Good to know that I don't have to scramble to read an entire article you've linked to just to know what you're claiming.

Anyway, again, nothing I've said depends on claiming that two-valued logic is sufficient to model human reasoning. So I don't know the relevance of your comment to me that two-valued logic is not sufficient.

Irrelevant ! — Gnomon

Here's what jgill responded to and his response:

"Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics
— Gnomon

Wrong. I and others have studied infinite regress in detail, as infinite compositions or iterations. — jgill

His response is quite relevant to your claim that infinite regress is not addressed in mathematics.

Addition to an earlier post by me:

what has incensed some posters in this thread is the supernatural implications of the OP. Which they hope to demolish by turning a broad philosophical question into a narrow technical definition. — Gnomon

I don't know who you claim are the "some posters", but at least I have not "hoped to demolish" the poster's notions about "supernatural implications". If the poster thinks it is supernaturally implied that Pi is a circle, then I don't have much to say about that except that it is worthwhile to mention that P is not a circle, from which one can take whatever supernatural implications one thinks there are to take.

And as to "demolishing", the poster himself invited:

Anyone wanna trash this theory? — invicta

His response is quite relevant to your claim that infinite regress is not addressed in mathematics. — TonesInDeepFreeze

Tones, apparently you didn't read the OP, and responded only to some abbreviated second & third replies to assertions about Pi & circles & infinity. I would have to be an idiot to make the "claim" you pin on me above. Perhaps that prejudicial misunderstanding is why some posters are treating as an idiot, or worse a woo-monger. I am not arguing with your mathematical acumen, just with your mis-interpretation of what is being said.

What I actually said was that his OP was not a scientific or mathematical assertion, but a philosophical "theory" for discussion. He was disagreeing with Aristotle's use of "infinite regression" as a reason for proposing a First Cause. Then, he offered an alternative metaphor of a snake eating its tail, raising the issue of whether a circle is an example of infinite regress, due to its association with the irrational never-ending number PI. He even asked if "anyone wanna trash this theory?". Would anyone in his right mind ask that of a mathematical fact?

I actually disagreed with his use of the Ouroboros metaphor. But when others began to make an issue of the PI/infinity concept, I simply pointed out that it was used in a metaphorical context, not as mathematical fact. So, get off his back. If you want to get technical, PI is indeed an infinite series of numbers*1, and a circle -- no beginning or end -- is sometimes used symbolically as a metaphor for infinity*2. Unfortunately, he continues to argue with Banno about interminable terms that have no bearing on the original post -- just digging himself deeper into the shallow end of philosophical debate. :smile:


*1. The approximate value of pi is calculated to be 3.14159265…. and is an infinite decimal number. Therefore, it can be concluded from the above explanation that pi is an irrational number.
https://unacademy.com/content/question-answer/mathematics/is-pi-a-rational-or-irrational-number/

*2. Why is infinity not represented by a circle?
Why is the infinity symbol not a circle? Because it was already being used by the number zero, the letter 'O,' the composition operation for functions, and the degree symbol, among other things.
https://www.quora.com/Why-is-the-infinity-logo-shaped-like-an-8-and-not-like-a-circle

Pi, spiral, symbol, math, infinity, irrational number :

Again, here is the problem with the OP:

I find his dissatisfaction with infinite regression unsatisfactory for if infinite causes are the chain of sequences ad infinitum does such a chain not imply a closed loop, like that primordial snake ouroboros eating it’s own tail. — invicta

An infinite causal chain does not imply a causal loop. Not even metaphorically.

apparently you didn't read the OP — Gnomon

It's not apparent, because it's false.

I would have to be an idiot to make the "claim" you pin on me above. — Gnomon

I can't help you there. You made the claim:

"Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics — Gnomon

jgill replied:

Wrong. I and others have studied infinite regress in detail — jgill

You replied:

Irrelevant ! — Gnomon

But jgill's reply is relevant, by saying that there is mathematical study that addresses infinite regress.

some posters are treating invicta as an idiot — Gnomon

For the record, whether or not other posters have done that, I am not one of them.

What I actually said was that his OP was not a scientific or mathematical assertion — Gnomon

But you also said, "Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics". Then, when jgill mentioned that there is mathematics that addresses infinite regress, you declared that to be irrelevant. Obviously, it is relevant to reply to "X is not addressed by Y" by saying that one has specifically studied Y addressing X.

He even asked if "anyone wanna trash this theory?". Would anyone in his right mind ask that of a mathematical fact? — Gnomon

You wrote:

Obviously, what has incensed some posters in this thread is the supernatural implications of the OP. Which they hope to demolish by turning a broad philosophical question into a narrow technical definition. — Gnomon

invicta starts with some non-mathematical musings but then also connects that with mathematical subject matter.

(1) I asked before, who do you claim is incensed?

(2) Whatever may nor may not be the case with other posters, I have no interest in demolishing his non-mathematical musings.

(3) invicta himself invited his post to be "trashed". I mentioned that in connection with your protest that posters are hoping to demolish the "supernatural implications" of his post.

(4) When a poster connects non-mathematical musings with mathematical subject matter, it is reasonable to point out where the poster is seriously confused about that mathematics.

(5) It is a not mere a "narrow technica[lity]" to mention that, for example Pi is not a circle.

when others began to make an issue of the PI/infinity concept, I simply pointed out that it was used in a metaphorical context, not as mathematical fact. So, get off his back. — Gnomon

For the record, whatever may or may not be the case about other posters, I made no comment on the acceptability of invicta's notion of Pi vis-a-vis the notion of infinity. Instead, I just gave the relevant mathematical definitions if anyone might care about the mathematics, and a suggestion that, as far as the mathematical aspects of the conversation, disagreements about definitions are not necessary.

As to metaphorical couching, invicta moves between non-mathematical musing and mathematics. At any given point it may be difficult to know whether he's being merely metaphorical or intending to be mathematical. But at certain points, he is explicitly mathematical, as he even challenges ANOTHER post to raise HIS game to mathematical precision:

Pi is exactly the ratio of circumference to diameter. It is not infinite — Banno

Ok then mister, please give me the exact value of Pi — invicta

Pi is not a circle — Banno

Of course it’s a circle what is the value of the line when you’ve performed the calculation circumference/diameter…it’s Pi of course. — invicta

It is just not the case that one has to accept everything invicta says as merely metaphorical when he himself presses others to be mathematically exact.

If you want to get technical, PI is indeed an infinite series of numbers — Gnomon

Most technically that is not the case. Depending on the approach, Pi is an equivalence class of Cauchy sequences of rationals, or Pi is a Dedekind cut. Perhaps one may also attempt to define 'is a real' as reals being denumerable sequences, but that is not common. (2) Pi also is the sum of an infinite summation. That is, Pi is the limit of a sequence.

a circle -- no beginning or end -- is sometimes used symbolically as a metaphor for infinity — Gnomon

Of course. And a symbolic metaphor for a thing is not that thing. When invicta says that Pi is a circle, and even presses others to be mathematically exact in disputing that claim, it is unreasonable to disallow that he is himself speaking about mathematics not merely his non-mathematical musings.

/

That graphic of digits of pi arranged in a circle is probably lovely, but I don't know what one is supposed to infer from it.

One can arrange digits of any number on any figure you please. One could arrange digits of Euler's constant on a triangle. That doesn't make Euler's constant a triangle. Not even a metaphor for a triangle. One can arrange digits of Pi along a hexagon. So Pi is no less a hexagon than it is a circle. And if one says, as does invicta, that Pi IS a circle, then a circle is a hexagon.

Wonder when Invicta's period of suspension will be over?

But you also said, "Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics". — TonesInDeepFreeze

Again, I did not say what you attribute to me. The "not addressed" is your imaginary addition to what I said. Such irrelevant insinuations often diverge mundane philosophical threads off-topic into long sub-threads on peripheral technical or emotional issues. The open-ended OP --- an essay question, not true/false --- regarding opinions about "First Cause", was of mild interest to me, but not the nitty-gritty facts of mathematical infinities.

This whole off-topic series of accusations & counter-accusations is what I was referring to as "the shallow end of philosophical debate". I hope to have a more productive discussion with you on a different topic, where polarizing hot buttons have not been pushed --- accidentally or deliberately. Let's get back to sharing opinions on general philosophical questions, not specific mathematical technicalities. :smile:

Referring to as "he" :
"Unfortunately, he continues to argue with Banno about interminable terms that have no bearing on the original post -- just digging himself deeper into the shallow end of philosophical debate."

But you also said, "Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics".
— TonesInDeepFreeze
Again, I did not say what you attribute to me. The "not addressed" is your imaginary addition to what I said. — Gnomon

That is nothing less than bizarre for you to say.

You wrote:

"Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics — Gnomon

And I said that you wrote: "Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics".

Then you say that you did not say it and that it is an imaginary addition to what you wrote.

You did write it; it's not an imaginary addition:

"Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics — Gnomon

/

This whole off-topic series of accusations & counter-accusations is what I was referring to as "the shallow end of philosophical debate". — Gnomon

You said that jgill's comment was irrelevant. I pointed out that it is relevant. And then you rejected that, on the bizarre basis that you didn't write ""Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics".

Shallowness is not preferred, but neither is incoherence. jgill's comment was not shallow and it is preferred that it be defended against your exclamation "Irrelevant!", and it is preferred that a thread not be so incoherent that a poster claims that another poster fabricated a quote that was not fabricated.

There is no "addition" to my quote of you. On the other hand, a few times you've added bold to quotes by me, without indicating that the bold was not original. That's not a huge deal, but it is inaccurate and it's apropos to mention it in contrast to your bizarre claim that I added to a quote of you.

Disagreements about terminology are unnecessary. Discussants can instead acknowledge the clear definitions in mathematics: — TonesInDeepFreeze

As to accusations, I haven't made any. On the other hand:

Tones, apparently you didn't read the OP, — Gnomon

False accusation.

bear-trap Banno — Gnomon

That's not an accusation, but putting a pejorative moniker on an interlocuter is less than high minded. I don't mind that kind of thing, but pointing it out goes to highlighting that you are mentioning shallowness while you also contribute to it.

what has incensed some posters in this thread — Gnomon

That is tantamount to an accusation that other posters have posted in anger. I said I don't which posters you claim to be incensed; but you still don't say.

they hope to demolish by turning a broad philosophical question into a narrow technical definition. — Gnomon

That is an accusation. And it's not clear that it's true. I'm not convinced that anyone has acted as if philosophic claims must be reduced to technical claims. But when philosophical claims do invoke technical matters, then it is wholly legit to talk about how those technicals are being treated.

/

Let's get back to sharing opinions on general philosophical questions, not specific mathematical technicalities. [with smiley face in original] — Gnomon

In other words, I am being asked not to post on an aspect of the conversation that interests me. Yet, I have explained quite well why that aspect is important. Invoking mathematics into a philosophical argument deserves not mangling that mathematics. Posting incoherently about the mathematics is a set up for degraded discourse from the start.

At best, the poster should say from the start: "I use a lot of mathematical terminology. It is not to be construed that it has anything to do with the ordinary mathematical meanings. Rather, it's just my own personal use of technical language. And while I don't stay with ordinary meanings found in mathematics, or even in everyday use, I don't define my personal use either. I expect that readers put aside their own understanding of the terminology, but still see what I personally mean though undefined. Any confusions therefore are not my fault but the readers' fault."

So, yeah, anyone is free not to comply with your suggestion that we stick only to the aspects of the subject you want us to stick to. Again, when philosophical questions or arguments are couched with mathematical claims, then it is not just appropriate, but it is very helpful, to discuss whether the mathematical aspect is being well treated.

The open-ended OP --- an essay question, not true/false --- regarding opinions about "First Cause", was of mild interest to me, but not the nitty-gritty facts of mathematical infinities. — Gnomon

And other people are interested in the mathematical aspects that were mentioned. In particular, I contributed a table of definitions so that, at least, discussants don't need to get bogged down in disagreements about mathematical senses.

Surely, you don't think a discussion should be limited to only the aspects that interest you?

Note that in the Ouroboros symbol, the snake that seems to be recreating itself, actually has a head and tail, a beginning and end. — Gnomon

Let's stick with the philosophy and not get bogged down in the nitty-gritty facts about ancient symbols and illustrations. [sarcasm, of course] Oh, but wait, maybe posters should not talk about the mathematics mentioned in relation to philosophy, but, on the other hand, there should be no preference that Gnomen not talk about ancient illustrations mentioned in relation to philosophy. [more sarcasm, of course]

/

Referring to invicta as "he" :
"Unfortunately, he continues to argue with Banno about interminable terms that have no bearing on the original post -- just digging himself deeper into the shallow end of philosophical debate." — Gnomon

Just to be clear, you are quoting yourself, not me.

I'm not sure what your point about the pronoun is*. Just to be clear, you first used male pronouns for invicta.

* Though I would agree, especially since 'invicta' is feminine, without knowing the poster's gender, that it is presumptuous to use male pronouns. But one, such as yourself (and me and others, later), might be forgiven for that lapse.

These stand:

It is just not the case that one has to accept everything invicta says as merely metaphorical when [invicta] [...] presses others to be mathematically exact. — TonesInDeepFreeze

Of course. And a symbolic metaphor for a thing is not that thing. When invicta says that Pi is a circle, and even presses others to be mathematically exact in disputing that claim, it is unreasonable to disallow that [invicta] is [...] speaking about mathematics not merely [...] non-mathematical musings. — TonesInDeepFreeze

/

One can arrange digits of any number on any figure you please. One could arrange digits of Euler's constant on a triangle. That doesn't make Euler's constant a triangle. Not even a metaphor for a triangle. One can arrange digits of Pi along a hexagon. So Pi is no less a hexagon than it is a circle. And if one says, as does invicta, that Pi IS a circle, then a circle is a hexagon. — TonesInDeepFreeze

Invoking mathematics into a philosophical argument deserves not mangling that mathematics. Posting incoherently about the mathematics is a set up for degraded discourse from the start. — TonesInDeepFreeze

:up: :clap:

That is nothing less than bizarre for you to say.
You wrote:
"Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics — Gnomon — TonesInDeepFreeze

I owe you an apology. I assumed the subject of the sentence was obvious. But, in retrospect, apparently not. Mea culpa.

Therefore, to avoid contributing to the ongoing confusion, I should have emphasized that it's the "philosophical concepts" that are not addressed by mathematics. "Infinity" is a legitimate mathematical topic, but "Infinite Regression" is an ancient philosophical conundrum. Hence, to get into mathematical technicalities is irrelevant to questions about a world-creating act of Causation. An Uncaused Cause or Prime Mover is a Platonic/Aristotelian notion of Metaphysics, not Physics, nor Math. Does that make sense to you? Or do you think philosophical questions can be solved mathematically?

In the OP, A self-drawn circle is the theory to be "trashed", not the definition of Infinity. Since the topic is hypothetical/metaphysical (an idea, not an object), Plato used creation myths, not math, to illustrate his concept of a First Cause. Likewise, Invicta was using symbols & metaphors to make his point. Unfortunately, by introducing PI into the discussion, he opened himself to mathematical criticism. But I still maintain that the discussion veered off-topic into irrelevant technicalities. Apparently, in the face of such sniping, Invicta bailed on his own thread. :smile:


For those interested in the actual topic of this thread :

From OP : "But hang on a second, if it was self caused then there can’t be an infinite regression of causes. Anyone wanna trash this theory?"
That's a big "IF", but IMHO he's correct that a self-existing First Cause*1, would be the initiator/creator of causation in our contingent world*2. Hence, by positing a First Cause, the Greeks were avoiding the absurdity of infinite regression*3 . If we can all agree with that interpretation, maybe Invicta will get back in the game.

*1. first cause, sustaining cause, unmoved mover, necessary being :
On the one hand, the argument arises from human curiosity as to why there is something rather than nothing or than something else. It invokes a concern for some full, complete, ultimate, or best explanation of what exists contingently. On the other hand, it raises intrinsically important philosophical questions about contingency and necessity, causation and explanation, part/whole relationships (mereology), possible worlds, infinity, sets, the nature of time, and the nature and origin of the universe.
https://plato.stanford.edu/entries/cosmological-argument/
Note -- Do the general questions listed above have mathematical solutions?

*2. First Cause : Though they often disagreed, one principle of philosophy on which Plato and Aristotle agreed was that existence and the universe required a First Cause or Prime Mover - a god of some kind. Their argument was basically as follows. Every finite and dependent being has a cause.
Note -- Therefore the regression of finite causation ends at the beginning.

*3. Infinite Regress Arguments attempt to refute a position by showing that the position leads to an absurd infinite sequence. This argument strategy is used in collaborative reasoning in everyday life, in science and in philosophy.
https://www.nottingham.ac.uk/humanities/departments/philosophy/research/research-projects/infinite-regress.aspx
Note -- Maybe Invicta will add to his theory an explanation for why Infinite Regress of Causation is deemed Absurd by some thinkers, even though that's exactly what the Multiverse theory postulates.

Apparently, in the face of such sniping, Invicta bailed on his own thread. :smile: — Gnomon

Apparently he/she has just been released from suspension.

Not necessarily implied that lines makes circles but that a line with irrational extension would snake its way when drawn.

Make a circle with a line one foot long and the circumference is one foot (if no contraction/expansion). This simply means the diameter of the circle is irrational, 1/pi .

But the diameter is a straight line…

https://en.m.wikipedia.org/wiki/Diameter

But the diameter is a straight line… — invicta

And the importance of this obvious fact is . . . . ? :roll:

What proof is there of 1/Pi…creating irrational diameter ?

Mathematically speaking ?

What proof is there of 1/Pi…creating irrational diameter ? — invicta

Let C = 1.
Pi = C/D.
So 1/Pi = D
Toward a contradiction, suppose D is rational.
So there are integers n and m (m not equal to 0) such that D = n/m.
So Pi = m/n.
So Pi is rational.
But P is not rational.
So a contradiction.
So it is not the case that D = 1/Pi is rational.

Mathematically speaking ? — invicta

As opposed to what? Philosophically speaking, artistically speaking, athletically speaking?

/

Anyway, your claim that Pi is a circle is false.

/

a line with irrational extension would snake its way when drawn — invicta

I don't know what you mean by 'irrational extension' or 'snake its way when drawn'. But this is the case:

The decimal expansion of any real number is denumerable. The set of points on a circle is uncountable. So there is an embedding of the decimal expansion into the circle (with points in the circle ordered in the obvious way of "left to right" from highest point to lowest point and "right to left" from lowest point to highest point).

But there is an embedding of the decimal expansion into lots of kinds of geometric figures. There is an embedding of the decimal expansion of Pi into a triangle, into a hexagon, into a line... And there's nothing special about Pi in that regard. The decimal expansion of any real number can be embedded ("arranged") into a circle, or triangle, or hexagon, or line...

Pi is not a circle. But the decimal expansion of Pi can be embedded into a circle. If you find philosophical significance in that, then okay. But then why not find philosophical significance also in the fact that the decimal expansion of Euler's constant can be embedded into a triangle? Or what greater philosophical significance with one over the other?

Wonder when Invicta's period of suspension will be over? — jgill

Never, as it turns out.

Wonder when Invicta's period of suspension will be over? — jgill

Never, as it turns out. — Banno

It's hard to know if he was putting me on. has a great deal of patience dealing with these things. Thanks, Tones. :cool:

— Gnomon

That is nothing less than bizarre for you to say.
You wrote:
"Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics — TonesInDeepFreeze

The bolding is not mine. You've quoted me a few times as you've added bolding. I already asked you to note that the bold or emphasis is added. Are you not familiar with that convention?

I assumed the subject of the sentence was obvious. — Gnomon

Yes, the subject is:

"Infinite Regress" and "First Cause"

The predicate is:

are philosophical concepts that are not addressed by Mathematics

That is a claim that "Infinite Regress and "First Cause" are (1) philosophical concepts and (2) they are not addressed by mathematics.

jgill mentioned his own studies in which mathematics do address those concepts.

Interesting that you immediately pounced to declare "Irrelevant!" when jgill shared his knowledge that there is mathematics concerning the subject of your sentence.

"Infinity" is a legitimate mathematical topic, but "Infinite Regression" is an ancient philosophical conundrum. Hence, to get into mathematical technicalities is irrelevant to questions about a world-creating act of Causation. — Gnomon

That is dogmatic. It is not precluded that mathematics may inform philosophy. It is not precluded that different areas of study may illuminate one another.

Moreover, separating out my earlier part in this discussion, the mathematics I mentioned was not meant to confirm or dispute any philosophy, but rather to offer standard definitions to the extent that the discussion did go into mathematics. But then also to flag the blatantly false claim that Pi is a circle.

Indeed, invicta has gone on to challenge other posters in explicit mathematical terms. I pointed this out to you twice, but you SKIP it, I surmise because for you to recognize it would be to recognize that your claim is false: It is false that it was only other posters who wanted to follow up on the mathematical aspects of invicta's postings while invicta merely wished to use mathematical terminology in a metaphorical way.

Here is is yet again; this time explicitly challenging in a mathematical context:

What proof is there of 1/Pi…creating irrational diameter ?

Mathematically speaking ? — invicta

[bold added]

invicta has been mixing mathematical terminology and mathematics subjects with his personal philosophical musings. It is quite appropriate for people to check the mathematical usage and mathematical claims. It is not incumbent on anyone to limit discussion to your own judgements as to what is and what is not relevant, especially when the original poster has explicitly challenged other posters as to mathematics qua mathematics.

And you don't need to say 'technicalities' over and over, as if the fact that mathematics is technical disqualifies it here. It's mathematics, which, of course is a technical subject.

An Uncaused Cause or Prime Mover is a Platonic/Aristotelian notion of Metaphysics, not Physics, nor Math. [...] Or do you think philosophical questions can be solved mathematically? — Gnomon

I hope you don't propose that as a dichotomy.

Of course, one may propose that mathematics may inform the metaphysical questions while not claiming that mathematics solves the questions.

An Uncaused Cause or Prime Mover is a Platonic/Aristotelian notion of Metaphysics, not Physics, nor Math. — Gnomon

Then it would be a good idea for anyone who wants to divorce that subject from math to not bring math into it.

Moreover, again, different fields of study may illuminate one another. Much of philosophy has been informed by mathematics and by science.

Anyway, again, it was invicta who invoked mathematics, so naturally people will comment on it.

A self-drawn circle is the theory to be "trashed", not the definition of Infinity. — Gnomon

Whatever other posters have in mind, I haven't said anything about 'self-drawn circle'.

And, at this point it is egregious that you keep SKIPPING the point I have made a few times already:

I posted the mathematical definitions of the terminology 'is infinite' and 'points of infinity' so that, to the extent when 'infinity' is mentioned in a mathematical context or context that mixes mathematics with philosophy, we may avoid pointless terminological contestation. Moreover, to highlight the crucial distinction between the adjective concept 'is infinite' and the noun concept 'infinity'.

Apparently, in the face of such sniping, Invicta bailed on his own thread. — Gnomon

You don't have a basis to infer the reasons for invicta's posting frequency.

For those interested in the actual topic of this thread — Gnomon

Of course, one may be interested in invicta's philosophical gravamen while also being interested in the mathematical notions he mentions.

philosophical questions about contingency and necessity, causation and explanation, part/whole relationships (mereology), possible worlds, infinity, sets, the nature of time, and the nature and origin of the universe. — Gnomon

Of course those are informed by mathematics and science.

contingency and necessity. That is informed by modal logic, which is a study in formal logic very closely related to mathematical logic.

mereology. Also studied in formal logic.

possible worlds. Again, informed by modal logic. Also, analogous to semantics for intuitionistic logic for intuitionistic mathematics.

infinity. The notions 'is infinite' and 'points of infinity' are informed by mathematics.

sets. Informed by set theory and class theory, which are mathematics and are themselves foundations for mathematics.

the nature of time. I don't know about 'the nature of', but the subject of time is, of course, informed by mathematics and physics.

the nature and origin of the universe. questions about the universe are of course addressed by cosmology, which is informed by mathematics.

It is curious, at best, to me that a person would want to dogmatically declare that philosophy should not be discussed in cross-context with other subjects. Especially when the original poster her(or him)self introduced mathematical aspects and not merely metaphorically. On the contrary, intellectual curiosity, intellectual creativity and open mindedness invite cross-study/conversation, not shutting it down.

Yes, the subject is:
"Infinite Regress" and "First Cause"
The predicate is:
are philosophical concepts that are not addressed by Mathematics
That is a claim that "Infinite Regress and "First Cause" are (1) philosophical concepts and (2) they are not addressed by mathematics. — TonesInDeepFreeze

Again, that is not my claim. It's your erroneous interpretation, but not my intention. "Infinite Regress" and "First Cause" are examples of the subject content, acted upon by the predicate. Instead, it is "philosophical concepts" that the predicate modifies with "not addressed". And it's the "Infinite Regression"*1 argument, not the definition of "Infinity", that is in question.

However, I admitted above that the sentence construction could be misconstrued --- by someone with a pre-conception. Especially after the impassioned mathematical side-track had been going on for a while. That's why I added the bold, to indicate the subject of my sentence.

I suspect that we are actually in agreement about the math of PI & Infinity, but perhaps not about the philosophical concept of a pre-big-bang First Cause. Unfortunately, seems to be insisting on a colloquial usage of "infinity", while you are insisting on technical definitions. Therefore, on the side issue of Number Theory, the post is at an impasse. But the philosophical notion of a causal-regression-halting First Cause (or Prime Mover) has not been addressed & resolved in this thread, so is still an open question.

Consequently, the Pre-Big-Bang state of being (Ontology) remains a contentious issue among philosophers. Yet I maintain that it is a valid enigma, that serious scientists have attempted to resolve, not with math, but with the endless regression of a god-like eternal Multiverse*2 (Many Worlds), without beginning or end. :smile:


*1. Infinite Regress Arguments :
An infinite regress is a series of appropriately related elements with a first member but no last member, where each element leads to or generates the next in some sense.
https://plato.stanford.edu/entries/infinite-regress/
Note -- The relationship between elements is Causation, not mathematical value. The "first" member is the element in question.

*2. Why the Multiverse is a “God-of-the-gaps” theory :
"God’s existence is not provable by observations. The Multiverse is not provable by observations. God explains the Universe. The Multiverse explains the Universe. The Multiverse, then, is a lot like God. Weird, right?" ___by astrophysicist Marcelo Gleiser
https://bigthink.com/13-8/multiverse-religion/
Note -- You don't have to "waste time" by clicking on the link. I included a summation in the quote.

You did it again: You bolded in my quote without indicating that the bolding was not original.

I have asked you at least three times not to do that, but instead to indicate that the bolding was added.

Clearly, by this point you are egregious.

One more time: If you add bold in a quote of mine, then note that the bold was added.

that is not my claim. It's your erroneous interpretation, but not my intention. — Gnomon

It's literally what you wrote. So, what you wrote is not what you meant. Of course, one may always correct what one wrote to align with what one meant. But it's not jgill's fault nor my fault to have replied to exactly what you literally wrote.

Instead, it is "philosophical concepts" that the predicate modifies with "not addressed". — Gnomon

Wrong. The word 'are' begins the predicate.

Subject:

"Infinite Regress" and "First Cause"

Predicate:

are philosophical concepts that are not addressed by Mathematics

This could not be more clear as basic English. 'are' begins the predicate.

The sentence says that "Infinite Regress" and "First Cause" ARE (1) philosophical concepts and (2) not addressed by mathematics.

Jack and Jill are happy kids who like to play.

The subject is Jack and Jill. The predicate begins with 'are' and the predicate is 'are happy kids who like to play'.

I hope you understand by now.

I admitted above that the sentence construction could be misconstrued --- by someone with a pre-conception. — Gnomon

Blame the reader for a "pre-conception". No, the two readers here read your sentence at face value, literally what you wrote.

And even IF you had written the sentence so that 'philosophical concepts' were part of the subject:

"Infinite Regress", "First Cause", and philosophical concepts are not addressed by mathematics

then still, it is the case that mathematics (and science) may be used, and is (are) used, to inform philosophy.

It is only dogma that mathematics should not be discussed in this thread and that, even more generally, mathematics should not be discussed in addressing certain philosophical questions. Not only is that arbitrary self-serving dogma, but it is deleterious to the benefits of cross-study and an expansive discussion about various subjects.

And your would be controlling dogma is untenable anyway as to this discussion, since the original poster first brought mathematics into the discussion (and not just "metaphorically", and indeed the original poster did not qualify that the mathematics she or he invoked was merely metaphorical) and later the poster explicitly challenged ANOTHER poster to be mathematically "exact" on a point of mathematics and then explicitly challenged another poster to provide a "mathematical" answer on a point of mathematics.

You have SKIPPED my adducing that fact at least two times now.

And it's the "Infinite Regression"*1 argument, not the definition of "Infinity", that is in question. — Gnomon

I never said that the definition of 'infinity' is in question with that particular comment of yours. Whatever you meant by "Infinite Regress" and "First Cause" is up to you. But they are the subject of the sentence you wrote, not 'philosophical concepts'.

impassioned mathematical side-track — Gnomon

That you go, argument by mere characterization.

I haven't been impassioned, nor was jgill impassioned.

And to say it's a 'side-track' is question begging, since whether mathematics is apropros to the subject is what we've been disagreeing about.

Your position is blatantly untenable:

It is invicta who first introduced mathematics into the discussion. And then invicta later even challenged another poster to justify a point mathematically. And then invicta explicity challenged for "mathematical" response.

And you SKIPPED the points I made about mathematics and philosophy interacting.

I suspect that we are actually in agreement about the math of PI & Infinity, but perhaps not about the philosophical concept of a pre-big-bang First Cause. — Gnomon

I haven't stated any opinion on first cause. And, by the way, 'big bang' is ordinarily understood to be a subject of physics and cosmology, a scientific notion, so it too is informed by mathematics.

invicta seems to be insisting on a colloquial usage of "infinity" — Gnomon

Please quote what you regard as invicta saying that she or he means only a colloquial sense.

while you are insisting on technical definitions. — Gnomon

That is a major STRAWMAN.

(1) I have not insisted that usage be confined to only the technical definitions. I offered the technical definitions so that there would not be pointless disputation in regards the mathematical aspects of the conversation.

(2) I did not address invicta's notion of infinity. Rather, I addressed his claim that Pi is a circle. And later his arguments about inscribing the expansion of Pi in a circle.

You have imposed on me things I did not say. Perhaps due to YOUR preconception. Philosopher, heal thyself.

This also should not have been SKIPPED over:

philosophical questions about contingency and necessity, causation and explanation, part/whole relationships (mereology), possible worlds, infinity, sets, the nature of time, and the nature and origin of the universe.
— Gnomon

Of course those are informed by mathematics and science.

contingency and necessity. That is informed by modal logic, which is a study in formal logic very closely related to mathematical logic.

mereology. Also studied in formal logic.

possible worlds. Again, informed by modal logic. Also, analogous to semantics for intuitionistic logic for intuitionistic mathematics.

infinity. The notions 'is infinite' and 'points of infinity' are informed by mathematics.

sets. Informed by set theory and class theory, which are mathematics and are themselves foundations for mathematics.

the nature of time. I don't know about 'the nature of', but the subject of time is, of course, informed by mathematics and physics.

the nature and origin of the universe. questions about the universe are of course addressed by cosmology, which is informed by mathematics.

It is curious, at best, to me that a person would want to dogmatically declare that philosophy should not be discussed in cross-context with [added: certain] subjects. Especially when the original poster her(or him)self introduced mathematical aspects and not merely metaphorically. On the contrary, intellectual curiosity, intellectual creativity and open mindedness invite cross-study/conversation, not shutting it down. — TonesInDeepFreeze

Of course, the Greeks were mathematical pioneers, but they had not formed a mathematically satisfactory account of the notion of infinitude. That does not entail that one should not apply modern concepts and knowledge to questions ages old.

And, of course, the Greeks never said that Pi is a circle.

Do the general questions listed above have mathematical solutions? — Gnomon

Seems that I didn't include my reply to that.

It is not clamed that mathematics solves those philosophical problems. It is only claimed that mathematics may inform solving the problems.

Anyway, again (because this fact keeps getting SKIPPED by you) in context of this thread, it was invicta who invoked mathematics to defend her(or his) argument, and not with a proviso that that was merely metaphorical, and later explicitly challenged for "exact" mathematics on a mathematical point and then explicitly for a "mathematical" reply on a mathematical point.

You did it again: You bolded in my quote without indicating that the bolding was not original. — TonesInDeepFreeze

Yes. I emphasized the subject of the sentence, to show where you missed the point of the original statement. Apparently, that didn't have the desired effect. But I'll continue to do it again, if you continue to misinterpret my meaning. In the words of Paul McCartney, "let it be". :smile:

You did it again: You bolded in my quote without indicating that the bolding was not original.
— TonesInDeepFreeze
Yes. I emphasized the subject of the sentence, to show where you missed the point of the original statement. Apparently, that didn't have the desired effect. But I'll continue to do it again, if you continue to misinterpret my meaning. — Gnomon

You say you'll do it again. And you did just do it again. The bolding you put in was not mine.

And you did it just to prove that you can - a childish, petulant act.

You are wrong.

(1) Even people who radically disagree at least respect the honesty of not misrepresenting a quote to make it appear the quoted person emphasized words that he did not emphasize. That is just BASIC common sense and intellectual honesty. I have seen even the worst Internet creeps - demagogic, specious opinion writers, bloggers, and forum posters who at least indicate where they have added emphases in quotes. But you insist on putting yourself beneath even that minimal convention of honesty.

(2) I didn't misinterpret anything. I took your statement literally as you wrote it. A school kid could diagram the sentence to show its subject and predicate. As I said, if you meant something different, then that's not my fault. And I have not insisted that you did NOT mean something different - only that it's a plain fact that it's not what you literally wrote, therefore jgill and I were not incorrect to respond as we did to what you literally wrote.

(3) Even IF (which is not the case) I misinterpreted you, there is a distinct difference between even willful misinterpretation and misrepresenation (which are not acceptable) and willfully fabricating emphases in quotes. The latter is just pure blatant dishonesty above even arguable disingenuousness.

(4) As to misunderstanding, you intentionally STRAWMANED me, as I noted in one of my previous posts.

Meanwhile, all the points I made in previous posts still stand.

In the words of Paul McCartney, "let it be". — Gnomon

In my own words, "You're vastly better at quoting songs than you are at making sense."

You’re saying im being irrational just like Pi.
— invicta

Hmm. Well, it seems you both go on forever. — Banno

:rofl:

That's the funniest thing I've seen in quite some time. I probably should not be promoting it, but damn... that was funny. I momentarily lost control of myself.