Emoticons are as eloquent as you ever get.

You deploy that "aw shucks" shtick repeatedly. It's so transparent.

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

That is blatant strawman. Especially after I have over and over stated and explained that I don't object to informal rumination in and of itself. What I object to is making false claims about the actual mathematics you presume to criticize without understanding even its basics..

Please do not persist to so egregiously mischaracterize my point of view, as your mischaracterization is blatantly refuted by the actual posting record.

an attempt to whack the stubborn pupil over the head with the textbook. — apokrisis

Nope. Over many months (a year or even more?) I have offered the poster the copious explanations. My purpose is not to merely rhetorically bludgeon, but rather it's as I described in previous posts. But, as I mentioned, after a certain point, it emerges that the poster is unwilling to desist from posting disinformation. At that point, I am not obligated to just give up posting the corrections and also to point out that the source of that disinformation is crankery.

I mean it is not as though "actual mathematics" doesn't have textbooks by Norman J Wilderberger as well. — apokrisis

Wilderbeger in a particular aside, you skipped that I already said that I am enthused that there are alternative mathematics. I have never, in any way, advocated that the only reasonable context is ordinary classical mathematics. Indeed, I very much appreciate that there are reasonable intuitive and philosophical quandaries about classical mathematics. On the other hand, self-malinformed cranks dogmatically claim, with terrible ill-reasoned arguments, that ordinary classical mathematics is not acceptable by any means or has certain problems (that it actually does not have).

So, rather than me be burdened by a strawman, I'll reiterate:

(1) I do not urge that all philosophical and mathematical discussions be anchored with respect to classical mathematics.

(2) I have never said anything that can even remotely be fairly construed as a claim that mathematics trumps philosophy.

(3) I am enthused that there are alternative philosophies and mathematics.

(4) I'll add that I admit my own personal framework for understanding mathematics is not itself a developed philosophy of mathematics and that there are quandaries that I don't claim to explain.

(5) So I am quite the opposite of dogmatic concerning mathematics and philosophy of mathematics.

(6) The crank, though, dogmatically, and from a position of ignorance on the subject, claims that classical mathematics is wrong.

(7) When the crank proposes a philosophical discussion in which classical mathematics is to undergo examination, then when the crank (as invariably he does) misstates what that classical mathematics is or how it works, then it is not improper to correct the crank about that, no matter how long he persists. And it is not mere formal nitpicking to do that.

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.

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?

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.

I should have made clear that I'm not opining about RussellA's posts, but rather I meant my own post as a rendering of my own explanation, not necessarily as agreeing with or disagreeing with RusselA's perspectives.

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.

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.)

But perhaps not all that clearly. — Banno

No, with utmost clarity. You can go back to the posts.

If one sets (ϕ &~ϕ) as true — Banno

One does not do that.

Again, statements are true or false (and not both) per a given model.

If a theory has a statement of the form P & ~P, then the theory has no model.

If one says "'P & ~P' is true", then one has simply stated a falsehood. It doesn't follow from that falsehood that everything is true.

You are conflating the syntactics with the semantics.

Yes, syntactically:

P & ~P |- Q

But semantically:

The above syntactical principle doesn't provide that Q is true in any particular model. All it does (via the soundness theorem) is provide that Q is true in any model in which P & ~P is true. But there are no models in which P & ~P is true.

then since (ϕ &~ϕ)⊃ρ where ρ is any wff, — Banno

Please go back to my post in which I explained with exactitude why that is not the case.

Get a good book on mathematical logic to learn the notions of provability, truth in a model, entailment, etc.

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.

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.

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.

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.

I don't know what that means.

So, if you posted it to make us even, you succeeded.

if contradictions (p & ~p) are allowed, "every proposition is true" — Agent Smith

No, that is not the case. I explained in detail why.

Now Banno's misconception has been inherited by you.

So the argument from the principle of explosion ( ex contradictione sequitur quodlibet) is, in fact, the circular argument: — Agent Smith

What argument are you referring to?

The proof that from a contradiction all statements are provable is not circular.

contradictions are unacceptable because contradictions are unacceptable. — Agent Smith

Speaking of ... the above is petitio principii.

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 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.

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.

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.

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).

One of the numbers one needs in a lifetime is the greatest number. — god must be atheist

Of course that is a plausible idea. But I don't know that there is a limit on how long there will be conscious beings.

existence on the timeline of our individual beings or of the species is supposedly finite — god must be atheist

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

Good point.

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.

AS did not argue that there is a greatest number... he argued that there is a greatest number we'd ever need. — god must be atheist

I am going by these:

it hasta be relatable in re my apperceptive mass, my experiences. — Agent Smith

there's got to be a finite number such that it's, for all practical purposes, ∞ to us. — Agent Smith

Probably those are not exact enough to say whether he means "there is a greatest number" or "there is a greatest number that will ever be needed". He can say for himself. But I would be very interested if he said "No, there is no greatest number. But there is a greatest number we'll ever need." If he said that, then it would be hard for me to dispute him, since I have no idea whether there is a greatest number that anyone (and let's include any conscious being in the universe now or ever) would ever need.

But still, again, as far as mathematics is concerned, there is no compelling reason that mathematics should limit to only numbers that are not greater than the one we guess to be the greatest ever needed for practical question. When I have a hankering to add one to that number, what's going to happen? The universe will tell me I can't do that?

this situation could go on indefinitely without any progress — Metaphysician Undercover

Yes, your obfuscation seems to be inexhaustible.

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.

I'm not in any way trying to say my way or the highway. — Agent Smith

No, you're not. But you hold to your position even though it can't withstand easy objections.

I changed my reply. I didn't notice that it was you who posted and not the other poster. Then I realized that you were making the same point as I was.

automatic is to dogmatic as karma is to dogma. Cute.

Yes, the game is a funny way of making this point.

/

Yes, chess is determined. Either there is a winning strategy for white, or winning strategy for black, or a strategy for both to draw. von Neumann made that observation. But we don't know which it is.

I also proved it for myself before I heard that von Neumann already had. It's kinda trivial really. Induction on the number of moves, if I recall.

We would have to restrict oursleves to specific units of measurement. — Agent Smith

You're claiming that there is a greatest number. It's not 186000. And there's no law of thought that says I can't use different units of measurement. And there's no law of thought that says I can't add 1 to whatever number you claim is the greatest number.

Your view is dogmatic.

I am most definitely not an expert on mathematics.

So what? We agree that 186000 is not the greatest number. Nor is 186000 x 1000, which is the speed of light in milliseconds. Etc.

we can never attain a speed of 186000 m/sec and that, in a sense, is infinityish. Wouldn't you agree? — Agent Smith

No, I don't agree.

The the number of states my lamp can be in is 2 - on or off. There is no counting past the number 2 when counting the number of states my lamp can be in. You can never attain more than 2 possible states for my lamp. So 2 is infinityish?

/

If 186000 is infinityish is then so is 186000 x 1000, since 186000x1000 m/millisecond is the speed of light. Etc.

Choose the highest number you will allow

You would admit that someone else might choose a higher number.

And whenever someone chooses their highest number, someone else can choose one plus that number.

So which should we take to be the highest number we allow?

Mathematics should be limited to only the numbers you will personally allow?

/

Suppose there is a highest number any living human can now conceive in the manner you require. It is not ruled out that future humans may conceive higher numbers. So when that happens, we will reformulate mathematics to accommodate the new highest number? And if the person who conceives the highest number dies, then we'll reformulate mathematics to bring down the highest number? Then every day, we'll check the newspaper to see what the new highest number is?

/

Consider a music CD, with about 850 mb. Consider all the possible combinations of those 850 mb as zeros and ones. Big number. I can conceive it though, since I can conceive of changing every one of the bits on the disc. But I can also conceive of 8 billion discs - one for each person on the planet - and each of those dics having capability of changing every zero and one. A bigger number. But I can also conceive of each person on the planet having a 100 terrabyte computer to store lots and lots of 850 mb music albums, and then to switch the ones and zeros around on each of them as many ways as combinatorically possible. A bigger number. But I have to check with you each time I proceed to a bigger number whether you also can conceive it?

Don't you see that mathematics is general - not confined to only numbers that particular human beings can visualize in the way that you require at a particular time in the history of the universe.

For any natural number n, there is the natural number n+1. So there are infinitely many natural numbers. That is not thwarted by your limitations of what you can personally conceive at this particular moment.

De nada.

I hadn't already recommended this?:

First:

Logic: Techniques Of Formal Reasoning - Kalish, Montague and Mar

That is to get a solid understanding of the first order predicate calculus, which is the ground level for formal mathematics and formal philosophy.

Supplement:

Chapter 8 of Introduction To Logic - Suppes

That is for the best explanation of formal definitions I have found.

Supplement:

The introductory chapter of Introduction To Mathematical Logic - Church

That is for the very best overview of the subject of modern logic one would ever find.

Then:

Elements Of Set Theory - Enderton

On it! — Agent Smith

Oh really? What book?