So those who're learning are guilty of intellectual dishonesty? — Agent Smith

I said nothing that can be construed as "learning is intellectual dishonesty".

I don't know what that emoticon you keep posting means.

/

I found out more about the -(1/12) thing. It requires taking the infinite sum in a different sense from the usual sense. It doesn't imply that there is a contradiction in mathematics.

I don't know what that emoticon you keep posting means.

/

I found out more about the -(1/12) thing. It requires taking the infinite sum in a different sense from the usual sense. It doesn't imply that there is a contradiction in mathematics — TonesInDeepFreeze

Okey dokey! Muchas gracias kind person! Please cut me some (more) slack. I'm a only a beginner as you already know.

For many months you have continued to post disinformation, even repeating items on which you were already corrected or refuted. That is a pattern not merely of a beginner, but of a crank.

And you recently lied about me personally.

I am happy you have finally found a number to use in place of infinity. You could show us how that works with the Lorentz factor. :cool:

This has to be exciting news for theoretical physics!

For many months you have continued to post disinformation, even repeating items on which you were already corrected or refuted. That is a pattern not merely of a beginner, but of a crank.

And you recently lied about me personally. — TonesInDeepFreeze

I'm sorry you feel this way! Good day.

This has to be exciting news for theoretical physics! — jgill

Indeed there's potential there to revolutionize science! Glad that you see it.

I'm sorry you feel this way! — Agent Smith

It's not a matter of feelings. They're facts.

revolutionize science! — Agent Smith

Come the revolution everyone will like strawberries and cream.

A dialogue between Georg and Ernst:

G: How's your rock collection these days?

E: I sold all my rocks. Now my collection is empty.

Ha ha, nice try Tones. Ernst's proper reply would be: "I have no collection of rocks. I sold all my rocks".

OED, collection: 1. the act or process of collecting or being collected. 2. a group of things collected together, esp. systematically. 3. an accumulation; a mass or pile (a collection of dust)."

I really don't know how you can conceive of a group of thing, or a mass or accumulation, without anything there.

Sure, you can't conceive of an empty set. But lots of people do.

But the problem is more fundamental with you. You can't conceive of abstract objects.

Here's a difference between you and me: You're a dogmatist. I am not.

In these kinds of matters, you cannot be bothered to give fair consideration to frameworks other than your own. Not only do you know nothing of the mathematics involved, you know hardly anything (if anything) of the many views of modern philosophers of mathematics. And you willfully avoid knowing anything about them. So you are brutally stunted in your capability to view from different perspectives, to intelligently compare different frameworks, to conceive. No matter that there is a rich, intensive, and intellectually competitive cornucopia of thinking in and about mathematics, you insist that all of those very smart and dedicated people must be wrong all the way to the core, while you alone stand above.

On the other hand, I can see the attractions of various points of view - from among even physicalist, materialist, idealist, phenomenologist, platonistic, nominalist, structuralist, finitist, constructivist, intuitionist, etc. Unlike you, I don't demand that my own personal framework for understanding mathematics is the only reasonable framework.

Sure, you can't conceive of an empty set. But lots of people do.

But the problem is more fundamental with you. You can't conceive of abstract objects.

Here's a difference between you and me: You're a dogmatist. I am not. — TonesInDeepFreeze

As I explained, I readily conceive of abstract objects, but I maintain a difference between abstract objects and physical objects, as necessitated by sound ontological principles. You it appears, do not seem to be ready to accept the dualism required for a true understanding of "abstract objects". That's the real difference between you and me, I understand abstract objects from sound and consistent metaphysics, while you simply assume "abstract objects" for the purpose of mathematics, without any kind of understanding of what an abstract object might consist of.

In these kinds of matters, you cannot be bothered to give fair consideration to frameworks other than your own. — TonesInDeepFreeze

This is untrue. I've given you adequate opportunity to explain the principles that you adhere to, which I find contradictory. I'm very willing to proceed with you, but not until we resolve apparent contradictions in your primary principles. I refuse to proceed from faulty principles. That would be nothing but unsound logic and a waste of time. So I give you fair consideration, but it is you who has not given fair consideration to the ontological problems I have raised. Instead of addressing my concerns, you now insist that I ought to just drop them, and take up some "different perspectives", even though I still apprehend your perspective as based in contradiction because you have done nothing to resolve this problem.

So, as I proposed, we can have an empty set, so long as "set" refers to the category, or type of thing which is going to belong to the collection, not the group of things itself. If the group had no members it could not be a "set" if "set" referred to the group itself. No members, no group.

This proposal allows that we could have a type, but no things of that type. Would you agree with this as a compromise principle? Then the "set", which is a category or type, is not a group, so that it can be empty, and the members of the set have a distinct kind of existence from the set itself, being the things which are categorized as being members of the set. So we have sets, and we have members, such that there are these two aspects of any set, the set (category), and the members (things classed as within that category, and there might not be any. And, we might even classify sets as things of a sort, such that we could have a set where the members are sets. But the set which has sets as members, would be a special type of category. So for example, "colour" could be a set which would have sets as members. The members would be "green", "red", etc., each being a category, or set on its own.

A few posts ago:

I cannot agree that abstractions are objects, unless we restrict "object" to refer only to abstractions. — Metaphysician Undercover

Now:

I readily conceive of abstract objects — Metaphysician Undercover

We should stop right there.

But you also put words in my mouth:

do not seem to be ready to accept the dualism required for a true understanding of "abstract objects" — Metaphysician Undercover

I haven't said anything about duality. This is yet another instance of you putting words in my mouth (except weaseling with "do not seem").

I've given you adequate opportunity to explain the principles that you adhere to — Metaphysician Undercover

I don't advocate any particular philosophy. But I have explained to you crucial notes about the mathematics itself, and I have touched on certain aspects of frameworks in which mathematics is discussed. You have made it a point to either ignore, evade, misconstrue or strawman all of it.

you now insist that I ought to just drop them, and take up some "different perspectives" — Metaphysician Undercover

I don't insist that you do or don't do anything (other than that you don't put words in my mouth or lie about me).

And I did not even hint that you have to "drop" your philosophy. I only said that you are not capable of also giving fair consideration, let alone study, to other points of view in the philosophy of mathematics, not to even the basics of mathematics on which you have such vacuously dogmatic opinions. It's characteristic of childish mentality to think that you can't look at things from other people's points of view without giving up your own.

And putting "different perspectives" is scare quotes is also jejune. Even if you disdain other perspectives, it should not be at issue that the notion of a different perspective is common and doesn't need scare quotes. That's not even a big point, but it is an emblematic detail.

Two posts now I've attempted compromise, but you still haven't addressed my proposal. It appears very much like you are the one incapable of giving fair consideration.

You've been addressed:

A few posts ago:

I cannot agree that abstractions are objects, unless we restrict "object" to refer only to abstractions.
— Metaphysician Undercover

Now:

I readily conceive of abstract objects
— Metaphysician Undercover — TonesInDeepFreeze

But you also put words in my mouth:

do not seem to be ready to accept the dualism required for a true understanding of "abstract objects"
— Metaphysician Undercover

I haven't said anything about duality. This is yet another instance of you putting words in my mouth (except weaseling with "do not seem"). — TonesInDeepFreeze

Friend, I think it's time to back away. You're debating with circle-squarers. It's like attending a flat-earthers' convention and joining a debate on what causes the phases of the moon.

Notice that most TPF folks are giving this topic a wide berth. Don't keep propping up their soapbox.

You could show us how that works with the Lorentz factor. :cool: — jgill

When v = c, $\gamma = -\frac{1}{12}$

But the Lorentz factor is always positive, so how can that be? :chin:

Nevertheless, you're on an amazing roll. :clap:

But the Lorentz factor is always positive, so how can that be? :chin: — jgill

You, as a mathematician, are better equipped to answer that most intriguing question.

Nevertheless, you're on an amazing roll. :clap: — jgill

You jest!

But the problem with setting a largest number is that it rules out irrational numbers such as pi, sq-root 2 etc because they cannot continue to infinity as decimals and therefore become expressible as ratios — unenlightened

This gets more and more interesting by the minute.

Take the irrational number $\sqrt 2$. To what decimal place of accuracy must we calculate it to construct the dome of the Hagia Sophia (google for details)? I read a book that relates how the engineer used a rational approximation instead of the actual value of $\sqrt 2$.

Remember high school when $\pi$ was $\frac{22}{7}$? We could use rational approximations that are accurate to an arbitrary number of decimal places for $\pi$ and other irrational numbers and I think modern calculators do exactly that.

The same logic is true in this case too - replace the infinite decimal part with a finite one using a rational approximation. My guesstimate is we won't be needing the actual value of $\pi$ ever; a rational approximation accurate to the required number of decimals will be just fine.

Likewise, infinity, no need! A very large but finite number will suffice. If memory serves the Greeks did just that - they used arbitrarily large numbers in place of infinity.

Friend, my admonition to you is the same as that for TDIF : when you see certain names pop up on math topics, run the other way. Otherwise, you're wasting your time.

Without an audience, they will go away.

(My understanding is that banishment can be initiated given a low quality of posts. So I caution the posters trying to tear down 3,000 years of well-established mathematics and invent their own. If any of the moderators have a knowledge of math, they may frown upon such repeated nonsense as "infinity = -1/12". These ideas are not up for debate in math. Such ridiculous pronouncements would not be tolerated on a "purely" philosophical thread.)

You quote the first line of a post and you ignore the rest. I see no point.

These ideas are not up for debate in math. — Real Gone Cat

Sorry to disillusion you Real Gone Cat, but this is a philosophy forum, not a math forum.

You quote the first line of a post and you ignore the rest. — Metaphysician Undercover

The rest doesn't mitigate your contradiction. I've been through this before with you where you shift your position making coherent discussion impossible.

this is a philosophy forum, not a math forum — Metaphysician Undercover

Philosophy of mathematics requires knowing the mathematics being philosophized about.

The rest doesn't mitigate your contradiction. — TonesInDeepFreeze

Sorry Tones, You have not pointed out any contradiction. If I remember correctly, you define contradiction as saying 'is' and 'is not' of the exact same proposition. "I cannot agree to abstractions as objects, without specific restrictions", does not contradict with "I can readily conceive of abstract objects". All conceptions require restrictions, that's what conception is, understanding the specified restrictions.

"I cannot agree to abstractions as objects, without specific restrictions", does not contradict with "I can readily conceive of abstract objects". — Metaphysician Undercover

What you wrote:

I cannot agree that abstractions are objects, unless we restrict "object" to refer only to abstractions. But then we could not use "object" to refer to anything else, or we'd have equivocation. And we would have to create a special form of the law of identity, such that when 'the same' abstraction exists in the minds of different people, we can still refer to it as "the same" abstraction, despite accidental differences between one person and another, due to different interpretations. The current law of identity requires that accidental differences would constitute distinct 'objects' which are therefore not the same, so we'd need a different law of identity. — Metaphysician Undercover

So I take it that restricting 'object' to refer only to abstractions is not acceptable to you. Thus, indeed you do not agree that abstractions are objects. Thus, indeed you contradict yourself when you also said:

I readily conceive of abstract objects — Metaphysician Undercover

To put it starkly:

"I cannot agree that abstractions are objects" is tantamount to "abstractions are not objects".

"We restrict 'object' to refer only to abstractions" is tantamount to "only abstractions are objects".

So what you said is tantamount to: Abstractions are not objects unless only abstractions are objects. But you also deny that only abstractions are objects. Thus you affirm that abstractions are not objects.

Or:

Let 'P' stand for 'abstractions are not objects'.

Let 'Q' stand for 'only abstractions are objects'.

You say 'P unless Q'. But you deny Q. So you affirm P.

You host a continually silly shell game. I shouldn't indulge in responding indefinitely.

this is a philosophy forum, not a math forum. — Metaphysician Undercover

If part of one's philosophizing about mathematics includes criticisms of certain actual mathematics, then one should know enough about that actual mathematics that one doesn't misconstrue and misrepresent it. And if one proposes a certain alternative philosophy of mathematics, then it is natural to ask "To what actual alternative mathematics does your alternative philosophy pertain?"

No, set theory does not say that there is a proper subset of a set such that the proper subset is the set. Set theory does say that there are sets such that there is a 1-1 correspondence between a proper subset of the set and the set.

This is another example of you running your mouth off on this technical subject of which you know nothing because you would rather just make stuff up about it rather than reading a textbook to properly understand it. — TonesInDeepFreeze

It's kind of funny in retrospect how arrogant you came off in accusing Agent Smith, while, unknowingly, you are completely wrong! Part and whole have nothing to do with set and subset: one is mereological, the other is set-theoretic, yes, they can overlap, but no, they're not the same thing.

To interpret his statement set-theoretically, when "part and whole" are specifically the technical terms used in formal mereology, is either (1) delibarately uncharitable or (2) you not being aware of what he's referring to. But whatever the case is, (1) or (2), it does not excuse your hostility.

In any case, (non-proper) parthood is a transitive, antisymmetric, and most importantly reflexive relation such that ∀x P(x, x): every whole is a (non-proper) part of itself. This axiom is true in virtually all of contemporary formal mereologies (X, M, AX, GEM, AEM, AMM, EM, etc.) and is perhaps the least controversial mereological axiom: even the transitivity of parthood is sometimes disputed!

So AgentSmith was correct, and your "correction" of him is a result of conflation of mereology with set theory on your part, so before telling him to do his homework, do your own.

Is infinity a contradiction? It does lead to some rather odd conclusions: a part is equal to the whole and all that. No wonder many mathematicians (recall Kronecker's vitriol against Cantor) were dead against it. — Agent Smith

No, set theory does not say that there is a proper subset of a set such that the proper subset is the set. Set theory does say that there are sets such that there is a 1-1 correspondence between a proper subset of the set and the set. — TonesInDeepFreeze

Part and whole have nothing to do with set and subset — Kuro

I didn't say that subset and set align with the mereological notions of part and whole.

Agent Smith said that said set theory allows that a part can be equal to a whole. I correctly pointed out that that is not true. (For that matter, 'part and whole' are not even terms of set theory). And I correctly pointed out that what set theory does say is that in some cases a proper subset is equinumerous with its superset.

And Agent Smith made no reference to 'part' and 'whole' as technical terms of mereology. And it doesn't matter anyway. Whatever mereology has to say, set theory does not say that a part can be equal to a whole.

does not excuse your hostility — Kuro

I am hostile to him only in a broad sense that includes that I decry his continual (over many posts and many months) ignorant and willful falsehoods, misrepresentations and confusions of the subject.

So AgentSmith was correct, and your "correction" of him is a result of conflation of mereology with set theory on your part — Kuro

You are either confused about the context of the posts or you are willfully fabricating about it.

What I responded to:

Is infinity a contradiction? It does lead to some rather odd conclusions: a part is equal to the whole and all that. No wonder many mathematicians (recall Kronecker's vitriol against Cantor) were dead against it. — Agent Smith

He's not talking about infinity per mereology. He's talking about the Cantorian notion. The mathematicians who were against Cantor's notion of infinity were not taking Cantor to have presented a mereology but rather indeed a mathematical notion of sets.

Agent Smith is claiming that the notion of infinity, as in set theory (for example, as he mentioned, set theory engendered by Cantor), leads to the conclusion that a part is equal to the whole. And I correctly replied that that is not true, though it is true in set theory that in some cases a proper subset S or T is equinumerous with T.

/

Bringing a mereological perspective to the subject is fine. But it is a red herring to put my exchange with Agent Smith in context of mereology when the context was clearly set theory.

You are either confused about the context of the posts or you are willfully fabricating about it. — TonesInDeepFreeze

I responded based on the quotation of him where he says "part is equal to whole" - this is what you've included in your post in whole with no further passage/text in the quote. Perhaps you could've made a larger quotation for context, but otherwise I do not think my presumption was particularly irrational (since, reading "part is equal to whole" at face-value, just is a mereological truism.)

You are entirely correct in that if he refers to proper subset and set by "part and whole", which, per context seems to be the case, then it is completely inaccurate.

What I quoted and my reply:

a part is equal to the whole
— Agent Smith

No, set theory does not say that there is a proper subset of a set such that the proper subset is the set. Set theory does say that there are sets such that there is a 1-1 correspondence between a proper subset of the set and the set. — TonesInDeepFreeze

I made clear that I was responding regarding set theory. Granted, I didn't include in his quote the part - that makes even more explicit that the context is set theory - where he specifically mentioned 'infinity' and 'Cantor'. Also, I didn't belabor that the previous context was infinity especially as Agent Smith faults the notions of infinity and set theory (with your comments about mereology running alongside but separate from the particular exchanges between Agent Smith and me). In all that context, if one paid attention to the conversation, rather than just knee-jerking to one quote in it, it was clear that set theory was what was being discussed at that juncture.

"part is equal to whole" at face-value, just is a mereological truism — Kuro

(1) It's my very point that Agent Smith seems to have conflated the set theoretic notion that an infinite set T has proper subsets equinumerous with T with the mereological notion of part/whole.

(2) Agent Smith was rejecting the notion that a part is equal to a whole. Obviously, that is not about a non-proper part being equal to a whole, but rather a proper part being equal to a whole. So that he's not adducing the truism you mentioned.


/

I would have made it easier for you if I had quoted him more fully. But even then, I did not distort him by quoting more narrowly. I was correct in my reply to Agent Smith. It was not arrogant of me. You were wrong to claim I was not correct or that I was arrogant about it.