Nice to meet you Pie!

Or be revealed as poetry that can't be combed into a formal system ?

Could you please elaborate on what you mean by this? At prima facea, I don’t see how the essay would be poetry, as I am thinking of “writing that uses rhythm, vivid language, and often rhyme to provoke an emotional response “. In the essay, I am attempting at defining, clearly, a sine qua non and, thereafter, that the principle of regulation can be regarded as a such: I am not sure what emotional response can be derived therefrom, but I would be interested to hear what you think!

Bob

Can we have a sine qua nons for an unbounded infinite. Yes, but there is only one. That would be "not X". If not X were true, then X would not follow. Anything more specific may be a sqn for a bounded infinite, but it cannot be a sqn for an unbounded infinite.

My issue would be that “not X” is a bounded infinite and so is “without numbers”: they both must conceive of the concept in toto to negate it. Therefore, “without numbers” really is an assertion that negates itself: for I am forced to conceive of “numbers” in toto, which is a complete whole (i.e., a traditional numeric “one”) which entails I have not, in fact, omitted numbers thereby.

In saying this, I think (although correct me if I am wrong) I am, at prima facie, not only agreeing with your examples but also supplementing them here.

That is why a sine qua non is not “one” in a traditional, numeric sense: it is an infinite in total as opposed to in toto. I can posit as many in toto conceptions I want, systematically, (i.e., numerical wholes—one) within a sine qua non (as being negated) without contradiction.

Likewise, I also agree that two unbounded infinites is a contradiction in terms and, therefore, I will interpolate that into the essay (as I believe I can prove it without further axiomatic importations).

In other words, “one” sine qua non is not “one” in the sense of a numerical whole but, rather, in total; that is, the analysis of what it approaches without the ability to encapsulate it. Perhaps a distinction of a “numerical one” (i.e., “in toto one”) and a “in total one” would be useful in the essay?

The same applies to the principle of regulation. Within X words, Y meaning, and Z contexts we are still bound by words, meaning, and context. Let simplify this further. W = { X, Y, and Z } all without "numbers" or explicit individual representations. W is still bound by X, Y, and Z. The only way for W to be unbounded is just "W".

Again, I would say that all of this, including any conceptions “without numbers”, for all intents and purposes, is being conceived numerically (that is, in toto). “just ‘w’” could very well, depending on how one is noting its form, be “one” (in toto) or “one” (in total)--I am unable to discern given the context thus far.

In terms of the arguments for our contingency on words (as an example), that argument is ultimately contingent on PoR. A set of implicit or explicit superordinate rules were utilized to derive the conclusion (reasonable and rational conclusion I must add) that a human being is contingent on words to explicate their messages (or at least, heavily contingent, as body language is a thing technically). However, the argument from the essay is that without PoR not “a human being is contingent on words”.

Can thinking things within this limit form and use conclude the logic of the principle of regulation is necessary. Absolutely. But can this be concluded from "W" alone? No, I don't believe it can.

I am not quite following what you mean by “’W’ alone”: could you please elaborate a bit? The point of noting the form of an infinite is for the expression that one cannot omit it without absurdity in relation to the definitions provided: it, simply put, cannot be bounded. I feel like we are more in agreement then we may have realized.

No, I'm not stating this. I'm stating an unbounded infinite is not a concept. The moment we create a concept within it, we are now within a bounded infinite. As such, there is only one unbounded infinite. Anytime any explicit infinite is proposed, it is by nature bounded.

I view this as you defining “concept” as having an essential property of “bounded form”; however, it is possible to define it as “bounded or unbounded in form” and I do not see, as of yet, why this would be a contradiction or an absurdity. Therefore, I think, so far, we are merely semantically disagreeing. If by “concept” you mean something with necessarily bounded form, then I simply would have to come up with a different term. I think what you are trying to convey is that that term I create, whatever it may be, is necessarily bounded in form: but why? At the bare minimum, I can conceive of a concept which prohibits boundaries as a continual process (therefore, not merely within a context of space or time or what have you).

You shouldn't need sqn's to prove the principle of regulation to logically thinking minds. And even if you do, perhaps its something you could come back and show later? Is the concept of a SQN within an unbounded infinite absolutely needed to continue your line of thought from the PoR proposal? If you just started the sentence with, "If we have the ability to derive, the principle of regulation logically arrives," would that hamper what you want to do? I feel you have so much more to say, and possibly introduce greater thoughts that I would hate to see stopped over focusing on what may be a technical, and perhaps unnecessary detail to show us what you have planned.

I agree! I think that I am going to begin building off of the essay and, once I am done, I will post them all together (as I think doing it in segments has only produced more confusion). I think that this essay will be readily available to reference if a conversation requires it, but there’s no need to squander time on it right now. With that being said, I still would love to hear what everyone thinks, so continuing to contend with infinities is totally fine with me: I will just be allowing myself to continue my adventure whilst that is occurring.

This right here is where I think you should go into detail. Prove not only to yourself, but that none of us can conclude anything differently. If you do this, I don't think anyone is going to need the infinite. How in the absence of derivation must we all necessarily have the principle of regulation? If I am not a being able to derivate, could I conclude I could not derivate?'

Regardless of how one puts it, whatever they derive utilized the principle that the subordinate rule(s) could not contradict the superordinate ones. However, the tricky and slightly confusing aspect is that, they can most definitely utilize PoR in a manner where they are convinced that it is not true or the case.

For example, if I were to postulate a concept of “a being that cannot derivate”, then I am doing so by means of deriving something which cannot derive. Consequently, whatever concept I derive for “non-derivation” is contingent on derivation to have been manifested.

As another example, if I were to postulate a concept of a derivation that “is not the use of subordinate rules not being able to contradict the superordinate rules”, then I can readily identify the superordinate rules I utilized to even derive that very concept itself. As a particular example:

I concluded X.
Y was the sole superordinate rule within the derivation of X (i.e., I determined it solely off of X, let’s say).
X is and is not true of Y.
Therefore, PoR is not applicable to this derivation.
Therefore, PoR is not true.

If I take it as granted that each is true (e.g., Y actually was the sole producer of X), then I can dissect this further to realize it is being derived by PoR (as it is a mere facade that it is not applicable by means of the possibility of negating it). For example, for me to have concluded X, I abided by the rule that the following could not be true and false within the derivation: X can be true and false of Y and Y can still determine X, but thereof cannot be true and false lest “I concluded X” is indeterminate as is. Likewise, to determine something as the “sole contributor” requires its own set of derivation with this same exact relation (and PoR being not applicable by some deductive or inductive argument, and PoR not being true by some deductive or inductive argument, etc.). Likewise, my argument that it is required requires one, and so forth. I can quite literally keep abstracting, particularlizing, and more generally deriving this infinite nest whereof it never rests upon an absolute foundation, so to speak.

This even functions for irrational or absurd derivations, such as:

I think 1 = 2 is true and 1 = 1 is true

We can perform analysis on this in any direction, with any goal, in mind—but one of particular interest is that they seem to be committing to the idea that 1 is and is not 1 (i.e., the absence of the law of noncontradiction): that would be an implicit superordinate rule.

In explicating that to them, they may reject that notion as well:

I accept the law of noncontradiction and “1 = 2 and 1 = 1” is still true.

Assuming, for all intents and purposes, that they aren’t merely conceptualizing things differently or semantically refurbishing well known concepts, they are still abiding by some set of superordinate rules to be able to possibly derive it in the first place. It could be that they hold the law of noncontradiction as exempt from itself or some other goal motivating their derivation, but the point is that we never get to a point where we can rest metaphorically upon absolute grounds, so to speak. Even if I conclude that “they simply derived it arbitrarily”, then the rule of arbitrary randomness governed their derivation. And my conclusion thereof and its justification will be by superordinate rules as well.

Bob

I asked my questions about time vis-a-vis PoR because I want to know who does PoR as sine qua non have as his neighbors? I was conjecturing that time is one of PoR's neighbors. As such, time does not prove PoR as sine qua non. Instead, time is one of PoR's neighbors, which is to say time & PoR are a matched set. One always implies the other.

If I am understanding you correctly, then I would say that there is no “neighbor” to PoR. I think, and correct me if I am wrong, you are essentially arguing that time and PoR are biconditionally related. However, an argument for time (and, I would say, space) encompassing all one’s cognitive faculty requires the use of axioms which do not lie within the essay. The axiom, so to speak, for the essay is two-fold: (1) an engagement in the attempt to derive a sine qua non and (2) implicitly the use of the definitions without contradiction.

With that being said, I agree that “derivation” implies “time” (and space): it is just that that would require axioms not granted nor required to accept PoR.

I haven't forgotten your explanation to the effect that, by definition, two sine qua nons are mutually exclusive and thus cannot both belong to one set.

I think that, upon further contemplation, I can prove, without the importation of other axioms, that two or more sine qua nons cannot be true. For example, if there were two true sine qua nons, then they would, by definition, have to independent, but, also by definition, they would be, as independent “without which, not”, biconditionally dependent on one another. In other words, for one to be a sine qua non, the other would have to be dependent on it; but, since likewise for the other, they would really be two biconditionally dependent concepts, which would not be sine qua nons by definition. Therefore, there can only be one true sine qua non. I think I will interpolate that into the essay here shortly.

Some other candidates for neighbors of PoR might be superordinate & subordinate rules?

PoR is the principle that the subordinate rules cannot be affirmed and denied in accordance to the superordinate rules within the given operation of derivation (as a recursive principle). The terminology of “superordinate rule”, “subordinate rule”, “rule”, “in toto”, “in total”, etc. are merely a means of describing PoR itself and, therefore, I, as of now, do not see them as “neighbors” of PoR but, rather, more like a means of explication.

If PoR has no neighbors, how can it fulfill the role of sine qua non in total isolation?

I apologize: I may have lead you astray by not acknowledging that only one sine qua non can be true. A sine qua non is not isolated but, on the contrary, it is that which everything in total (as opposed to in toto) is contingent upon (including “contingency” as a primitive faculty of reason). Therefore, it is ever present (in total that is, not in toto).

When the temporality of an object is undecidable, is not the location of said object also undecidable?

PoR is what we utilize to determine what “time”, “undeterminancy”, “location”, etc. is. It is what we utilize to determine what is is, etc. It doesn’t have a location like a physical object in space (I would argue).

My underlying premise here is that even a purely cognitive "object," holding a priori status, by force of causality (inter-relatedness) obtains location. In this example, location of sine qua non is first member of a sequence.

I don’t think it is a priori or a posteriori because both require PoR to classify anything therein or to even construct the terms themselves. I don’t think it would make sense to classify it as a priori, for example, because that is merely something else we derive, given a set of implicit or explicit superordinate rules.

I'm starting to suspect that sine qua non, as absolute solitary, without neighbors covering peers & subordinates alike, in parallel to the singularity of the Big Bang, cries out for conceptual revamping that addresses the deeply problematical boundary ontology of origins.

Although I may just be merely misunderstanding you, I do not view a sine qua non as isolated whatsoever.

Bob

Hello Philosophim,

Wonderful points as usual! Let me try to respond adequately.

I don't think we can say an "unbounded infinite of negations". That's really, a "bounded infinite of negations"

By “negation”, to be more precise, I mean a “complete negation”; that is, that the entirety of what is negated is completely obliterated (so to speak). Therefore, I do not mean a “partial negation”. Consequently, I am in agreement with you that “not X” necessarily entails that X is bounded (which is what I noted as “being conceived in toto”) because to negate it I must implicitly treat it as completely not (as opposed to “partially not”).

However, as far as I am understanding you, you seem to be asserting that an “unbounded infinite of negations” (which, we are in agreement, is an “unbounded infinite of nots of bounded concepts”) is somehow entailed to be equivalent to “a bounded infinite of nots of bounded concepts”. In other words, it seems as though, from my point of view, you are rightly identifying the bounded nature of the contents of the unbounded infinity and, in virtue of that, extending it (or maybe misassigning it) to its form.

I can see an unbounded infinite negated, because an unbounded infinite is the base from which all bounded infinites are formed.

Categorically, I think it would be a contradiction in terms to posit the negation of an unbounded infinite: that is actually a bounded infinite. Let me try to explain:

But if we say that all possible bounded infinites are negated, isn't that the same as stating an unbounded infinite is negated?

I don’t think these are the same concepts that you just described and I think it is the root of our dispute. Firstly, it is important to note that I am not, at this point, attempting to prove that there is an unbounded infinite but, rather, I am merely trying to prove there is a valid concept of such that is at your disposal—for, as of now, it seems as though your contention lies in the denial of an “unbounded infinite” as a valid concept (i.e., it is really a “bounded infinite” assigned a new name).

To simplify it down for all intents and purposed for now, it seems as though, to me, you are essentially stating: an unbounded infinite of nots = not an unbounded infinite.

I would describe it as a difference between conceiving in toto and in total. Bundling up all those negations found within the unbounded infinite into a “complete concept” is to necessarily contradict the very concept (that is, attempt some operation which necessitates it to be conceived in toto). By “concepts” I am not entailing that it have a bounded form, which is what I suspect you are at least partially committing yourself to.

You are conceptually performing a different task to completely negate an unbounded infinite. What you seem to have done is analyzed the content of an unbounded infinite in terms of the sum of its parts to derive what it approaches (i.e., in total) and, thereafter, conflated that with in toto--thereby considering “not an unbounded infinite” valid; However, nothing about the sum of the parts of a concept entails that it can be conceived as a whole (that is, nothing about being conceivable in total entails that it is conceivable in toto).

This is the exact issue that required of me to explicate that, in the essay, a sine qua non is “without which, not” not “without which, none”; that is, the natural and swift leap from the sum of the parts of the content of a concept cannot entail its form in any way whatsoever (and nothingness is a great example of that). The unbounded infinite of nots does not necessitate nor prove a complete concept of nothingness (i.e., in the essay: “none”). The essay itself, consequently, does not even attempt to prove that “without the principle of regulation, there is nothingness”, because the PoR is also valid of the statement “without PoR, not nothingness” and “without PoR, not everythingness” (and so on): there is nothing which “escapes” it, so to speak.

The issue you may be having conceptualizing it is quite understandable, as with everything else we tend to swiftly conceive of finites and bounded infinites in toto based off of in total: but I have separated the two modes of thinking. For example, if one were to postulate what an infinite of empty sets would exist as in space, then they are more than likely going to quickly derive the summation of the parts to conclude that it would be nothing. This, however, in the sense of separating the two modes of thinking, is only valid by positing the form of the infinite as bounded. Therefore, I am noting the two different modes of thinking involved in the assessment:

First, the individual determined in total the infinite of empty sets, which is 0. This mode of thinking requires simply the ability to conceive what a sequence approaches (e.g., I cannot actually perform 0 + 0 forever, but I can nevertheless reasonably conclude it results in 0).

Second, the individual implicitly shifts their mode of thinking to in toto to “package” and “bundle” their conclusion into a wholly conceivable concept (e.g., 0 in space is nothing); that is, they assume that their evaluation in total of the infinite of empty sets warrants the ability to substitute the infinite for a bounded counterpart equal it in total (e.g., the total of the infinite is 0, therefore where ever I utilize the infinite I can substitute 0 for it). But, there is a distinction here, I think, in that they are not necessarily equivalent and, thusly, they are not always guaranteed to be valid of substitution: performing substitution of a bounded for an unbounded necessarily means that the form of the concept has been reshaped (by means, I would say, of utilizing a different mode of thinking). This substitution is only valid if the intents have no bearing on the form of the infinite: if the form matters, then 0 cannot be a valid substitution for an infinite of empty sets. Admittedly, a vast vast majority of the time I think the form is dismissable; however, my essay (I would argue) is an example where the distinction is vital.

The best I can think of is that we must be able to make conceptualizations out of/within the unbounded infinite. Because if something could not, then nothing could create any sort of differentiation between bounded, and unbounded. Does this somehow fit within your PoR?

I may be misunderstanding you here, but PoR can be utilized to make distinctions, but the very concept of PoR is also via itself. Therefore, the indifferentiation or differentiation of PoR from other things is via PoR. In that sense, PoR cannot be separated from anything, including nothing.

This again is where I have a hard time. Without a sqn, nothing can be. Which means without a sqn, concepts cannot be either. The way I read the essay and your explanation, it seems to imply without a sqn, the infinite, bounded or unbounded could not be.

Another great point Philosophim! This, I would say, is your other major contention with my work (which is not the same as what was previously mentioned). Let me explain it back to you (to ensure that I am understanding correctly) and then I will attempt to adequately address it. Here’s what I think you are essentially saying:


#1
p1. A sine qua non is “without which, not”
p2. Therefore, by definition of #1p1, a sine qua non contains “without which, not “concepts””

#2
p1. A unbounded infinite is a concept
p2. By substitution property and #1p2, a sine qua non contains “without which, not “unbounded infinite””
p3. By #2p2, it is a contradiction in terms to assert an unbounded infinite as a sine qua non.
p4. Therefore, an unbounded infinite cannot be a sine qua non.

The issue I would have is:

1. #1p2 is only partially true: I am allowing a “concept” to be incomplete in form and, therefore, a sine qua non only contains “without which, not “concepts with a complete form””. The mode of thinking matters to me.

2. Therefore, a sine qua non cannot contain a concept with an incomplete form.

Note: by “incomplete form”, I do not mean a concept merely conceived as incomplete in content (e.g., an incomplete apple) as that is complete in form (e.g., a complete concept of an incomplete apple).

Now, at face value, my response seems to be a contradiction: if a sine qua non is an unbounded infinite of negations, then it seems as though I ought to be able to negate it within itself, otherwise it cannot be deemed true. The answer is that one can subvert a sine qua non through itself; however, that is to necessarily erode its form to that of being bounded (i.e., to shift my mode of thinking to in toto), which is not really a sine qua non: I am thereafter dealing with an imposture so to speak and not the real thing.

Likewise, if only complete forms are allowed, then it seems as though there is something which persists with the negation of a sine qua non: concepts with incomplete forms, which contradicts the idea of it being a sine qua non in the first place. However, again, an incomplete form is an unbounded infinite or a contradiction in terms (e.g., either unbounded with infinite content or a contradiction wherein it is unbounded with finite content). In terms of the latter, it is invalid. In terms of the former, we must contend with it: does an unbounded infinite persist, as a concept with incomplete form, without a sine qua non? The answer is no, because, again, to posit an unbounded infinite as without a concept necessarily shifts the mode of thinking in toto, which contradicts the term itself. If this operation is permitted, then the unbounded infinite simply (1) is not an unbounded infinite and (2) does not persist without a sine qua non because its eroded bounded conception is wholly within the jurisdiction of a sine qua non (“without which, not”). Therefore, I submit to you that an unbounded infinite is not out of nor within wholly and, therefore, it stands not outside (without) a sine qua non and, in turn, it does not pose a threat to the concept thereof.

Again, I think that our dispute first lies in whether an “unbounded infinite” is valid as a concept, which hopefully I have proved herein, and, after that we can then discuss whether there is such a concept. As always, I could merely be wrong about the concept itself.

Bob

In isolation, I agree that your quote of mine makes little sense; however, in the context of the entirety of the response where it is contained I think it makes sense. I would suggest reading this post in its entirety (if you haven't already) and then feel free to ask specific questions about it.

If I had to extract certain parts of the linked response, then I would provide further context:

Within the scope of the essay, I would disagree (albeit incredibly reasonable to assume). Yes, it is reasonable to infer that the procedure and proof of the essay is necessarily that of temporal relations (sequences in succession of one another). The important thing is that, as of now, I find such a conclusion (i.e., derivation or the principle of regulation is temporal) to only be found by importation of other axioms (or, in my terms, superordinate principles which are not apart of the standard terminology nor proof explicated in the essay. My point here is not to completely discourage your conclusion here, but only to expose that it is by means of other superordinate rules other than what is required (I would argue) to prove PoR to be true. In other words, it is entirely possible for one to accept PoR as true and immediately thereafter assert PoR is in time, is time, is sans time, neither in or outside of time, etc

…

I am not entirely certain that a stable methodological approach can be establish to examine the properties or existence of PoR, but that is something I am currently contemplating. I find compelling arguments to assert it is aspatio-temporal (because there is no where which would reasonably pertain specifically to PoR and any derivation of its temporal sequences of derivation are simply via it), but, in contradistinction, I find it compelling to argue for its spatio-temporality (because being sans time & space seems merely to be a conceptualization under space and with time); however, I think both arguments are within the real of critique of derivation (as they are both inheriting from this PoR meta-derivation if you will) and, therefore, I think that, with respect to PoR itself, the best way to conceive of it for the essay is neither true nor false of the former nor the latter. It just simply seems inapplicable, but correct me if I am wrong.

Nothing about it has to do with the fundamentals being proven in the essay (i.e., that the principle of regulation is a sine qua non--being a true statement) I would say. If it is still confusing, then please let me know and I can elaborate further.

Another member of TPF has in the past submitted a lengthy and sophisticated essay on a theory of everything (or roughly that), starting with an assumption every fact in the universe can be encoded for use in Turing machines. But doesn't explain how.

I am not familiar with the essay you are referring to, but it seems disanalogous to mine. It seems as though the point of their proof was to show that their claim is true, yet their proof was vague: I don't find that my proof is vague, but correct me if I am wrong.

In terms of your other post:

This essay might get a larger following if all this infinite stuff were in mathematically acceptable nomenclature. Just a thought.

What exactly would you suggest in terms of mathematically acceptable nomenclature? What about our discussion of infinities is confusing within the apperception of mathematics?

Bob

It is true that 1=1 in the world defined by the definitions and rules of mathematics. The rest of us just accept this truth on blind faith based on the accomplishments and power of mathematics to be useful in the sciences.

I have brought up the pitfalls of 'true' in metaphysical reasoning. For metaphysics akin to mathematical reasoning, True is a binary value for evaluating dichotomies, any other use of truth is common but can be shown to be invalid or unsound. Since '1' is just like any other concept, it can not be true that '1' and '1' is anything other than '1'. Just as 'orange' and 'orange' are 'orange' and nothing else. However, instantiations of 'orange' are countable. 1 orange +1 orange = 2 oranges. And 1 apple +1 orange = 2 fruit

I would like to clarify that the essay pertains to the higher principles involved in the example given therein, as opposed to a critique of the derivation itself (i.e., of the example derivation of 1=1). Therefore, within the scope of the essay, nothing about it is meant to prove that you must accept 1 = 1 as true. This seems to be what you are contending with: am I correct? If not, please correct me where I am wrong.

Indexical means 'relative to context of utterance' - like 'he' or 'here', as you say. The term 'existence' does not seem relative to context in that way. You go on to say that it has different senses, which is different from indexicality.

Upon further contemplation, I agree with you that ‘he’, as an indexical use of language, is not analogous to my use of different senses. However, what I was really trying to convey in terms of “indexical” is “of or relating to an index”, which I do still think applies (although my example of ‘he’ was fallacious).

You may well be right. Hamlet exists as a character in a play and does not exist as a flesh and blood human being. So sure, there are different kinds of existence in that way. But to say for example that Hamlet exists but does not [open italics]actually[close italics] exist is confused and confusing.

I still think that there is a meaningful distinction to be made the sense of existence of a thing and there are different terms for such. For example, ‘ontic’ (e.g., noumena and phenomena) usually refers to the being of things and ‘ontological’ is the discussion of being of being (e.g., dasein). In terms of ontical consideration, I would simply dividing it up further:

There is a ‘colloquial’ sense of ‘existence’ wherein laymen tend to denote an objects tangibility.
There is a ‘phenomenological’ sense of ‘existence’ wherein in a person denotes that an object exists as an appearance, with no immediate classification of what it may exist as otherwise.
And so forth…

Now, to be honest, I slightly blundered in my use of ‘ontic’, in hindsight, as what I really was trying to convey was what sense they were meaning the term more generically than that.

When you say it is a confused outlook, I would agree if what you mean is that it would be a contradiction to assert that, for example, something exists phenomenologically and does not exist phenomenologically. However, I would be hesitant to concede that making such contextual sense of “existence” are unwarranted or that they are confusing.

You chose the cup in your hand as a straightforward example of something which exists, distinguishing it perhaps from the tiger in your hallway which (ex hypothesi) does not.

A cup does not uncontroversially exist, unless you are referencing a colloquial use of the term (e.g., it is tangible). Many philosophers, some of which I already mentioned, would not state a cup exists ontologically (or they may have other distinctions such as a cup as a noumena verses a phenomena).

It's a useful example specifically because it won't let us wriggle away from its existence.

If by “tiger in your hallway”, you mean an imaginary tiger, then I would say an imaginary tiger exists in the imagination: that’s still qualified as existing. Again, if you are thinking of colloquial “to be”, then, yes, an imaginary tiger is not tangible, therefore it does not exist (and that is a meaningful distinction in its own right).

The problem is that your cup doesn't exist sans your consciousness and the cup in your dreams also does not exist sans your consciousness. We are left with the problem of distinguishing a cup in the hand from a dreamed cup. That is, a real cup from an imagined cup.

This is true, and the subject can do so however they so please. In a colloquial setting, I typically denote a tangible cup (i.e., non-imaginary) as “a real cup” because I know most situations that is how everyone is thinking about it (they aren’t philosophers); however, I can easily and reasonably (I would say) assert that both the imaginary and non-imaginary exist in their own respects. Therefore, an imaginary cup is not the same as a non-imaginary cup, but nevertheless they both certainly exist.

Similarly, the cup in your dreams also exists contextually to phenomena and for all I know it may exist as one infinite substance as well.

I think you are committing an equivocation: just because two things are phenomena doesn’t mean they are equivalent. Just because I conceive of a chair and a table under the concept of “object” does not mean I can thereby assert them equal to one another. An imaginary and non-imaginary cup are both phenomena, but are nevertheless distinguishable in many meaningful ways. Likewise, one can most certainly reject the “phenomena” vs “noumena” distinction, as my main point pertained to possibility and not favoring one over the other.

But at some time, possibly outside the philosophy laboratory, we are going to have to distinguish the cup of our dreams from the cup in our hands, the car that hit ours from the car that did not, the positive bank balance from the negative.

Practicality is a worthy consideration, but I genuinely don’t see, as of yet, how one cannot pursue such within what I have posited hitherto. Nothing about what I stated necessarily determines imagination and non-imagination indistinguishable, an inability to distinguish different cars, nor an inability to discern bank balances.

I mean, while we enjoy this delicious atmosphere of confusion we must still keep a concept of 'existence' tucked in our back pockets for use when we actually need it and not just for when we are playing at metaphysics. And that, I submit - the concepts tucked away for use when we are serious - is our metaphysics.

I understand: it seems as though you are arguing for the practical over what you would deem the philosophical; however, I think the deeper issue is that they aren’t incompatible with one another whatsoever.

If the terms mean something like the interpretation I gave them, then I can get little sense out of this - except perhaps that if we fail to follow rules of logical inference, then we will fail to make logical inferences.

If there’s any way you think I can provide better clarification on the essay, then please let me know! What I can say is that it is not about “failing to make logical inferences”, as that is a contemplation of logic, which is not determined nor argued for in the essay.

Bob

I apologize for the belated response ucarr! I had a hefty week or so. With that being said, let me dive into your post.

WRT = with respect to

Thank you for the clarification: I was not familiar with that acronym.

Context ≅ Environment. In my thinking, environment suggests state of affairs, which suggests reality.

I wouldn’t quite go as far as to claim context is synonymous to environment (maybe that’s why you used a tilde equal sign?--to suggest an approximate equivalence). I would be hesitant to confine “context” to “reality” (which I would agree is implied with environment, at least to some degree). Therefore:

In your usage here, is individual… can transcend their own context an action symbolic or literal?

In terms of object relations, I would say that I can meaningfully produce contexts sans-my-body (e.g., I can see red, but they cannot).

In terms of consciousness, it is much harder to produce anything (or at least anything rational) without admitting the contingency of other objects on the sensations and perceptions of my object (i.e., the body). However, it is possible for a subject to posit things without their bodies (no matter how irrational/rational it may be), as it is possible to deny the contingency of something on such and, not only that, but people can produce meaningful predictions that involve positing their non-existence. So I wouldn’t holistically grant that I cannot posit sans-my-consciousness.

In terms of reason, I think that, although an individual can still assert its omission, the most rudimentary thereof is without omission (in possibility). This is the area of discourse which I am attempting to convey with the principle of regulation.

Now whether that is literal or symbolic, as I do not entirely know how you are utilizing those terms, I will leave up to you.

An essay is, at bottom, the logical language of argumentation

I think, in the sense you are positing it, I would agree. However, I would distinguish “logical language” (in the sense of a formal or informal theory of logic) from hyper-logic (maybe “meta-logic”?--I am not too sure as of yet). If you mean it in terms of the latter, then I agree. If in terms of the former, I disagree.

The stuff of logic is a continuum of conditionals that unfold sequentially, thus implying a temporal process

Within the scope of the essay, I would disagree (albeit incredibly reasonable to assume). Yes, it is reasonable to infer that the procedure and proof of the essay is necessarily that of temporal relations (sequences in succession of one another). The important thing is that, as of now, I find such a conclusion (i.e., derivation or the principle of regulation is temporal) to only be found by importation of other axioms (or, in my terms, superordinate principles which are not apart of the standard terminology nor proof explicated in the essay. My point here is not to completely discourage your conclusion here, but only to expose that it is by means of other superordinate rules other than what is required (I would argue) to prove PoR to be true. In other words, it is entirely possible for one to accept PoR as true and immediately thereafter assert PoR is in time, is time, is sans time, neither in or outside of time, etc.

Although logical expressions can be conceptualized as atemporal mental objects, continuity is always empirical & temporal

I would personally agree that derivation is always empirical and temporal; however, I don’t find, as of yet, that that is necessary to hold to prove PoR. Please let me know if you think I am wrong here.

If, as I interpret you to be saying with the above two claims, sine qua non is not of anything, and, moreover, is not at all contextual, then I get the impression the whereness of sine qua non is more mysterious than the position of an orbiting electron at any given moment. Is that the case?

I am not entirely certain that a stable methodological approach can be establish to examine the properties or existence of PoR, but that is something I am currently contemplating. I find compelling arguments to assert it is aspatio-temporal (because there is no where which would reasonably pertain specifically to PoR and any derivation of its temporal sequences of derivation are simply via it), but, in contradistinction, I find it compelling to argue for its spatio-temporality (because being sans time & space seems merely to be a conceptualization under space and with time); however, I think both arguments are within the real of critique of derivation (as they are both inheriting from this PoR meta-derivation if you will) and, therefore, I think that, with respect to PoR itself, the best way to conceive of it for the essay is neither true nor false of the former nor the latter. It just simply seems inapplicable, but correct me if I am wrong.

I now have an impression of your essay’s essence via use of a helpful metaphor wherein your sine qua non holds status akin to the singularity that precedes the Big Bang.

If there’s even a particle of truth in application of my pre-Big Bang metaphor to your metaphysical claim, then hopefully I can proceed to an understanding you’re wrestling with the boundary ontology of origin.

If I am understanding the analogy correctly, then I think I would more or less agree. PoR is simply what (I think) can be proven to be a sine qua non, which essentially means that it is the meta-derivation (so to speak). Although I think there’s a strong case to make that I am acting as if PoR is what ontologically exists, I can’t say I am able to place that within the essay itself (for the same reason as my previous elaboration on spatio-temporality).

One could, I suppose, think of PoR as a spark of derivations. Is that what you mean?

I would emphasize that the essay is not making reference to “reality” though, so it is not entirely analogous to the Big Bang.

Boundary Ontology of Origin – continuity via hyper-logic across the super-position of a non-localized QM event.

By QM, do you mean Quantum Mechanics? If so, the essay is not meant as an exposition of any quantum mechanical principles (nor is it meant to assert for or against any given scientific principle). Again, the essay is meant to be a inquiry into higher reasoning (or lower depending on how one wants to visualize it).

In terms of superpositioning, do you mean to reference its use from quantum mechanics? If so, I would say the same thing as previously, but please correct me if I am misunderstanding you.

The above definition is my best-to-date exposition of a hairy beast of a concept that is one of my works-in-progress. I won’t elaborate it’s possible pertinence to your essay because that would entail an inappropriate digression from your work. I will say I expect it to inform some of my commentary upon your work henceforth.

I appreciate and respect your effort to keep our conversation pertinent to my essay, but if it helps you elaborate on your views (in contrast to mine), then please feel free to discuss them!

Since you reject time_sine qua non, I think it imperative you state (If you have not done so) whether PoR_sine qua non is temporal, or atemporal.

I don’t find time to be a consideration necessary to prove PoR as a sine qua non and, furthermore, any assertion of atemporality, temporality, spatial references, etc. is via PoR (thereby dependent on it). As I alluded to earlier, I think for the sake of the essay it may be best to conceive of a sine qua non as neither in time nor not in time.

I’ve been understanding regulation in the everyday sense of a transitive verb that controls & shapes an object under its influence. I don’t presently see this function as being atemporal.

I agree, but by “regulation” I was meaning “to govern or direct according to rule”, which (I think) coincides with my construction of superordinate and subordinate rules. I am honestly not sure what “modulation” would entail beyond “regulation”, but if you think it is a better term for what I am trying to convey then please feel free to critique me!

Your above statement, speaking potentially, has a lot to say to the project to bring the rules of inference into congruence with QM.

If I am understanding correctly, I don’t think our ideas are perfectly aligning, but are similar. Maybe in due time we will determine them to, indeed, be equivalent.

If the above claim contains a particle of truth, then your sine qua non, as presently perceived by me, embodies something akin to the Original Utterance, itself, in turn, akin to the pre-Big Bang Singularity, itself, in turn, akin to God’s “Let there be light!”

I hope you’ll forgive the tincture of theism_Jungian psychology pooling into my assessment of your essay.

Might sine qua non, per your essay, be your Logos?

Although I don’t mind you invoking theology, I don’t think PoR is synonymous with the vast majority of conceptions of God, Logos, or the Original Utterance. The essay isn’t positing it as what created the universe, it is simply where I hit bedrock: it is the most rudimentary aspect of me (that is, me as reason: the subject).

If you think it is more alike to theological conceptions than I would grant, then I would love to hear why!

Bob

I entertain hope that your above claim expresses a/the crux of your essay's purpose.

I think that the two biggest cruces are (1) whether the individual at hand can transcend their own context (which is what you and Philosophim brought up, I would say) and (2) whether the idea of the essay preceding “logical languages” (or theories of logic) is question begging. Those, I would say, are the most concerning aspects, fundamentally, of the essay. So I would agree with you on that.

PoR can never be excluded from context

I agree, but I want to clarify that, more abstractly, it is “PoR can never be excluded”--it isn’t just contexts. For example:

Proving this logically renders PoR as sine qua non WRT context.

I am not sure what “WRT” stands for, but a sine qua non has no prepositions (as noted in the essay), so it is not sine qua non of WRT context. This may be me just splitting hairs though, because a context that is universal I really wouldn’t constitute as a context, but if that is what you mean, then I would agree in saying that PoR is a sine qua non (without a preposition).

Does this imply the concomitant> Derivation can never be excluded from context.
Does this lead us to> Context contains at least (2) sine qua nons: PoR & Derivation

Although I completely understand why you were inclined to conclude this, I don’t think it is correct. Firstly, a sine qua non is “without which, not” (where “not” is an unbounded infinite negative) and, therefore, the possibility of “without PoR, not derivation” invalidates “derivation” as being a sine qua non. Secondly, this is exactly why, derivation not being a sine qua non, produces the possibility that someone can completely remove it within their derivation (no matter how irrational it may be, as someone else could easily mention that I just literally said “someone can remove derivation from their derivation”), whereas they cannot remove PoR without utilizing it. Let me know if I need to explain more, as this is definitely where it starts becoming necessary to be precise with my terminology.

Likewise, time is by no means something one can posit as sine qua non, as “without PoR, not time” and, honestly, there are many principles that are required for it to be affirmed in the first place (i.e., faculties of reason which allow one to determine that time is enveloping of oneself, or that there is a non-temporal true claim, or neither true nor false, etc.).

I think where you may be misstepping (or I may just be wrong) is that the essay does not utilize a logical language and, therefore, many axioms that most people are more than comfortable swiftly deploying is beyond my reach in the essay. All that is utilized is the use of PoR to derive if there are any sine qua nons and, thereafter, the proof of one.

Likewise, you may have also noticed that it isn’t logically (meaning from a constructed logical language) coherent (at least on most logical theories) to claim multiple sine qua nons as true—for if there existed two then they are thereby not sine qua nons (that’s a contradiction). In other words, if a sine qua non is “without which not”, if we allow ourselves the importation of useful logical axioms, then only one can be true by definition (otherwise we have a situation where two principles are supposed to be negatable in relation to one another, but yet the source of an unbounded infinite of negations respectively). However, this is not argued for in the essay because it is, albeit enticing, something which would require the use of logical axioms and, therefore, I don’t think, as of yet, it can be argued for.

Please elaborate how regulate & modulate compare.

By “modulate”, what are you referring to? I am not completely following.

Bob

On this view, from the proposition that X exists we may not infer that X actually exists - it is not 'necessitous.' That's awkward. If you have a theory that your cup may not actually exist (having proposed it yourself as a straighforward example of something that uncontroversially does exist) then you've made a muddle.

I would say not quite. “existence” is indexical: is it awkward that I can refer to different people with the same word ‘he’? I personally don’t think so. I can posit, without contradiction, that the cup in my hand “exists” (by constituting, for example, its existence as phenomenal) while denying it as existing in an ontic sense. I gave a couple examples, such as Spinoza to illustrate this clear distinction: do you disagree with that distinction as demonstrated in the examples? If I were to posit, for example, that the cup in my hand exists (contextually to phenomena), but really exists as one infinite substance, then, regardless to its truth, there is a distinction being made there within the concept of “existence”. Another example is that a cup may exist in the sense that I can interact with it, yet not exist sans my consciousness. Again, just an example of how there is a distinction here to be made.

To ask "What does it mean for something to exist?" is sensible enough. To give an answer that denies actual existence to the very thing you have chosen as an example of something that exists is confused.

It is confusing if and only if one is conceptualizing “existence” as one universal context (as opposed to separate contexts). Again, I can say “this thing exists as a phenomena and not as a noumena”.

It may be that your cup exists but that your cup is not the thing that I think it is. Just as, for example, stars exist but stars are not the things that the ancients thought they were. They may not even be the things that we think they are.

I think that if one is to accept that something may not exist as they deem it, then there’s necessarily a split between “existence” which I constitute of things and “existence” as things-in-themselves (or potentially things from someone else’s perspective or what have you). If you are, on the other hand, uniting “existence” under one context, then I don’t see how you can state “this star exists as X, but its actual existence could be completely unrelated to my conjecture”: there’s an implicit separation into two contexts there.

You think it's clear but I say needs an example or two. E.g. a 'subordinate rule' is 'Don't walk on the grass' and a 'superordinate rule' is 'Notices in this park are posted with authority of the Town Council'. 'Derivation' is 'If p, then q. p. Therefore q.' 'Derivation of derivation' is 'If 'if p, then q. p. Therefore q', then 'If p, then q. Not-q. Therefore not p'. 'Recursive' means, well, I don't have an example. A 'sine qua non' is for example. Examples are the baby-walkers of the mind.

There is an example in the essay (as you note later on), but I suspect you found it unsatisfactory (which is totally fine).

An example of a subordinate rule can most certainly be ‘Don’t walk on the grass’ and a superordinate rule, contextually to that subordinate rule, could be “because notices in this park are posted with authority of the Town Council”. I don’t see anything wrong with this example if it makes more sense to you (it’s perfectly fine). I would note that this can be continued further (if one wants) to question the authority of the sign, etc. and through the whole process, continually, one is performing it via PoR.

By “derivation of derivation”, I mean to derive “derivation” itself. So, instead of discussing whether a particular set of premises and conclusions are true, it is a consideration of the process of derivation itself (i.e., how is derivation itself possible?). If conceptualizing that as specifically “if p, then q. p therefore q” for derivation and “if if p then q. p therefore q, then p. p therefore q” as second order derivation (i.e., derivation of derivation) then that is fine: that would be an example within the realm of “logic”, which is a form of derivation.

By “recursive utilization”, I mean that the idea is to abstract up to higher orders of derivation until (if at all) we reach a recursive use forever. By “recursion”, I mean, like a program, the utilization of itself by itself. This is most common in software engineering, wherein programmers will code functions that invoke themselves some finite set of times. However, within the essay, it would be a recursive use for an unbounded infinite (that is, to be more precise, an unbounded infinite of negations). A sine qua non is not an example, I would say, of a recursive principle, as it is merely a definition: without which, not. If some principle were to exhibit that sort of concept (i.e., sine qua non), then it would be an example of a recursive principle that is unbounded infinite of negations. It is entirely possible to have finite set of recursions, like in programming, which is not the focus of a sine qua non.

What makes this a rule? What makes it superordinate?

The reason it was a superordinate rule was because it was, within the context of the example, “a regulating principle (rule) having greater importance or rank as another”. In other words, it was meant as an example of an explication of the implicit overlying guiding affirmations of the subordinate rule (in this case: 1 = 1 was the subordinate rule, which can be also simply noted as an conclusion).

It looks like a proposition. I have say it also looks false

As noted explicitly in the essay, the focus of the example is not the truth or falsity of the derivation, it was about the higher principles involved: it is about what is occurring for the derivation to occur:

“However, before the demonstration, a couple clarifications must be noted. Firstly, the proof of the principle of regulation has no bearing on the derivation demonstrated in the example but, rather, on the higher form of derivation itself; that is, the higher procedure, as abstracted, utilized to perform derivation itself. Therefore, the reader is urged to focus heavily on the higher principle(s) engaged in the derivation of derivation as opposed to focusing on the derivation.”

You can most certainly negate my example derivation (for example, that “1” and “1” are actually indiscernable as opposed to what I claimed) by means of deriving that conclusion which, in turn, inevitably is by means of the PoR. The point is the overarching process in play, not the specific conclusions themselves. With that being said, let me address your contentions with the derivation:

I take 'indiscernible' to mean 'impossible to tell the difference between'. I have never been able to tell the difference between "1" and "1" or between 1 and 1. I can tell the difference between several instances of mentioning the number 1. I would happily buy the proposition that 1 is identical with 1 and that to mention "1" at the start of a sentence is different from mentioning it at the end. Is that what you mean?

I mean more of what you said at the end there: the law of identity. That is, we use 1 and 1 interchangeably for most situations but understand that they are discernible. As you noted, location and time are arguably the two biggest factors that make 1 and 1 most definitely not equivocal. Nevertheless, I am still able to postulate, assert, command, state, etc. that 1 = 1.

If so, that seems OK, but it does not look like a rule. It looks like an observation helping to distinguish an entity from the mention of an entity.

By “rule”, I mean “a regulating principle”. Within the context of my derivation in the example, 1 and 1 being identical but not indiscernible was the superordinate rule guiding my conclusion that 1 = 1 (in part); in other words, a regulative principle determining the course of my derivation. Does that make more sense? If not, let me know!

Bob

bam! You hit the nail on the head! That's what I was trying to ask and you answered it very well I might add.

I am glad I finally was able to understand and address your contentions properly!

So now hmmmmm... So then whats the next essay? I'm dying to see how this all ties into the next part not that I'm smart enough to know how to do anything with it LOL but nonetheless I'll pretend like I am lol

The next essay will pertain to the investigation of the obligation to affirm PoR (or lack thereof) and the consequences of affirming PoR. However, I do not want to actually spend the time writing it until I think that all the contentions with this essay are resolved (someone may convince me that I am partially or holistically wrong, which would render any further essay that builds off of it useless to me).

Bob

why are they beyond the scope?

The reason that the consideration of what exists and what is known (or lack thereof) is outside the scope of the essay is because to conclude anything with respect to either is to import an epistemology and/or ontology, which the essay is not aimed to lock anyone into or against any given epistemology or ontology; for the essay pertains not to derivation (which is what would be utilized to construct any resemblance of either) but, rather, the process of derivation itself and, therefore, the essay is true regardless of what one posits for either. Derive that this particular epistemology is most suiting to you and it will have no direct relevance to the principle of regulation; derive that this particular epistemology is not suiting, downright false, absurd, etc. and, likewise, it will have no effect on the principle of regulation (nor sine qua nons). Same goes for ontology, logical languages (i.e., theories of logic), etc.

In attempt to resolve some of the confusion, let me try to explain what I think you are asking and, thereafter, you correct me where I am wrong. Moreover, let me, for the sake of the conversation, step past the bounds of the essay to hopefully help guide the discussion.

I think that you are essentially inquiring how one can truly deem any given proposition true given the fact that they are limited in their faculties of reason and, therefore, it could be entirely possible that one is really analogous to a child who is right given the context of their limited faculty, but, on the contrary, wrong in relation to an adult (who is typically capable of much more sophisticated reasoning).

If I am understanding you correctly, then here is my response:

Firstly, this can be posited for any given theory, statement, assertion, etc. For example, one can most certainly question whether humanity can deem something true of anything: is Special Relativity true or are we simply like children that think they are the best bicycle rider? How can we be certain, in other words, that some of the top discoveries, the top minds, aren’t just ignorant of their child like boasting?

Secondly, I think this is, abstractly, really an issue pertaining to the postulation of something outside, or completely transcendent, of oneself: truth, knowledge, existence, etc. For the sake of conversation, let me step outside of the bounds of the essay and acknowledge that any of the aforementioned (i.e., truth, knowledge, existence, etc.) can be viewed, prima facea, as transcendent of oneself. If one does that, then they are faced with this dilemma I believe you are voicing: how do we ever know, prove to be true, or claim existence to anything when we cannot be certain that what we deem so truly coincides with that transcendent truth, knowledge, existence, etc. The problem here, I would say, is that, in a deeper sense (i.e., not prima facea), nothing transcends reason (in relation to the subject at hand): not even the very concept of nothingness. There is no transcendent truth, knowledge, existence, etc. It is a contradiction in terms to hypothesize about something “sans reason” when reason was what derived “sans itself”.

So, when I claim that the principle of regulation is “true”, I do not mean “truth” in the sense of something which transcends, in relation to me, myself, nor, in relation to you, yourself. To be honest, it’s not that I would deem it a figment of the imagination but, rather, simply a contradiction in terms.

and that was the point that I was trying to use to compare is that you're giving parameters and limitations and within those parameters and limitations the tools appear to be real and do work in the manner that they need to because when we question them we're questioning them within the parameters you've set and when we do that they are rendered as real and usable and good but is that only because we're stuck within that narrow parameter?

I can only ever provide what I deem worthy as true, which could be false (I don’t consider myself God (; ). Furthermore, I cannot prove it aligns with some sort of transcendent of myself “truth”, if that is what you are asking. In terms of the simple child analogy, I can deem it to be proven to consume all derivation, which removes the possibility for its exclusion; however, I could be wrong (as always).

If we were to expand further past would we find something else?

There’s two ways I am interpreting this: (1) expansion in the sense of allowing other considerations (e.g., importing a wide range of other held view, beliefs, etc.) and (2) the expansion of the understanding (i.e., reevaluation in hindsight).

In terms of #1, I think it is proved in the essay that expanding into other considerations is all in vain—for all of those importations would be via derivation, which the process of which is performed via the PoR. If there’s anything you would like to introduce into the mix in terms of consideration that you think would potentially invalidate my essay, then please do!

In terms of #2, I cannot, in all honesty, ever solidify any of my views as 100% guaranteed to be right, in the sense that I could guarantee that I will never be able to negate my current views. So, in this regard, I don’t really see it as an issue as this can be posited for anything.

The hidden #3 would be, I would say, the idea of expansion into what transcends the subject at hand—such as a “truth” which is “sans subject”. I think I already addressed this: there’s no such thing. However, I want to clear that, in some of this, I am overstepping the bounds of what is required to prove PoR: one can hold there are truly transcendent “truth” via PoR.

Now I'm by no means calling your essay limited stupid youthful barbaric or any of those other things by any means it's actually way more complex than my brain is used to dealing with but I was simply using the analogy in comparison of limitations not of complexity by any means.

No worries! I completely understand!

But regardless you're still not getting the point that I'm trying to convey and I'm having hard time trying to figure out how to convey it so bear with me while I try to gather my thoughts

Let me know if I did a more adequate job at addressing your contentions. If I am still completely missing the mark, then please correct me as you deem fit.

Bob

@MAYAEL & @Cuthbert,

I would also like to clarify that, despite ontology and epistemology being considered out of bounds of the essay, I don't want you to feel like you cannot argue for why it should be a consideration (if that is something either of you wish to do). As of now, they are considered beyond the scope, which I can elaborate further if either of you would like, but I am completely open to any counter arguments you may feel inclined to provide.

Bob

Like you were saying this entire essay in subsequent essays might work under the rules established in the original essay and everything might function perfectly fine but like you said how do we know that it's real beyond the confinements of the essay itself like you said if we take the essay and throw it away what are we left with how does it affect other things because although it might function the way it says it will function within the essay does it actually function that way in the real world or is it just a mirage

Within the essay, it is proven to be true. I am arguing for its proof as utilized as an unbounded infinite, which quite literally means that someone cannot even posit what “is real” without its underlying (or overlying) utilization. Even if someone were to negate the entire thing, then I would argue they still utilized it. Does that sort of answer your question?

And kudos to Bob for being so patient with us he truly has a virtuous personality LOL it's like a single daycare worker working overtime by themself with a room full of 3-year-old brats that their parents forgot to pick up from school and somehow in the midst of this he remains calm if that ain't zin then I don't know what is LOL

I appreciate the compliment, but I wouldn’t regard anyone in this discussion board (thus far) as a “brat”: I think that some of my contenders are conceptualization the essay in a different light than I am, which more conversations will help each of us understand each other better.

Let's say there are two kids playing with their bicycles one kid does this cool stunt going really really fast totally impresses the other kid so when they go to school the other kid is bragging about his friend and how fast he was and says he's the fastest bicycle rider in the world now when other kids hear this they want to test him so they go out and have a little competition and he beats all of them

now does that mean he's the fastest bicycle in the world?

The claim that this kid is the fastest bicycle rider in the world is false, because we can prove it. For example, let’s say we are constituting the fastest by means of the current record holder. If that is the case, then we can prove, deductively, that he is not when we time him and find out it is nowhere near the world record.

Likewise, let’s take this more literally: let’s say, by “fastest bicycle rider in the world”, we mean that literally out of every single person on the planet they are the fastest. Now, the world record is usually recorded in a manner that requires a hierarchical competitive structure, which usually omits people who didn’t have the opportunity to race. There are many factors that go into bicycle races, which I will spare you the boredom of meticulously exposing. My point here would be that we deductively know that the claim, as posited now, is an induction; that is, the premises do not necessitate the conclusion and, therefore, we cannot know that anyone is the fastest bicycle rider in the world right now.

This is not the case whatsoever with the essay (I would argue) that I wrote. It is proved deductively (which rules out the idea of my second aforementioned example of an inductive argument) by means of proving it to be true and, therefore, it is not open ended like the bicycle example.

Likewise why aren't we questioning if that is in fact what is happening with the things presented in your original essay?

Questioning anything within the essay to be true or false is perfectly within the scope of the essay, and, furthermore, I would love if you did!

However, right now, I don’t think you have contended with the actual proof in the essay, which is meant to prove it is true. If you think that the essay is not, in fact, proving that it is true, then I would love to hear why!

I believe you answered this and you replied to me saying that that was beyond the scope of this essay which is fine if that's the case but my question is why?

So, what I meant is that epistemology and ontology are out of the bounds of the essay (i.e., “is it known?”, “does it exist?”). However, questioning its truth (as in, whether it is true) is perfectly within the scope of the essay. Although I may be misremembering, I don’t think you have actually, as of yet, argued why it is false (or, at least, if not false, why it isn’t proven to be true).

The essay is most certainly meant to prove that the principle of regulation is true.

Me personally I tend not to waste my time with things that aren't as true as possibly can be and I don't find interest in exercising my brain with exercises that don't actually reflect a bigger picture usability and only work within the scope of their intended use because I feel like that can create bad habits and or give a person a false sense of reality kind of like playing video games too much makes you less sociable with people because it's not a good representation of actual reality likewise I only entertain things that are as real as can be

So, you seem to be using “as true as possibly can be” and “real as can be” synonymously; however, I am merely clarifying that (1) the principle of regulation is argued as true, and (2) epistemic and ontic claims are beyond the scope of the essay. Let me know if I need to clarify further on this, as I may still just be misunderstanding you.

I'm not saying I'm judging your essay by any means in a negative way I understand people like to do mental exercises for various reasons and that's totally cool I was just stating my personal preference

I totally understand! I think the more we discuss, the better we will be able to narrow down our differences and potentially come to an agreement!

Bob

So your cup exists but it does not really exist. It exists in a colloquial sense but not in an ontic sense.

The ontic sense is clarified by adding italicised 'really' to 'exists'. But this does not seem to add anything to the sense. I'm writing this post. Am I really writing this post? If I'm writing it, then I'm really writing it. If I'm really writing it, then I'm writing it. 'Really' is an intensifier, adding to emphasis, but not to sense.

I wasn’t claiming the cup does or does not exist in an ontic sense but, rather, the meaningful distinction I find between different usages of the term “existence”. Let me try to clarify with an example: let’s borrow a couple different philosophers to demonstrate what I am attempting to convey (that is, by means of my interpretations of them).

Let’s say I am holding a cup in my hand.

From my interpretation of Spinoza, he would not deny the existence of the cup in my hand as it appears, but would deny it in an ontic sense—as he would claim that the cup actually exists, in an ontic sense, as apart of one absolutely infinite substance (i.e., God).

From my interpretation of Kant, he would not deny the existence of the cup in my hand as a phenomena, but would deny it in an ontic sense—as he would claim that what exists is actually noumena, of which we can only ever know it by means of negative judgments. In other words, he would claim, in a nutshell, that the noumena conforms to the mind a priori (most notably time and space).

From my interpretation of Schopenhauer, he would deny that there is a valid separation between phenomena and noumena, and, thusly, would posit that they are the same thing; furthermore, he would posit that what actually exists, in an ontic sense, is an infinite will. In other words, the cup exists as an object (phenoma are noumena), but what really exists is an infinite, blind will.

My point here is that, to my comprehension, there’s a meaningful distinction between objects put forth in front of me and what lies at the bottom of existence (or what actually is existence); that is essentially what I am trying to convey. It is most certainly possible to assert that what “actually exists” is the same as what “exists” (which would be essentially claiming that whatever is deemed “existent” must be also in an ontic sense), but my point here is that that is not necessitous at all (personally I would find it problematic).

Are they useful tools?

“useful” is relative to the individual at hand. I can attest that I find it useful to understand, metaphysically, how derivation works, but that doesn’t necessitate that others find that useful.

What did you create them in order to achieve?

I created sine qua non (the term) and discovered whether there are any ‘true’ sine qua nons: I would clarify that I didn’t simply create the principle of regulation.

I wanted to discover whether such foundations exist, or whether it is essentially arbitrary (or contextual).

Are they valid - do they exist?

This is where, I would argue, it becomes necessary to be precise: “validity” is not necessarily linked to “existence”. One can most certainly package them together, but that is not necessary. That is why the essay proves that the principle of regulation is true (being defined precisely in the essay, which would be constituted as valid) and not what exists. So, I would answer two-fold: yes the principle of regulation is valid, and the essay doesn’t state yes or no to its existence (in an ontic sense specifically).

What questions or problems are you trying to address - what task did you create the tools for?

The task, or purpose, is to derive if there are any sine qua nons, of which one is determined to be true (i.e., principle of regulation). Given the definition of sine qua non, it essentially is meant to derive whether there are actual foundations to derivation or not. I think that is a pretty fair and important purpose, but please correct me if you think otherwise.

You seem to be looking for validation that they are good, useful tools.

Not quite, I would say. Again, the essay explicitly states that value is of no consideration therein (i.e., usefulness I would attribute to that area of discourse) and by “good”, I am not sure what you mean: can you please define it?

On the other hand, I am looking for critique of the essay, so in a way anything that remotely critiques it is fair game (so if you think the essay should address its usefulness or unusefulness, then that would be a fair critique to explore!).

But the essay proves, as it has been written as of yet, that the principle of regulation is true. Not that it is useful.

I am sorry that I can get little sense out of the one you emphasise most. The principle of regulation as formulated seems not to have a clear meaning.

By “the one you emphasise most”, I am starting to suspect that you may be under the impression that the essay proves multiple sine qua nons: it only proves one (i.e., principle of regulation). So I just wanted to clarify that that is the only one proven.

In terms of not having a clear meaning: how so?

I asked whether this principle can be denied or asserted with equal consequence. Suppose I say - hang on, the opposite is the case - what difficulties would that create for me, what absurdities or contradictions would it land me in?

The absurdity would be that the denial of the principle of regulation thereby utilizes it. However, it is still, nevertheless, possible for someone to simply reject it (as anyone can reject anything). I am not positing that the principle of regulation is something which can be separated from the subject at hand. For example, if we were to debate about whether redness is an inherent property of the cup I am holding, then we could, upon ending our discussion, continue our lives without such a consideration—as many concepts are completely independent of whether redness is an inherent property of a cup. This is not the case with the principle of regulation: if I reject, then I used it (and vice versa)--but that doesn’t negate the possibility of someone simply living their life ignorant (willfully or not) of their utilization thereof. Maybe that clarification will help resolve some of the confusion; otherwise, feel free to hammer me harder.

Bob

With my scant knowledge of philosophy (or metaphysics) I can't tell whether Bob is out on the cutting edge or is being cleverly deceptive, ala Sokal affair. Has he taken simple ideas of generational derivations and convoluted them on purpose, or am I just failing to appreciate his insight?

Although I may be misunderstanding, I am slowly extrapolating that you may be refraining from voicing your full concerns (pertaining to the essay) because you are not vastly knowledgeable in metaphysics: my friend, I want to clarify that I would nevertheless love to hear your contentions—regardless of your knowledge on the subject at hand. If you don’t want to, then that is completely fine as well though.

On a separate note, I can assure you that my intention is not even in the slightest to convolute a simple idea; however, if you think that is the case, then I would love to hear why! I think, with respect to the essay, it is incredibly easy to deviate from the intentions of it and, therefore, I am doing my best to be as precise as I possibly can. I think for some it is being interpreted as mere whimsical, superfluous verbiage that means arguably less than nothing, but I can assure that that is not my intention and, consequently, I am genuinely interested to hear everyone’s contentions.

Bob

I can't speak for Mayael but I can say how I understood his questions. By 'tools that actually exist' I understood the question to mean the same as I asked. Let's suppose that everything you wrote is the exact opposite of the truth. Let every sentence be negated. Let the principle of regulation be rejected and let sine qua nons go back to being what they were before. If we do that, what has been lost? What problems would that create for us? Is the whole thing a chimera, an airy nothing - a non-existent - a pretence? I am putting the matter more starkly - rudely - than Mayael - who in any case may not have had quite that in mind. So, for what it's worth.

I can see how your contention is similar to Mayael’s; however, I have not understood, as of yet, Mayael to be making your contention (but I could be wrong). Thus far, I need further clarification from Mayael to help me understand what they are precisely trying to convey.

In terms of your contention, if you could please review my response here, then that would be much appreciated. Perhaps you did respond and I simply missed it?

Please feel free to refer me to your response if that is the case; otherwise, I would love to continue our conversation if you could provide a response to mine.

By "a tool that is what it says it is" I understood to mean use of language with clear sense and purpose and without equivocation or confusion

As far as I have comprehended, Mayael is speaking much more broadly than “use of language” as a tool: it seems as though, although again I could be wrong, they are speaking in terms of “a means to an end”. However, Mayael can most certainly provide an alternative definition if I am misunderstanding here.

'Ontic' means 'related to existence' and there is no special ontic sense of the word 'existence'. Ontic existence is a kind of existence only in the way that canine dogs are a variety of dog.

Let me clarify what I meant by “ontic”.

Language is utilized most definitely not used in one universal contextual sense and the most generic subdivision is “colloquial” vs “formative” usages of languages: by the former I mean a looser, but adequate for everyday life, use of a term, whereas the latter is a highly specialized and precise definition for the branch of study (or even particularized further if you will) meant for the formation of new ideas (or critiques or what have you of existing ideas within that given field). A word can quite literally be the exact same and be posited in an utterly different manners depending on the context (and each within their own rights and proper justifications).

By “ontic”, I do not merely mean “related to existence”, I mean something related to “ontology”--which is a branch of study pertaining to what “really exists”. It is, as I was utilizing it, quite literally a contextual usage that is not within the realm of colloquial use (i.e., it is within a formative sense). For example, I may proclaim to my friends, at a casual gathering, that “this cup I am holding exists” and everyone , unless it is a highly philosophical moment, will know exactly what I am referring to—as I am merely deploying the term “exists” in a loose, colloquial sense (and that is totally fine). However, that was not an ontic claim, whereas if I were to claim that noumenon, one substance, one will, etc., then that would be. Ontology is about what “really exists” as opposed to a looser, colloquial use of the term (which usually is deployed to merely depict something resides outside of imagination or what have you). Therefore, that is why I was asking for clarification and I can assure you it is no pointless, superfluous invocation of fancy terminology.

Bob

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