Stating my own argument about it.

Whether you reply to my statement of my argument about your contradiction is entirely your own prerogative. — TonesInDeepFreeze

There was no argument made by you, just a blatantly false accusation, that my previous post was contradictory.

And, since you seem now to be leaning toward a claim that I called you back to defend your argument, I withdraw my comment that I might have taken you too literally. — TonesInDeepFreeze

You clearly demonstrated that you never even understood what I said, calling it obfuscation. Now you confess to not knowing whether you took it literally or not. Admit the facts, you have no understanding whatsoever, concerning the ontological principles I stated. So you decided your best course of action was just to publicly state that what I said is contradictory, (even though it clearly is not), instead of asking me to clarify. That is bull shit!

There was no argument made by you — Metaphysician Undercover

Yet again you repeat your false claim that is refuted by content of the posts.

If memory serves, [Widlerberger is] a finitist.
— Agent Smith

That is quite missing the point. Wilderberger, as I glean, is an ultrafinitist. — TonesInDeepFreeze

Then I mentioned that, more particularly, he's an ultrafinitist. — TonesInDeepFreeze

Your notion of “mentioning” is as disingenuous as your definition of “being constructive”. We can leave it there.

Your notion of “mentioning” is as disingenuous — apokrisis

Granted, I didn't just say that Wilderberger is an ultrafinitist but that it is quite missing the point to refer to him merely as a finitist. In my post just quoted, I didn't intend that my saying that I mentioned that Wilderberger is an ultrafinitist was meant to elide that I also said that it is quite missing the point not to more specfically say he's an ultrafinitist.

That you read into such details that I am dishonest for referring to myself has having mentioned something is nutty.

your definition of “being constructive” — apokrisis

I gave no definition. I just said that there is a sense in which I think posting replies to cranks is constructive. And I as much as happily granted that that is limited.

Yep. Just trying to help you counter the three-headed anti-modern-math beast.

The OP is too clearly an example of ultrafinitism to be an accident. All protestations aside, I think someone is trolling.

What do you mean by "ultrafinitism to be an accident"?

I think someone is trolling. — Real Gone Cat

I think Agent Smith is sincere that he thinks there should be an alternative to infinitistic mathematics. And he thinks he's contributing to that goal when he broaches certain considerations and (what are to him) juicy tidbits about mathematics.

Where he is not sincere is in not bothering to learn very much about the subject while he serially misrepresents the infinitistic mathematics he objects to.

I sense that where he's actually trolling is in his cutesy, self-effacing, would-be disarming, [parody:] "Aw shucks, I'm just a poor country boy educated in an old one room country school" shtick.

I did reply half-seriously to what was the actual OP. Cosmology does recognise that the visible universe is a bounded region with a maximum entropy condition. It contains some finite number of degrees of freedom.

The OP is too clearly an example of ultrafinitism to be an accident. — Real Gone Cat

That is nuts. You think @Agent Smith is pretending to be a finitist when he is really an ultrafinitist at heart?

This little drama sounds more and more like that scene in Life of Brian…

You think Agent Smith is pretending to be a finitist when he is really an ultrafinitist at heart? — apokrisis

That's addressed to Real Gone Cat, but for myself, I don't think he's pretending that. He doesn't even know what the scope of the rubric 'finitism' includes, and he didn't even know what ultrafinitism is until (maybe) he looked it up an hour or so ago.

Anyway, it's not clear to me what his view is: Does he grant that there is no greatest number, while suggesting that there is a greatest practical number? Or does he hold that there is a greatest number period?

You think Agent Smith is pretending to be a finitist when he is really an ultrafinitist at heart? — apokrisis

:snicker:

I find that really amusing! I'm afraid my acting skills aren't up to the mark, I wouldn't be able to pull off such a stunt.

Anyway, it's not clear to me what his view is: Does he grant that there is no greatest number, while suggesting that there is a greatest practical number? Or does he hold that there is a greatest number period? — TonesInDeepFreeze

All of the above. :grin:

His position is vague. But one can develop it in a fruitful direction - like ultrafinitism.

The enquiry can be fruitful. But poorly so if the vines are mangled and torn apart by misinformation and unnecessary confusion.

His position is vague. But one can develop it in a fruitful direction - like ultrafinitism. — apokrisis

Muchas gracias for understanding.

I recall @andrewk (hope s/he's well) said something to the effect that we could be like the finite calculator I hypothesized in my post to @jgill [a calculator that can't calculate beyond 5 would display 5 (the arbitrarily large number) for both the queries 2 + 3 = ? and 3 + 29 = ?]; he asked, paraphrasing, how can a finite brain grasp infinity? What follows is there hasta be a finite number to think of which would require every single neuron in the brain to be activated, let's call it N_max. Any number larger would be, in a way, truncated to N_max whatever that is (a cognitive numerical ceiling).

$\infty$ = ERROR!

All this hullabaloo about an error message!

how can a finite brain grasp infinity — Agent Smith

Depends on what 'grasps' means. If it means mentally seeing an infinite number of concrete or abstract objects all at once, then probably it can't be done.

But if it means grasping that a certain property is held by more than a finite number of objects, such as we describe that situation as there being a set of all and only those objects, then I grasp that easily.

In that regard, I have little difficulty in grasping, for example, that there is the set of all and only the natural numbers. And I am not dissuaded by such mere facts that, for example, there is a bijection between the set of even natural numbers and the set of natural numbers. I don't find that baffling. Especially I don't think I need to reject that fact only because at an earlier stage in my life, as a child, I didn't think about such things so that I might have mistakenly jumped to the conclusion that a proper subset of a set T cannot be in correspondence with T (though that incorrect intuition wouldn't have been stated in those terms when I was a child).

I don't find that baffling. — TonesInDeepFreeze

Most interesting. — Ms. Marple

I hypothesized in my post to jgill [a calculator that can't calculate beyond 5 would display 5 (the arbitrarily large number) for both the queries 2 + 3 = ? and 3 + 29 = ?]; he asked, paraphrasing, how can a finite brain grasp infinity. — Agent Smith

I did? I'm old. Maybe I was closing up shop for the night. :chin:

Then there is the heuristic question: What practical advantage would there be in throwing out the methods of infinitistic calculus for an ultrafinitist approach? Again, how is it any better for me to have to know what degree of accuracy my friend needs when instead I could just say, "pi is the value" and let him use whatever accuracy he needs in its practical application?

And, from a formalizing perspective, we can pretty much anticipate that an ultrafinitist system would have a much more complicated axiomatization.

From an aesthetic point of view: At least for me, it is unbeautiful to pick some particular number, either arbitrarily or on the basis of some physicalist constraints, to be the greatest number. I lean toward being more sympathetic with a system of greatest possible generality, not particularized by whatever physical science determines at any given point in the developments of the sciences.

But there are puzzles I find with infinite sets in certain aspects of mathematical logic. I admit that my framework of understanding hits a wall in those particular aspects.

I did? I'm old. Maybe I was closing up shop for the night. :chin: — jgill

:lol: :up:

I suppose my question boils down to: is infinity necessary? We really don't use 3.14159... (the real value of $\pi$). Put yourself in an engineer's shoes and answer that question? In other words, at least in the case of $\pi$, an approximation (finite) will do just fine.

Is $\infty$ like God as Cantor believed? Lt. Worf said of Klingon gods, "We killed them. They were more trouble than they were worth."

I'm no mathematician but I believe it's a simple rule of thumb that if a mathematician wants to propose a new idea, s/he'll use $\infty$ only if absolutely necessary and that too with much reservation.

When I said "too clearly an example of ultrafinitism to be an accident", l was implying that these ideas most likely originated from an ultrafinitist source. I suppose you could arrive at such a conclusion on your own, but not if you've taken math at university, or even high school. The opposite is taught in math today. (Isn't this why you keep admonishing AS to get some learnin' on the subject?)

Not telling you anything you don't know, but adopting ultrafinitism leads to some odd results

• Pi must be truncated, and becomes rational. Thus the circle cannot be closed, and circles should be open to squaring.
• Irrational numbers don't exist, and thus lines do not consist of points.
• Limits cease to exist, and rhe epsilon-delta definition for the derivative is removed.

Why am I nuts?

Ultrafinitism is usually defined as the belief that really large FINITE numbers do not exist because of constructive limits - what is physically realizable in the universe. And what does the OP posit? That there is a maximum number needed to describe the universe. Anything bigger doesn't need to exist. Did I get something wrong?

is infinity necessary? — Agent Smith

First, as I've said ad nauseum, (with exceptions of figures of speech) mathematics doesn't have a noun 'infinity' but rather an adjective 'is infinite'.

You keep using 'infinity' as a noun. Okay, then what is your definition? What object do you think is named by the noun 'infinity'?

And as I've said ad nauseum, infinite sets are necessary for the ordinary system of the mathematics for the sciences. There are alternative systems, for many approaches, but I don't know of an actual ultrafinitist systemization. (Maybe there is one? Someone can adduce one? Quite some time ago I did read through a lot of Lavine's book, but I don't recall how formally satisfying his proposal is.)

We really don't use 3.14159... (the real value of π). Put yourself in an engineer's shoes and answer that question? — Agent Smith

You skipped what I wrote about that. That is your M.O., in true crank style: Skip responding to points that don't support your own position and instead just keep reiterating your position.

Is ∞ like God as Cantor believed? — Agent Smith

Oh come on, why do you keep harping on something that died over a hundred years ago? Mathematicians, at least in their actual formal mathematics, don't relate to the part of Cantor in which he equated an Absolute Infinity with God. That's just not on the table. Forget about it. It's a huge red herring.

it's a simple rule of thumb that if a mathematician wants to propose a new idea, s/he'll use ∞ only if absolutely necessary and that too with much reservation. — Agent Smith

When you make claims like that, I ask you to provide your basis. By what actual evidence, from what actual sources, do you make that claim?

It's patently false anyway. Many mathematicians freely make use of infinite sets. All over in analysis and other other branches. Not to mention set theory itself which is a branch of mathematics. Day one of even a high school class: The real number line. That's an infinite set of points ordered by the less than relation. Day one of freshman calculus: A sequence converging to a limit. That's an infinite sequence. Infinite sets are as basic to ordinary mathematics as wheels are to automobiles.

You're just making claims straight from your smoke blowing orifices, with no regard, no sense of responsibility, for supporting those claims or even thinking for one moment whether you are right about them. Pure crank.

Isn't this why you keep admonishing AS to get some learnin' on the subject? — Real Gone Cat

I say he should learn about the subject so that he'll desist from spewing misinformation about it. He fancies himself a critic of classical mathematics but he persistently makes false claims about it. One might as well go into a biology discussion group and say, "Academic biology is all wrong. Just look at the concept of a cell. They say a cell is an organ of the body. That makes no sense. Look at their concept of carbon. They say carbon is the fluid that runs through veins. How much more wrong could they be?"

But I don't agree with the utilitarian framework you apply here*. First, I don't think utilitarian result is the only consideration. Second, for utility it doesn't matter anyway: The crank will continue to spew disinformation no matter whether left unresponded to or responded to with correction.

* I don't claim you adhere to utilitarianism. I am just saying that in this particular context your framework is utilitarian. — TonesInDeepFreeze

If you know a thing or two about that quote you agree with, you'd know that I'm not employing a utilitarian framework here* (though I'm delighted that utilitarians and Kantian deontologists alike would also agree with me): this is simply the framework of Hellenic virtue ethic theories, and I'm saying that, in a less blunt way, that in not acting rightly one retracts from the virtue of their character, which is less so a property of any particular fault or flaw in action rather than those habits which become second nature to them and come to form their decisions & methodology (which is what the discussion came about, the generalized implications versus the particular one, hence the relevance of the quote).

*I'm not saying this to imply that what I said disagrees with what utilitarians or deontologists have to say, just that I'm not myself using their theories.

Why am I nuts? — Real Gone Cat

If you believe @Agent Smith was being that cunning and conspiratorial in framing his OP.

What would be the point?

I'm not employing a utilitarian framework here — Kuro

My main point is that I don't accept your argument of posting in terms of what is "productive" or outcomes ("fanned flames"). Evaluation per what is productive or outcomes, as I would think in that framework, productive outcomes are good and unproductive outcomes are at least less good. That is what I meant by a utilitarian point of view. My comment about the quote was that I agreed with that part of it that I quoted (no comment on the rest of it), but also I don't accept the "utilitarian" (the productivity and outcomes of posing) part of your argument; I did not all intend to suggest the quote itself is from a utilitarian point of view. Indeed, I would have no reason to think it is.

Is that clear? There's the part of the quote that I quote, which I agree with. And there was another part of your argument that I don't agree with. I don't take the quote to be from a utilitarian point of view. But I find an productivity and outcomes argument to be, at least generally put, utilitarian.

But I accept that you don't consider 'utilitarian' as a correct description of your productivity and outcomes argument. Indeed, my point doesn't rely on the particular rubric 'utilitarian' but rather that I reject your productivity and outcomes argument, whatever rubric it correctly falls under.

Also, I don't claim that evaluation of the merits or advisability of posts cannot include productivity and outcomes as a factor. Just that I don't think it is in and of itself determinative and may be trumped by other factors including even a poster's own prerogative to express himself and as a post may offer others access to expressive and cogent and/or well articulated thoughts even if they are not productive in the immediate context of a particular posting exchange. Even further, sometimes it is simply fitting that a poster gets stuff off his chest.

Hate, emotions generally, is/are so weird, both to feel and express. Sometimes, I conjecture, two incompatible feelings e.g. love-hate become so intense that the mind splits into an appropriate number of pieces, each compartmentalized and separated from the other, as a defensive mechanism, to prevent a mind crash (re Dissociative Identity Disorder). The compartmentalization may not be fail-safe, remember the Titanic!

You're correct, of course. I apologize to AS.

I now realize that AS is asking for something even more restrictive than the ultrafinitists. Correct me if you disagree :

Finitism rejects the existence of an actual infinite set (sometimes, as in the case of Hilbert, allowing for a potential infinity). Ultrafinitism rejects the existence of very large integers (sometimes positing that only what is constructable in this universe, or by humans, exists) - and by extension, irrationals. AS rejects any number that is not useful to humans, such as Pi beyond a few decimal digits. Ultra-ultrafinitism?

My bad.

AS rejects any number that is not useful to humans, such as Pi beyond a few decimal digits. Ultra-ultrafinitism? — Real Gone Cat

That does have some sense if you wanted to play with it as a conjecture. What would be the best rebuttal? Would we start by saying we couldn’t limit the scope of future human ambitions and the numbers that would involve?

There is a line of thought if you wanted to be serious about dismissing it.

Likewise he made the point that animals and even tribal human cultures don’t require a number sense beyond one, two, a few and many. So where does that leave our love affair with an unbounded capacity for assigning distinct names to an infinity of values?

Again a perfectly fair start to a discussion that can draw on plenty of scholarship.

How often do random or confused starting points lead to entertaining discussions on PF? Far more often than the dogmatic exposition of something anyone could read up as the received view in an undergrad textbook I would say.

So yes, give AS a break. :smile:

Yet again you repeat your false claim that is refuted by content of the posts. — TonesInDeepFreeze

The claim was not false, as I showed with a number of explanations. You would not even address the content of my replies, insisting they're too confused, obfuscatory, rambling, dishonest and ignorant.

In other words, you could not understand what I wrote, and instead of asking for clarification you decided that it must be contradictory, so you just kept repeating that it is contradiction. That's not only disingenuous, it's bull shit!

You skipped what I wrote about that. That is your M.O., in true crank style: Skip responding to points that don't support your own position and instead just keep reiterating your position. — TonesInDeepFreeze

How familiar. Now I can call you a "crank", by your own description.

Ultrafinitism is usually defined as the belief that really large FINITE numbers do not exist because of constructive limits - what is physically realizable in the universe. And what does the OP posit? That there is a maximum number needed to describe the universe. Anything bigger doesn't need to exist. Did I get something wrong? — Real Gone Cat

There's a very simple ontological principle to employ. Potentialities do not "exist". To "exist" requires actuality. So when I say tomorrow I might build myself a new chair, that chair does not exist because it's only an idea, a potentiality, or possibility, without actual existence.

First, as I've said ad nauseum, (with exceptions of figures of speech) mathematics doesn't have a noun 'infinity' but rather an adjective 'is infinite'. — TonesInDeepFreeze

Many mathematicians freely make use of infinite sets. — TonesInDeepFreeze

OK, let's see if you can clarify what is meant here to make sure you are not contradicting yourself. "Infinite" is an adjective. There is something which is said to be "infinite" and that is a "set". Now, a set is not an object, otherwise the set would be an infinite object, and this would be an infinity. But "infinity" as a noun, is not a word used in mathematics, so a set is not an object.

So what type of existence does a set have? It's not an object, or else it would be an infinite object (referenced by the noun "infinity"). What is this 'thing'?, called a "set", which we cannot say is a thing, referenced with a noun, otherwise it would be an infinite thing, i.e. an infinity. How is it that "infinite" can be predicated without a thing to be the subject of that predication?