You yourself have said you have no philosophy to defend on this forum, just a self-appointed need to police it for its mathematical thoughtcrimes and disinformation campaigns. — apokrisis

Having no philosophy is not a disqualifier. Posting is not paintball where you can't participate unless you you are on one of the teams. Not having a philosophy doesn't entail that one doesn't have meaningful things to say. And I find it refreshing when a person doesn't have a philosophical ax to grind.

There are no thought crimes. On the contrary for me. As I don't hew to a particular philosophy, I don't have strong oppositions to other philosophies; and I relish that there are so many tantalizingly different philosophies of mathematics and formal systems; and I believe that freedom to imagine is to be cherished. Spewing of disinformation though is abundant. Moreover, much of my posting is not just making corrections. Your categorical reduction is false. And beneath you, just as your multiple strawmans earlier

I've seen that cartoon, and it is funny.

Having no philosophy is not a disqualifier. Posting is not paintball where you can't participate unless you you are on one of the teams. Not having a philosophy doesn't entail that one doesn't have meaningful things to say. And I find it refreshing when a person doesn't have a philosophical ax to grind. — TonesInDeepFreeze

Have you noticed how much you assert the negative so as to avoid having to support the positive?

What is life without some form of ontological commitment?

Have you noticed how much you assert the negative so as to avoid having to support the positive? — apokrisis

I don't usually support the affirmative because I'm humble enough to admit that I don't have the vision, education, confidence and constancy to arrive at a fixed philosophy. If I were a philosopher, I'd be nowhere in that way. But I'm not a philosopher.

What is life without some form of ontological commitment? — apokrisis

That is a great line.

But I'm not a philosopher. — TonesInDeepFreeze

Hey. Now you are on a site where you get the chance to learn! Don't waste it.

Your strength is deductive rigour. Pragmatic philosophy stresses that rational thought involves the three steps of abduction, deduction and induction.

A scientific mindset means making the creative leap of forming a hypothesis, properly deducing the general constraints of that hypothesis, then inductively confirming the truth or otherwise of that hypothesis in terms of the observed particulars or practical consequences.

So think of this site as presenting you a true intellectual challenge. There is an arc to thought that transcends all forms of human rationality. If you are strong in one of the three aspects of reasoning, why would you be content with leaving the other two weak?

Can you just make an inspired guess, a creative leap in the dark. Can you follow through a formal model to its practical and measurable consequences?

The deduction of a theory is indeed a formal exercise. But pragmatism explicitly recognises that its inductive confirmation is necessarily informal. And that is OK. Theories make predictions and we find confirmation in the messy real world business of making measurements. We say the facts fit, even if we only have the first two or three significant digits. Three sigma could be good enough if not a lot is at stake.

So when you hammer on posters, some are indeed just fools or cranks. But also, they might at least be discovering something about how to abductively form hypotheses, or inductively confirm their theories.

You clearly are confident in your logical rigour. But Pragmatism tells you that that is only one third of what you need to be a "reasonable person" in this world we share. Time to be properly humble and get involved with PF in ways that challenge your weak spots.

Now you are on a site where you get the chance to learn! — apokrisis

I glean a thing or two here and there. But posting is only a side hobby. I don't have ambitions for philosophy. Sometimes, though, I see things in discussions that I can't resist finding out about more, then I look them up or grab a book.

A scientific mindset means making the creative leap of forming a hypothesis, properly deducing the general constraints of that hypothesis, then inductively confirming the truth or otherwise of that hypothesis in terms of the observed particulars or practical consequences. — apokrisis

Of course.

If you are strong in one of the three aspects of reasoning, why would you be content with leaving the other two weak? — apokrisis

I don't know that I am so terribly relatively weak. And I'm never content. But there's so much else I also need to be doing. Forumcombing is itself a distraction that I probably shouldn't allow myself as it eats so terribly into my time needed for my main pursuits.

So when you hammer on posters, some are indeed just fools or cranks. But also, they might at least be discovering something about how to abductively form hypotheses, or inductively confirm their theories. — apokrisis

That's disastrously overgenerous. I've studied cranks for over 20 years, in forums from here to Timbuktu, and (speaking of inductive inference) one thing is clear: They never learn. They are dogmatic, irrational, intellectually dishonest, and narcissistically self-sure to the core. They persist in their favorite forum for years spewing confusion and disinformation.

reasonable person — apokrisis

I am reasonable in forums. Almost always, my first posts to a crank are without attitude. Merely a statement of the correction. Then, over time, the crank entrenches with even more dishonesty and often with passive put downs and things like that. Eventually, what becomes salient is the crank himself. And eventually I frankly say what is up with them. Believe me, I have so many times practiced restraint hoping that a crank might, miraculously, come to reason. Never happens. And that is not a function of my style. Hundreds and hundreds of other posters in many forums have tried with cranks, and they always fail to get anywhere with it. Not even a millimeter. Always.*

In this thread, you're seeing only recent interchanges. But there is a context with this poster going back over a year(?) or two years(?). I don't know whether you've read much of those threads. If not, then I would understand that you think my approach is arbitrarily harsh. (By the way, this poster is not as overtly dogmatic as usual cranks. Indeed his skill is to deflect by feigning that he is considering the corrections, which I perceive to be disingenuous.)

/

Your comments in your above post are well taken though. Even if I am in countering mode in this post, probably soon later I'll reflect more and benefit more from your point of view.

But now that you've given me advice, I will return the favor:

Your annoyance with me should not permit you to read into my plain words things that are not in them, not even plausibly, not to willfully misconstrue what I say in the worst way, and not to strawman me over and over as you did yesterday. That is beneath you.

/

* Except that one fellow I wrote about recently. The sole counterexample.

I don't know that I am so terribly relatively weak. — TonesInDeepFreeze

That is my hypothesis. The evidence continues to mount.

Forumcombing is itself a distraction that I probably shouldn't allow myself as it eats so terribly into my time needed for my main pursuits. — TonesInDeepFreeze

Of course. We are not worthy of you. That makes your pointless asterisking of "dangerous disinformation" even more pointless.

(By the way, this poster is not as overtly dogmatic as usual cranks. Indeed his skill is to deflect by feigning that he is considering the corrections, which I perceive to be disingenuous.) — TonesInDeepFreeze

So someone is different in lacking a prime characteristic of the true crank. And yet you only hammer harder when that someone finds you being overly hostile and wants to laugh you off?

Your comments in your above post are well taken though. Even if I am in countering mode in this post, probably soon later I'll reflect more and benefit from your point of view. — TonesInDeepFreeze

Great.

Your annoyance with me should not permit you to read into my plain words things that are not in them, not even plausibly, not to willfully misconstrue what I say in the worst way, and not to strawman me over and over as you did yesterday. That is beneath you. — TonesInDeepFreeze

You wildly exaggerate. But it is true I hadn't read any of your posts before this thread.

Forumcombing is itself a distraction that I probably shouldn't allow myself as it eats so terribly into my time needed for my main pursuits.
— TonesInDeepFreeze

Of course. We are not worthy of you. — apokrisis

You did it again! You falsely twisted what I said to reflect it in the worst possible way, little doubt as a spite you're exercising. You are incorrigible.

To say that I have other pursuits, closer to my heart, that I sometimes neglect for posting, does not at all entail that I think that there are not posters worth reading. I could even say that the ghost of Kurt Godel himself visits me each night and wants to give me free lessons, but I can't take him up on it, because mathematics is far from my main pursuit. That wouldn't entail that Kurt Godel is not worthy of me! Get a grip, man.

lacking a prime characteristic of the true crank — apokrisis

He's a variation.

And yet you only hammer harder when that someone finds you being overly hostile and wants to laugh you off? — apokrisis

I have recently.

Your annoyance with me should not permit you to read into my plain words things that are not in them, not even plausibly, not to willfully misconstrue what I say in the worst way, and not to strawman me over and over as you did yesterday. That is beneath you.
— TonesInDeepFreeze

You wildly exaggerate. — apokrisis

Not this time.

You did it again! — TonesInDeepFreeze

:lol:

To say that I have other pursuits, closer to my heart, that I sometimes neglect for posting, does not at all entail that I think that there are not posters worth reading. I could even say that the ghost of Kurt Godel himself visits me each night and wants to give me free lessons, but I can't take him up on it, because mathematics is far from my main pursuit. That wouldn't entail that Kurt Godel is not worthy of me! — TonesInDeepFreeze

Too bad I don't have an emoticon to express that for you.

Just to let you know that I haven't disregarded your post. I wish to give it more thought. I hope eventually to reply.

:rofl:

What, no leminscate to go with that?

Having no philosophy is not a disqualifier. — TonesInDeepFreeze

Your lack of training in philosophy really shows. And, it is very annoying for a philosopher, when a person without philosophy comes to a philosophy forum, and enters into a philosophy of math discussion, insisting that philosophers ought not discuss the metaphysical principles upon which mathematical axioms stand, if they have not first studied mathematics. Clearly, it is philosophy which is being discussed in the philosophy of mathematics, not mathematics.

I am reasonable in forums. — TonesInDeepFreeze

The above is unreasonable behaviour. And, you personally increase the degree of unreasonableness with the use of insult. When you do not understand the philosophical principles being discussed, because you have no philosophy, you simply hurl insults at the philosopher. Try some introspection, to reveal to yourself, your unreasonableness. You may find the way toward respect.

If, a big if, there did exist a finite number N_max that could stand in for, salva veritate, $\infty$, we could prove/disprove all mathematical conjectures via proof by exhaustion (brute search) with the help of existing supercomputers. Math would instantly become a boring subject, with no problems to solve, but it would be complete.

For instance take the Goldbach conjecture. If the N_max were 10, I would do the following

4 = 2 + 2. Check.
6 = 3 + 3. Check.
8 = 3 + 5. Check.
10 = 5 + 5. Check.

There, I just proved the Goldbach conjecture to/for kindergarten kids! :cool:

If, a big if, there did exist a finite number Nmax that could stand in for, salva veritate,∞, we could prove/disprove all mathematical conjectures via proof by exhaustion — Agent Smith

It might be the case that an ultrafinitist system would not be subject to the incompleteness theorem? I don't know. We'd have to see the system or at least a sufficient statement of its relevant properties.

/

Nothing can be understood to stand in for what you think the leminscate stands for, unless you say what you think the leminscate stands for.

Adopting an ultrafinitist system leads you to several conundrums not faced with infinitism. Here are two :

1. The real numbers no longer form a continuum

If $N_{max}$ is the largest possible number, then $\frac{1}{N_{max}}$ must be the smallest (Otherwise, if there exists some k such that $k\lt\frac{1}{N_{max}}$, then $\frac{1}{k}$>$N_{max}$, a contradiction). This smallest number in turn implies that the set of reals is discrete (i.e., no more irrationals). Thus, the diagonal of the square is now commensurable with its side, which we've known to be untrue since the time of the Pythagoreans! (Also, points have size!)

2. Series can be expressed that have no (acceptable) sum

Consider the series 1 + 2 + 3 + 4 + ... If the last term is $N_{max}$ (which should be allowable), then the series sums to a quantity greater than $N_{max}$, a contradiction.

For these reasons (and others) ultrafinitism is inadequate to describe modern mathematics.

irrationals — Real Gone Cat

Is it a coincidence that the word "irrational" means illogical/makes zero sense? I recall starting a thread on how irrational numbers could be the smoking gun that there's something seriously wrong with mathematics and the universe itself.

I remember watching a video about how math teachers generate problems with numbers such that the answer is a nice whole number. The point? If you're ever find that your calculations lead you to an answer that has a decimal expansion then you've made a mistake. As you can see even ordinary fractions (rationals) are red flags, forget about an irrational number as an answer.

As for series sums, what about modulus arithmetic?There is no 13 o'clock on an analog watch; there's 1 o'clock though.

Is it a coincidence that the word "irrational" means illogical/makes zero sense? I recall starting a thread on how irrational numbers could be the smoking gun that there's something seriously wrong with mathematics and the universe itself. — Agent Smith

You have got to be kidding! Please tell me you are kidding!

Yin-Yang (Taijitu). Worst $\to$ Good $\to$ Better $\to$ Best $\to$ Bad $\to$ Worse $\to$ Worst. Return to base immediately pilot!

Is it a coincidence that the word "irrational" means illogical/makes zero sense? — Agent Smith

Consider the root of "rational" is "ratio". Now think about an irrational ratio such as that expressed as pi, and you'll get a glimpse at the problems which pervade mathematics.

pi is not a ratio of two rational numbers.

pi is the ratio of the circumference of any circle and its diameter. But if the diameter is rational then the circumference is not. So still pi is not the ratio of two rational numbers.

So there is not a contradiction.

I don't know what "problems" in mathematics are supposed to have been caused by pi.

https://www.jpl.nasa.gov/news/on-pi-day-how-scientists-use-this-number

So I guess people that don't like pi being used in mathematics have not need for such things as satellite technology, etc. Fair enough.

Is it a coincidence that the word "irrational" means illogical/makes zero sense?
— Agent Smith

Consider the root of "rational" is "ratio". Now think about an irrational ratio such as that expressed as pi, and you'll get a glimpse at the problems which pervade mathematics. — Metaphysician Undercover

Irrational numbers can't be expressed as a ratio of two whole numbers. That didn't jibe with the way math was supposed to be in the eyes of the Pythagoreans. If memory serves Pythagoras discovered that harmonious musical notes were rational i.e. the note combinations were pleasant to the ear when the length of string producing one was a whole number multiple of the length of string producing another. Since music is numinous in nature, it being somewhat of a bridge between us and the universe, the Pythagoreans probably extrapolated the math found therein to the universe itself.

The discovery of irrationals, kind courtesy of Hippasus of Metapontum who was thrown overboard to prevent word of this getting out, threatened to overturn what was up to that point a perfect world. A simple and yet magnificent way mathematics could serve as the foundation of the universe had to be abandoned. I wonder what Max Tegmark has to say about this?

Will we, somewhere in the future, come across a kind of number that would do to us (mathematical universe hypothesis) what $\sqrt 2$ did to the Pythagoreans (mathematical universe hypothesis)?

Stick with your earlier theory that irrational numbers are bad because 'irrational' also means illogical. That one is a doozy.

I recall starting a thread on how irrational numbers could be the smoking gun that there's something seriously wrong with mathematics and the universe itself. — Agent Smith

There's nothing wrong with math, so it must be the universe. I wouldn't put anything past that sucker!!!

Now think about an irrational ratio such as that expressed as pi, and you'll get a glimpse at the problems which pervade mathematics. — Metaphysician Undercover

It'll take more than a glimpse for me. I know, I know, pay no attention to the man behind the curtain. :cool:

There's nothing wrong with math, so it must be the universe. I wouldn't put anything past that sucker!!! — jgill

:smile: Couldn't there be something wrong with both?

Couldn't there be something wrong with both? — Agent Smith

No

Mathematicians come up with general formulas, involving pi and other irrational numbers. Isn't it the case that engineers make use of those general formulas, from which they can decide what specific specific values to use as close enough for the task at hand?

If that is the case, then it's a mistaken premise that we can decide on a greatest practical number, or greatest number of places to approximate pi. Science and engineering doesn't work with just specific numbers but also rather with general formulas. I take engineers at their word that they use trigonometry with pi all over the place. Not that they plod along with just individual values.

Couldn't there be something wrong with both? — Agent Smith

Couldn't there be something wrong with you?

Sadly, it seems math discussions on TPF are doomed to descend to the level of farce. Notice that most folks on TPF avoid these topics like the plague. This is most likely because they've seen what happens far too often before.

Consider the latest comments regarding irrationals. Let's draw an analogy. Imagine that every time you saw a topic where consciousness was under discussion, you stepped in and declared that consciousness obviously did not exist because the first three letters of the word spelled "con". How long before you got canned for the low quality of your posts? That's the equivalent of what's happening here.

Some TPF worthies are convinced they know more about math than some of the greatest minds that humanity has produced over the past 5000 years. They know what they know, and there's no arguments that will convince them otherwise. How foolish of us to question the folk wisdom of anonymous forum posters!

Some months ago, on another thread, I implored one of these commenters to write up their math musings and send them off to prestigious math journals. The world languishes without access to these amazing insights. (I don't think he took my advice.)

Communication is bad because 'communication' is from the same root as 'communism', which is bad because communism is Marxism, which is bad because Richard Marx sang lousy songs.