I surmise that I am not mistaken that, ordinarily, physics uses classical mathematics, which has infinite sets and is ordinarily axiomatized by set theory. That seems salient. So, from my admittedly non-expert point of view, it would seem plausible that we might combine formal mathematics with whatever parts of physics have been, or might be, formalized. At least one example of a basic portion is, as I mentioned, in Suppes's logic book, though it is not so ambitious to undertake relativity, quantum, etc.

$\sum\limits_{1}^{\infty }{n}=-\frac{1}{12}$

:scream:

deleted

I surmise that I am not mistaken that, ordinarily, physics uses classical mathematics, which has infinite sets and is ordinarily axiomatized by set theory. That seems salient. So, from my admittedly non-expert point of view, it would seem plausible that we might combine formal mathematics with whatever parts of physics have been, or might be, formalized. At least one example of a basic portion is, as I mentioned, in Suppes's logic book, though it is not so ambitious to undertake relativity, quantum, etc. — TonesInDeepFreeze

It doesn't work that way.

It's true that physics "uses" the real numbers. And it's true that the real numbers are formalized using infinite sets. It does NOT follow that physics uses or is formalized by infinite sets.

I don't have the philosophy vocabulary to name this phenomenon, where A is a part of B and B is a part of C but A is in no way even remotely a part of C. Perhaps others can suggest the right concept.

Regardless, it's just not true and it's not valid thinking to say that "physics uses math and math uses infinite sets therefore ..." It's wrong, I just can't verbalize why.

ps -- To add a little. If you want to use the real numbers, you can just take their properties as given, namely that they are a complete totally ordered field. That uniquely characterizes them, there's only one model. (The completeness is second-order, that's why this works. I'm a bit fuzzy on that aspect of the logic but I think that's what's going on).

Now if you are doing math and you want to show that you can cook up a complete totally ordered field within set theory, you use one of the standard constructions involving the use of infinite sets. But the ontological commitments, if that's the right phrase, are of a different type. Physics uses real numbers and mathematicians formalize real numbers using infinite sets, but there's no ontological commitment in physics to infinite sets.

deleted — TonesInDeepFreeze

1+2+3+ ...

It does NOT follow that physics uses or is formalized by infinite sets. — fishfry

I didn't say it does. And I am not saying that it would be consistent if it did. I am saying that I haven't seen an argument that it would be inconsistent if we added to set theory, primitives and axioms for physics, and that it seems plausible that we might be able to do so.

Did you think I argued that physics uses or is formalized by infinite sets? If you did, then that would be yet another example, from different threads, in which you read into what I posted claims that I did not make in those posts.

there's no ontological commitment in physics to infinite sets. — fishfry

And using set theory doesn't entail that physics would take on an ontological commitment. Again, I am asking about a possible axiomatization. That is syntactical. Consistency is syntactical.

Yes, I deleted my reply because immediately after posting it, I read about the Euler and Riemann sums.

I am saying that I haven't seen an argument that it would be inconsistent if we added to set theory, primitives and axioms for physics, and that it seems plausible that we might be able to do so. — TonesInDeepFreeze

So that I can understand what you mean, can you give an example? What kind of axiom would we add to set theory that would be an axiom for physics?

I'm going to address your question. But I have some other remarks first, and I'll quote from some earlier posts that are important still in the context of this post.

My main interest is this claim:

The axiom of infinity is in contradiction with known physics — fishfry

If there is not some formalization of physics in mind, then it is not clear what it means for a formal axiom to be in contradiction with a set of unformalized statements. It might mean that any conceptualization of the meaning of the axiom of infinity is incompatible with the concepts of physics, or something along those lines. I don't make a claim pro or con about such informal senses of 'contradiction', but I am interested in the question whether any possible reasonably sufficient formal axiomatization of physics would entail the negation of the axiom of infinity. If such a theory can't formulate the axiom of infinity in the language of the theory, then, a fortiori, there is not a contradiction with the axiom of infinity, so that would settle the question. On the other hand, if the theory includes set theory or any variant of set theory (such as set theory with urelements) that includes the theorem "there exists an infinite set", then the question is whether it is possible to have a consistent system that combines set theory or such variant with a reasonably sufficient set of physics axioms. (I'll leave tacit henceforth that we might need a variant such as set theory with urelements. But moving to a variant would not vitiate my point, since the variant would still include the "there exists an infinite set", which is the supposed source of inconsistency. Also, I'll take as tacit "reasonably sufficient".)

There are two questions: (1) Can there be a consistent set of axioms for physics? I don't opine, especially since I have no expertise in physics. (2) If there can be an axiomatization for physics that combines with set theory, then would any such axiomatization be inconsistent? My point is that I have not seen an argument that it is not at least plausible that there might be a consistent axiomatization that combines physics with set theory, and that I do think it might be plausible.

Some earlier points bear on the question and need to be kept in mind:

The axiom of infinity is inconsistent with known physics since there is no principle of modern physics that stipulates the existence of any infinite set,
— fishfry

That doesn't entail inconsistency. Just because a theory doesn't have a certain principle doesn't entail that adding that principle causes inconsistency. But if physics had a principle that it is not the case that there exists an infinite set, then yes, there would be inconsistency. But even if physics had a principle that there are not infinitely many particles, that is not itself inconsistent with the existence of infinite sets, such as infinite sets of numbers if numbers are not axiomatized to be particles. — TonesInDeepFreeze

contemporary physics can not accept the axiom of infinity as a physical principle.
— fishfry

I never said that it would be a physical principle. It would be a mathematical theorem to which are added primitives and axioms for theorems of physics. — TonesInDeepFreeze

Physics has not been axiomatized at all. — fishfry

I don't know that there are not axiomatizations of any part of physics or even of a large part of it. At the very least, Suppes provides an axiomatization of particle mechanics. Granted, that's not an axiomatization of modern physics. But at least the question of infinity is addressed, as Suppes combines infinitistic set theory with added physics primitives and a definition of a system of particle mechanics such that the set of particles is finite. I was along those lines when I said that the existence of infinite sets is not inconsistent with having a finite set of particles. Also, not claiming an axiomatization of physics, but arguing for the plausibility that certain questions in physics might be affected by set theory: http://logic.harvard.edu/EFI_Magidor.pdf at page 10.

/

What kind of axiom would we add to set theory that would be an axiom for physics? — fishfry

I will not suggest any particular axioms, as I am not expert in physics. It is better anyway that anyone may nominate, at their own will, any postulates of physics (or any formulas of physics deemed fundamental and productive enough) for axioms. These can be, for example, the postulates of special relativity. (Nota bene: Again, I am not claiming that this project would be successful. I am saying only that it might be plausible.) Examples from Suppes for particle mechanics:

The set of particles is finite.

The mass of a particle is a positive real number.

For particles p and q, and elapsed time t, the force of (p q t) = - the force of (q p t).

I won't defend any particular formulations from possible criticism. The particulars are not my point, on an assumption that any details that raise objection could be adjusted to suit whatever formulation the physicist more prefers.

The set of particles is finite. — TonesInDeepFreeze

Contradicts axiom of infinity.

The mass of a particle is a positive real number. — TonesInDeepFreeze

What's a particle? What's mass? These are axioms, remember? Everything's defined in terms of a single primitive, $\in$. You've claimed you can add physics axioms to the axioms for set theory, so the burden on you is to challenge yourself to see if your idea holds water.

The set of particles is finite.
— TonesInDeepFreeze

Contradicts axiom of infinity. — fishfry

No it does not. If you can't see that, then discussion with you is hopeless.

That some sets are finite does not contradict that some sets are infinite.

What's a particle? What's mass? — fishfry

They are primitives.*

Everything's defined in terms of a single primitive, ∈ — fishfry

No, we add primitives for physics. I covered that very clearly in previous posts. You are just skipping the explanations given you.

I did not say that physics can be formulated using only the axioms of set theory. I explicitly said that we take the axioms of set theory and add primitives

* Technical note: Strictly speaking, Suppes doesn't add primitives, but instead he defines a 'system for particle mechanics' as a tuple with certain properties. The tuple is a structure or sometimes called a 'system', in the same way as an algebraic structure or other structures in mathematics and science. Anyway, this is not an essential difference from adding primitives. His definition of a certain kind of structure can be easily transformed into adding primitives. Moreover, defining a certain a kind of tuple adds even less to set theory. Moreover, the physics axioms also could be conveyed instead as properties of the structures.

You have ignored and outrageously misconstrued what I wrote, yet again. I didn't want to comment on the discussion itself again, but your reading confusions, as seen in this thread and other threads, are quite remarkable.

You have ignored and outrageously misconstrued what I wrote, yet again. I didn't want to comment on the discussion itself again, but your reading confusions, as seen in this thread and other threads, is quite remarkable. — TonesInDeepFreeze

You haven't convinced me of your point in the least.

discussion with you is hopeless. — TonesInDeepFreeze

Perhaps we can mutually agree on at least this. I'm always for achieving agreement.

You haven't convinced me of your point in the least. — fishfry

What possibly could refute that it is consistent that some sets are finite and other sets are infinite?

discussion with you is hopeless.
— TonesInDeepFreeze

Perhaps we can mutually agree on at least this. — fishfry

What I wrote is:

If you can't see that [it is not inconsistent that some sets are finitie and some sets are infinite], then discussion with you is hopeless. — TonesInDeepFreeze

You continually ignore and terribly misconstrue what I write, and now you can't even see that the finititue of a particular set does not contradict the axiom of infinity. So if you persist that way, then discussion with you is pointless.

The claim that "the set of particles is finite" contradicts the axiom of infinity is shockingly wrong.

then discussion with you is pointless. — TonesInDeepFreeze

We're quite in agreement. We tend to talk past each other and I'm content to leave it at that.

The claim that "the set of particles is finite" contradicts the axiom of infinity is shockingly wrong. — TonesInDeepFreeze

I'll concede that point. But if you adopt as an axiom claims that are subject to experiment and investigation, your science won't get you very far.

We tend to talk past each other and I'm content to leave it at that. — fishfry

No, you regularly ignore and misconstrue, sometimes even to the point of posting as if I said the bald negation of what I actually said. Meanwhile, I respond on point to you, and make every reasonable effort not to misconstrue you or mischaracterize your remarks, and I'm happy to correct myself if I did.

That is not an equivalence.

But if you adopt as an axiom claims that are subject to experiment and investigation, your science won't get you very far. — fishfry

Meanwhile, your original point that the axiom of infinity combined with physics is inconsistent has not been sustained. I don't know whether you recognize that now.

Next, as to your new point, perhaps I don't understand what you're saying. Axioms can be interpreted and then the interpretations subjected to experiment, so that either the experiments support the axiom as interpreted or refute the axiom as interpreted, in which case the theory would need to be reformulated, if possible, with different axioms. I don't see a problem with that.

In any case, again (since so much effort was spent to get to this juncture): It has not been shown here that the axiom of infinity is inconsistent with possible axiomatizations of physics.

I'll concede that point. — fishfry

I am truly curious why you even disputed it to begin with, and then persisted in yet another post. Especially as this is typical with you. You weren't reading correctly? Your weren't reading correctly because you mostly only skim? A mental lapse? A mental lapse because you have a continual preconception that when I disagree with you or question whether your claim is supported that I am bound to be wrong about it?

No, you regularly ignore and misconstrue, sometimes even to the point of posting as if I said the bald negation of what I actually said. — TonesInDeepFreeze

Is it possible that you're not always as clear in your meaning as you think you are?

Meanwhile, I respond on point to you, and make every reasonable effort not to misconstrue you or mischaracterize your remarks, and I'm happy to correct myself if I did. — TonesInDeepFreeze

Can you see that it's possible that this is not my perception?

I am truly curious why you even disputed it to begin with, and then persisted in yet another post. Especially as this is typical with you. You weren't reading correctly? Your weren't reading correctly because you mostly only skim? A mental lapse? A mental lapse because you have a continual preconception that when I disagree with you or question whether your claim is supported that I am bound to be wrong about it? — TonesInDeepFreeze

I humbly apologize for whatever grave offense I may have caused. Peace be with you, my friend.

ps -- But ok, you asked a fair question and you deserve an answer. You said "The number of particles is finite." Now you proposed that as an axiom to be added to the standard axioms of set theory. Being familiar with the latter, and not knowing what a "particle" is, I assumed you meant mathematical sets, or mathematical points. In which case your formulation would indeed be in contradiction with the axiom of infinity.

So I asked. And you THEN -- after I challenged you on this point -- admitted that "particle" is a primitive, something you had not said before. After you said that, it was clear to me that there could indeed be only finitely many of them without creating a contradiction.

Can you see that I had to ask you twice in order to dig out your hidden assumption that "particle" is a brand new primitive in set/physics theory? Without that information, your statement that there are only finitely many particles makes no sense.

Therefore can you see that my asking twice was necessary in order to smoke out the hidden information you didn't bother to say up front? And that this would be a perfectly sensible explanation for my having to ask you twice about your claim?

You see you are not always as clear as you think you are. If you want to add new primitives to the theory, and you don't bother to tell me that, then it's perfectly understandable that I would have confusion about your meaning.

(ps, a couple of hours later) Hilbert's sixth problem is to axiomatize physics. It's still an open problem. So if you think you have an idea, or if you even claim it's logically possible, the burden is on you to be crystal clear in your thoughts; because nobody in 120 years has axiomatized physics, let alone unified it with set theory, which seems logically contradictory on its face (to me at least).

The vast majority of mathematical principles, like pi, and the Pythagorean theorem which we discussed, are not fictional, and that is why mathematics is so effective. — Metaphysician Undercover

Pi and the Pythagorean theorem are not mathematical "principles."

So there is nothing UNREASONABLE in the effectiveness of mathematics. You can argue from ridiculous premises, as to what constitutes "true", and assume that the Pythagorean theorem is not true, as you did, but then it's just the person making that argument, who is being unreasonable. — Metaphysician Undercover

If you knew or understood more math, you'd understand the point. That you come up with "pi" as an example of a mathematical principle exemplifies the problem. Pi is a particular real number, known to the ancients. Hardly a principle.

The word "set" is a physical thing, which signifies something. — Metaphysician Undercover

If you're not willing to agree that set is a term of art in math that designates a purely abstract thing, having nothing to do with the physical world, we just can't have a conversation.

And it only has meaning to a human being in the world, with the senses to perceive it. Therefore sets, as what is signified by that word, are bound by the real world. — Metaphysician Undercover

Are you saying that because humans are physical and sets are a product of the human mind, that sets are therefore physical? By that definition everything is physical, yes, but you are ignoring the distinction between physical and abstract things. Makes for a pointless conversation.

Now you're catching on. — Metaphysician Undercover

Well then your point is trivial and pointless. Everything is physical if we can imagine it. The Baby Jesus, the Flying Spaghetti Monster, the three-headed hydra, all physical because the mind is physical. Whatever man. Pointless to conversate further then if you hide behind such a nihilistic and unproductive point.

Consider though, that the physical forces of the real world are not the "reason why" we think what we do, as we have freedom of choice, to think whatever we want, within the boundaries of our physical capacities. The physical forces are the boundaries. So we really are bounded by the real world, in our thinking. We do not apprehend the boundaries as boundaries though, because we cannot get beyond them to the other side, to see them as boundaries, they are just where thinking can't go. Therefore it appears to us, like we are free to think whatever we want, because our thinking doesn't go where it can't go. — Metaphysician Undercover

What a bullshit argument. I'm not going to play. Can we please stop now?

You will not understand the boundaries unless you accept that they are there, and are real, and inquire as to the nature of them. The boundaries appear to me, as the activity where thinking slips away andis replaced by other mental activities such as dreaming, and can no longer be called "thinking". We have a similar, but artificial boundary we can call the boundary between rational thinking and irrational thinking, reasonable and unreasonable. This is not the boundary of thinking, but it serves as a model of how this type of boundary is vague and not well defined. — Metaphysician Undercover

So everything is physical because some mind thought it up. What a childish talking point to deny abstract objects.

I skipped the rest, this is too childish. All the best. You've talked yourself into an unsupportable position. Everything is physical because a human thought of it. Therefore there are no abstract objects. I can't continue. I see no continuation. You won't acknowledge the existence of abstract or fictional objects not bound by the world. What basis is there for me to continue?

Is it possible that you're not always as clear in your meaning as you think you are? — fishfry

Not only do I think it is possible, but I bet it's true. I am keenly aware that (1) It is difficult to write about these topics on-the-fly and in the confines of posts, and therefore, no matter how hard I try, I'm bound to sometimes falter, and (2) Looking back at some of my posts, I see that what I wrote could have been clearer or needs certain corrections.

But I don't think that is the main problem with you. With you, even things that really are quite clear get misconstrued. There was even an incident in which you continued to insist that I made a certain claim, but I actually wrote the explicit negation of that claim. You had overlooked the word 'not' in my post. Sure, such a mistake can happen to anyone, but it was remarkable that you persisted even after it had been pointed out to you and even claimed the word 'not' did not appear! And then, after another poster also alerted you that the word appeared, as I recall, you still did not post that you recognized it finally.

And, time after time, even when I state clear and simple things, chronically, you read into them things not there nor implied.

And there have been even a couple of bizarre incidents (even lately) where you conflated what you said with what I said. Again, it can happen to anyone - but you persist in such incidents even after your error has been pointed out to you.

Meanwhile, I respond on point to you, and make every reasonable effort not to misconstrue you or mischaracterize your remarks, and I'm happy to correct myself if I did.
— TonesInDeepFreeze

Can you see that it's possible that this is not my perception? — fishfry

Indeed I do. But I don't recall an instance in which I unintentionally misconstrued you, then refused to recognize it when pointed out, let alone went on and on doing it over the same point, as you do with me. And, though I can't recall the specific incidents, I think there were one or perhaps two times when I misunderstood you and posted that I recognized that when it was pointed out to me.

You said "The number of particles is finite." Now you proposed that as an axiom to be added to the standard axioms of set theory. — fishfry

Just to be clear, I wrote it as a report of what an author wrote. I made clear that I don't personally propose any particular axioms for physics.

Being familiar with the latter, and not knowing what a "particle" is, I assumed you meant mathematical sets, or mathematical points. In which case your formulation would indeed be in contradiction with the axiom of infinity. — fishfry

No! You're doing it again! You're ignoring what I posted. I wrote explicitly about the alternatives (1) particles are sets or (2) particles are not sets but instead are urelements.

https://thephilosophyforum.com/discussion/comment/563405

[Note: I just now marked some edits to that post. But even with the pre-edited version, it was explicit that that there are two approaches, and in one approach particles are urelements not sets.]

And even if particles were sets, having the set of them being finite still would not violate the axiom of infinity. You're repeating the mistake on the point you conceded just a few posts ago!

Even if particles were sets (which, as I mentioned, we can avoid anyway) it is not inconsistent with the axiom of infinity to have the set of particles as a finite set.

So you blew right past my earlier post. I can see at least four possibilities (1) You skip reading a pretty good amount of the posts or (2) You read them but have a comprehension or retention problem or (3) You are nuts or (4) You willfully mangle the conversation for some kind of trolling effect. My guess is that it's a combination of (1) and (2).

whatever grave offense I may have caused — fishfry

I duly note what I take to be your sarcasm. But there's no grave offense. Hardly even offense. More like a feeling that it's too bad that someone who is not altogether uninformed sometimes reads so poorly, reasons so abysmally, and is so characteristically recalcitrant about it.

And you THEN -- after I challenged you on this point -- admitted that "particle" is a primitive, — fishfry

To ZFC, add a 1-place predicate symbol — TonesInDeepFreeze

When we add a symbol without definition, then it is clear that we are adding a primitive.

And I said over and over in various posts, that we add primitives and axioms for physics.

Suppes combines infinitistic set theory with added physics primitives [emphasis added] and a definition of a system of particle mechanics such that the set of particles is finite. — TonesInDeepFreeze

And even if 'particle' weren't meant as a primitive, but were defined, it would not detract from my point of giving you examples of axioms.

A reasonable conversation would be:

F: Is 'particle' primitive or defined?

T: Primitive.

F: Okay, now it's clear.

or

F: Is 'particle' primitive or defined:

T. Defined.

F. Then what is its definition?

T. There is a chain of definitions leading up to it. I can't practically type it all out here. But my point is not to convince you of the Suppes's cogency, but rather just to give an example of an axiom.

Even if I hadn't earlier mentioned 'particle' as added, that would not have been misleading you, since any lack of details can still be supplied on request. There is nothing I posted or didn''t post that was my fault of you misconstruing me.

Alice: C is the case.

Betty: That's wrong [or, That's problematic, or whatever criticism].

Alice: No, it's right, because [fill in S, which is support for C, here].

Betty: You withheld the information S.

Alice: I didn't include S when I said C, but that doesn't justify claiming that C is wrong, especially as It is not the case that C is wrong. Instead, you could have said, "You claimed C, but have not supported it", to which I could respond (1) "Even if I don't personally support it, it is still the case that P" or (2) "Here is the support S".

What you are arguing essentially is that there is something wrong with my arriving at (2). That's illogical.

And anyway, I did mention previously that 'particle' is primitive.

Without that information, your statement that there are only finitely many particles makes no sense. — fishfry

Wrong. You make no sense. Even if I didn't give any information about the set of particles other than it is finite, that doesn't entail that saying that it is finite makes no sense. You are again abysmally illogical.

After you said that, it was clear to me that there could indeed be only finitely many of them without creating a contradiction. — fishfry

Again, the consistency doesn't depend on the predicate being a new primitive. Your notion is ridiculous. Even if the set where made without a new primitive, it still is not inconsistent to have a finite set while other sets are infinite.

Your illogic is stunning.

Can you see that I had to ask you twice in order to dig out your hidden assumption that "particle" is a brand new primitive in set/physics theory? — fishfry

Nothing was "hidden". (1) Even if I didn't mention it at a particular juncture, that doesn't entail that I am "hiding" it. (2) I did mention in previous posts that we add primitives and axioms. (3) In an earlier post, I did mention that we add 'particle' as a predicate, and without giving it a definition; so of course it would be primitive. (4) I did mention that Suppes himself adds primitives and axioms (except with an inessential technical qualification that I explained). So one may allow that it is primitive in his axiom, or if one doesn't want to take that as granted, then one can ask. But there was no misleading you about it.

And you failed to count to to even the number one. When you FIRST asked me about primitives, answered you IMMEDIATLY in the next post:

What's a particle? What's mass?
— fishfry

They are primitives.* — TonesInDeepFreeze

And you make the false claim that you had to ask me twice, not as a causal matter of fact, but rather while claiming that I was "hiding" and you had to "smoke it out". Yeah, you had to "smoke it out" by asking and then receiving my immediate reply. And even IF you had to ask twice that's not so bad really. Meanwhile, so many questions and points I've made to you that you have ignored; you continually make arguments that I rebut and then you ignore the rebuttal but still go on repeating your more basic misconstruing and strawmen. You are bizarre.

If you want to add new primitives to the theory, and you don't bother to tell me that, then it's perfectly understandable that I would have confusion about your meaning. — fishfry

It is perfectly reasonable to say I didn't mention it or to ask about it. It is very unreasonable to claim that I was "hiding" or that you had to "smoke it out" (especially as I answered you about it immediately). And I did mention 'particle' as an added to the language in an earlier post, and I did mention at least a few times that we add primitives and axioms, and one might take from context, in Suppes's formulation that it is primitive or, if not taking it from context, ask before falsely claiming that without the information you are justified to claim there is a contradiction. And, even more basically, even if it were not primitive, then it is still ludicrously illogical to claim there is a contradiction between stating a given set is finite and having the axiom of infinity.

So if you think you have an idea, or if you even claim it's logically possible, the burden is on you to be crystal clear in your thoughts; because nobody in 120 years has axiomatized physics, let alone unified it with set theory, which seems logically contradictory on its face (to me at least). — fishfry

I have been clear. (I noticed today that I botched a formulation in an earlier post, but it is not material to the particular argument we are now having.) Also, what I claimed to be consistent is merely the initial setup of adding a 1-place predicate, and adding that there is a unique set all and only those objects that have the predicate and adding that that set is finite. And it is consistent with ZFC. It's trivial that is consistent. Anyone can trivially see it for themself.

Meanwhile, the first claim on this subject was YOUR claim that the axiom of infinity contradicts physics. You have not supported that claim. And, again, here's what I said about that:

If there is not some formalization of physics in mind, then it is not clear what it means for a formal axiom to be in contradiction with a set of unformalized statements. It might mean that any conceptualization of the meaning of the axiom of infinity is incompatible with the concepts of physics, or something along those lines. I don't make a claim pro or con about such informal senses of 'contradiction', but I am interested in the question whether any possible reasonably sufficient formal axiomatization of physics would entail the negation of the axiom of infinity. If such a theory can't formulate the axiom of infinity in the language of the theory, then, a fortiori, there is not a contradiction with the axiom of infinity, so that would settle the question. On the other hand, if the theory includes set theory or any variant of set theory (such as set theory with urelements) that includes the theorem "there exists an infinite set", then the question is whether it is possible to have a consistent system that combines set theory or such variant with a reasonably sufficient set of physics axioms. (I'll leave tacit henceforth that we might need a variant such as set theory with urelements. But moving to a variant would not vitiate my point, since the variant would still include the "there exists an infinite set", which is the supposed source of inconsistency. Also, I'll take as tacit "reasonably sufficient".)

There are two questions: (1) Can there be a consistent set of axioms for physics? I don't opine, especially since I have no expertise in physics. (2) If there can be an axiomatization for physics that combines with set theory, then would any such axiomatization be inconsistent? My point is that I have not seen an argument that it is not at least plausible that there might be a consistent axiomatization that combines physics with set theory, and that I do think it might be plausible. — TonesInDeepFreeze

But I don't think that is the main problem with you. — TonesInDeepFreeze

I read this far and gave up. You started out by agreeing that your exposition was unclear and that I was asking clarifying questions. I became hopeful that a productive and interesting conversation could ensue. Then you go back to the personal insults. Have a nice day.

ps -- Also my name's not Betty.

Pi is a particular real number, known to the ancients. Hardly a principle. — fishfry

This is clearly wrong. The ancients did not have real numbers, so they could not have known pi as a real number. They knew pi as the ratio of a circle's circumference to it's diameter. Further, they discovered that this ratio is irrational. You really amaze me with the nonsense you come up with sometimes fishfry.

Are you saying that because humans are physical and sets are a product of the human mind, that sets are therefore physical? — fishfry

No, I was saying that human actions are limited by the physical world, and mathematical thinking is a human action therefore it is limited by the physical world.

Well then your point is trivial and pointless. Everything is physical if we can imagine it. The Baby Jesus, the Flying Spaghetti Monster, the three-headed hydra, all physical because the mind is physical. Whatever man. Pointless to conversate further then if you hide behind such a nihilistic and unproductive point. — fishfry

Obviously, I wasn't saying "everything is physical". Metaphysically, I believe in the immaterial, or non-physical. But human thoughts, as properties of physical beings, do not obtain this status.

Can we please stop now? — fishfry

Sure, you seem to have run out of intelligent things to say.

This is clearly wrong. — Metaphysician Undercover

It's clearly wrong that pi is a particular real number? @Meta, please understand that you give me no basis to continue this conversation. Maybe we'll chat about something else in some other thread sometime. For what it's worth, and for your mathematical education, pi is a particular real number.

It's clearly wrong that the ancients knew pi as a real number.

It's clearly wrong that the ancients knew pi as a real number. — Metaphysician Undercover

What the ancients knew is you changing the subject. It has no bearing on the nature of pi or whether pi may be called a "principle of mathematics," which was yet another error on your part.

Sure, you seem to have run out of intelligent things to say. — Metaphysician Undercover

I got tired of you trolling me and have put a stop to it the only way I can.

Pi is the ratio of the circumference of a circle to it's diameter. Why is that not a "principle of mathematics"?

Pi is the ratio of the circumference of a circle to it's diameter. Why is that not a "principle of mathematics"? — Metaphysician Undercover

I don't want to be rude but at some point I have to stop responding and I'm at that point. The definition of a particular number is not sufficiently general or broad or foundational to be called a principle.

But Pi obviously is a principle, the ratio of the circumference of a circle to it's diameter. So, clearly it's you who is wrong, to say that pi is "the definition of a particular number". Again, you really amaze me with the nonsense you come up with sometimes fishfry.

You started out by agreeing that your exposition was unclear — fishfry

I didn't mean in this particular argument. Granted, I could have been made it explicit that I recognize that I can be clearer sometimes but that I am not saying that I was unclear in this argument.

and that I was asking clarifying questions. — fishfry

I did not say that. You are making that up out of thin air. Again, bizarre.

And, let's take this one point again:

You said that you had to ask me twice. But you asked me and then I IMMEDIATLY answered.

Sure, one can make a mistake like that innocently, but with you it's a dominant pattern and you won't recognize such instances when they are pointed out to you.

Then you go back to the personal insults. — fishfry

When your posting is so bizarrely off-base and patently illogical, through so many different conversations, then it's reasonable to point that out and to wonder aloud what is the source of your problem.

Again, you really amaze me with the nonsense you come up with sometimes fishfry. — Metaphysician Undercover

Then surely it's no loss to you to stop talking to me.

But pi is not a particular real number? How can I have a conversation with you? It's like a trained brain surgeon arguing about medicine with someone who just learned how to apply a band-aid. You lack the knowledge to be an interesting conversational partner. And then you get insulting about your ignorance.

Pi is not a particular real number? Wow.

And, let's take this one point again: — TonesInDeepFreeze

Like the girls in junior high school used to say: Let's not and say we did.