Ok so you have all of these things tools whatever you want to call them for simplistic speediness of referencing sake that way I don't have to elaborate on each individual one let's just call a tool like for instance your wrench is a "sine qua non"

Or any one of the other things you pointed out and explained

By “tool” I am understanding you to mean “a means to an end”. Correct me if I am wrong, but, for the intents of my response here, I will be assuming that definition.

So with that said everybody's got their tool belt on that you laid out in detail ready for the next essay to arrive for us to then use our tool belt on to work out whatever that essay is talking about

If by this you mean that the subsequent essay(s) will utilize the concepts explained in the antecedent essay(s), then I agree.

But my question is even though we can use these tools do they actually exist in the sense that it's possible to even have a tool that is what it says it is?

Can you please elaborate on what you mean by “actually exist”? For example, if you mean to question whether there is a sine qua non that exists outside of my body (or what have you), then I would say that the essay doesn’t argue for or against it: there’s no “objective” vs “subjective” consideration as such is only via the principle of regulation and, therefore, it holds its rightful place in a subsequent essay.

Likewise, can you please elaborate on what you are referring to by “have a tool that is what it says it is”? The concepts within the essay are defined concisely and precisely, so I am imagining you are more contending with where (if anywhere) they exist (in an ontic sense). Is that correct?

The one that's on the top of my head is the tool called "sine qua non" is it even possible to know a sine qua non?

To be incredibly precise with my terminology, as it relates to specifically the essay put forth, it was proven to be “ascertained” but purposely and explicitly not “known” (in an epistemic sense); that is, epistemology is not something which is constructed within the essay as that is out of the sphere of that essay’s jurisdiction, so to speak.

Whether a sine qua non can be known depends entirely on its reevaluation via the individual’s accepted epistemology, which has no bearing on what was being proved in the essay.

I know it's easy to say that something could be a sine qua non but are we even capable of knowing something like that can even exist there's so many variables in the world so many possibilities for things so much information that one person cannot know so then to say something like something is a
sine qua non seems to be stating something that is impossible to actually know if it really is a sine qua non or not

Again, I would need further, more precise elaboration on what you mean here. Are you questioning whether there is a sine qua non in the “outer world”? What exactly do you mean? A sine qua non is defined precisely and the principle of regulation is proven to be “true” in the essay. In another essay, I will demonstrate, given more than likely a set of axioms, that the principle of regulation resides within “reason” of a given “subject”, contrary to being grounded in an “object”, but that is beyond the scope of the current essay in the OP. Is that the realm of discourse in which you are contending?

So my question is why don't we question if these tools can actually truly exist or if we're just pretending that they exist

The essay is meant to prove its truth, not prove that we ought to pretend it is true. If you don’t think that was adequately proven, please elaborate further on what exactly was inadequate about it. Furthermore, “existence” (in an ontic sense) is out of the scope of the essay; however, feel free to continue to utilize it to convey your contentions and I will do my best to respond.

Bob

If by "complicated" you merely mean that it is more complex than the provided illustration, then I agree.

Bob

Thanks. It's a matter of chains of encompassing superordinate categories with possible overlaps, I suppose. If so, I can see where you deal with infinities.

If I am understanding you correctly, then, as a simplification, yes. With respect to the image you linked, the all encompassing circle would be the superordinate and the smaller ones within would be subordinate. Now, imagine that contextual relation continued forever.

Bob

Same question: Why does metaphysics tend to have foundations that use ∞?

To be honest, I think this is an entirely separate question from the essay, as you are questioning the entirety of the branch of metaphysics: which is not addressed therein. Honestly, I cannot authoritatively assert why, in a generic sense, philosophers have posited countless formulations of limitless foundations for their views; but I can state that any other form of "foundation", with regards specifically to the provided essay, would simply not be a foundation. A limited foundation, to me, begs the question of its further, higher abstraction--unless, that is, it is posited as axiomatic or arbitrary (or something similar), which, in that case, it simply is conceded as not foundational in the sense the essay is contending with.

With respect to your other post:

In short, your system/theory is based not on knowledge but on ignorance

I don't honestly think that the proposed sense of an unbounded infinite in the essay is a grounding in ignorance. If you could specify exactly what about a sine qua non is problematic to you, then I would be able to respond more adequately.

Also, I would like to note that nothing within the essay is based on knowledge (and, moreover, the essay explicitly states that): it is ascertainment, which is defined very precisely therein. There's no epistemic consideration, in a formative sense, as the essay's sphere of discourse is meant of that which precedes the formulation thereof.

Bob

Lets look at the true infinite as all possible numbers. Within that infinite, you can have bounded infinites. For example, all numbers that end on the tenth's place is a bounded infinite within the true infinite. A bind is a limit. To speak of an unbounded infinite, is to speak to something without limits.

Although that is fine if you would like to use that kind of distinction, I would like to note that that is not what a “bounded infinite” is defined as in the essay. All possible numbers would be, with respect to the essay, a bounded infinite. I can abstract, for example, its contingency on distinction which thereby erodes it to a bounded infinite (i.e., conceived in toto); for I cannot posit the omission of that hypothetically “unbounded infinite” of possible numbers without conceiving it as in toto, of which its omission is entirely possible if everything was oneness. That’s just one example of many principles that it presupposes. Perhaps my essay, on that section, was misleading—as I did mention that the regards of postulating natural numbers can be possibly either “unbounded” or “bounded”, but what I was meaning to say is that it has no direct relevance to the point I was making therein (i.e., in toto vs in total). Maybe I should refurbish that paragraph if you think it was misleading.

Within the infinite, I can create many bound ways of comparing numbers. I can create bounded ways of adding, substracting, etc. But does the negation of one of these comparisons negate the true infinity of numbers? No. But if we think about numbers for a second, we realize they are bounds as well. Each "number" is a bounded concept. So we get rid of numbers as well, and we are finally left with true infinity.

Again, I would argue that the concept of all possible numbers as an unbounded infinite can only occur by means of the misapprehension of thinking it is such while actually conceiving it in toto. The idea of an unbounded infinite of possible numbers is contingent on many principles and faculties of reason (e.g., possibility, necessity, spatiotemporality, etc.).

Now, to your point I think, it is entirely possible to posit hierarchical structured infinities. For example, you and I can most certainly posit a bounded infinite wherein each element contains a bounded infinite and so on. I could postulate that there is a contingency structure (wherein the lower is contingent on the higher) that looks like so:

{All possible numbers}

{n + 1, …} {n + 2, …} {n + 3, …} etc.

The infinite sets of the iteration over each possible number + 1, + 2, +3, etc. is, as you said, contingent on the concept of there being an infinite set of possible numbers; however, this is a bounded infinite of bounded infinities: any permutation you choose, I would argue, is bounded—which I don’t think we are agreeing on as of yet.

By true infinite, I think you are talking about something entirely different than me, but I could be wrong.

When you say a sqn is needed, because without it an unbounded infinity is negated, I'm not sure that's possible.

This is where it gets incredibly subtle, but equally incredibly vital: it is not “without it an unbounded infinity is negated” but, rather, without it there are an unbounded infinite of negations. Sounds kind of like the same thing, doesn’t it? I agree, but yet they are entirely different ideas.

In terms of the former (your version), I would have no choice but to concede that a sine qua non is simply a misapprehension; that is, not an unbounded infinite is to necessary conceive of it in toto to thereby flip its affirmation into a denial (i.e., negation): therefore, it would be nothing more than the masking of a bounded infinite under the name of an unbounded infinite. However, in terms of the latter (my version), it is simply the negation, sequentially, of everything (i.e., not …, not not {…}). I think this is potentially where you may be misstepping (or I may be simply incorrect).

Is there a superordinate to 1? I'm not sure.

It is entirely possible to declare a particular derivation complete; that is, that it has been sufficiently justified and, therefore, can be put to rest. This doesn’t negate the principle of regulation’s truth: that assertion (i.e., that it has been sufficiently justified) is yet another conclusion which utilized the principle of regulation. This then can be further abstract to question its validity, which inevitably utilizes PoR. Likewise, it is entirely possible for it to remain implicit, which still utilizes PoR.

So, whether 1 has a superordinate or not, in the sense that you are asking, I think has not relevance PoR directly: you can posit whatever you want, which will be via PoR.

An unbounded infinity is something we can never understand in total, but only in toto as well.

Although I think this may be just that we are defining the terms differently, I want to clarify that the essay proposes the converse: a unbounded infinite is never understood in toto, but can be in total.

So when you declare a sqn is that without it, unbounded infinity cannot exist, it something that I'm not sure can ever be proven.

This is not, if I am understanding you correctly, what the essay defines as a sine qua non. To omit something is to thereby conceive of it in toto (as opposed to in total). So if you try to omit an unbounded infinity by any means it is thereby eroded to in toto. One cannot without a unbounded infinite, I don’t think at least.

Being in bounded infinites is not a bad thing however, as I believe its the only way we can have concepts. Perhaps we can simply reform your idea into, "A sqn is what is needed for concepts to exist." Basically try to find what is logically necessary for concepts to occur.

Unfortunately, that would defeat the point of the essay, as that is not a foundation (unless we speaking of contextual foundations). Likewise, a sine qua non is not deriving what is necessary for concept to occur, as that is within the sphere of critique of derivation (as opposed to its higher form of performance of derivation). Also, “existence”, to me, oversteps the bounds of the essay, as I am not trying to get into ontology therein.

Yes, we can prove this. To have a subordinate or superordinate concept, one must have two concepts. By the nature of a concept being a derivation, one must be formed before the other. If one cannot conceive of a single concept without the PoR, how does one conceive of the first concept?

One must conceive of that first concept prior to the second according to the PoR. That means one must be able to conceive of a concept without the PoR, because prior to the first concept, one has no concepts. If one can conceive of a concept prior to the PoR, than the PoR is not necessary to conceive of concepts. If this is the case, one could also conceive of a second concept that had no relation to the first concept. The ability to create concepts does not necessarily mean one will create derivated concepts, or use the PoR.

This would be true if the principle of regulation pertained soley to explicated superordinate and subordinate rules. It’s quite literally being postulated as an unbounded infinite of such. One can most certainly conclude something without explicating or even understanding how they were able to do so. Furthermore, all concepts are derived (that is, produced from the process of derivation): I am not positing that one can only formulate “derivated concepts”.

Thus we've shown that while the PoR is a way to view derivation itself, it is not necessary to hold or create concepts. Meaning that the PoR cannot be a sqn as the idea of "concepts" itself can still be conceived without it.

It cannot be conceived without its implicit use. However, it can most certainly be something the individual at hand has no clue about; nevertheless, concepts cannot be conceived without the principle of regulation.

Bob

Nice to meet you Agent Smith!

I fail to see why anyone in his right mind would want to use a highly controversial concept such as infinity as the bedrock of his/her thesis (on metaphysics)?

…

P.S. A quick question: Why, o why ∞?

I understand that many fields of study are still of yet formulating the behavior and kinds of infinite (e.g., mathematics), but I don’t see its controversy with respect to the essay: could you please elaborate specifically on what within the essay is controversial (with respect to its use of infinities)?

Nevertheless, from the posts I read, the OP gets points for being systematic, a quality that I respect (a lot). Bonam Fortunam OP.

I appreciate that my friend! If you could please elaborate on your contention with its grounding in an unbounded infinite, then I would love to explore that issue.

Bob

Sorry, Bob. See if you can parallel what he did in a short paragraph. A clear example with less abstraction. Give a clear example of the principle of regulation as well. Or just ignore me and continue on - I would not take offense.

I must concede that, at this time, I do not have readily available a short and simple explanation for the principle of regulation (that doesn’t erode some of the meaning thereby). However, with that being said, let me attempt to give you a brief, overly-simplified example.

Imagine I were to postulate that “A is true” wherein “A” is a statement (whatever you would like it to be, let’s say). “A is true” is the affirmation that “A is true”. This affirmation abides inevitably by superordinate rules (that is, it could not have been affirmed otherwise by the utilization of other implicit, in this case, principles that are affirmed). Let’s say, for example, I were to postulate that my affirmation of “A is true” (i.e., A being true) by means of mere whim (i.e., completely arbitrary and baseless—just a random thought that manifested in my mind). Now, that justification can be the shifted focus: I affirmed that the affirmation of “A is true” is by means of mere whim. This postulation, likewise, inevitably abides by superordinate rules, of which I can explicate (or simply move on and thereby they remain implicit). I can do this forever.


I want to emphasize that the above example is incredibly over-simplified, but let me know if that at least partially helps you understand. If not, I can try again.

Bob

Tones-in-a-deep-freeze is more an expert in this area. I'm from the generation of naive set theory. Your use of infinite is a philosophical excursion beyond my experience.

Oh I see: no worries my friend!

Bob, I recommend you do the same.

There is an example in the essay which I think explains it well: did you find it to be confusing as well?

Bob

Nice to meet you magritte!

My impression is that by reducing the process to what is 'true' you have already relinquished your quest in favor of strictly realist binary meta-possibilities.

For clarification, are you saying that defining what ‘true’ I have thereby restricted myself to some set of realist binary (so true or false) meta-possibilities? By “binary meta-possibilities”, do you mean that I am rejecting non-binary ones (e.g., like fuzzy logic)? By “meta-possibility”, what exactly are you referring to?

For example, there is no truth in science! In science true is replaced by correct or more likely or most likely the case.

I have no problem with using cogency as opposed to an absolute truth in relation to derivation and the conclusion produced therefrom (if that is what you are getting at: I am not too sure yet). But then we need to define what you mean by “true”? I do not mean it in an absolute sense at all.

In most aspects of personal life the only truth is death (and not even life according to our faithful judges)

Can you define “truth” for me (in terms of what you mean)? I was anticipating you would have claimed the opposite, as death is an induction and thusly “more likely” the case.

If this is so given that the process is not the same as its derivations, then you might limit yourself to closed objective identity and the PNC everywhere.

The principle of regulation by no means necessitates the principle of noncontradiction. Furthermore, I would argue that process of the performance of derivation abides by the principle of regulation but, more importantly, not that the performance of derivation is always exactly the same. One person could use PNC, another could not. Nothing about my essay favors either one (at least that I am aware of).

I may just be misunderstanding you, so please feel free to correct me!

Since I am a radical metaphysical pluralist I hope I am wrong in this.

I am by no means an expert on “metaphysical pluralism”, so if you could elaborate a bit on what you mean that would be much appreciated!

Bob

I define infinite as volume unspecifiable. This is a way of saying infinities cannot be made explicit. I believe this truth persists even in the instance of hierarchies of infinities.

Positing an infinite value (unspecifiable volume) within bounds is tricky because, in my opinion, territorial limit takes on a special meaning such that limit transforms into asymptote.

Perhaps curiously, an infinite value "warps" a (conceptual) boundary into a "curved space" that functions as an unspecified boundary in that it is a boundary that is never reached.

I think I understand. Basically (and correct me if I am wrong), an infinite within bounds actually simply approaches the limit as opposed to actually reaching it. So, for you, I would image that the contents of a line connecting two dots does not actually reach the two endpoints: it approaches them infinitely. Is that correct?

I think, if that is what you are saying, then this objection makes sense (in those terms as you proposed):

Is an unreachable boundary really a boundary?

In the instance of a bounded infinity, whose unspecifiable volume is quite free to expand forever, can we truthfully claim that it is contained?

To me, this still produces the same in toto claim (that is, a complete infinity): even if it asymptotes, every single point within the infinite of points of the finite line exists. For every possible point, it exists between the two dots on the line and the two endpoint dots exist for the line: therefore, the concept can be thought of as in toto (that is, complete, which is an encapsulation within a finite).

To be honest, I actually think that you are right, as you are discussing the rightful method of conceiving of a bounded infinite (I would say): the infinite content quite literally does approach as opposed to arrive at the ends. If it reached the endpoints of the line, then it wouldn’t have an infinite content.

Assuming I am not misrepresenting your view (which please correct me if I am), I would like to clarify that a bounded infinite is just like that line connecting two dots: there’s a form that is conceivable in a finite concept (i.e., the line from point X to point Y), but the content quite literally is infinite and, therefore, the points approach the endpoints which actually achieves a complete concept when combined with the endpoints themselves (i.e., an infinite approaching, asymptoting at by endpoints + the endpoints themselves is conceivable as a complete concept).

By unbounded, I meant that it cannot be conceived of as this sort of complete, in toto, concept: try to imagine a line that just continued forever and, with respects to its ends, never ended a particular point. For all intents and purposes, that would be unbounded in form and that cannot be conceived of as in toto. The best I can do is formulate its in total by means of a summation of its parts (potentially, that is, depending on what the parts are).

It occurs to my visualization that a bounded infinity is a configuration wherein an unspecifiable volume has PoR as a neighbor who speaks another language and thus, there is no dialogue between the two. In this situation, can we truthfully say PoR acts as modulator of unspecifiable volume?

I am sorry, I don’t quite follow what you are asking here: could you please elaborate further? What do you mean by neighbor? PoR, as I was postulating it, is, as opposed to a kin to, a unbounded infinite (or unspecificable volume that cannot be conceived in toto).

the inherent unspecifiability of an infinite volume implies its expansion towards a boundary is necessarily asymptotic.

I honestly have no problem with this premise: I think you are misled to a wrong conclusion by it though. A infinite volume that asymptotes as two finite endpoints is a bounded infinite, as it can be conceived in toto. I might just be misunderstanding you thought, so please correct me where I am wrong!

To far greater extent than Philosophim, there's much I neither know nor understand, thus I might be egregiously wrong when I use my argument above to expand Philosophim's doubt to include bounded contexts.

Having said that, I admit I do, now, have the audacity to entertain nascent doubt about the PoR's ability to modulate a bounded infinity.

In terms of Philosophim’s argument, I think it reveals a more fundamental dispute I will have to contend with: is it possible to extend this beyond the sphere of my individual context. I think it has been proven to be true, but there’s much to discuss (so I could be wrong). The problem, I think, is that one is perfectly capable of omitting themselves (i.e., their context) to see what remains and, thereby, if it is constrained to my context then that is self-defeating. However, I think it is a facade of sorts: one cannot actually conceive of sans themselves (in sense of derivation). When someone validly conceives of someone else’s context sans their own, this is all contingent on their derivation and does not transcend themselves whatsoever (I would argue). If you would like to discuss Philosophim’s objection as well, I would be more than happy too! I will leave it there for now and let you navigate where you would like to go from here.

Bob

No, that wasn't my intention. What I was trying to note was there are an infinite number of things I could postulate with "unmarried man", that I could not postulate without "unmarried man"

You are correct and this is why the form, as opposed to mere content, of an infinite is incredibly important. Let’s take my Y example again: without Y, there’s an infinite of postulations that cannot be proposed anymore (let’s call that infinite X).

There’s two ways (pertinent to this conversation, that is) we could conceive of this X: in toto or in total. In terms of the former, it is conceived of as bounded in form (i.e., complete in form). In this case, if Y can be omitted and there are still concepts which remain intact, then Y is not a sine qua non (although without it there is X). In terms of the latter, it is conceived as without bounds in form (i.e., never complete in form) and, in this case, there must be no exception to the negations (that is, every concept is being negated).

Therefore:

If we disregard all possible synonyms for "unmarried man" in all possible contexts, would this be a sqn?

It would not, because fundamentally we would have a situation where we are positing “without Y, there’s a bounded infinite of negative judgments”. That claim is not coherent if posited as an unbounded infinite because the omission of “unmarried man” leaves many concepts intact.

Of course, there are a potentially infinite number of derivations we can establish from "unmarried man" that we could not without the concept of "unmarried man". From the finite springs the infinite, though this infinite is bounded by the finite superordinate.

Exactly! It is still an infinite negative judgment, and valid at that, to assert the withouts of “unmarried man”, but it is bounded and not unbounded. Same is true of chains of infinities, cyclical infinities, etc.: they are only conceivable by means of eroding the infinite to a bounded one (that is, by means of conceiving it in toto: complete). It’s subtle, but an incredibly vital distinction (I think at least).

The problem I see you running into is when you note a "universal" infinite. Having worked with infinite before, its very easy to lose the real consequences of true infinity. Real infinity has no limit. Which means practically any formation within that infinite can also be negated.

…

As noted, continuous data is still a bounded infinite. Without the context of dimension, height just dissolves into the true infinite. There are an infinite amount of potential dimensions that we can create within that true infinite.

As you noted, continuous data (and height) is a bounded infinite; that is, must be conceived as in toto, which is not a sine qua non. I don’t have any contention with the idea that, in content, we can measure height infinitely. Maybe I am misunderstanding you, as I see nothing wrong with this.

However, I want to clarify that I do not use the language of “true infinite” (although you certainly can), and so I am interpreting that as an infinite (which is simply defined, generically, as limitless in content, which no specification of its form). Correct me if I am misunderstanding you here.

To your point, I'm noting that the rule of regulation too would dissolve into the true infinite without certain bounded contexts. If a sqn must be true universally, then it must be true in the unbounded infinite.

That is what my essay is arguing for: by being a sine qua non, it is an unbounded infinite.

This is still within your own bounded context. I take no objection to there existing a sqn within a bounded context. It is completely true that you thought everything you did, and could only come to one conclusion. But is that true of all contexts, of the true infinity?

Whenever I even attempt to derive other contexts sans my own, it is contingent on my own. I never once escape out of my context, not even in terms of conceiving of “escaping my own context”. This is why the principle of regulation is an unbounded infinite (more precisely, sine qua non).

The best I can do is postulate that, via my own derivation contingent on me, that if there were a duplicate reason out there of mine (to any degree in its manifestation), then this principle would apply. But that will always be inevitably self-referencing.

There are some people who cannot visualize in their mind. As in, they cannot think of images like most people can. They close their eyes, and the world is completely dark for them. Think of the host of conclusions and thinking you've done with your ability to visualize in your head, and then try to imagine the conclusions one can or cannot make if they cannot visualize.

If they react to their environment to any degree other than 0, then I think it is provable that it applies to them. By “conclude”, I mean it in the most affirmative & negative sense (affirmation and denials). It’s not that they have to explicate this process of the principle of regulation or that they have the exact same faculties of consciousness as me: it’s that their conclusions are regulated by this very principle.

In the same manner, a personal conclusion of thought within your own bounded context does not prove a universal context. In the same manner, we can imagine a creature that can think without the rule of regulation. Its difficult for those of us who use the rule of regulation on a daily basis to imagine this, but we already know that some things think differently from ourselves. This is what I was noting earlier. If you personally think using the rule of regulation, and nothing else, then yes, its a sqn for you. But that doesn't mean its a sqn for something that does not think like you do.

I cannot think of a creature that can think without utilizing (implictly at least) superordinate and subordinate rules. I can conceptually the omission of the concept of “principle of regulation” from my mind and attempting, thereafter, to derive what is left, but that inevitably utilizes it. If you can conceive of such a thing without its utilization, then I would be genuinely interested to hear more! How are you able to do that?

I will say that my approach, or argument, is that it regulates me and all human beings (and most likely creatures) that exhibit any form of life. Prima facea, I can trick myself into thinking sans “my context” to see what someone who wasn’t constrained to PoR would exist as, but that inevitably utilizes it as well! If there is a way to break the cycle, I would love to hear about it!

So, I guess, it depends on what you mean by “universal”. I cannot constitute it as not universal (in virtue of being my context) because “sans my context” is still contingent on PoR for me. Furthermore, I could postulate an if conditional of how it would be for an individual who didn’t have such a regulatory principle guiding their derivation, but that, again, is contingent on it.

Perhaps you have found the root dilemma of my essay!

I do want to clarify that I am able to derive other contexts sans me, but what do I mean by me? Can I posit a context sans PoR? No, and that is my point.

First, there's the idea that we're assuming our own basis of thought applies to all other thinking things. We cannot conclude that just because you and I think in the terms of the principle of regulation, that every other thinking thing does as well. All it takes is one thinking thing that does not, and then we don't have a universal sqn anymore. I'm not saying you can't come up with a universal sqn, but it must be provably true within the true infinite. I don't see the PoR doing that currently.

I would ask, in light of what I previously stated, for you elaborate on how you are able to omit the PoR when deriving conclusions of its omission. I would like to know how it is not recursively utilized therein. If you can demonstrate that, then that would be really helpful for me!

Second, we can speculate that a plant, or any other creature thinks with the PoR, but we have to prove that. The burden of proof is not on me within the true infinite, the burden of proof is on yourself. And even if we prove that, we must prove it for all plants of that type, then all plants, all creatures, etc. The PoR is not something provable, because it is a bounded idea that relies on certain bounded infinites thinking in a particular manner.

All derivation is subsumed under this principle for me, as a subject, and thus nothing escapes it (not even that idea of escaping). Therefore, it really is an unbounded infinite, universal if you will, but maybe I am missing something. Maybe it is possible to conceive of its omission without recursively utilize the principle itself: but, yet again, I just used it to postulate that possibility. Maybe you mean something entirely different than me by “universal”?

That being said, it may be that there are things I still don't understand, so please correct me if I'm in error. I also think the PoR is a fine principle within bounded contexts, and see nothing overtly wrong with it within these bounded contexts. I just don't think at this time that you've provided what is needed to show it is true universally, and not just within the contexts you've been thinking in.

If this is the case, I would love to know how. I wouldn’t say I am in agreement with you: I think it is proven to be universal, but I could be wrong as always!

Bob

Could you clarify with an example here? When you mean infinite, do you mean "All possible derivations in total/tota"? To compare again to the bachelor, we could derive another term called a bachelum, which is an unmarried man that is about to be married. Again, we could not derive the term bachelum without the superodinate "unmarried man". As such, there are an infinite derivations we could not create without the concept of "unmarried man", many which we do not directly know or have been invented yet.

I want to clarify that I think you are thinking of it conversely to what I was proposing. When you say:

As such, there are an infinite derivation we could not create without the concept of “unmarried man”

That proves that “unmarried man” is not a sine qua non, which I believe (and correct me if I am wrong) you are thinking it would prove it if there’s an infinite amount of things that could be postulated without “unmarried man”. It isn’t that “if without A, there’s an infinite of other things we could postulate, therefore A is a sine qua non”: it is “if without A, we are met with an infinite amount of negations (nots)” (e.g., “without A, not this”, “without A, not that”, etc. until we realize by proof that it can be abstracted to infinity as “without A, not ...” if you will).

One of the reasons I made the distinction between “bounded” and “unbounded” infinities is because one (not necessarily you) may be incentivized otherwise (that is, if it is just postulated as “infinity”) to counter the validity of the idea of a sine qua non by means of asserting that they can conceive of and derive infinities of negations (as a concept) as without another concept. For example, one may be inclined to determine that they can categorically define that Y is without X and Y is an infinite of negations. That can most certainly postulate it, but I wanted to clarify that that is by no means a counter to the validity of a sine qua non (as an idea). You see, as I would argue, that concept of Y, valid as it is by means of derivation, is a bounded infinite because I can abstract further by questioning the grounds of that very concept of Y, thereby invalidating it as an unbounded infinite.

Could you give an example of what you mean by context here?

By “context”, I just loosely meant an idea that is sandboxed. So it is perfectly possible that “A IFF D” is only true within a sandbox, so to speak, and not true universally.

If it is unbounded context, I cannot see a sqn forming simply by the fact language and thinking can change. Lets look at the principle of regulation. A fine principle, but can it be proven that its a sqn in unbounded context?

I am not entirely sure if I am understanding, but by “unbounded context” I am envisioning a sandbox which has no bounds in form. That seems kind of like a contradiction in terms to me: a context, by definition, has a limited form, otherwise it is not a context.

If you are trying to inquire how it can be proven sans context (i.e., unbounded context), then I can provide further detail: I continually performed abstraction to its highest point, whereat I could not longer abstract higher and, thereafter, determine what (if anything) produces the negation of those abstractions if removed (or it could be thought of as the negation of particulars too, if you will). The principle of regulation was the only thing that remained. Now, at this point in my thinking, it was not so discernible whether it was (1) an unbounded infinite, (2) a bounded infinite, or (3) indefinite.

To keep it brief, I determined it not to be #2 by virtue of the proposed definition of sine qua non the negations cannot be conceived in toto and, therefore, it is not possible to prove a in toto conception without the utilization of the principle of regulation in the first place (as a separate, out of scope of the essay, derivation). I determined it not to be #3 because the derivation of without the principle of regulation was recursive (thereby solidifying its infinite nature as opposed to be undetermined bounds in content).

What if something does not think in a derivative manner? This may be due to low intellect, or simply a brain that does not process in such a way. Does a plant think in terms of the principle of regulation for example?

Firstly, I would say that the essay is meant only to prove in relation to the subject at hand (or more modestly, me as the subject). I by no means disproved or even mentioned solipsism. However, with that being said, I think it is easily arguable that this principle extends to the vast majority of non-brain-dead human beings: the principle is observable without postulating an actual subject as the originator. In terms of low intellect, I think they still exhibit the principle, just not as rationally as we do. Even the most primitive use still counts to me.

In terms of animals, I think most would fit the bill and maybe plants. To be honest, I haven’t contemplated that aspect enough to give a substantive response. However, I do think, off the top of my head, plants, for example, exhibit the abidence of such a regulatory principle (e.g., a plant does make binary decisions, which does require superordinate/subordinate rules, albeit it primitive).

The problem with an unbounded infinite is we can always come up with a situation that negates another.
To your end, I believe you are implying a bounded context. For example, in individuals who have the capacity to only think in superordinate and subordinate manners, we could say the principle of regulation holds. Because people in this context have no other way of possibly thinking, it is impossible to think differently. Among creatures that had alternative thinking processes, the principle of regulation does not apply to them.

Maybe if you provide an example I could respond better: what about the principle of regulation do you think doesn’t hold for a plant that demonstrates it reacts to its environment (which, I would argue, pretty much happens in virtue of them being alive—no?). I certainly don’t think a plant would be able to affirm the principle of regulation, but I think I can affirm that they use it (which is a different claim, I would argue).

I look forward to hearing from you,
Bob

With a view towards answering the above question, I'm making an attempt to get my general bearings within your project by elaborating the overview below. Let me know if it's sufficiently accurate to be helpful.

Sounds good my friend: hopefully I can provide a substantive and helpful response here.

Schematic of Foundational Metaphysics of Derivation

If I am understanding this title correctly, then I actually think it is a really good title! It could be thought of as a scheme of the foundations of the metaphysics of derivation (kind of a bit wordy, but I think is true nevertheless).

A scheme to establish an algorithm for expressing & establishing a causal chain of derivatives culminating in a conclusion. This algorithm will be expressed in terms of the widest generality.

I wouldn’t use this terminology, but I think it suffices. My concern is that it isn’t quite narrow (or precise) enough; but for intents and purposes that is fine. I would say to keep the concepts very the most generic senses of the terms. For example, “causal chain” would be incorrect if it were to assert for or against it being physical, mental, or where this causal chain is originating from. But in the sense that there are a series, if one wills, of connectives: that’s basically derivation.

If you would like to use that kind of terminology, then I think that is fine (for all intents and purposes): I will do my best to interject when I think your use deviates from what is meant by a sine qua non.

Some key elements that hold priority within the scheme:

If by “key elements” you mean key terms being used in the essay, then I think that most of your list is fine. Except:

{Infinite Series} bound, unbound, indeterminate

There is no “indeterminate” category proposed for infinities: it is indefiniteness—which I wouldn’t hold means the exact same thing (but if you just mean that in the sense that the bounds in undetermined, as opposed to indeterminate, then I think that is fine). For me, I am defining “indeterminate” as not able to be determined, whereas “undetermined” simply means it hasn’t yet been determined.

{Ground} not subjective, not objective

Since you included this as an element in the list but not others (like how it is not indubitable), I feel inclined to ask if there is some sort of significance you are extrapolating from this particular claim that isn’t found in the other (such as the aforementioned example)? By “Ground”, I am thinking of an ontic claim: is that what you mean? In that case, I am not saying it is or is not grounded in the subject or an object (or objects or what have you): I am claiming it is simply not addressed, purposely, in the essay. Attempting to argue for any sort of ontic claim, even its own ontic grounding, is beyond the scope of the essay.

By convention, the derivatives are configured in accordance with the established rules of inference.

By “established”, I would like to clarify that they can be either implicit or explicit.

By “derivatives”, I am thinking of “conclusions produced via the process of derivation”. Please correct me if that is not what you meant.

By “rules of inference”, I would agree if you mean the relation between superordinate and subordinate rules. They can be, for intents and purposes, thought of as “inferred” in the sense that they are “intuited”, which I mean in the sense that we don’t necessary explicate them.

The upshot of the scheme is elaboration of a plan applicable to the entire edifice of derivation to a conclusion.

If I am understanding correctly: exactly!

Successful execution of the scheme will, by design, entail the establishment of a foundational metaphysics of derivation to a conclusion.

If I am understanding correctly: yes! I would slightly refurbish to be “establisment of a foundational metaphysics of derivation itself” or “of derivation to any given conclusion”: just to clarify that it is not just a particular conclusion. That might just be knit picky though (:

This foundational algorithm will embody a logical imperative for all derivations to conclusion.

I would have a problem with the use of the term, semantically speaking, “logic”. However, I see this as one of the potential weaknesses of the essay; that is, it could be considered a “logic”, but as the nth-order logic where n is actually an unbounded infinite series. You see, in that sense, it could be considered a higher-order logic (maybe that’s what you meant in your previous post?), but I don’t think it is constituted as a second-order or third-order logic (as it is an actually abstraction to an unbounded infinite use). If you have any ideas on this, then I would love to hear them!

Other than that, yes it is an imperative (the principle of regulation) of all derivations to a conclusion. Well said ucarr!

Bob

I asked what difficulties would be caused by denying everything you wrote - for example, supposing there never is such a thing as a principle of regulation, never has been and never need be. Does that cause a problem in any way? The answer to that might give me an idea about the value of the theory - that is, why it might be needed.

I think I understand what you are asking (but correct me if I am wrong), and, unfortunately, I anticipate that my answer will not be satisfactory. You see, for me, I consider an axiological evaluation outside the scope of the essay itself. If I were to respond with any given problem, then it would necessarily presuppose some set of values (which I am not attempting to argue for nor against in the essay): that is kind of my dilemma. In other words, a “problem”, to me, entails necessarily an underpinning value (e.g., if I value being well fed, then something which contradicts that, at least prima facea, may be a problem for me—but it is no problem if I reject the underpinning valuation).

It is simply an inquiry into how the process of derivation operates as opposed to critique of a derivation itself. I think it is and will be useful for my subsequent essays, but I am not arguing for its value in the essay.

With that being said, I feel like I didn’t really answer your question. I think that its usefulness is found in after it is found to be true (regardless of the value of endeavoring on a such a journey in the first place). For example, albeit outside the scope of the essay, I think that the principle of derivation (being a higher order, so to speak, than derivation itself—or at least, for all intents and purposes, can be visualized that way), once it is affirmed, proves the relativist nature of any particular derivation. That will play a significant role in my epistemology, for example, which will not assert its construction as built on any absolute conclusion from my derivation (assuming I am not persuaded to change my mind by the time I start writing that essay). Maybe that will help you understand its “value” to some degree (or maybe not).

If that wasn’t a satisfactory answer, I apologize and please feel free to grill me harder on it and I will do my best to provide something which I think isn’t extending into the sphere of speculation (on my end).

Bob

Not at all. I just pop in now and then whenever math is mentioned and provide my perspective. Most in my profession are not in foundations. In the most recent 24 hour period only 1 in 58 papers submitted to ArXiv.org were in that subject (logic, set theory, etc.).

Oh, I see! I would love to have a conversation about infinities (e.g., set theory) if you are interested: my knowledge of it is by no means expert level and would love to hear what you think of it. However, for this discussion board, if the discussion of infinities doesn’t pertain to the essay in the OP, then I would like to respectfully ask if we could shift that discussion to occur somewhere else (that is, if you would like to continue that discussion). Feel free to DM me on this forum whenever you would like! Or maybe you would like to open up a discussion board specifically pertaining to infinities (or maybe there already is one that I am not aware of)? Otherwise, no worries.

I appreciate your friendly attitude! :cool:

Same to you my friend! (;

Bob

I am trying to suppose that derivation has no foundation and no derivation; or that derivation cannot be abstracted; or, if it can be abstracted, it cannot be abstracted towards a utilization

At the beginning of the endeavor of writing the essay, that is exactly what I was wondering as well. That’s why I kind of postulate it as a purpose rather than a formal problem: nothing about the essay states that there must be sine qua nons but, rather, only that there is one that is provable. If I went into the essay trying to prove there were any, then I would be just fulfilling a bias.

I realized, to keep it brief, that even if I concluded that there was no foundation to derivation, or no derivation, it is all by means of the principle of regulation (or whatever one wants to call it).

; or, if it can be abstracted towards a utilization, it cannot be abstracted to a specifically recursive utilization; and it may be that, even if all that can be settled, the recursive utilization may be unbounded but not infinite (like the surface of sphere) or it may be infinite but not unbounded (like the sum of a convergent series) or it may be neither infinite nor unbounded or it may not even be the kind of thing that could described as either.

Well, let me see if I provide my thoughts (although I may be misunderstanding you):

Not a recursive utilization: I think that the principle of regulation proves that it is. By recursion, I mean that it utilizes itself and that’s as far as I can seem to go. Every step I take, every definition I utilize, every connection I make, and every conclusion I perform is inevitably regulated by superordinate and subordinate rules.

It may be unbounded but not infinite: I may just be misunderstanding you, but an unbounded finite seems like a contradiction in terms to me. Finite content entails finite form. In terms of a sphere, it depends on how you are specifically using that analogy if I would agree or disagree. For example, if I continually walk around a sphere endlessly, then that action is an unbounded infinite. The content of the sphere itself, on the other hand, is finite and therefore the bounds of the sphere is finite (it has a finite form). What exactly were you trying to explain with it? I don’t see as of yet how it would be ever an unbounded finite.

Infinite but not unbounded: Things like the sums of convergent series is what I was describing in the essay as in total (as opposed to in toto) and are what I would consider the summation of an unbounded infinite. I do not think that the limit of X approaching infinity is a bounded infinite nor the summation of infinite parts. A bounded infinite would be if one were to posit, I would say, that there are an infinite amount of points in a line that connects two dots and yet the line itself is bounded in form.

I should add that whilst I'm attempting to make these suppositions, I am not succeeding well. I can't get much sense out of any of them - either supposing their truth or their falsity. So I wonder: what problems or questions are you addressing?

Oh I see. I understand that, but the problem I am addressing is exactly that: the consideration you yourself just claimed you could suppose their truth or falsity. The question of derivation of derivation (and its abstraction towards recursive use—meaning of derivation of derivation of derivation of …): are there any sine qua nons? That is the question. Otherwise, there is simply the arbitrary.

How have other people addressed them? What difference would it make if you changed your mind and decided to deny everything that you wrote in the essay - say, there is no principle of regulation, never was and never needed to be - what difficulties would that cause for us?

It is really a question of whether derivation is arbitrary (i.e., axiomatic) or grounded in a sine qua non. I wasn’t stipulating one as supreme over the other: I simply wanted to derive if there is. If not, then my subsequent essays would have been derived from axiomatic principles for “foundations”. Is that what you are asking?

Bob

Hello Philosophim! I am glad to see you again!

Let me see if I can sum up your argument. sine qua non means "without which, not". Which means, "If this does not exist, this derivation cannot follow"?

So “without which, not” is meant as an unbounded infinite negative (i.e., if not A, then an unbounded infinite of negative judgments). It is not meant to negate only one particular derivation.

As an example, A -> B. But also, C -> B. If we removed A from the derivation, we would still have C. So neither A, nor C, are a sqn. If however we had A -> D, and in the removal of A, it is no longer possible to ever derive D, we have a sqn. Does this approximate the idea fairly?

A sine qua non is not denoted by being the anchor of a biconditional statement (such as D IFF A); for that could entail that it is only valid within one or a finite set of contexts. For example, it’s possible that A IFF D is true of context C1 but not true of context C2. That would not be a sine qua non.

If so, this is similar to a contrapositive of derivation. Perhaps a way to view it is a bachelor is an unmarried man. The term bachelor is derived from the "unmarried man". Without an unmarried man, there can be no bachelor. A man is a bachelor if and only if he is unmarried. Being an unmarried man is the foundation of a being a bachelor. In this case, we could call "unmarried man" to be a superordinate rule. The subordinate rule would be the creation of the term "bachelor".

It is not the contextual superordinate and subordinate relationship (of the principle of regulation) that is meant as a sine qua non: it is the principle itself. Therefore, an “unmarried man” would be, given your definition, a superordinate rule in that context but it would not be a sine qua non (the more abstract principle of regulation is). I am not sure if that is what you are implying there (in that case I would say it is incorrect) or if you were merely giving an example of a superordinate/subordinate context (in that case, I think it is correct).

However, to clarify, a sine qua non is not in itself a contrapositive conditional, but superordinate rules can regulate the derivation to have such (if that makes any sense).

I think what you also wanted to note was that a superordinate rule can be a subordinate rule in relation to its previous derivation as well. So, I could look at the term "man", and note (as an example, not denoting the correctness) that some creature with an 46 chromosomes in an XY structure exist, and from there, we derive the word "man". In this case, the chromosomes would be the superordinate, while the term "man" would be the subordinate.

Yes! And the very derivation of the process you just described (i.e., the defining of a word, the definitions of those words, the definition of defining, the regressive pattern, the cyclical pattern, patterns themselves, etc. can be abstracted to superordinate rules that govern the ones within the context of your example). Does that make sense?

That being the case, we can create superordinate clauses that work, but do not negate the subordinate when removed.

I am not sure what you mean here: maybe I am misunderstanding you. The process of derivation is simply the production of affirmations or denials in relation to the implicit or explicit superordinate rules.

It is not necessary that I know of chromosomes to derive the word "man". I could note its a "human with particular reproductive anatomy". Thus while the chromosomes can be a superoridinate to man, it is not a sqn.

Even if chromosomes were considered essential to the given definition of “man”, it would not be a sine qua non: is that what you are stating here? Within the context of the given definition of man (let’s say that an essential property is having chromosomes), it would follow that a man without chromosomes is a contradiction in terms. When I derived that just now (that it is a contradiction in terms) I also, subsequently, utilized superordinate rules to assert it (and that can be continually abstracted towards higher superordinate rules). I could posit that man is not defined by chromosomes or what have you, but that would be a different context. The main point here would be that chromosomes is not persisting across an unbounded infinite of contexts, even if it is essential to one. I think you may be thinking that sine qua nons are when the superordinate is in a contrapositive kind of conditional, but the sine qua non proposed is the process of all the possible contexts of superordinate and subordinate relationships.

I look forward to hearing from you,
Bob

Sorry to have gotten off on this tangent.

Not all my friend! I am just not entirely sure the relevance to the essay itself: are you contending that I ought to remove the unbounded vs bounded distinction because it is not highly disputed amongst mathematicians? Even in that case, I think they are necessary (and I elaborate further if you would like).

I don't understand your philosophical argument. To me "derivation" means putting together certain things, and this can involve the passage of time. Hence, a kind of reverse iteration of causations.

By derivation, I simply mean the procedure of producing conclusions. I wouldn’t, for the intents of the essay, pose it as involving time (although I think a good argument can be made for it). The consideration is very narrowly scoped for the essay—and purposely so. It is a consideration of foundations, and I do not consider time to be a foundation in the sense of a sine qua non. I can elaborate further if you would like. But I understand what you mean and, in terms of practicality, I would presume that kind of conception of it works very well.

Bob

Well, evidently I have no idea what I am doing...I thought you were opening a discussion on a focused topic. Please disregard my previous comment.

Absolutely no worries my friend! I think we are mutually just as confused as each other with respect to conversation. Perhaps I can clarify the purpose of this discussion board: it is to discuss the essay linked in the OP. If you would like to contend with it or give comments, then please feel free!
Bob

Hello ucarr! I appreciate your analysis and response: let me try to respond adequately.

examination of derivation-of-derivation means establishing continuity between phenomenal experience and first causes.

I would say that it depends on how you are defining “first cause” whether my essay is participating in that kind of business. Although it may merely be semantics, I personally don’t think that a sine qua non is a first cause. To me, a or the first cause implies an arbitrary discontinuation of a chain of causation (whether that be mental or physical or what have you) at a supreme or ultimate element. This utlimate element is usually eternal, which is usually meant in an actual infinite sense (that is, a bounded infinite which has been proven in toto to exist).

For example, let’s take your example:

An example is Aristotle’s unmoved mover as the cause of all motion.

I wouldn’t constitute an unmoved mover as a sine qua non. It requires a specific derivation (with certain presumed axioms) which can be possibly omitted.

analysis & derivation share important common ground to the effect that derivation is a type of analysis.

By derivation, I mean the procedure of producing conclusions. So I would agree that “analysis” is being utilized pretty synonymously with “derivation” (if I am understanding you correctly). By “of derivation of derivation”, I mean the analysis of derivation itself (i.e., analyzing the procedure of producing conclusions if you will).

I would like to clarify, briefly, bound vs unbounded infinities, as you seemed to a bit confused on what I meant:

What’s the difference between a bounded finite & a bounded infinity?

So, first, I am making the distinction based off of the grounds of “form” vs “content”. Form is the boundaries of the concept. Content is what is contained in the form. Therefore, a bounded infinite is conceived in toto by means of a form with boundaries, whereas an unbounded infinite is only conceivable in total by means of a form with no boundaries. Now, you brought up a keen insight:

Is content sans form intelligible? Is there a type of form that has no boundaries? What’s an example of boundaryless form? If there can a content without boundaries, how is it differentiable from other contents? How is a set composed of boundaryless contents intelligible as a set of discrete things?

It depends, first and foremost, what you mean by “intelligible”: my immediate reaction is to say that a content sans form is not conceivable in toto, but conceivable in total. I think the issue you were running into is that you were trying conceive of an unbounded infinite implicitly in toto and, thereafter, rightfully determining that it is a contradiction in terms (which is what I also noted in the essay)(i.e., limited limitless). Therefore, I think, and correct me if I am wrong, you may be thinking only of content and form as inseparable and, to a certain extent, I would agree; however, I don’t think that that negates what I am saying either (but correct me if I am wrong).

Form is like the shape, if you will, of something, whereas the content is what is actually contained therein.

Can you visualize content that is discrete & perceivable and without form?

Can you visualize form that is composed of nothing?

So an unbounded form is not “not form” or “sans form”: it is a form that can’t be conceived in toto. If a conception is of without a conception (i.e., not-A is without A), then the form of “without A” is nothing (0) because its content is nothing (0). The form requires some sort of content to be conceivable (other than 0, let’s say) (in toto or in total—or potentially, if you will, conceived of as 0 in toto or 0 in total would suffice for all intents right now). The visualization, thus, of something composed of nothing is nothing. I don’t see anything paradoxical nor contradictory about this: am I wrong?

Let me take your example to try and clarify:

Consider the set of all natural numbers. Imagine the set is a bag & the natural numbers are colored balls being thrown into the bag. This can be but an asymptotic approach to bounded infinity, as any specifiable boundary cannot hold or bind an unspecifiably large volume.

In set theory, they quite literally postulate the set (i.e., {N}) of natural numbers as an actual infinite, which is considered a complete set of infinite elements (i.e., a set, formally speaking at least, is a bounded form).

Think of it this way, if one accepts the intermediate value theorem, then there is exists an actual infinite of points between two points on a graph. Therefore, the line that can be drawn by connecting those two points is said to have an actual infinite of points that compose it; however, the interesting thing is that the conception of the line itself is as a bounded form (i.e., a line which begins at one point and ends at another) but yet is said to have content (that is, is composed of) an infinite amount of points. This would be what is traditionally called an actual infinite (of which I term a bounded infinite).

The problem with your example, I think, is that we don’t, unlike a line, conceive of a bag as holding, prima facea at least, an infinite amount of balls: we assume it can hold a finite amount. However, we could say that a given ball is constituted by an infinite amount of points (which would be a better example of a bounded infinite).

With that being said, let me go back to your paradoxes:

Let me assert a premise – All origins are paradoxes.

Your narrative ventures into paradox.

“1” and “1” are identical but not indiscernible. This implies that “1” simultaneously
is/is-not itself, a paradox.

Firstly, you could, for the intents of the essay, postulate “all origins are paradoxes” as a superordinate rule, within the context of your derivation, and continue down that derivation to determine the exact conclusion you made: this entire process (that is, derivation itself) is still abiding by the principle of regulation and that is the main focus of the essay. My premise that “1” and “1” are identical but not indiscernible was apart of my example of derivation (which I was defining the law of identity) which a critique of that premise has no bearing (I would say) on the principle of regulation. Even if it is the case that my premise implies that “1” simultaneously is and is-not itself is a paradox, that whole procedure abided by the principle of regulation. The principle of regulation doesn’t dictate what I or you think is rational but, rather, what is possible (including the very concept of possibility).

You support the above with,
It must also be regarded, briefly, that law of noncontradiction can possibly be negated by the individual at hand by means of this principle of regulation and, therefore, the principle of regulation can be regarded as the most abstract form of the law of noncontradiction.

I was not meaning here to postulate a logical axiom that the principle of regulation is the law of noncontradiction, just that, abstractly, it could be regarded as similar since it disallows “affirmation and denial” within an incredibly specific sense. That sense is so specific that I don’t honestly think it is synonymous at all with the law of noncontradiction but, to be fair, I mentioned it. If it helps you understand, then please regard the principle of regulation as completely separate from the law of noncontradiction.

At this point, principle of regulation has expanded its scope to encompass the super-position of QM (in cognitive mode). Importantly, in so doing, it contradicts itself super-positionally.

I don’t see how this is the case, but if you elaborate further then I can more adequately respond.

Now your essay seems poised to utilize higher-order logic henceforth.

Could you please define “higher-order logic”? You may be right: I am just not sure specifically what you mean by it.

First causes, I assert, possess transcendent boundaries, which is to say, non-local boundaries. As such, these boundaries of first causes require examination by higher-order analysis.

If you could elaborate, then that would be appreciated. At first glance, I don’t think my essay is dealing with “first causes” nor “transcendent boundaries”, but it depends on how you are defining them if I would agree or disagree definitively.

Axioms are the metaphysical boundaries of 3-space phenomena.

If the above is true, then analysis, in the instance of derivation from non-local origins, must be higher-order analysis, which means a multi-dimensional matrix above our 3-space matrix. This higher-order matrix is the tesseract, a 4-space matrix + time.

Firstly, my essay is not grounding itself in objective nor subjective reality (therefore, not a consideration of 4 or 3 dimensional space). Secondly, as a side note, I don’t think anything transcends human reason (not even the very concept of transcending human reason).

I look forward to hearing from you,
Bob

Nice to meet you Rocco!

What is the first question?

I apologize: I am having a hard time understanding this question. Could you please reformulate the question? What exactly are you asking (what is "the first question")?

What basic rules or laws have you decided are unchallengeable (that which cannot be contradicted)?

The essay depicts one sine qua non, which is the principle of regulation; that is, as defined in the essay, "the subordinate rules cannot be affirmed and denied in accordance to the superordinate rules within the given operation of derivation". This principle is not argued, in the essay, as "unchallengeable", indisputable, irrefutable, or indubitable: it is considered, on the contrary, a sine qua non.

I suppose these unchallengeable laws are related to what you have determined to be sine qua nons (absolutely necessary)

Sort of. Again, it is not argued in the essay as "unchallengable". Moreover, in the essay, it is directionally related in the converse manner to what you seem to be conceptualizing it as: a sine qua non is what is being related to the law/principle. The essay is not arguing for an "unchallengeable law" which, thereafter, is related to a sine qua non: the law is determined to be a sine qua non, and that is all the essay covers. Likewise, it is not argued as absolute nor necessary (although I understand one's urge to commit to that idea, it is strictly separated from the specific, narrow sphere of argumentation that the essay is supposed to cover).

By its very nature, "Metaphysics" is a type of "thinking outside the box."

We may be utilizing the term "metaphysics" differently (and that is fine!). For me, I am using in the sense of "a study of what is outside objective experience" and "a division of philosophy that is concerned with the fundamental nature of reality and being and that includes ontology, cosmology, and often epistemology". The reason I termed it "foundational metaphysics" is because the foundations are what I deemed not a matter of objective or subjective experience: it is the pinpoint, so to speak of all derivation (however, it is specifically "all" in the sense of an unbounded infinite negative as opposed to a bounded infinite void). With that being said, I am completely open to the idea that "metaphysics" is not the best term, so please correct me if you think I am wrong!

The entire concept of "infinity" [(positive or negative)(bounded or unbounded)] is alien to Metaphysics

I am not sure how you derived this conclusion? Many metaphysical discussions pertain to eternity, for example, which is a infinite of some sort. I don't see how metaphysics is alienated from the discussion of infinities. Of course, I understand that certain specific infinities are out of the discussion, such as physical causation chains.

In each study, inquiry or, investigation, of that which is determined to be a Metaphysical event is explained in the portion of the outcome or product that deals with methodology.

I am not entirely sure what you mean here: could you please elaborate further? I've tended to see metaphysics pertaining to the logical explanation of the overlying instantiation of the physical world. For example, platonic idealism would postulate that Universals explain the phenomena of particulars in the physical world: that is an explanation, regardless of its validity, of the overlying instantiation of the physical, particulars of the world. Is that what you understand metaphysics to be as well? Please correct me if I am wrong.

Thank you,
Bob

I still don’t think I fully understand what you are meaning, but I think I have a better idea now: thank you for the elaboration! Let me try to clarify.

Firstly, the essay is not meant to be taken as a dogma: it is not positing sine qua nons as indubitable, irrefutable, or supreme. I don’t find anything about it suggesting anything analogous to a cult, but I would be interested to hear what exactly you thought was meant dogmatically (if anything)?

Perhaps it would be beneficial if you specified one example within the essay that exemplified what you are trying to convey, as then I could do a better job at addressing your contentions.

I mean for example "Prima facea" would be one of them it would be a "tool" and by tool /semantic / metaphysical concept I'm just sticking labels on the same thing over and over again to try to make sure I cover the whole thing in stickers because I don't know exactly what the preferred thing to call it is but I'll call it a tool because it's something you utilize

So, for clarification, is everything constituted as a “tool” to you to some degree? Is that the idea?

By semantics, I usually am referring to argumentation pertaining to what underlying meanings should be attached to what words to optimize the expression of the view at hand. Are you defining it differently?

By “metaphysical concept”, are you referring to something that is not merely a “concept”?

Hmmm I'll try , so what I mean is that how do we know that the "tool" is even the very thing that it's name claims it to be

I am not entirely following: maybe a specific example would help. All areas of inquiring must start with definitions, whether they be implicitly or explicitly defined. My essay is merely explicating those definitions to provide the utmost amount of clarity possible. If there is a definition of a term you don’t think is correct, then I would be more than happy to engage in semantics about it: I just, as of yet, don’t really know what terms you are contending with my essay.

I realize you explain each one of them in great detail about how to use it specifically as well as its nature however we never question if that's a facade

A facade is when something is not of the nature one supposed it was. What about my terminology is a facade? I think they are clearly defined and justified. One can most certainly contend with those definition if they would like: maybe in toto isn’t the best word for conceiving a conception as a whole? There’s nothing dogmatic about that definition: it is just for means of conveying my main message and that term was just the most suiting.

because it's impossible for a human being to invoke that tool or even impossible for the human brain to know if something like that existed being the only one of its kind and things of that matter

This essay is to be considered prior to ontology and epistemology. Therefore, it is not a discussion of knowledge (i.e., of whether a human brain knows X). Likewise, there isn’t an assertion that there is a brain or that it is ontologically what exists as a material substance: none of which, for or against, is addressed in the essay.

An example being my personal view on time we use this concept called time or "tool" called time and according to the parameters we're told we're allowed to judge Time by it works and according to the parameters we're told to use time it works and usually we never question it because it works however I view time as just a concept that has been overlaid on an action that actually exists to make it look as if time is the thing that actually exists when it's not it's like a facade

Time may very well exist, ontologically, or maybe it doesn’t. If the former, then it isn’t necessarily a consideration of a tool, as it is possible, prima facea, that what a human utilizes as time isn’t how time actually exists. I would agree though that a lot of our ever day-to-day ideas of time are typically socially constructed; but, that doesn’t mean that time doesn’t exist at all nor that it is completely socially constructed. I could, for example, measure only by the hour; or only by the day; or never at all; or only by means of a generic change; all of which does not prove time is holistically a facade.

I believe that there's change change happens to different things at different speeds and this happens in space so you could say SpaceTime but actual time linear the one that pseudoscience says eventually we'll be able to go back in time or hop to the Future in as if there's a version of us waiting somewhere in a filing cabinet to be messed with that concept called time does not exist yet it's easily usable and works in most scenarios and most people go their whole life without questioning it so that's the kind of situation I'm wondering could occur with these other tools.

Are you referring to Special Relativity vs the colloquial use of time? I don’t think are should be disbanded of: there’s not much use for special relativity in the laymen lives. It’s contextual.

I am just not sure what about the “tools” of my essay are a facade or even suggest it: could you provide an example?

Things like time is a tool the theory of gravity is a tool things of that nature the segments of your essay are discussing the mechanics of a tool I just don't have a better word to use so I'm confusing everybody using my weird bucket of random words LOL my apologies

No worries my friend! I am trying to understand your view; however, I am just not quite following as of yet.

What I mean is there's so many steps in so many guidelines I think it's impossible for somebody to put down all their bad habits and all their good habits for that matter and use the format laid before us in this essay in its entirety I think there's too much to it too many steps I think that not only are people going to forget how to use the tool the way you said to use it but I think we're just going to revert back to our old habits when reading your next essay because your first one was so complex

Firstly, I think this objection is irrelevant to whether the essay is true or not.

Secondly, this could be said of anything that surpasses any given individual in terms of their potential (or faculties of reason). Most people can’t fully grasp many academic concepts, even basic math. Are they all in vain in virtue of that? I personally don’t think so.

I guess what I'm trying to say is that a person can make almost anything logically look true and be usable so long as you control what is considered to be true and how people use it

Again, my definition of “true”, in the essay, is not dogmatic. Within all fields of study, and even colloquially, some definition of “true” must be formulated. This is why I gave a very precise definition of “true” and “false” in the essay.

I think I should clarify that the principle of regulation is not by any means something enforced upon people: it is being argued as something that is always occurring. It’s not that being need to be consciously aware of such a principle: it is being argued as always there.

Also, many principles are utilized all the time in the field of logic (e.g., law of noncontradiction) which are by no means dogmatic in virtue of being a law or principle.

It's easy to use and it works when used but are we actually using it properly?

So using it properly I would deem apart of the sphere of the next essay, which will depict the consequences of its affirmation. The purpose of the essay put forth here is a proof that it is true that it is being used as a sine qua non.

Can we actually really know if a situation qualifies the use of the term "sine qua non"?

The essay’s purpose is to (1) endeavor exactly on that journey and (2), thereafter, prove that the principle of regulation is qualified as a sine qua non. Do you think that it isn’t true?

How can re really know if there's no other option for a thing or situation I can we really know?

Firstly, again, the essay is prior to knowledge in a formative, epistemic sense: so a sine qua non is not being postulated as known in any manner.

Secondly, When you ask if you could ever rule out an unknown extra option: nothing about a sine qua non determines that, in your derivation, that you could not arrive at that conclusion.

Thirdly, a proof of the principle of regulation being “without which, not” (i.e., an unbounded infinite negative) lies in the essay: I am not sure what about it you are specifically contending with? Is the proof invalid?

Bob

It's simply a process that's unbounded.

It depends entirely on what you are referring to as unbounded: content or form? For example, the set of all natural numbers is regarded as an actual infinite (what I deem in the essay a bounded infinite) because, although it is unbounded in content (i.e., there’s a limitless amount of natural numbers), the form is of a set (which is a conception of natural numbers as a whole, in toto, which has bounds). I would say that an “infinite” is denoted by being limitless in content (with no immediate regard to its form), which I think is the only aspect that interests you (which is totally fine). If you are using “infinite” to denote something which is limitless in content (with no subsequent regard to its form, which would require a subdistinction of some kind), then as long as you are conceiving “without which, not” as an unbounded infinite negative (which you would term simply an infinite negative) that is fine. The subdistinction is still vital as the form of the infinite is important in the essay. For example, that is why it is “without which, not” and not “without which, none”. If you are able to discern that without postulating any subdistinctions of infinities, then I have no problem with that.

In math an actual infinite potential (I've never heard it called that - but I don't live in that mathematical world) is vague unless it corresponds to a cardinality.

I have never heard of an “actual infinite potential”: the debate, philosophically and mathematically, is between actual and potential infinities. In other words, the valid form or forms of infinities is highly disputed, regardless of them all being limitless in content.

Tones-in-a-deep-freeze could go into this in a much more rigorous way.

I think that, for you, going deeper than limitlessness is futile or maybe redundant (or extraneous maybe?). However, the distinction is prominent enough for me to deem it worthy of specification. If you are still able to understand how a sine qua non is not a bounded infinite negative (i.e., a proof of nothingness if without a conception) without positing a “bounded infinite”, then that is fine: I just don’t see at this time how it would be beneficial to erode away that distinction.

I would have guessed more precise.

I think we are both right in this regard, because we are anchoring precision on converse goals: I was using “precision” in the sense of the goal being to get to the most complete abstract of a concept (as opposed to particulars), whereas you seem to be (and correct me if I am wrong) utilizing “precision” in the sense of the goal being to get to the most particular of a concept (as opposed to abstract). Therefore, I meant it in the sense that my goal is not to define “infinite” in the sense of one particular example (of many); whereas, you seem to be thinking the converse.

Give me an example from the real world of what you are talking about.

The classic example is natural numbers: a full set of natural numbers is an actual infinite, whereas the continuation (in form) of natural numbers forever is a potential infinite. Another example is to take physical causation (as I believe you referenced earlier): the conception of the totality (what I would call in toto to be precise) of all physical causation is an actual infinite, whereas the conception of the continuation of some chain of physical causes/effects would be a potential infinite.

Bob

There's no significant dispute that I know of. Most of us not in foundations or set theory are not concerned with "actual" infinity.

I think there is a big enough recognition of it, for the sake of the essay, to clearly and concisely define the terminology. However, I agree that more than likely most people think of one “infinity” when they conceive of that concept.

I assume what you are talking about is moving backward through causation chains with no recognizable beginnings.

In terms of infinities, here’s what I mean:

“infinite” = limitless in content (with no specification, at this general level, of its form)
“unbounded infinite” = limitless in content (infinite) and unbounded in form.
“bounded infinite” = limitless in content (infinite) and bounded in form.

So an example of an “unbounded infinite” could be moving backward through causation chains with no recognizable beginnings; however, that is not the definition: it is an example of one specific defined infinite I discussed in the essay.

Like backward iteration in which there is no end to the number of iterative steps, but the process is either bounded or unbounded.

So, in the sense you put it here, a bounded backward iteration with no end to the number of iterative steps would be what is traditionally called an actual infinite and unbounded potential—which is what I was essentially noting in the essay (when defining). However, just to clarify, I am not defining an infinite nor bounded/unbounded infinities in that manner, but I could see them as less precise examples. Am I understanding you correctly?

Bob

I apologize my friend! I honestly could not tell, but I see now that it was most certainly in good faith! With that being said, let me address your questions.

But then you go on to explain the perspective that we should have on several different semantic metaphysical concepts and tools yet not one time question if any of those tools should even be considered to actually be what they came to be?

Before I can adequately respond, I would like to inquire exactly what you mean by “semantic metaphysical concepts” and “tools”? Are you saying that the essay defined terminology but yet didn’t elaborate why they weren’t simply semantically defined differently?

You tell us how we should view and use and judge each of these semantic tools but once again not once question if they should be tools or if it's even possible to know if they actually are what they say they are before contemplating if they should be added into the tool belt or not

If you could give me an example, then that would be appreciated—as I don’t think I am quite following. Are inquiring why an in toto and in total were defined the way they were? As opposed to simply defining them differently?

And as far as my understanding goes when you investigate something you investigate it is far down to the root core as you can which in my eyes means investigating if we should even consider it a tool if it's possible to call it a tool and if it could ever actually be what it says is before then learning how to utilize it

The essay doesn’t invoke the term “tool”: what exactly do you mean by that term? I am not attempting to ban its use but, rather, just wondering what exactly you are referring to?

And lastly you touched on so many different tools and in such great depth on each one of those tools do you really expect people to do what you said? Or should I say do you think it's possible that a person can sat their tool belt down and pick up that one you just laid out in your essay? Do you think a person can remember that many new tools?, and utilize only those tools in the exact way you explained in your next essay that you write?

The essay concedes that anyone can reject it; however, a sufficient proof has been established for it being true regardless of whether it is affirmed by any particular human being. Again, if you could elaborate, then that would be appreciated.

I'm not even sure if that's possible I don't know if anybody could remember that many methods of how to use that many tools and properly utilize them without their old habits kicking up causing them to judge things the way they're used to

Prima facea, I think this is a different contention than the validity of the actual content of the essay. As far as I am understanding you (and correct me if I am wrong), it seems as though the entirety of the essay (and subsequent essays) could be true and yet there is still the contention that people may not be able to remember it. Is that correct?

Or am I just completely missing the entire boat on this one? Let me know please

I wouldn’t say you are missing the boat, my friend! I am just not of yet completely understanding what you are conveying and that’s on me.

I look forward to hearing from you,
Bob

Nice to meet you Cuthbert!

From the OP I get the impression that you think people may not behave well in the discussion

I have observed many discussion boards on this forum which do not exemplify what I am envisioning as a productive conversation and, therefore, I was merely, by established some rules, attempting to ensure some (what I would deem) methodological principles of discourse. My intention was not to make any commentary on the forum as a whole or to foreshadow a wave of bad actors.

and now you have raised a suspicion that someone is trolling - on no grounds at all that I can see.

I was incorrect in that judgment, although I think there are grounds to argue such (just given the one post), but that is why I simply responded to them stating that I wasn’t sure what to make of it (and if it was trolling, then to stop or if it is of good faith, then I cannot wait to hear their feedback). I hope that my response was not taken with any offense: if so, then I apologize.

Do you think you might go with the flow of posts to some extent and see what results? You may get different and interesting points of view that way.

I am all for the idea of allowing the conversations to flow as long as they pertain to the essay (i.e., the OP). I do not see how the few rules I declared stunt any conversations, unless they are derailments. If you think that they are hindrances, then I would appreciate further elaboration on how. Nevertheless, I agree in that allowing a flow (as opposed to rigid, constant policing) is preferable and is my intention.

Regarding the essay, I think it is so far an answer without a problem - or at least without a problem having been stated clearly. Maybe we need a principle of regulation. Maybe we don't. What problem(s) are you trying to solve by proposing one?

What exactly are you referring to by “problem”? A problem that majority constitute as such? What I constitute as such? The essay is meant as an articulation of the foundation(s) of my views and, hereafter, further essays will build off of it. I guess if one wanted to, they could view the problem as whether or not there are sine qua nons or not. The way I was positing the essay was more about a purpose rather than a problem—and that purpose is clearly stated in the introduction. Someone can most certainly come along and hold no value in it (as I specified in the essay): I find nothing wrong with that, as this essay is for those who would like to discuss foundations in the sense that I described as a sine qua non. Is that what you are asking?

In other words, if one doesn’t want to partake in such a purpose, they don’t have to.

How have other people approached those problems?

I have a couple in mind that were influential in my thinking, but they have no direct relevance to the essay: the essay is not meant to expound on the history of ideas (or the history of solutions to problems). If you have someone in mind (or some idea or solution) that you think contests with my views in the essay, then I would love to hear about them!

Bob

Although I understand the point pertaining to the dispute amongst mathematicians over "potential" vs "actual" infinities, I am not sure how that objection relates to my essay. If you could please provide further elaboration, then that would be much appreciated.

Cheers,
Bob

Nice to meet you my friend!

To be completely honest, I am not sure if your post was out of good faith or simply trolling. If the former, then I look forward to your assessment of the essay! If the latter, then I respectfully urge you to refrain from further trolling.

Thank you and have a great day,
Bob

Absolutely no problem! Take as much time as you want: I would imagine we both prefer substantive responses that take some time over swift, insubstantial ones. I have no doubt that you are an excellent, well-educated philosopher and, therefore, I am incredibly interested in what you make of the essay.

In terms of the question-begging, specifically as it relates to logic, I share with you in that concern and hopefully I can provide elaboration on why I don't think it is the case. For now, to keep it brief and allow you to navigate the discussion as you please, let me provide the following:

By a "logical language", I mean a formal logic (e.g., classical, intuitionist, paraconsistent, etc.) or an informal logic (which I am defining in its most general form: the attempt or practice at deriving logical thought and principles of logic outside of a formal setting). I am using "logical language" and "theory of logic" synonymously for the intents of the essay.

The proposition in the essay does not pertain to the logical axioms utilized in the examples (which would be what I was constituting as a consideration "of derivation" as opposed to the consideration of derivation of derivation--and its abstraction towards its recursive use). It is about the higher performance of derivation itself and, in the case of the essay, a proof of the principle of regulation as being a true sine qua non.

In other words, to keep this brief, the reader can most certainly reject and utilize whatever axioms they would like (or even attempt with none, at least prima facea), as the attempt to produce a logical language (i.e., formal or informal theory of logic) is only by means of the principle of regulation (as a sine qua non).

That is why I did not, to my self-assessment at least, invoke logical axioms as the grounds of any of the proof but, rather, only as an example derivation to demonstrate the proof of the sine qua non: I could have, for the sake of what I was trying to convey, utilized even the most irrational of premises (I just thought it would be harder for people to understand if I did). If there's anywhere that you deem question-begging in terms of logic, please let me know as I would love to reevaluate the essay if that is the case.

I look forward to hearing from you,
Bob

@Philosophim,

First and foremost I want to thank you for a wonderful discussion (as always)! I appreciate you taking the time to respond the points I made that had no relevance to your epistemology and for being willing to discuss it in this forum. However, as you suspected, I don't think you quite understand my epistemology (and that's no fault of your own) nor do I 100% understand yours. I think it is best if we actually just pause the conversation here and reconvene after I post my epistemology. Then, you will have a fair grasp of what I am trying to convey and we can revisit our conversation of your epistemology. Then we can juxtapose them and explore them more adequately. With that being said, I think it is best that I actually leave it with your last post having the last word: although there is much I would like to say, it will all be addressed properly in my epistemology post (once I get the time to post the whole thing).

I look forward to our next conversation,
Bob

Hello @Philosophim,

Hello again Bob, this was more delayed than I had liked due to Memorial week activities and summer starting here, thanks for waiting.

As always, take your time: no worries! I have no problem waiting for substantive, well-thought out replies (:

The goal of this exploration was to see if someone could poke holes in the d/a distinction within the argument itself. I feel that has been adequately explored. At this point, it seems to be the dissection of your theory, and I'm not sure I want to do that on this thread. It is unfair, as you have not had the time and space to adequately build it up from the ground floor.

That is absolutely fair. This is your thread and, thusly, I want this conversation to be directed exactly where you would prefer: if you think that the discussion has met its end (in this discussion board at the least), then by all means we can conclude whenever you deem so! I completely understand the desire to prevent irrelevant derailments on the thread, and I can see how diving into my epistemology could do just that. With that being said, someday soon I am planning on posting an in depth analysis of my epistemology and, as always, feel free to rip it apart (: It may be a little while though as I want to ensure its quality before posting.

With that being said, I will respond to your post with the intention of keeping it relevant to your epistemology but also very briefly responding to some of the points you made about mine (or alluded to them in your responses). After that, if you wish to cease the conversations on grounds of derailment, that is totally fine my friend.

To be honest, I don't think you are entirely understanding what I am trying to convey, but that is by no means your fault and it is entirely possible that you do and I am failing to perceive it. To keep it brief, let me address your points on PoN and how it relates to what you defined as PoI.

Lets list what the PoN is. In Western Philosophy it is often associated with Aristotle and comprises several principles. The law of the excluded middle and the law of contradiction for example.
'if p, then not not-p,'
'if not not-p, then p.

My contention here would be that the LEM (law of excluded middle) is by no means apart of the law of noncontradiction even with respect to classical western logic: they are completely separate principles. Instead of positing it as "not-p" and "p", which are meant to presuppose the use of LEM and PoN together, there separability can be more easily demonstrated as follows:

"B cannot be A and not A" (or more precisely "B cannot be A and not A at the same time")
"B is either A or not A"

The former does not directly necessitate the latter in this terminology, but using "not-A" instead of "not A" implies LEM--as anything that is A = not not-A and thusly anything that isn't A is a not-A, which means that the if conditionals "if A, then not not-A" and "if not not-A, then A" directly necessitate the law of the excluded Third. But within the refurbished terminology it is quite clear that B necessarily not being "A and not A" does not necessitate that B is thereby one or the other. This is the wiggle room where paraconsistent, paracomplete, and, as you noted, eastern logic, such as catuskoti (tetralemma) notions, are able to be conceived. Also, as you noted, the kotis actually do allow for B to be A and not A . To keep it brief, my point is that my use of PoN is not meant as a logical construct like those, and its precise definition holds no immediate favoritism on the battle between paraconsistent vs consistent logical languages. I am defining PoN in the form of predicate-logic:

"a predicate cannot contradict its subject concept"

Or even more precisely:

"a predicate cannot be true and false of its subject concept"

This move is admittedly subtle, potentially sneaky, which turns out to be vital. This is not equivocal to "B cannot be A and not A" nor "B cannot be A and not A at the same time"! To keep it brief, here is an example where the distinction matters:

"circles are green and not green" (aka: "Bs are A and not A")

A more classical logic enticed individual will deny this sentence in virtue of the obvious (A and not A), while a more paraconsistent minded individual will allow it in at least some circumstances. However, using the predicate-logic definition of PoN, the aforementioned sentence, at face value, is not violating PoN, contrary to popular, classical logic belief. Firstly, let's allow ourselves to refurbish the subject concept "circles" how we please (with the exception of holding fast to the concept of plurality: i.e. circles), given that the sentence wasn't given any prerequisite definitions of the concepts. One particular scenario of the definition of "circle" pops out: what if "circle" is defined to contain "has essential property of being green and not green". Now the sentence "circles are green and not green" makes perfect sense: apart of the definition of being a "circle" is to have a "contradictory" state of greeness, which is perfectly definable and describable by human reason. Now, this definition of "circle" is perfectly coherent, yet does not entail any sort of "circles in 'reality' that are green and not green". Secondly, let's analyze it from the understanding of the colloquial use of the term "circle": nothing in the concept of a "circle" necessitates a certain color nor that it cannot be "green and not green". However, we have violated the predicate-logic PoN in the colloquial use of the term "circle" because stating is permits the non-necessity of color in the definition of a "circle" with its necessity in a coexistent state, which amazingly has nothing to do with the fact that we posited the color in contradictory states, this violation can also occur without it:

"circles are green"

Given a "circle" inheriting the colloquial definition, this violates PoN. With a bit more clarity, we can also violate PoN with the contradictory greeness:

"a circle, by definition, can be any color"
"circles are green and not green" (which could equally violate PoN with proposing any color even in a "non-contradictory" state in this case)

Now, I am skipping a couple steps here, but I think you get the point. This is why subjects can posit and bend "PoN", because they are not referring to what I am referring to. It is perfectly possible to hold sincerely that something is A and not A without contradiction as long as the subject concept is not contradicted by the predicate: this is the aspect of reason which is always abided by, not "B cannot be A and not A" or "B cannot be A and not A at the same time". If someone defines B as X and then posits B is not X, they will not hold it unless there is some other variables at play which resolve this predicate contradiction as no longer existent or they simply do not recognize the contradiction (regardless of how valid their derivation actually is or is not). The important aspect here is that I am trying to derive and convey how reason works as opposed to developing a logical language. Maybe PoN is the wrong term? People can most certainly construct PoN how they like as long as they abide by the PoN I am proposing (I would argue).

And, yes, I am using a constructed logical language's, predicate-logic's, form of PoN and still claiming that it precedes constructed logic, because this is analogous to simply deriving that one discretely experiences by constructing it from discrete experience. I can most definitely propose a constructed logical language which embodies a more fundamental principle than logical languages.

Now, with that in mind, let me address your PoI. Yes, one could, prima facea, construct a logical language wherein the classical logic PoN is accounted for but LEM is non-existent (which is exactly, I would say, what you did in creating PoI). In fact, there are many logical languages which deny LEM without any issues, such as fuzzy logic (https://www.globaltechcouncil.org/artificial-intelligence/fuzzy-logic-what-it-is-and-some-real-life-applications/), which doesn't utilize boolean logic (which by virtue of being boolean requires LEM) but, instead, uses values from 0 to 1. It is actually very useful in certain situations where boolean logic doesn't cut it. Logical systems, such as fuzzy logic, necessarily cannot hold LEM as that would necessitate it to be boolean logic, which would defeat the purpose.

Now, what you described in PoI is a much bolder constructed logic which is like but not equivocal to our fuzzy friends: you posited three outcomes (true, false, and indeterminate). Firstly I want to note that this is entirely possible to construct, prima facae, using the predicate-logic formulation of PoN. One can produce sentences with PoI in which the subject concept is not contradicted by its predicate, such as:

"B is in an indeterminate state"

That's fine. This makes no inherent position on what "state" must be in terms of possibility (it doesn't contradict its subject concept)--it doesn't specify that an indeterminate state must be either A or not A (LEM). Indeterminate could be ineffable, neither both, both, true and not false, or false and not true (the kotis for example). Let's take your sentence:

"Somewhere out there, I believe we'll find a thing that both exists and doesn't exist at the same time"

The reason this is possible for you to construct this sentence is because the subject concept, implicit here, isn't contradicted by its predicate: the concept of ignorance could potentially be enough wiggle room for one to posit such a sentence about the unknown. My main point with respect to your epistemology is that you are using, inadvertently, this more fundamental PoN (more like the form of predicate-logic) to formulate discrete experience. I was never trying to convey that you have been involuntarily using classical logic PoN and LEM.

What we cannot do is applicably know such a thing, which is why it is not used by anyone seriously within science.

Although I understand what you are trying to convey, logicians and mathematicians (and scientists) do not disregard logic simple based off of classical logic principles. There are perfectly applicable logics, like first-degree entailment logic, which allow for koti-like truth value systems: f (false and not true), t (true and not false), b (both true and false), and n (neither true nor false). Wherein the output of a given function is a set: {f}, {t}, {t, f}, and {} (empty set being n).

But more in terms of every day to day application, four possibility systems are also applicable, albeit not as applicable as classical logic is. Imagine I am eating cereal and claim:

"I am eating bread"

That's false and not true. Imagine I am eating cereal and claim:

"The bread I am eating is purple"

Well, I am not eating bread. So I am neither eating bread that is purple nor bread that is not purple, because I am not eating bread. Therefore it is neither true nor false. Imagine I am eating cereal and I claim:

"this sentence is false"

I could simply concede that the liar paradox outputs {t, f}, which is essentially the same thing as defining a liar paradox sentence as having a property of being contradictory (just like being green and not green). I could also simply deny its truth-aptness, which is the exact same thing as claiming the output is {} (i.e. n). As you can probably see, there are application, even in mundane life, for first-degree entailment logic.

This is incredibly relevant to how you are trying to resolve this within your epistemology:

But after determining the d/a distinction, I can then go back and ask myself, "Is the PoI something I can applicably know?" No, using the theory from there, I determine I cannot applicably know the PoI. Therefore its a distinctive theory that cannot be applicably known, and is unneeded. At best, it would be included as an induction.

You are subscribing your epistemology to LEM and PoN, most notably as described by classical logic. This rules out the actual applicable usages of paraconsistent, fuzzy, and first-degree entailment logic. My epistemology still accounts for these within their own respects.

Thus I would conclude using the POI that what is distinctively known is what we discretely experience, and I would add the claim we could discretely experience both something, and its negation at the same time.

I don't think you can posit this unless you are redefining discrete experience: the subject concept necessitates, categorically, that it be distinct, which necessitates that one cannot experience both something and its negation at the same time in the same place. As you described it, technically speaking, that is possible. I could experience a blue car and a not-blue car at the same time as long as they are not in the same place. My main point here, in relation to predicate style logic PoN, is that the subject can only posit your claim here if they either don't recognize the contradiction in the predicate or they convinced themselves of some sort of wiggle room (which requires, I would argue in your case, some refurbishing of the term "discrete experience").

What I could do is form the PoN to make the proof cleaner, but it is not required.

You can most definitely posit it without classical aristotilian logic which uses PoN and LEM, but that's not what I am referring to. You cannot help but use predicate style PoN to determine discrete experience.

Without the d/a distinction, there is a problem that the PoN must answer. "Just because I have not experienced an existence and its contradiction at the same time, how do I know I won't experience such a thing in the future?

You could, if it isn't in the same place at the same time. But let's refurbish the claim to append "at the same place" into your inquiry here to try and steel man it: the concept of space and time (in terms of their overlying references and not different theories out there such as string theory) would be contradicted by a predicate which states "Space/time contains A and not A in the place at the same time". This is why it is important to note the necessary inseparability of time and space, for the sentence "Space contains A and not A" does not violate predicate logic PoN, nor does "Time references A and not A at the same time": it's only when combined, the union of the two concepts, where the predicate contradicts the subject concept. I don't see how this is a problem for PoN as I've described it.

You have never observed these contradictions, but as noted earlier, how do you explain that this gives you knowledge that it is not possible somewhere in reality?

It doesn't. Firstly, I am deriving the possibility of reason, not constructing rationality. Secondly, there is application, rationally, for logical systems that do not use LEM and even some that do not use traditional PoN (from classical logic). What isn't possible is to sincerely posit a claim wherein the predicate contradicts its subject concept. It is only possible if one refurbishes the terminology or simply doesn't recognize the contradiction: that's the only way. At this point, I am not attempting to construct a logical system I deem most rational for a given context, I am noting the possibility of reason and therefrom asserting the fundamentals thereof.

Then this is absolutely key. If there is any doubt or misunderstanding of the idea that we discretely experience, that has to be handled before anything else. Please express your doubt or misunderstanding here, as everything relies on this concept. You keep not quite grasping the a/d distinction, and I feel this is the underlying root cause.

I think I understand that we discretely experience. However that doesn't necessitate it is a fundamental. We utilize predicate logic style PoN to derive we discretely experience. Someone could possibly deny this by introducing "wiggle room" into the concept of discrete experience to abstract applicable non-LEM scenarios or even non-PoN scenarios. Maybe my use of PoN is misleading, maybe I need to use a different term?

Without applicable knowledge, how can your theory compete with someone who uses a completely different theory using different definitions for words and concepts?

They would be using mine fundamentally. I cannot say the same for classical logic, fuzzy, etc. I can't say the same for every definition of PoN, LEM, law of identity, etc. I am speaking much broader than I think you may believe me to be.

Yes, absolute truth outruns proof.

That's not quite what I meant, but I agree. I'll refrain from further elaboration to keep this shorter and more relevant to your epistemology.

A potential infinite regress is an induction. You can deductively ascertain this induction, but it is an induction. Potential means, "It could, or could not be." If your theory has a potential infinite regress, you have an unresolved induction as the base of your argument.

Every valid epistemology must have an absolute as its point of derived contingency. Mine is no exception. A potential infinite regress is not an induction. Again, uncertainty is not equivocal to an induction. The absolute wherefrom contingency arises is utlimately reason in my epistemology. A potential infinite, of the type I am describing, is not claiming "it could, or could not be", it is claiming that a particular finite operation would be infinite if given the sufficient resources to continue. For example, counting the positive integers starting at 1 is a potential infinite. This claim is not an induction whatsoever. I deductively know that given sufficient resources counting the positive integers would be an finite operation occurring infinitely: there is no uncertainty in the claim here, only uncertainty in whether there is sufficient resources or not (which is not the actual claim here). This is clearly different, I would say, than an induction, such as, for example, if I were to claim that because I've seen white swans my whole life that all swans are white. Any sort of epistemology which grounds itself in an induction is faulty.

Mine contains no potential infinite regress.

I think it does. You can construct PoN and LEM based off of my definition of PoN, but cannot prove my definition of PoN without recursively using it. This is just like how you can't ever stop counting positive numbers granted enough resources and claim you've hit the last positive integer.

The key between us at this point is to avoid repetition. I fully understand that two arguments can be made, and eventually it may be that each side is unpersuaded by the other. It may be time where if you feel you are repeating yourself, feel free to state, "I disagree because of this previous point." and that is acceptable.

I feel I understand your positions at this point, and they are well thought out. But there are a couple of fundamental questions I've noted about your claim that the PoN is fundamental that I think need answering. Neither are a slight against you, you are a very intelligent, philosophically brilliant individual; the best I have encountered on these boards. So, if you would like, either we can start a new thread addressing your knowledge theory specifically, or we can simply spend the next post only going over your theory from the ground up, without the d/a distinction. I leave it up to you!

I understand and that it completely fair. If you would like to end the conversation in this discussion board here, that is totally fine! Sometime soon I will post a discussion board of my epistemology anyways. If you feel like this post has been utterly repetitive, then feel free to simply respond stating that, there's no need to repeat yourself countering my claims herein if you think you will indeed be reiterating.

I really appreciated our conversation, and I look forward to many more! You are also a brilliant, respectful, and genuine philosopher, and I respect that. It may be that we just agree to disagree, and continue this conversation (if you are interested) on another discussion board in the future.

Bob

I think they did. They had doctors.

"Psychological and mental illnesses were viewed as the effect of nature on man and were treated like other diseases.Hippocrates argued that the brain is the organ responsible for mental illnesses and that intelligence and sensitivity reach the brain through the mouth by breathing. Hippocrates believed that mental illnesses can be treated more effectively if they are handled in a similar manner to physical medical conditions"

I don't think this really contended with anything I wrote. The main point was that the reason "self-consciousness" didn't exist back then for the greeks is simply because contextually they didn't view it that way. Another example is still mental illness: I was speaking predominantly not in terms of one particular. The greek mythology clearly indicates a lack of "mental illness" in greek culture. That's why plato isn't writing in those terms (nor in terms of self-consciousness in that sense). One person paving the way towards acknowledging mental illness does not negate what I was trying to convey.

Science claims only physical particles are real.

Not at all. That is ontological naturalism and, by extension, materialism, which is not synonymous with "science". The only requirement to partake in science is methodological naturalism.

Christianity claims the spirit is real.

"spirit" is not necessarily equivocal to "subject". Moreover, there's a multitude of religions which claim there's a spirit. Hindus claim it is all one spirit, is that also something science is dependent on?

Thus science is the outer and Christianity is the inner. A dialectical relation.

Not at all. One can claim there is a "subject" or "subjects" without ever subscribing to Christianity. One can even scientifically posit a "subject" without invoking any religion. There's no dialectical relation here between Christianity and science: at best, there is a relationship between positing 3rd person knowledge and 1st person knowledge, that's it.

Same metaphysics. Science needs to treat subjectivity as an opposite.

This is true of every metaphysics that even hints at any kind of "subject" / "object" divide. This has no specific reference to Christianity and science. Moreover, to perform scientific investigation, one must, at a minimum, adhere to methodological naturalism, which is not required for one to practice Christianity. Likewise, most scientists tend to be also ontological naturalists, which is incompatible with Christianity. The metaphysics is drastically different, but not necessarily mutually exclusive. In other words, their metaphysics (in totality) is not even remotely close.

First person, third person. Isomorphic. Back and forth, back and forth. Each concept depends on the other.

This did not originate nor is specific to Christianity, so I am not understanding why you are specifically comparing the two. Likewise, this doesn't entail that two metaphysics are equivocal in virtue of sharing some particular aspect. Science and Christianity do not depend on one another.

Yes. Notice the fruitless debate between science and religion. They need each other to protect their knowledge domains.

How so? Science and religion are not yin and yang. They are not the same as cold/hot. Yes science needs "subjectivity" to assert "objective facts", but that has nothing to do with religion. Religion is not the source of the concept of "subjectivity".

Why did Aristotle and the ancient Greeks never talk about self-consciousness?

Same reason the greeks didn't have such a thing as "mental illness", instead they attribute it to contact with a god: during their time the knowledge they had suggested no such thing as brain malfunctions. We are heavily influenced by the context of our era.

Was there some huge leap in evolution where the brain developed self-consciousness? I think not.

I am not sure what you are trying to imply in that question. They were self-conscious back then, but that has no bearing on whether such a term or any notion of it existed back then. Contextually to us, mentally ill people existed back then, even though it didn't "exist" for them (in their context, it was a god of some sort inflicting or supplementing the person). Nowadays you hear God, you are schizophrenic, back then it was divine experience. Nowadays a psychedelic trip is simply the manipulation of neurotransmitters, but for them you were meeting god(s).

Subjectivity is that which, generally speaking, pertains to the 1st person experience of an individual. I think science actually denies any such truth in its methodology: it necessarily approaches empirical knowledge from the perspective of 3rd person as a methodological approach.

The Christian tradition--which science participates in--uses subjectivity as the site of truth.

I am not sure how science participates in (1) christian tradition or (2) subjectivity: with respect to the latter, it tries to eliminate it into 3rd person light and with respect to the former I see no relevance whatsoever.

Sometimes called inner experience, it is supposed to make the reality of humans unique, which other things in the universe do not have.

I think both more materialist and idealist minded people would agree to this. Even if one is reducible to the brain, that doesn't eliminate the real 1st person experience.

The error is that only humans can have or use intelligence. Thus intelligence is a function of the human mind and the subjective.

How is this a flaw? Ideally, what would constitute as "without flaw" then?

Hello @RolandTyme,

I may not be able to solve the dilemma in its entirety for you, but, as this was an issue I used to have constantly as well, perhaps I can provide a bit of exposition.

As you explicated in your post, your contentions (or more like doubts) pertain to a very specific flavor of Christianity, and that is totally fine. However, at face value, I think you can rule out the possibility of a literal hell, in the sense you described, because in order for someone to be in eternal torment, they must necessarily have the capacity to feel it, and there's legitimately no possibility of feeling without a body: there's no possibility of pain without objects. This inevitably transitions the conversation towards a transference of an individual from their body to another body, as any non-spatialtemporal consideration of a "being" would be incoherent with the conceptualization of a burning hell. With regards to physical-to-physical transitions from one "world" to another "world", prima facea, it would not be impossible but it has no grounds. If one were to fret about every possible proposition, regardless of what grounds it may stand, then they would have an infinite amount of highly intensive claims to contend with, of which they definitely won't be able to deny outright. For example, I could claim to you that the mind, once the body dies, transfers to another body and depending on your karma you will either be one of the unlucky individuals that gets tortured your whole life or one of the lucky ones that lives lavishly. This proposition, even if it is deemed "possible", does not entail any legitimacy. Likewise, I could worry every second of every day that someone is always scheming to kidnap and torture me, without a shred of evidence, but what about the concept of possibility necessitates that I ought to take it seriously? I submit to you: nothing. Again, it could be the case that there's a drunk driver on the road and they could hit me with their car if I decide to go take a walk, but if such a mere possibility were to guide my actions then I would never take a walk!

Now, at a deeper level, I do think that transcendent concepts, like most conceptualizations of God and an afterlife, are contradictions: there are no actual infinites. The idea of eternity only exists insofar as it exposes a concept that encapsulates a contradiction (albeit not obvious). The concept of eternity simply concatenates the concept of a potential infinite with the concept of actuality, which doesn't actually produce a new concept beyond a potential infinite. Likewise, to claim there's an actual infinite of anything implies that the claim is truth-apt but, in fact, it is not. If I told you there's an undetectable unicorn next you right this very moment, is that truth-apt? I submit to you that it is not. To try and pursue an answer (i.e. true or false) with regards to that proposition is in vain because to pursue it implies it is truth-apt, which it is not not: therefrom the contradiction arises. So, I would submit to you, at a deeper level, an eternal damnation is, at best, nothing more than a potential infinite of inflictions on an object that produces some form of pain, which would be a contradiction to even attempt to prove that it actually occurs forever (transform it to an actual infinite), and, at worst, it simply exposes a concatenation of concepts, as opposed to a unionization, in a contradictory manner (no different than concatenating the concept of "square" and "circle" together, which does not produce a union of the two).

To keep it brief, I will stop there. I hope that helped a bit.
Bob

Hello @Philosophim,

Please do Bob! You have been more than polite and considerate enough to listen to and critique my epistemology. At this point, your system is running up against mine, and I feel the only real issue is that it isn't at the lower level that I'm trying to address. Perhaps it will show a fundamental that challenges, or even adds to the initial fundamentals I've proposed here. You are a thoughtful and insightful person, I am more than happy to listen to and evaluate what you have to say.

I appreciate that, and same to you! Most of my conversations on this board, apart from ours, hasn't been very fruitful. It seems as though most people on here like swift abrupt responses and then get bored and move on to the next topic. I, and I think you as well, like longer, thought-out discussions that really go much deeper. That's why I really enjoy our conversations, as you are very respectful, genuine, and are providing thought-provoking responses.

The fundamental issue between us is becoming clearer and clearer for me, and I suspected as much but now I think it is pretty solidified. I think this is the pinnacle of our fundamental disagreement:

Philosophically, you seem to be taking a heavy realist methodological approach whereas I seem to taking a heavy anti-realist methodological approach.

Consequently, I am performing derivation starting with the mind and working my way outwards onto the "real" world, whereas you seem to be starting with the "real" world and working towards your mind. Now, firstly, I want to disclaim that I am not in any way trying to put words in your mouth or unfairly fit you in a category, I am merely explicating what I think is the root issue here, which is reflected quite clearly (I think) in our disagreement in terms of what a "fundamental" is. Secondly, when I stated you seem to be working "towards your mind" from the "real" world, obviously you are thinking and therefore are starting with your mind in that sense, but what I mean is that you are grounding fundamentals in the "real" world, whereas I don't. Subsequently, I think you would hold (correct me if I am wrong) that your mind is from a brain (which the latter would be more fundamental than the former) and, as you mentioned, the atom is would be more fundamental than the brain. That kind of derivation, if I am allowed to say so, is a realist approach which I would gather, if I may guess, you are probably somewhere along the lines of an ontological naturalist. Again, not trying to put words in your mouth, just trying to get to the root of the issue between us, as I don't think that our disagreement is as easy as "fundamental" semantics.

I, on the other hand, although I used to be in that boat of thinking (ontological naturalist, materialist), approach it from a heavy anti-realist position. It took me a while to recognize the shift in my thinking over the years, but in hindsight it is quite obvious. I start with the mind and, therefore, only subscribe to methodological naturalism (as opposed to ontological).

I think, in light of the aforementioned, it is glaringly clear to me why I am thinking PoN is a fundamental whereas you think it is discrete experience. I don't think going back and forth about "you had to use PoN to claim that" (me) and " one cannot think about the PoN without first being able to discretely experience" (you) is going to get us anywhere productive. I would simply respond with the same counter argument that you already know well, and thusly I don't think you find it productive either.

I think, and correct me if I am wrong, you are arguing for discrete experience in virtue that the brain (or whatever object is required, to keep it more generic) must produce this discrete experience for me to even contemplate and bring forth PoN (in other words, I must discretely experience). Now, I don't think that is how you explained it, but I think that is a pretty fair (admittedly oversimplified) generalization.

I understand that, and in contemplation of my body as an object I agree. In contemplation of other bodies, objects, I agree. But in relation to myself, wherefrom derivation is occurring, I start with PoN and derive the relations of objects (and one conclusion is that the brain produces discrete experiences wherefrom it makes sense contemplation of PoN can arise). However, to claim that that is truly a fundamental in relation to the subject is to take a leap, in my opinion, to bridging the gap between mind and brain, which, as of now, I do not hold.

Before I dive into direct responses, I want to explicate clearer what I mean by "fundamental". I am not talking about a contextual fundamental in relation to another object. Yes, atomic theory is more fundamental than molecular theory (I vaguely remember that conversation, and if I argued the converse then I was mistaken) contextually within that relation. I am talking about, do I dare say, the absolute fundamental. By absolute I need to be careful, because what I don't mean is that it is unquestionable: I mean that amongst all contexts (and the derivation of what a context is in the first place) it is necessarily true.Now, what I mean by "all contexts" is in relation to the subject at hand: I am not extending this out objectively or inter-subjectively at this point.

Let me try to explicate this clearer in my direct responses:

Discrete experience is the fundamental simplicity of being able to notice X as different from Y. Non-discrete experience is taking all of your experience at once as some indesciphable.

This is simply outlining the fundamentals of how a brain works. I find nothing wrong with this. I do not hold the brain as the subject, which I think is clearly where we are actually disagreeing (realist, materialist vs anti-realist, idealist--generally speaking, I'm not trying to force us into boxes).

You are explicating a correct derivation of a fundamental contextually in relation to when discrete experience arises out of objects (this is an analysis of the mereological structure of objects, which is fine in its own accord) . However, the flaw I think you are making is bridging the gap, so to speak, between mind and brain in virtue of this: there are aspects of the brain which will never be explained from it. The brain is simply a representation of the mind, which can never fully represent itself.

But we could not begin to use deduction about discrete experience, without first being able to discretely experience. We cannot prove or even discuss the PoN without being able to understand the terms, principle, negation, etc.

Apart from the fact that, again, you are fundamentally positing objects as more fundamental than subjects, I want to clarify that explicating PoN and utilizing PoN is not the same thing. I am not talking about what is necessary to argue for PoN, I am talking about the actual utilization of PoN regardless.

Yes, but you must first understand what the terms "true" and "false" are.

I don't want to be too reiterative, but this argument is sound in relation to the utilization of PoN: without PoN, the best way to describe it would be "indeterminacy". That claim doesn't thereby grant you some kind of obtainment outside of PoN, or what exists beyond it because you just thereby used it.

In the most radical example, if I could hypothetically prove without a doubt PoN was false (even just in terms of some kind of distinction), that would be in relation to PoN. Again, I think this disagreement is really at a deeper level than this because I suspect you were anticipating this response.

While I do believe that fundamentals can be applied to themselves, an argument's ability to apply to itself does not necessitate that it is a fundamental.

In terms of fundamentals contextually in object relations, you are correct. But in terms of the absolute pin point of derivation, I think you are incorrect: that is why PoN is called an axiom: you can't prove it in the sense that you can prove something via it.

I will create the PoN using the a/d distinction now. Instead of truth, its "What can be discretely experienced", and instead of false its, "What cannot be discretely experienced. What is impossible is to discretely experience a thing, and not the very thing we are discretely experiencing at the same time. Such a claim would be "false", or what cannot be discretely experienced. As you see, I've built the PoN up from other fundamentals, demonstrating it is not a fundamental itself.

I appreciate you demonstrating this, but I think it is fundamentally still using PoN. First your entire derivation here is utilizing it: "truth = what can be discretely experienced" is an argument from PoN and so is "false = what cannot be discretely experienced". To claim that impossibility is to discretely experience and not discretely experience in the same time is utilizing the more fundamental aspect of your mind: spatiotemporality. Our minds will not allow for something to be in two places at the same time, nor one place at the same time. This is because the mind considers it a contradiction in its continuous understanding, which inevitably is based off of PoN. I don't think this is going to be productive, but my ask back to you would be to try and "create" PoN using the a/d distinction without utilizing PoN: you can't. Likewise, try to justify not that one thing being at two places at the same time is a contradiction but why it is a contradiction without using PoN: you can't. Try to point to something objective to prove it, I don't think you can: not seeing something right now in two places at the same time is not a proof that it cannot occur.

Fundamental to me means the parts that make up the whole

In mereological consideration of objects it does: not holistically. I am using it more in terms of (from https://www.merriam-webster.com/dictionary/fundamental):

"serving as an original or generating source"
"of central importance"
"belonging to one's innate or ingrained characteristics"

I am not referring to what constitutes as the parts of an object or all objects (like fundamental particles).

I've used the a/d distinction to demonstrate an explanation for why the PoN is not a fundamental as it is made out of component parts

Hopefully I demonstrated why it is not made of component parts. You aren't contending with PoN itself but, rather, utilizing it to define it differently (which is completely possible).

Barring your agreement with my proposal, you would need to identify what "true" and "false" are.

It is the transcendental aspect of the mind which determines what is a contradiction and what is not. I didn't choose that something cannot be in two different places at the same time, nor that two objects cannot be at the same place at the same time. Likewise, I didn't choose the validity of the causal relations of objects. The contemplation of the understanding is fundamentally in terms of spatiotemporal references (e.g. I can redefine PoN in terms of something else as long as it does not violate these underlying principles, if I were to define it as "discrete experience of X and Y at the same place in the same time" then that obviously wouldn't fly, but why?--because I am inevitably playing by the rules of my own mind and so are you regardless of whether either of us realize it). This happens before consideration of what must exist for us to transfer our views to one another.

I am not sure how relevant defining "true" and "false" are with this respect, because "true" is simply a positive affirmation, and "false" is a negative affirmation (denial). I think this derails quickly though because I can posit PoN for the terms as well: it isn't that X can't be "true" and "false", it is that it can't be true and false at the same time. Likewise, if X had the capability to be in two different places (even merely in abstract consideration), then X can be "true" and "false" at the same time because it isn't in the same place.

I think the problem is you are trying to use terms for synonyms to the a/d distinction. It is not as simple as "abstraction vs non-abstraction" or "creation" vs "matching". I can use these terms to assist in understanding the concept, but there is no synonym, as it is a brand new concept. Imagine when the terms analytic and synthetic were introduced. There were no synonyms for that at the time, and people had to study it to understand it.

I can assure you I am not meaning to straw man your position: if it is the case that not even "certainty" and "uncertainty" relate to it, then I am not sure yet what to do with your distinction. I am not saying it is wrong in virtue of that, I am simply not understanding yet.

I think part of the problem is you may not have fully understood or embraced the idea of "discretely experiencing". If you don't understand or accept that fully, then the a/d distinction won't make sense

I most certainly have not fully embraced it. I am not sure how that would make the a/d distinction make sense, but you definitely know better than me.

You are still at a higher level of system, and assume that higher level is fundamental.

For you it is higher, for me it is lower. For you "higher" is the mind, "lower" is the objects which constitute the production of the mind. For me, "lower" is the mind, and "higher" is the derivation of the objects. For me, "lower" and "higher" aren't really sufficient terms because they more relate to mereological structure, which pertains to objects alone.

Can you use your derived system without my system underlying it? No. Until that changes, it cannot be used as a negation of the very thing it uses to exist.

I feel like my response so far should clear up the confusion here (not saying you are going to agree with me though of course (: ).

"I" is the discrete experiencer. You've been attributing the "I" as having free will. I have not meant to imply that or used those terms.

I have no problem if you aren't trying to convey any position on free will in your epistemology, my problem is that when you state "I've noted you can create whatever system you want distinctively", that implies free will of some sort (I am not trying to box you into a specific corner on the issue). I don't see how that could imply anything else. If I walk up to a hard determinist and say that they are definitely going to catch on to that implication very quickly.

Where does the idea of negation come from? True and false?

Metaphysically the mind. Explain to me how you can derive PoN without using PoN to derive PoN. I don't think you can. Explain to me how you can validate causality holistically: the best one can do is systematically validate one connective (relation) of two objects by virtue of assuming the validity of another connective (or multiple): this occurs for a potential infinite.

Did you mean to say, "One cannot distinctively know their own definition before they perform application to obtain that?" That doesn't work, because distinctive knowledge does not require applicable knowledge.

The entire point was not to conflate or omit your terminology, when I used "application" I was referring to "applicable". I should have been more clear though: the point is that one does not know distinctively anything without performing application to know it. Your distinction is not separable in that sense like I would imagine you think it is.

Please clarify what you mean by this in distinctive and applicable terms. I didn't understand that point.

Of course. Forget for a second that you have obviously imagined a "pink elephant" before (or at least odds are you just did). Now image you "discretely experience" "pink", in isolation. Now, imagine you "discretely experience" "an elephant". Now, without imagining a combination of the two, you assert "I have imagined a pink elephant". That is a conceptual conflation. You did not, in fact, imagine a pink elephant. The concatenation of concepts is not the same as the union of them.

What I meant by "proving itself" is it is consistent with its own rules, despite using some assumptions or higher level systems like the PoN.

I wasn't referring to consistency, I was referring to completeness. Consistency is when the logical theory proves for all provable sentences, S, either not S or S. Completeness is when the logical theory proves all sentences in its language as either S or not S.

Also, I am not using truth. If you wish to use Goedel's incompleteness theorem in relation to this theory, feel free.

I was never attempting to argue you were using "truth". You are arguing for what is "true", which is "truth", but you are refurbishing its underlying meaning (to not be absolute). That is what I meant by "truth outruns proof".

What I am noting is that an infinite regress is something that cannot be applied, and therefore an inapplicable speculation.

It is applied. I think I noticed clearly in my previous post how one could negate it. Also, I want to clarify I am referring to a potential infinite regress, not actual.

My system can be constructed distinctively, and applicably used, while not using infinite regress

You just previously conceded "despite using some assumptions...like PoN". You can't finitely prove PoN. It is not possible.

Mine does not rely on such an induction, and is therefore more sound.

If I were arguing for an actual infinite regress, then it would be an induction. A potential infinite regress is deductively ascertainable.

Because I am not fully understanding (I would suspect) the a/d distinction I am going to end this with a step by step analysis of your definition here and you tell me where I am going wrong (thank you by the way for elaborating):

Distinctive knowledge is a deduced concept. This deduced concept is that I discretely experience. Anytime I discretely experience, I know that I discretely experience. This is distinctive knowledge. This involves, sensation, memory, and language. This is not the definition of the Principle of Negation, though we can discover the principle of negation as I noted earlier.

1. Distinctive knowledge is a deduced concept.

Makes sense.

2. This deduced concept is that I discretely experience.

The justification for this seems to be "Anytime I discretely experience, I know that I discretely experience". The question is why would this be valid? I would argue it is valid in virtue of PoN, spatiotemporal contemplation, etc. You know it because your mind related the objects in that manner in accordance to the rules you inevitably submit to. Causality are simply the connections of your mind. There's nowhere to point to in objective "reality" that validates the causal connection of two objects in space and temporally in relation to time: it is a potential infinite regress of validating connectives in virtue of assuming the validity of others and so on and so forth.

3. This involves, sensation, memory, and language.

I think all of these are aspects of the brain in a derivation of objects and their relations. But the relations themselves are of the mind. This is why I am careful to relate my position to reason as opposed to consciousness.

4. This is not the definition of the Principle of Negation, though we can discover the principle of negation as I noted earlier.

I agree that it is not PoN, but you are necessarily using it here. Just because you can discover it doesn't mean you weren't using it fundamentally to discover.

I look forward to hearing from you,
Bob

A moral interpretation of the phenomena implies that phenomena have inherent morals, as interpretations are phenomena.

A moral interpretation of a phenomena implies a distinction between "phenomena" and "the interpretation". An interpretation is not a phenomena and is likewise not an object (I would hold phenomena and object as synonymous). The main point I was trying to make is that morality is projection as opposed to discovery, so to speak. A moral interpretation does not imply anything moral about the objective nature of the phenomena (or object) in question.

That means that there are no goodness and badness in people or other creatures, which is contradicted by the phenomena.

Other humans are subjects, not objects. Subjects are not phenomena. In other words, there is no inherent moral "goodness" or "badness" in objects.

In practice though, what is interpreted as good or bad, can be annihilated.

I agree. But that wasn't what I was explicating: there's a difference between annihilating what one interprets as bad or good and annihilating what is bad or good. I don't think there are any valid ontic or phenomenological traits or properties or essence of objects that make them bad or good, nor any relations that produce "badness" or "goodness": it is solely a matter of contemplation of subjects.

History is full of examples.

I agree that history is full of examples of trying to fight (or even annihilate) what people (in their time) interpreted as wrong or right: that's doesn't have any relation to any objective morality.

The question is, should we allow irrational annihilation of the interpreted evil?

The way that question is framed heavily implies a specific answer (e.g. irrational annihilation pretty much turns the question into a statement hidden as a question). I'm not sure what you mean here. I think most humans would agree that we are striving to remove "evil" or even "annihilate" it if you will. Do you mean more like "should we walk to the edge of extinction to prevent 'evil'"?

Isn't annihilating interpreted evil even bigger (and objective!) evil than the evil being annihilated?

Again, I don't see how it would be objective. But, furthermore, how is annihilating evil, evil? Is this a question of "does the end justify the means"? I think the question would need to be formulated more precisely for me to give a substantive response.

Still, it seems to be happening.

If by "seems" you are trying to convey that it seems as though humans are naturally going to self-extinction, then I think that is a defensible position (I am not thoroughly convinced of it though).

The path of western man away from nature seems a path away from a natural moral.

I don't see how advancing society away from nature strays away from "natural" morals because they don't exist: morals aren't something objectively real in the universe. Sure, there's benefits to being connected with nature, but I don't see how that has anything to do with straying away from morals: our morals and ethics have progressed substantially over the millennia.

The digression from this moral translates in natural chaos and chance of natural annihilation.

There's no "natural" morality. Deviating into what most people may consider "evil" nowadays (or what they considered it three thousand years ago) does not imply that "natural chaos" ensues.

Let's face the fact. The evil is undeniably with us. It's an undeniable part of us. Of me, of everyone, of the universe, of the eternal gods.

I would take more of a cognitivist anti-realist position on morality: there are no moral phenomena, only moral interpretations of phenomena. I don't think the universe instantiates any "good" or "evil".

The question is, what shall we do with it?

"good" and "evil" are essentially the projection of subject's onto the world. Depending on the intellectual capacity of a given subject's faculties of reason, they will have a different interpretation of what the terms encompass.

However, this doesn't mean no one is correct (or more cogent) or wrong (or less cogent) in their views: varies based of off their intellectual capacities. I think the best we can do is slowly progress towards the most cogent positions by means of those subjects who can contribute, but ultimately there's no telling the capacities (and thusly interpretations) of those in power (or/and the masses) as time moves forward.

Shall we let it persist, shall we restrict it, even annihilate it?

What one annihilates today as "evil", is only an annihilation of what they considered "evil": there's nothing objective to annihilate that instantiates evil.

The last seems even worse than evil itself, for shouldn't we then annihilate the whole universe?

Do you interpret existence itself as "evil" or partially so?

Is this chance of total annihilation a means of the universe to cleanse itself from the evil we introduced, to restore the balance.

I don't think the universe has some sort of plan to restore "the balance". Humanity may annihilate itself, but I don't see how that equates to somehow "annihilating evil", unless one is referring to the fact that interpretations arguably won't exist anymore: I guess it is amoral at that point.

Hello @Philosophim,

No need to apologize for long pauses between replies, I believe we are both out of our comfort level of easy response at this point in time. I find it exciting and refreshing, but it takes time to think.

I likewise find it exciting and intriguing. If one isn't out of their comfort zone, then they aren't learning.

The problem I have with your fundamental concepts, is I do not consider them the most fundamental concepts, nor do I think you have shown them to be.

I suspected this would be the case, and I agree to a certain level: in my previous post I purposely refrained from going into a meticulous derivation of the fundamentals so as to prevent derailing into my epistemology as opposed to yours. I can most certainly dive in deeper.

The most fundamental concept I introduced was discrete experience. Prior to discretely experiencing, one cannot comprehend even the PoN.

"discrete experience" and any argument you provide (regardless of how sound) is utilizing PoN at its focal point. Nothing is "beyond" PoN. Therefore, I view "discrete experience" as a more ambiguous clumping of my outlined fundamentals. There's nothing wrong, at prima facea, of thinking of them in terms of one lumped "discrete experience", but this cannot be conflated with "differentiation" nor "spatiotemporality".

That being said, I don't necessarily disagree with your fundamentals as system that can be derived from the fundamental that you discretely experience.

You derived this via PoN. A common theme that I view as a misunderstanding is to think that the derivation of a "fundamental" should be what one can determine as what they are contingent upon: they were required in the first place. It is not what one can derive via PoN as the grounds which is the fundamental, it is what was used in the first place to derive it (e.g. PoN). A "fundamental" is that which is an unescapable potential infinite of the subject's manifestations ("thoughts", "reasoning" if you will). I claim PoN is false, it is thereby true. I claim X, it used PoN, I verified that because PoN is true. I verified "because PoN is true" via PoN: it is a recursive potential infinite. That is the nature of "reason": a succession of finite operations which are constrained to necessary principles.

But I don't think you've shown that it isn't derived from the more fundamental a/d distinction.

At this point, I still don't think a/d distinction is very clear. Some times you seem to use it as if it is "abstract" vs "non-abstract", other times it is "creation" vs "matching": these are not synonymous distinctions. Sometimes it is:

I've noted you can create whatever system you want distinctively.

Other times it is:

Free will is not necessary to my epistemology. Free will is a distinctive and applicable concept that is contextually formed.

The former implies some form of "free will" regardless of whether the term is constructed or not. The latter denies any such implicit necessity.

The way I understand it is:

- If distinctive knowledge is "creation", then by virtue of the term it implies some form of "free will" to "create" whatever one wants. Unless you are positing a "creation" derived from an external entity or process that is not the subject.

- If distinctive knowledge is "abstract", then it renders "free will" irrelevant, but necessarily meshes "creation" and "matching" into valid processes within "distinctive knowledge" due to the fact that "abstraction" can have both.

Quite frankly, your descriptions are "free will" heavy (in terms of implications): I think you are frequently mapping "distinctive knowledge" to a distinction of free construction, whereas "applicable" is outside of that construction. I don't think you have offered an adequate reconciliation to this issue (but I could be simply misunderstanding).

Furthermore, being able to always classify something under one of two categories does not entail that that those two categories are fundamentals. Your a/d distinction is like a line drawn in a potential infinite beach of sand, whereas I am trying to examine it by granule. Sure, the granule is either on the left or the right of the line, but that doesn't have anything to do with fundamentals.

What is necessary is the concept of a will.

Is this will "creating" the distinctive knowledge? I get heavy vibes that that is not what you are saying, but I could be wrong. If not, then there's a heavy "free will" implication. Even in terms of this will, if it is directing the constructed "distinctive knowledge" and it isn't an act of free will of some sort, then it isn't the subject "creating" anything: therefore they cannot do whatever they want distinctively, but maybe the rudimentary will can?

But, when your reason is placed in a situation in which it is provably uncertain, the deduced results of the experience are applicable knowledge.

This leads me to believe, instead of "creation"/"abstract" vs "matched"/"non-abstract", you are really trying to convey "certainty" vs "uncertainty", which, again, is not the same thing.

Let me invoke your definitions from a while back:

Distinctive knowledge - A deduced concept which is the creation and memorization of essential and accidental properties of a discrete experience.


Applicable knowledge - A deduced concept which is not contained within its contextual distinctive knowledge set. This concept does not involve the creation of new distinctive knowledge, but a deduced match of a discrete experience to the contextual distinctive knowledge set

This is a "creation" vs "matching" distinction. "creation" does not equate to "abstract consideration". "matching" does not equate to "non-abstract consideration".

You've typically been thinking at a step one higher, or one beyond what I've been pointing out. Your ideas are not bad or necessarily wrong.

I think it is essentially the converse. However, what makes it tricky is that your definitions think higher and equal to mine, which clouds the waters.

I am talking about a system from which all systems are made, while you're talking about a system that can be made from this prime system.

I am arguing the exact same thing conversely. I don't think your "discrete experience" is the fundamental: it is an ambiguous lumping of the fundamentals into one term. It works fine prima facea, but as I have been examining your epistemology it slowly breaks down when one gets to a/d. Neither of us can derive a/d, or any distinction, without first using PoN, connectivity, negations, equatability, spatiotemporality, and a will. These are not after nor do they arise out of discrete experience. PoN is the focal point and thereafter the other fundamentals follow logically. "discrete experience" is an ambiguous sort of equivalent to the lumping of these concepts: it is the realization that one is experiencing differentiation via the PoN, connections, negatiability, equatability, and spatiotemporal references: we cannot go beyond those, they are apodictic.

As you've noted, you had to use the d/a distinction to use the concepts that you created. I'm noting how knowledge is formed to create systems, while you are creating a system.

I wasn't trying to note that I used a/d: I was meaning that it seems as though (in anticipation) that I am given the murky waters in the definitions of a/d. You are drawing a line in the sand, I am noting the granules and the granules that make up those, etc to derive what is necessarily always occurring in the finite procession of the manifestations of reason. I am not convinced that a/d somehow is being used to derive PoN, when PoN was required to derive a/d.

As I mentioned earlier, your fundamentals are not fundamentals. I can both distinctively and applicably know what you claim to be fundamentals. I distinctively know the PoN, and I applicably know the PoN.

Being able to categorize one granule of sand either as on the left or the right does not have any bearing on what is fundamental. Even if the a/d distinction works for all granules, it wouldn't thereby be a fundamental. The derivation of a/d, I would argue, utilizes my fundamentals to get there. Try to derive a/d without using PoN. Try to derive anything without it.

Likewise, depending on what distinction you mean by "distinctive" and "applicable" it may or may not be the case that one can derive PoN in those two contexts separately. There's a definition of "PoN" in my head, which I abstractly had to perform application to know that, and I abstractly apply it to my previous abstract thoughts to determine whether it holds as apodictic: and it does. I would suppose I had to "applicably" know that I "distinctively" knew, not the other way around, because I don't know I had a definition of "PoN" until after I perform the necessary abstract applications to determine I do. "Application" and "definitions" is a murky distinction (just like creation and matching), no different than a/s.

One cannot know of their own definition before they perform application to obtain that. Once they know, then they can distinguish that from whether the definition's contents hold. It would be a conflation to claim that the definition proves it owns validity beyond it: which doesn't have any bearing on a/d. I claim "I cannot hold A and not A". I didn't know I made that claim until I applicably determine via PoN that I did claim it. Thereafter, it is a conceptual conflation to claim that in virtue of the claim it is true: this is the distinction I think should be made.

Conflation is not a function of my epistemology, but a way to demonstrate separations of knowledge and context

That is my point: there is only one form of knowledge. No matter what distinction is made, the subject is necessarily following the same underlying process. All the issues your distinction are supposed to be demonstrating can be resolved simply by noting conflations.

If you imagine a pink elephant combining your memory of pink and elephant, that is distinctive knowledge. There is nothing wrong with that.

Depends on what you mean. If you are conflating concepts, then there is something wrong. A "pink elephant" in combination is not the same as "pink" + "elephant" in isolation, it would be wrong to abstractly conflate the two.

If we distinctively identify a square and a circle to have different essential properties, than they cannot be the same thing distinctively.

This is necessarily the case because we fundamental utilize PoN as the focal point. This is not a choice, it is always abided by.

But my point was that concepts can be conflated abstractly and, potentially depending on how you are defining "distinctive", distinctively.

I may try to apply whatever my contextual use of square is, and find that I run into a contradiction

The real underlying process here I think is trying to relate, whether abstractly or non-abstractly, concepts to one another and whether it results in an invalid conflation. You tend to be using "applicable" as if it is "non-abstract".

But, when you make the claim that your derived system invalidates the underlying system, you are applicably wrong.

There is no underlying system. My proposed system is meant as the underlying system. Your definition of "possibility" implicitly uses mine. The mind necessarily considers in terms of how I defined it. Now, semantically, that is a whole different question. Your possibility's function was to note a contextual conflation, which is accounted for in my system without redefining possibility in a way that creates confusing different "could" terminology (i.e. "I speculate I could" vs "I possibly could").

This would be a flaw in your proposal then...An infinite regress cannot prove itself, because it rests on the belief in its own assumptions.

Firstly, a finite regress of reason should never prove itself: that is circular logic. Secondly, a system cannot prove all of its true formulas. Goedel's incompleteness theorems thoroughly proved that truth outruns proof: it is an infinite regress wherein a system has at least one unprovable, but yet true, formula which is only proven by using another system (aka it is non-computational).

Although I am interested to hear your reasoning, I didn't get the impression that your epistemology proves itself in that sense: it is consistent, but not complete. There's nothing wrong with that.

Thirdly, I think this is a strength of my system is that it explicates the true nature of reason: potential infinite regressions and one circular reference. This is why PoN is the focal point, as it is the one valid circular reference:

It is a potential infinite circular cycle of "X is true because of PoN", where X can also be PoN. There's nothing wrong with that: that is why it is an axiom. The reason that isn't special pleading is because all other circular logic depends on PoN and we can demonstrate therefrom their invalidity. Apodictic doesn't mean complete, it means demonstrably true (not to be confused with absolutely true). When a subject tries to prove PoN, they have to eventually give up under the conclusion that it is true as they follow the potential infinite path of derivation, which is cyclical. I don't think, in action, you can demonstrate that to be false (as that very proposition is presupposing PoN). That's why it is an axiom.

The potential infinite regressions (recursions to be specific) is simply noting what concepts are and how they exist in a infinite recursive pattern. Similar to how PoN is cyclical but yet valid, noting that when one derives any concept they can perform the finite operation to all of its properties, sub-properties, sub-sub-properties, etc for a potential infinite. All concepts, even in your derivation, are referencing other concepts in a potential infinite fashion. This is provable by means of simply trying to invalidate it: try to come up with a concept that isn't derive from other concepts. The nature of reason is a continuity: there's no stopping point. This does not rest on its own assumptions.

If you are the creator of the definitions of A and B, then there is no uncertainty.

There's always uncertainty. When someone claims they are certain of what they defined as A, they really mean that they very quickly ascertained what they defined, but necessarily had to perform application to discover what it was. They had to dissect the concept of A, and the act of dissecting implies uncertainty. This is not the same as claiming they are formulating inductions.

Let me be clear by what I mean by distinctive. Distinctive is like binary. Its either on, or off. Either you have defined A to have x property, or you have defined A to have y property.

This is not " A deduced concept which is the creation and memorization of essential and accidental properties of a discrete experience", you have defined PoN here, which is true of both of your distinctions.

I really think going through the terms has helped me to see where you are coming from, and I hope I've demonstrated the consistency in my use and argumentation for the a/d system. Everything we've mentioned here so far, has been mentioned in prior topics, but here we have it summed up together nicely.

I appreciate your response, I hope I wasn't too reiterative from previous posts here.

Bob

Hello @Philosophim,

You have brought up some very thought-provoking points and, thusly, it has taken me some time to really give it its due. I realized, with aid of your contentions, that the synthetic/analytical distinction is also not actually directly exposing what I want (just as, I would argue, the applicable/distinctive distinction isn't) and, therefore, I can no longer invoke it legitimately to convey my position. Consequently, I was forced to really dive into what I am actually trying to convey and, therein, really clearly define each fundamental building block. So, I now going to share with you what I believe to be a much more clear, distinct representation of what I am trying to convey (but of course it could not be as well (: ).

As a general overview, I still do not think (as I alluding to above) either a/s or a/d properly convey the distinction I am addressing and, quite frankly, I don't think it quite explicates properly what you are trying to convey either. I think both distinctions are missing the mark: in hindsight, the a/s more than a/d. It is like at prima facea a/d makes sense, but at a deeper evaluation it diverges from the rightful distinction. Let's dive in.

First I need to start my derivation not at the distinction I want to convey but at the groundings, fundamentals, of everything. That is, a deeper analysis of reason to determine, recursively, what is occurring across all instantiations (because reason is the focal point of all derivation, I think we would agree on that at least generically). If this endeavor is accomplished, then I submit to you that it will be relevant, at the very least, to your epistemology as it would be the protocol by which all else conforms.

I think that, although I am open for suggestions, there are two groups of fundamentals worth mentioning right now: the most fundamental and some sub-distinctions therein. It is important to note, before I begin deriving and defining them, that I only giving ordering in terms of those groups and not in terms of the items therein: in the case of the most fundamental I am not particularly convinced one can make a meaningful order and in the case of the sub-distinctions therein I don't find it relevant at this point to parse it.

Most Fundamental:
In the case of the most fundamental, they are as follows:

- The principle of non-contradiction (PoN): subject concept which is not in contradiction by its predicate.
- Negatability: the ability to conceive of the direct opposite (contradiction) of a given concept.
- Will: a motive.
- Connectivity: the ability to construct connections via connectives.
- Connective: a concept which relates two other concepts in some manner (relations).
- Spatiotemporality: the spatiotemporal inevitable references of concepts.

These are the fundamentals which are such because they are the utmost (or undermost) conceptions that one can derive. Any other concept is thereafter.

It is important to note that by "spatiotemporal" I am not referring to "space and time" (as in two separate distinctions) but more as "space and time juxtaposed as one". Time and space cannot be separated in a literal sense.

Sub-distinctions Therein
There are two sub-groups worth mentioning at this time. First is the sub-group of connectivity:

- Possibility: a predicate which does not contradict its subject concept.
- Necessity: a predicate which is true of all possibilities of its subject concept.
- Impossibility: a predicate which contradicts its subject concept.
- Conditional (Contingent): a connective which relates two concepts in some sort of dependency. This includes, but is not limited to, biconditionals (IFF) and uniconditionals (IF).
- Unconditional (Not Contingent): a connective which relates two concepts in a manner that has no dependency (e.g. the connection that A and B are not related is a relation determined by a connective which dictates their unconditioned nature).
- Communal: two concepts share a concept.

The second relevant sub-group is of spatiotemporality:

- Quantity: A concept which is numerable. Such as "particular", "singular", "three", etc.
- Quality: A concept which is innumerable. Such as degrees on a spectrum from 0 to 1.

Immediate Productions of The Fundamentals and Sub-distinctions
Now, from those fundamentals, along with the understanding of the relevant sub-distinctions therein, arises immediate processes of reason which are identifiable, which are:

- Concepts
- Properties
- References
- Contexts
- Conflations
- Conceptual Conflations
- Contextual Conflations
- NOTE: probably many more, but the aforementioned are the relevant ones.

These immediate processes, derived ultimately from the fundamentals, are, in fact, arranged in order (unlike the two groups I mentioned previously) as their definitions rely on the previous to understand each other. They are what I would consider the "fundamentals" which can be constructed given the actual fundamentals (previously explicated).

Concepts:
A "concept" is spatiotemporal connection(s) composed of spatiotemporal connection(s).

E.g. Concept A is comprised of other concepts:

NOTE: apparently philosophy forum strips white space characters and won't let me upload any images, so I am going to have to represent by diagrams a bit odder.

'=' will be assigning operator
'[ ]' will be a set
'&' will be a reference operator
'<=>' biconditional operator
'( )' order of operations

A = [P1, P2]

Properties:
A "property" is a concept, P, which is connected (related) to another concept, C, in a manner of necessity as one of C's comprised parts. In the above example, P1 and P2 are properties of A.

References:
A "reference" is a connective, R, which connects its concept to another separate concept, wherein "separate concept" entails that the given concept is not a property of the other concept.

Concept A, which has two properties, is referencing concept B, which has a property that is not equal to either of A's:

B = [P3]
A = [P1, P2, &B]

Contexts:
A reference which dictates its concept as conditional on another concept in the manner of IFF (biconditional).

There are two concepts defined as A, but each is biconditionally referenced to concept B and C respectively (B and C would thereby be considered contexts):

B <=> (A = [P1, P2])
C <=> (A = [P3, P4])

It is important to note that the properties of both A's must be different, otherwise it is not a biconditional and, therefore, not a context.

Conflations:
The use of two or more concepts as synonymous when they are differentiable in terms of their properties or/and references (see subsequent examples).

Conceptual Conflations:
The use of two or more concepts as synonymous when they are differentiable in terms of their properties.

A = [P1, P2]
B = [P3, P4]

Conflation: B has property P1 because A has property P1.

Contextual Conflation:
The use of two or more concepts as synonymous when they are differentiable in terms of their references.

B <=> (A = [P1, P2])
C <=> (A = [P3, P4])

Contextual Conflation: A from C has property P1 because A from B has property P1.

Brief Explanation:
The entire point of the previous derivation is so that I can more accurately and precisely convey my point of view and is not in any way meant to derail the conversation into a discussion about a different epistemology (although it inevitably sort of requires such insofar as it is my position). To keep this brief, let me elaborate on my previous definitions in contrast to your epistemology:

Advantages Over Your Epistemology

Free will is irrelevant. The determination of "knowledge" is not related directly to control, which dissolves any issues or paradoxes related thereto.

Creation & Application are irrelevant. The distinction being made has no direct relevancy to whether a given concept was "created" or "applied", just that the conceptions appropriately align with the fundamentals. In relation to concepts, dissolving of the distinction of "distinctive" vs "applicable" resolves a lot of issues, such as the fact that contextual conflations can occur in distinctive knowledge which seems, in your epistemology, to be an exemption wherein no conflations can occur. Take the elephant example, here's your response:

Distinctively, there is nothing strange about taking the terms pink and applying it to an elephant. We create whatever definitions we wish. The part that doesn't make sense is stating there is some unknown distinctive identity apart from our imagination or fiction that matches to the identity of a pink elephant. The creation of distinctive knowledge does not necessitate such knowledge can be applicably known. The a/s distinction is what causes the confusion, not the d/a epistemology.

The problem is that I can conflate distinctively concepts. If I, in isolation, imagine the color pink and, in isolation, imagine an elephant, it would be a conflation to claim the concatenation of the two produced a literal "pink elephant". Given the nature of imagination, it isn't so obvious that there's a conflation occurring, but a more radical example explicates it more clearly: I imagine a circle and then imagine a square, I then declare that I distinctively know of a "a circle that is a square". What I really distinctively know is a square, a circle, and a contradiction (impossibility in this case).

The concept of "square", and its properties (essential properties in your terms), as a predicate (such as "this circle is square") contradicts the subject concept "circle" and is therefore "impossible". It contradicts it because the properties are related to the concept as necessitous by nature and therefore a contradiction in the predicate to the properties of "circle" (the subject concept) results in rejection (due to PoN): this is what it means to be "impossible".

Potential vs Possibility is now resolved. There's no more confusion about possibility because what you are defining as "possibility" is not fundamentally what it should be, however the distinction you made is still relevant. "Possibility" is truly when a predicate does not contradict its subject concept. Thereafter, we can easily explain and justify the validity of what you are meaning to distinguish with "possibility". We simply need to provide the concepts of "reality" and "self" (for example) and demonstrate that the two concepts have at least one different properties and, therefore, they are two different subject concepts. Therefore, it would be a conceptual conflation to relate a predicate to both by mere virtue of them being considered synonymous (because they aren't). It is important to note here, as I have defined it, that this would not be a contextual conflation but a conceptual conflation. This is because the approach previously mentioned is differentiating the two concepts by means of their properties and not their references to other concepts. If it were the case that "reality" referenced a context and "reality" referenced a different context, then the use of a predicate for both in virtue of being synonymous would be a contextual conflation. But in the case of comparing properties, the conflation is not occurring contextually. To be clear, a "conceptual conflation" occurs by means of properties and "contextual conflations" by means of references.

Further, notice that properties, as I defined them, are only essential (because they are utilizing a connection of the nature of necessity) and never accidental (unessential). I think this nicely portrays what the mind really does: if something is an accidentally property, what is actually happening is the mind is determining the accidental property to be "possible" (as I defined it) and therefore noting that the given concept could reference another concept but it is not necessitous. For example, if concept A has one property of "being circular" (to keep it simple) and concept B has one property of "being green", then it is "possible" for A "to be green" (reference concept B: A = [..., &B]) because "being green" does not contradict A. Now, what you are noting, and rightfully so, is that A referenced in the concept of "reality", so to speak, cannot be conflated with a reference to "imagination", which really looks like:

Reality <=> (A = [Circular])
Imagination <=> (A = [Circular])

A contextual conflation arises if one were to claim X of Imagination's A in virtue of Reality's A (and vice-versa) because of the referential difference (even though they are the same conceptually in this case, so there's no conceptual conflation). Likewise:

Reality <=> (A = [Green, Circular])
Imagination <=> (A = [Circular])

This would be a referential and conceptual conflation if one were to claim X of one in virtue of the other. In this case the conceptual conflation would determine that the concepts of A are not synonymous when compared with each other (in their contexts). Which I think is important as well.

I think, overall, this really gets at the fundamental situation of reason and how it operates, which is the pinnacle in relation to a given subject.

As you probably noticed, there is a recursive nature to my definitions: they are all concepts. This is purposely so because, quite frankly, it is an inescapable potential infinite regress of reason. Which I think is important to note that the epistemology is never complete, only consistent. The most fundamental is that which is apodictic.

The last thing I will say is that I can see how this all, at prima facea, seems like I really used what your epistemology states to even derive these terms (e.g. I "created" definitions and applied them without contradiction). However, I actually think that the previously mentioned process is what occurs as the fundamental building block of reason (at least human reason) and your epistemology happens to align with it pretty nicely, but the subtle but vital differences required me to really derive and explicate my position to figure out what wasn't quite adding up for me: I think mine explicates the situation more clearly and precisely. Hopefully that makes sense.

In terms of your post, I am now going to try to respond to what I think is still relevant to our conversation, but feel free to prompt me to respond to anything you think I left out.

I define a synonym as "Two identities which have the same essential and non-essential properties.

I would define synonyms as two concepts which have the same properties, where property is connected as necessary. Apart from the obvious difference in semantics, the important part is that non-essential properties no longer exist: they are references to other concepts determined by "possibility".

But there is no uncertainty involved. How I define A, B, and synonyms are all in my solo context.

There's a difference between saying A and B are synonyms, and trying to discover if they currently are synonymous. Maybe the latter is applicable knowledge? However, that would be solely abstract consideration, which I think you were stating was only possibly distinctive.

applicable knowledge always involves the resolution of a distinctive uncertainty

Would you agree with me then that there is such a thing as uncertainty distinctively? Because prior it felt like you were stating there's never uncertainty because I am "creating" the definitions:

Distinctive knowledge has no uncertainty.

I see this as a direct contradiction. Which I think is resolved in my position because we no longer need a/d.

No, taken alone, the process of distinctive and applicable knowledge do not explicitly involve context.

I think that I was wrong to think the distinction needed to be contextual conflations, it is actually simply conflations in general (both).

No, X alone is not an induction. "IF X" is an induction.

In the way you have defined it from the dictionary, I am no longer certain "hypothetical" is the correct term. There's a difference between stating "I believe it will rain" and "I don't know if it will rain". The former is an induction, the latter could be either: both are expressing uncertainty. The latter is not a hypothesis, it is a certainty of uncertainty (assuming it was deduced). if I state "IF it rains, THEN ...", I may not be claiming that I "believe" it will rain, I could be claiming "I do not know either way" which is not an induction. That's my only point.

Therefore it is more cogent to act as if the known certainties of today such as logic and needing to breath and eat to survive, will be the known certainties of tomorrow. My inductive hierarchy can justify itself. Can any other rationalization of inductions do so? I leave that to you.

I still think hume's problem of induction isn't really answered here. But I completely understand and agree that the most rational thing to do is the hierarchy of inductions. But more on that later as this is very long.

Bob