I don't know whether there is a limit on how long there will be conscious beings.
— TonesInDeepFreeze

True. But we are talking "we". Supposedly humans. That's what I'm sticking with. Computers are not humans. — god must be atheist

We could stick to humans. But there may be a time when humanity becomes some other kind of being. Also, for philosophical purposes, it seems arbitrary to confine this question to a particular species at a particular point in history.

I wasn't even talking about computers. I would take it though that any number needed by a computer that is used by a human (or whatever) is number needed by humans (or whatever).

But I don't know that there is a limit on how long there will be conscious beings. — TonesInDeepFreeze

Human beings are predicted to die out at the latest when the sun becomes a Red Giant. Whether we would escape the confines of the Solar system by then, is questionable.

However, if we are able to escape the confines of the solar system, then our lifetime as a species is still limited, even under the best of circumstances, because heat entropy will make all habitable environments inhabitable. That is to come in a trillion, trillion, trillion Earth years. (1 followed by 36 zeros Earth years.) There may have been some rounding error.

I did not make this up. I read it in a newspaper (before the advent of the rampant use of the Internet)

your refusal to define and adhere to a definition of "object" is inexcusable. — Metaphysician Undercover

You're mixed up again and lost your place in the exchange. The question is not how I define 'object'. And it's not even how you define it. Rather, no matter how you define it, you contradicted yourself about it, as I quoted you doing that.

I predict that now you'll write yet more rambling, obfuscatory paragraphs in which you elide your own posted words.

Also, for philosophical purposes, it seems arbitrary to confine this question to a particular species at a particular point in history. — TonesInDeepFreeze

if we become something else, we are something else but humans.

And like I said, I go by the title. The title clearly states the set of salient things who will ever need a number that is larger than all other numbers they will need. And the named set is "we". Since it was written by a human (supposedly), it is humans we talk about.

I'm just saying that, in principle, I don't know whether consciousness, even if no longer human or was never human, will end.

The question of what this particular species needs seems (at least to me personally) too quotidian to be much of a really philosophical question about mathematics.

I have already granted that if Agent Smith does agree that there is no greatest number (despite his persistent anti-infinitstic lobbying in other threads), then I misconstrued him, forgot to refer back to the title post, and a retraction by me would thereby be due.

There we go.

There we go. — god must be atheist

Yes, as I had gone already many posts ago:

But I still would be interested to know whether he does recognize that there is no greatest number. If he does, then I would need to retract some of my previous comments about this. — TonesInDeepFreeze

I actually can't see the UNIVERSAL advantage of unifying objects and terms of measurement. Sailors still measure velocity in knots; Americans still measure weight and volume in ounces and gallons and pounds. If there were an advantage to unification, everyone would be using the same system, and yet we don't. — god must be atheist

It would free us from the need for conversion, translation, in communicating with each other, which would of course be an advantage.

Rather, no matter how you define it, you contradicted yourself about it, as I quoted you doing that. — TonesInDeepFreeze

Oh, if that's how you interpreted what I said in all those posts, it's very apparent that you did not read what I said. I conclude that I was wasting my time.

I proved that I read what you posted, as I quoted it more than once and gave exact and detailed comments about it. And though my comments were clear as day and formatted quite perspicaciously, you couldn't intellectually cope with them.

I conclude that I was wasting my time. — Metaphysician Undercover

Indeed your confused, ignorant and intellectually dishonest postings are a waste of your time, as you'd do so much better for yourself by reading a book on the subject.

Has anyone read the Wikipedia entry on the so-called methodus exhaustionibus? Pioneered by Antiphon, and employed by none other than Archimedes to calculate $\pi$. To my knowledge, when computing $\pi$ (an irrational number), all we need is a certain level of accuracy, tailored to the task at hand. So, if I were making a wheel for an ox-cart, I could use 3 as the value of $\pi$, but if I were to machine a wheel to be used on a spacecraft, I'd need greater accuracy, say I'd need to use a value of $\pi$ correct to the fifth decimal place viz. 3.14159. As you can see these approximations can be arrived at without having to bring $\infty$ into the picture; all that's required is, as some have said, an arbitrarily large number.

What sayest thou?

How about, if I don't know what degree of precision my friend needs to complete his task, I just tell him that the value he need is pi, then he can use whatever approximation is suitable.

How about, if I don't know what degree of precision my friend needs to complete his task, I just tell him that the value he need is pi, then he can use whatever approximation is suitable. — TonesInDeepFreeze

Ok, but there's no need for $\infty$ oui?

You keep writing the leminscate but without saying what you mean by it.

I have explained over and over that in rigorous mathematics:

There are points of infinity on the extended real line

And there is the notation "goes to infinity" such that that notation is only a convenience as we can dispense with it by writing the formulas with greater rigor.

And there is the adjective 'is infinite' but not the noun 'infinity'

But when you use the leminscate, you do so without rigorous grounding to explain what you mean by it as actual mathematics.

/

And I have explained over and over the importance of infinite sets for axiomatizing mathematics.

/

And you keep pointing to the -1/12 thing. You brandy it around like a chimpanzee beating his chest, as if you've brought in some kind of killer refutation of infinitistic mathematics. Yet you ignore jgill when he explains that it's really just a gimmick that plays on purporting that a divergent series converges.

I really do not understand why someone would keep spouting the same mistakes over and over, even when explained to him, and while not bothering to actually learn something about the subject. Well, I can guess actually: vanity - the fun of fancying oneself as a thinker on a subject one thinks one doesn't even have to study.

How would it be if there were a Biology discussion group, and I serially posted that ordinary academic biology should be replaced with my own personal notions about biology, and yet I didn't even know what a cell is, didn't even know what a carbon atom is. That is essentially what you do.

/

And, by the way, in ordinary axiomatized mathematics, there is no pi if there are no infinite sets. You would see that easily if you only took a bit of time to learn something about this subject.

This thread has opened the door to a BIG NUMBER theory, a BIG BANG theory companion!

Oops, looks like there already exists such a Theory :sad:

:smile: I'm trying mon ami, to learn. Not exactly in the best of circumstances to do that. Cut me some slack, will ya? Danke.

BIG NUMBER THEORY! Yeah that sounds about right - if there's a finite number that exceeds a supercomputer's ability to grok it (returns an error), then a fortiori humans can't handle it. We could of course always program a computer to display an arbitrarily large number instead. Imagine a calculator that can't deal with numbers larger than 5. If I ask it to do 2 + 3, it does so and gives the result 5, but if I ask it to calculate 3 + 9, it should still give 5 as the sum (it doesn't "understand" 12, a number > 5).

I always thought from my experience that maths types were invariably into classical music. It was the physicists who scaled peaks. — apokrisis

I knew Lester Germer, a multi-dimensional person. He was a fighter pilot in WWI.

My oldest and best climbing friend ,Dave Rearick, was a math prof at the U of Colorado.

I have explained over and over that in rigorous mathematics: — TonesInDeepFreeze

I really do not understand why someone would keep spouting the same mistakes over and over, even when explained to him, — TonesInDeepFreeze

But you are on a philosophy site. And one that is far from rigorous in its willlingness to allow all types of speculative thought. So no need to continually clutch your pearls in shock at the rude habits of the nasty natives.

More productive would be to engage in the deeper issue being expressed - the fact that physics may indeed be in ontological conflict with maths on the issue of whether infinity is usefully thought of as potential or actual. The result of a generating process or the existence of an actual value.

The idea of a largest number makes no sense to either of these positions. But the idea of largeness being arbitrary does.

On the physicalist side of the debate, the ontological argument is that reality is relational. It is born of a structure of constraints. Stability can’t be taken for granted as existence is a process - the process of instability being stabilised.

In that light, we can well wonder what the numerical value of pi is in a real world where we are not even sure if the metric is flat - just flat to some currently measured degree of precision.

Likewise, if the values of numbers are being understood as the limits of terminating processes, it becomes legitimate to ask if all the irrationals have generating algorithms, or just some of them, like pi? So what is going on there.

If you come on to a philosophy site, you ought to expect a traditional rivalry - such as that between potential and actual infinity - to be treated as an open and interesting question, even if the level of discussion is lay.

I've said much of this before:

I do not object to broad and speculative philosophy, even regarding mathematics. And, of course, I appreciate that there are alternative mathematical systems and motivating philosophies - constructivist, predicativist, finitist, dialtetheist, etc. - and that it is philosophically relevant to compare mathematics with the sciences. But when a poster also brings the actual mathematics into consideration, especially to critique it, then the poster should not mangle or misrepresent that mathematics. Certain posters do this serially (over months and years) and willfully. To ignore multiple corrections and explanations while posting, over and over again, confusions and falsehoods about the actual mathematics is intellectual abuse. Crankery corrodes knowledge, understanding, clarity and communication.

You mention what is constructive to post. Crankery is dishonesty and it is destructive. It is honest and constructive to flag that dishonesty and destructiveness. (Anyway, a poster's intent is very often not to be constructive but rather merely to be expressive.)

To reiterate: I have no principled objection to people philosophizing as wildly as they want, but when they cite actual mathematics as part of the subject of that philosophizing, then they should not, from ignorance and self-misinformation, be posting falsehoods and confusions about that mathematics. And while I don't begrudge them the prerogative to do that, I don't begrudge myself the prerogative to refute it and denounce it.

Crankery corrodes knowledge, understanding, clarity and communication. — TonesInDeepFreeze

Sure. But again, this is you now setting your self-appointed standards for the site. And there are moderators who actually are responsible for deciding the limits of tolerance.

So I understand your point of view. But pragmatically, have you achieved a measure of success? By your own admission, hammering on @Agent Smith doesn't seem to have the desired effect. You can set him as much reading homework as you like, but that becomes performative if you have no real expectation anything will change.

And while I don't begrudge them the prerogative to do that, I don't begrudge myself the prerogative to refute it and denounce it. — TonesInDeepFreeze

This speaks of a joyless rigidity to life. And you are mistaken if you think "actual maths" trumps "actual philosophy" on a philosophy website. It's a simple category error.

The site could crack down harder on folk's critical thinking skills, of course. :grin:

this is you now setting your self-appointed standards for the site — apokrisis

I don't set any site-wide or general standards. Rather, I comment based on my own standards.

And there are moderators who actually are responsible for deciding the limits of tolerance. — apokrisis

Moderators don't censor cranks. And I don't advocate that moderators censor cranks. But that doesn't entail that I must refrain from my own comments about cranks.

have you achieved a measure of success? — apokrisis

Cranks never* come around to reason and knowledge. They go on for years and decades. They are, by nature, deeply stubborn and are narcissistic in criticizing the profound intellectual developments in mathematics over the last 200 years without feeling the slightest need to study to know anything about those developments.

But I find it worthwhile to post the corrections to the record. I don't have an inflated sense that this makes any "hill of beans" difference in the outcome of humankind or the world. It's just, for me, satisfying, even if only in principle, to articulate and enter my comments. And I believe it is constructive to do that.

And while I don't begrudge them the prerogative to do that, I don't begrudge myself the prerogative to refute it and denounce it.
— TonesInDeepFreeze

This speaks of a joyless rigidity to life. — apokrisis

Absolutely the contrary. I find real joy and solace in the fact that people are free to post what they like and I am free to reply as I like. Rather than the rigidity of disallowing people from posting as they like, I celebrate the freedom that they may post as they like and that I may reply as I like.

Moreover, it is presumptuous to extrapolate to life in general. Posting refutations to cranks doesn't nullify the joys of life such as friendship, art and study. Moreover, I find posting as I do to be a mildly gratifying pastime.

And you are mistaken if you think "actual maths" trumps "actual philosophy" on a philosophy website. — apokrisis

It's good that you phrased that as a conditional. Because indeed I don't think mathematics trumps philosophy. I said nothing like that. What I said, if you would be so kind as to reread it, is that when we bring in the actual mathematics as a subject of the philosophizing, then we should not misrepresent the subject we are talking about; we shouldn't misrepresent or cause confusions about how that mathematics is actually formulated.

/

* I've witnessed just one exception. Years ago, in a different discussion group, there was a poster who was abysmally confused about set theory, yet he kept posting ignoran, and blatantly incorrect purported proofs that set theory is inconsistent. Later, he kept popping up alternative formal proposals, but they were ill-formed nonsense. For a long time, I offered him suggestions on how he could fix his formalizations so they made sense. Gradually, he started to get the hang of it. Then it became clear that he is brilliant. Once he got his feet on the ground, he was able to propose a number of meaningful and interesting alternative foundational systems, to the point that he proved a result that was published, as a prominent logician took him under wing. Years ago he went way past my own meager knowledge, so that he talks about advanced subjects I can't even begin to keep up with. (Yet, he never seemed to let go of the habit of making large claims without adequate support or rigor; but he would retract and admit that he did have more work to do on it when it was pointed out to him.)

I'm trying — Agent Smith

You're not. Instead of thinking for even a moment about the corrections and explanations given you, you keep popping back to prorogate your misunderstandings and flat out errors about the mathematics you comment on.

But I find it worthwhile to post the corrections to the record. I don't have an inflated sense that this makes any "hill of beans" difference in the outcome of humankind or the world. It's just, for me, satisfying, even if only in principle, to articulate and enter my comments. And I believe it is constructive to do that. — TonesInDeepFreeze

I'm questioning your definition of "constructive".

I don't know what kind of person he is away from posting, but I find him to be flippantly dismissive in my interactions with him as a poster. — TonesInDeepFreeze

Now reading further back in the thread, your excuses seem even thinner. Don't you realise that the more dogmatic you become, the more flippant will be the reply in this situation. That is how the dialectics of real life social interaction works. So you are producing the very thing you are complaining of in the end.

Rather than stamping out crackpottery, you are fanning its flames. :clap:

Rather than stamping out crackpottery, you are fanning its flames. — apokrisis

This is similar to my diagnosis.

I find myself as frequently frustrated as Mr. Tones with respect to the mathematical, logical or other formal/technical errors that are somewhat frequent on this forum. However, a rude attitude seldom yields anything productive: there is the option of politely leaving a discussion, perhaps at no fault of your own but the inadequacy of your interlocutor, or explaining their mistake at a reasonable level.

"Fanning the flame", so to speak, is unnecessary in whole. As a wise Greek philosopher said:

We do not act rightly because we have virtue or excellence, but we rather have those because we have acted rightly. We are what we repeatedly do. Excellence, then, is not an act but a habit.

I'm questioning your definition of "constructive". — apokrisis

I suggested the sense I have in mind.

excuses — apokrisis

I don't make excuses. My posting doesn't require excuses.

reading further back in the thread — apokrisis

In this thread, I might have made a certain major error about the other poster's position. As mentioned, I would retract that error if needed clarification shows that indeed I was in error.

dogmatic — apokrisis

What dogmatism do you refer to?

Rather than stamping out crackpottery, you are fanning its flames. — apokrisis

That seems likely. It is a Catch-22. If one refrains from commenting on crank posts, then cranks more greatly dominate. But if one comments on crank posts, then that also causes cranks to post even more.

My approach has usually been to first simply state the corrections and sometimes to add explanation. But then the crank replies with even more ignorant, confused and intellectually dishonest posts, and usually skipping even recognition of the most substantive parts of the rebuttals (form of strawman). An indefinitely long back and forth ensues. And at a certain point, what becomes most glaringly pertinent is no longer the subject itself but the cranks' inability (or refusal) to reason.

I accept that. Again, I don't claim that such engagement is constructive in the sense that it leads to the crank desisting from posting disinformation. The crank will continue to post disinformation whether he is left alone to do it or whether he does it in response to being rebutted about it. Rather, I find that it is constructive at least to have on record that the crank was rebutted. That is the best that can be achieved.

rude attitude — Kuro

The very first time I post to a crank, I don't impart attitude*. I simply post the correction and sometimes added explanation. But after a while, the crank gets even more dishonest, especially by countering as if he has rebutted the corrections while skipping the most important substance of them. Or, often, the crank becomes snide or condescending. It's often a key element of the crank's bag of tricks to impart that dismissiveness, condescension and putdown so subtly that the crank is ostensibly on high ground while still getting his digs in.

At a certain point, what becomes most glaringly pertinent is no longer the subject itself but the cranks' inability (or refusal) to reason and his abject intellectual dishonesty.

At

formal/technical errors — Kuro

Keep in mind that these are not mere technical lapses, but basic and ongoing critical systematic disinformation.

/

* Possibly there have been an exception or two?

We do not act rightly because we have virtue or excellence, but we rather have those because we have acted rightly.

I agree with that.

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.

However, a rude attitude seldom yields anything productive: — Kuro

I think you can even be rude if you are funny with it. And hammering a crackpot could be constructive if you explain yourself well enough that others are engaged and learning something.

I think being too nice can be unproductive as well. Discussions have to have energy.

But this particular interaction seemed just an attempt to whack the stubborn pupil over the head with the textbook.

I mean it is not as though "actual mathematics" doesn't have textbooks by Norman J Wildberger as well. :rofl:

[No slight on Wildberger who I really enjoy.]

Norman J Wildberger — apokrisis

I know of him. Watched his History of Mathematics on youtube. If memory serves, he's a finitist. His reason, again if memory serves, was that the close bracket "}" doesn't square with the ellipsis " ... " preceding it in {1, 2, 3, ... }. I feel him in a way, but that's about it!

formal/technical [errors] — Kuro

Formalization, it's a big deal! TonesInDeepFreeze seems well-versed in that department. Hence, I suppose, his annoyance at my rather informal approach to math.