I'm excited I can't wait I'm about to read it and my slow mine will masticate on it for a couple of days most likely before I reply so consider this broken rule and a friendly hello

I need to reread the essay once or twice more before I comment. As an attempt at establishing a logical foundation for "logical language" (in a subsequent essay), the treatise seems implicitly question-begging on first read. I'll get back to you once I have a clearer grasp of what I think you're up to.

Quite a few mathematicians don't go beyond "potential" infinity. We're not all like Buzz Lightyear.

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

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

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

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

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

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

I look forward to hearing from you,
Bob

Nice to meet you my friend!

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

Thank you and have a great day,
Bob

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

Cheers,
Bob

From the OP I get the impression that you think people may not behave well in the discussion and now you have raised a suspicion that someone is trolling - on no grounds at all that I can see. Do you think you might go with the flow of posts to some extent and see what results? You may get different and interesting points of view that way. Regarding the essay, I think it is so far an answer without a problem - or at least without a problem having been stated clearly. Maybe we need a principle of regulation. Maybe we don't. What problem(s) are you trying to solve by proposing one? How have other people approached those problems?

I wasn't trying to troll you I was being sincere lol

But perhaps its my over powering ADHD that has me not holding my attention long enough to grasp the body of what you are building linguistically because I am confused about something,

You said "The primary purpose of this essay is a meticulous investigation of the foundation(s) of all derivation; that is, the consideration of the derivation of derivation and, subsequently, its abstraction towards a recursive utilization"

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

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

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

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

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


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

What problem(s) are you trying to solve by proposing one? How have other people approached those problems? — Cuthbert

Ninja'd. :cool:

↪jgill

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

There's no significant dispute that I know of. Most of us not in foundations or set theory are not concerned with "actual" infinity. I assume what you are talking about is moving backward through causation chains with no recognizable beginnings. Like backward iteration in which there is no end to the number of iterative steps, but the process is either bounded or unbounded.

Nice to meet you Cuthbert!

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

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

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

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

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

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

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

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

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

How have other people approached those problems?

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

Bob

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

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

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

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

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

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

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

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

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

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

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

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

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

I look forward to hearing from you,
Bob

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

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

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

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

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

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

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

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

Bob

So, in the sense you put it here, a bounded backward iteration with no end to the number of iterative steps would be what is traditionally called an actual infinite and unbounded potential — Bob Ross

It's simply a process that's unbounded. 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. Tones-in-a-deep-freeze could go into this in a much more rigorous way.

However, just to clarify, I am not defining an infinite nor bounded/unbounded infinities in that manner, but I could see them as less precise examples — Bob Ross

I would have guessed more precise. Give me an example from the real world of what you are talking about.

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

It's perfectly fine I can kind of see how it might have looked a little bit like some sarcastic narcissism so all in good faith no harm.



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

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



>>>If you could give me an example, then that would be appreciated—as I don’t think I am quite following. Are inquiring why an in toto and in total were defined the way they were? As opposed to simply defining them differently?<<<
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 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 and we only think that that's its nature and we're not actually tackling the root of it because we're using fixed parameters by which we are allowed to examine it because we're allowed to examine it a certain way but what if it shouldn't exist in the first place 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

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

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.



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

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




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

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

I'm not even sure if that's possible I don't know if anybody could remember that many methods of how to use that many tools and properly utilize them without their old habits kicking in people just reverting back to their normal way of doing things and judging things

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

Yes you are right they very well would be but 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

this is one of the fundamental building blocks of how cult leaders control their people is it might look illogical to everybody outside of the cult but to the people inside the cult they're only allowed to judge things a certain way and do things a certain way and as long as they stay within that framework things seem logical and they seem like they work but the moment you step out of that framework it crumbles

so in that same nature (although I don't think your essay is anything like a cult )but by in that same nature I mean that the same unrealization of something that might be there that we are not aware of

For instance the "tool" called "sine qua non"

It's easy to use and it works when used but are we actually using it properly? , Can we actually really know if a situation qualifies the use of the term "sine qua non"? How can re really know if there's no other option for a thing or situation I can we really know?

That's that kind of I'm talking about that I'm saying is not being done or at least I don't see it being done But I could be wrong

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

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

RE: Foundational Metaphysics
SUBTOPIC: Fundamental Issue
※→ Bob Ross, et al,

Please forgive old man.

• What is the first question?
  
• What basic rules or laws have you decided are unchallengeable (that which cannot be contradicted)? I suppose these unchallengeable laws are related to what you have determined to be sine qua nons (absolutely necessary).

By its very nature, "Metaphysics" is a type of "thinking outside the box." The entire concept of "infinity" [(positive or negative)(bounded or unbounded)] is alien to Metaphysics. 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.

Just my thought.


Most Respectfully,
R
Tuesday, July 12, 2022 (1)

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

My principle interpretation of your essay says>examination of derivation-of-derivation means establishing continuity between phenomenal experience and first causes.

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

A close second to my principle interpretation of your essay says>analysis & derivation share important common ground to the effect that derivation is a type of analysis.

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.

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.

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.

Now your essay seems poised to utilize higher-order logic henceforth. However, instead of this, its progress appears to snag on some basic questions.

{Infinity} bound/unbound/indeterminate are solely objects of a priori cognition. As such, they exemplify ideals along the lines of Plato’s Ideal Forms. I question placement of ideal objects at the foundation of metaphysics as it is supposed to examine the real, not the ideal.

Maybe you can refute some implications of my following questions.

What’s the difference between a bounded finite & a bounded infinity? I ask this question because, at one point, you say,

“… the content of an indefinite could possibly have bounds (thereby be finite)…”

This statement declares that bounding entails being finite, so how bounded infinity?

You also say,

“Now, the bounded infinite noted before should be clarified as not pertaining to the content of the infinite but, rather, its form and, therefore, does not constitute as indefinite.”

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?

The existence of a thing = all attributes of a thing, including its content & form. In separation from each other, content & form are unintelligible.

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

Can you visualize form that is composed of nothing?

Any intelligible description of infinite volume i.e., set of infinite volume>bounded infinity is merely reification to (asymptotic) sample as infinite is a cognitive abstraction that, when paired with a boundary, signifies a paradox> the limited limitless.

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.

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.

Metaphysics necessarily concerns itself with examination of the paradoxes of non-local boundaries.

If it’s true that all origins have paradoxical boundaries, which is to say, all origins have non-local boundaries, then derivation from origins (sin qua nons) is trans-logical, and thus epistemic, logical & ontological disciplines are only axiomatically justified by local origins (sin qua nons).

There is a gap separating local origins from analysis_derivation to phenomena. Theories that support analysis_derivation to phenomena must rest upon unanalyzable axioms.

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.

RE: Foundational Metaphysics
SUBTOPIC: Fundamental Issue
※→ Bob Ross, et al,

Well, evidently I have no idea what I am doing.

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")? — Bob Ross

(COMMENT)

I thought you were opening a discussion on a focused topic. Please disregard my previous comment.


Most Respectfully,
R
Tuesday, July 12, 2022 (2)

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. — Bob Ross

"Highly disputed" within a certain, relatively small, subset of mathematicians.

Dispute Over Infinity Divides Mathematicians

With the hypothesis unresolved, many other properties of cardinal numbers and infinity remain uncertain too. To set theory skeptics like Solomon Feferman, a professor emeritus of mathematics and philosophy at Stanford University, this doesn’t matter. “They’re simply not relevant to everyday mathematics,” Feferman said.

Sorry to have gotten off on this tangent. I guess 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.

Hello Bob, it is great to see you again! I'll address your paper the best I can.

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"?

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?

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".

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.

That being the case, we can create superordinate clauses that work, but do not negate the subordinate when removed. 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. This is simply a bounded capture of a man, but in tota, not in total.

Let me know if I'm on the right track or it needs some correction Bob!

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? — Philosophim

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

Nice :smile:

The way I was positing the essay was more about a purpose rather than a problem—and that purpose is clearly stated in the introduction. — Bob Ross

The primary purpose of this essay is a meticulous investigation of the foundation(s) of all derivation; that is, the consideration of the derivation of derivation and, subsequently, its abstraction towards a recursive utilization (i.e., an unbounded infinite).

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; 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.

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? 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?

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

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

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

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

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