Entropy can be reset to initial or previous state

he was a rastafarian. why? you don’t think rastafarians do honest philosophy? omg that’s so ad hominem.

When you hear something that seems to not make sense and you have to rely on thier reputation, you must then examine their politics and religion.

I don’t think that philosophy should be a product of ad hom. But reputation IS ad hom. If you say that because he has such a strong reputation he should be believed (which you have done) then you have already invoked an ad hom argument, merely in his favor rather than against him.

His reasoning or logic should stand alone. But it doesn’t appear to do so. He seems (by your own account) to be proposing the axiom that unless we directly experience something, it doesn’t exist. And that presumes complete inability to logically project. Science is a demonstration that logically projecting works extremely well when carefully checked for errors.

As it stands, what is said about him testifies that his words are contrary to the evidence that we have directly experienced (technology). His argument is defeated by his own proposition.

very nice, 524, and indeed true. the ad hom works both ways, and i do brag on W quite often, but i’d never encourage anyone to take his word just because he’s like grease lightening. i’d expect people to also notice and give some consideration to the peer review his ideas have received by other major philosophers, typically in the analytical tradition. but therein lies the rub; if you aren’t big on the analytical tradition and its history, you’d probably not find the significance of his thought.

That isn’t the problem.

That’s some hobby you got there. :open_mouth:
I do think your analysis of JSS is correct… his arrogance on his own ideas hindered him from listening to others… because he was right. Were his theories ever peer reviewed or proven?

Politics? I dabble too, but on the fence between volunteer and career.

Well… why not.

Lol… but it is funny. :laughing:

Ah some content, I knew I could find some somewhere in amongst the accusations - got faith in ya, buddy!

Who said the rule changed? The rule is the same, but the result it would get to, if it could, is not. One endless string of "1+1"s is not endless more than another endless string of "1+1"s. They’re both endless…

I get your simple mistake, instead of concluding that infinities result in paradoxes, you represent infinities paradoxically. Endlessness going on further than endlessness? - nice try, but no.

We already had plenty of content:

Did you think we forgot?

No. It’s amazing how you don’t see the connection here…

Like I just said, the rule doesn’t change for how you construct these sums, but what you get differs depending on whether they’re sums of a finite or infinite series:

This method is fine while “…” is a finite number of "1+1"s. Agree for finites, but disagree for infinites - like I already covered - not because the construction is different, but because what you tend towards defies this [n] structure you’re imposing on it. That structure is valid for finites because by definition they have ends to distinguish [n] from [n+1] but infinites by definition do not…

You’re distinguishing one endless string of "1+1"s from another during the course of the same summation i.e. imposing a bound: a finitude - to separate an endlessness in the middle of its endlessness.
It’s as though you’re saying that continuing an endlessness on a new line makes the endlessness different. New steps in the same endless process don’t give ends to an endless process.

Again, the method you’re using is fine while “…” is a finite number of "1+1"s that justifies a distinction that could be validly represented by the structure of [n] followed by [n+1] and so on.

More of the same.

More of the same - building contradictory assumptions to produce a contradictory result.

It’s like, because you don’t understand the basic distinction I’m making in your third grade elementary maths, you don’t think I get the elementary maths… even though I keep saying I agree with the elementary maths only for finites. I’ve been saying all along you’re using your intuitions about finites to apply to infinites. But somehow, because I’m showing you something you don’t seem to understand, “I’m distracting” from what you understand. So, to you, my explanations of what you don’t understand have been attempts to “forget” that we need to stick to your elementary mistakes. When you graduate from third grade elementary maths and eventually get to infinites you’ll see the difference (clue: it’s in the name!)

The alternative that you’re completely missing, that there’s something you’re missing, is what I’ve been covering all this time - but it all just completely bypasses you… how are you ever going to grow? At this point you’re making it very clear that learning and growing is not your intention. All I can do is continue to try and show you where you’re going wrong and put up with the presumption that if someone else is seeing something that isn’t covered by your understanding, they either don’t understand your understanding or are trying to distract from it. Your lip service to finding presumption “sinful” and understanding infinities is just that: lip service.

That was almost a definition. One times ANYTHING is that same thing. It doesn’t matter what that thing is. There is no “approaching”. It is a simple defined concept times one.

If infA = (1+1+1…+1) then
1 * (1+1+1…+1) = infA

How could anything be simpler?

Agree :slight_smile:

Now build on that simple definition to the point you’re missing that I’m trying to explain: is (1 * ) more or less endless than (2 * ), or even (n * ) ?

For finites it’s obvious: the ends of a series that equals “2n” get to twice the finite quantity more than the ends of “n”.
For infinities the paradoxes emerge: there are no ends of “2n” to be quantitatively twice as endless as the ends of “n”.

So that was NOT the first line that you disagreed with. You agree that it doesn’t matter what “…” stands for when you simply multiply by 1.

I think what you are trying to say is that you first disagree with:

Right?

I definitely disagree with the meaning that “2 * ” provides, as if you can be “twice” as endless as endlessness, and I definitely disagree with dividing endlessness into arrays of [n] and [n+1] etc. to get there (like you do with “1 x (1+1+1…+1) = infA[2]”).

I can’t currently see any definite issue with “1 x infA = infA”, but I suspect that issues could maybe arise through using the finite “1 x” part to insert finitude into the infinite expression of “infA”.
“1 endlessness” seems strange as it combines finite quantity to a quality that defies finite quantity by definition. So I’m warey of it, but provisionally I’ll allow it depending on what you do with it.

This is it, 524. Time to do this, man. You own it, you better never let it go. You only get one shot, do not miss your chance to blow. This opportunity comes once in a lifetime…

Ok, a hair of progress. :slight_smile:

Now, do you agree or disagree that the whole number set, infW, is smaller than the real number set, infR?

Realize that if you disagree, I believe that you are going to be disagreeing with almost the entirety of maths professionals.

…a pivotal nail-biting moment of a crossroads.

I mean, this is what I’ve been saying for a while now, but I’m glad you now see it as progress.

Which is worse? Disagreeing with almost the entirety of maths professionals, or disagreeing with almost the entirety of physics professionals by denying both relativity and the laws of thermodynamics? I think we’re both way past appeals to authority fallacies here.

Not a distraction, just something to bear in mind when we eventually apply all we’ve learned back with the topic of this thread.

If my logic is right, there’s something wrong with “infW” being smaller than “infR”, and authority doesn’t override that. Logic can though - so let’s get to that. I’m fully aware that there’s something I might be missing that elite mathematicians aren’t - but there needs to be a logical explanation from you that doesn’t contain contradictions, like we’ve had so far. I’d be quite happy to accept one if you have one, once you have it. Repeating anything you’ve already said doesn’t cut it for reasons I’ve explained a great many times by now. I’m looking forward to it :slight_smile:

So, unlike everyone else on this board, you do not simply accept ethos argumentation. My compliments.

So now to that proof that apparently surprised many people long ago.

That merely let’s us know that Georg Cantor got the credit for “proving” the idea that infR is bigger than infW.

The name of the method was “Diagnalization”.

Actually, I think there is an easier way to prove it but since belief is ruled by reputation and reputation is not ruled by performance, but politics, it wouldn’t do any good to bother with it.

If you have trouble following that explanation, we can go through it line by line but it is getting late for me, so it will have to be later.

Huh… that’s new.

I had no problem following your explanation, don’t worry. Funnily enough I was first familiarised with Diagonalisation through a YouTube channel called “Numberphile” - it’s a decent channel for explaining famous mathematical theorems and the like, if you’re not already familiar with it.

So the primary concern of Diagonalisation is to pair elements between two sets. For example, if the number 2 is in both, you can match them together, or if you have two in one and two squared in the set of square numbers, you can match them together - and the goal is to see if there’s anything left over. If there’s something left over in one and not the other, then that infinity of numbers is said to be bigger than another. Diagonalisation is a way of finding these leftovers.

I think it’s easy enough to dispute that simply by pairing positions of elements in each set. If both sets are infinite, every single position in one will presumably have a corresponding “same” position in another, forever. The intention behind the method of Diagonalisation is to make it appear as though one set is “deeper” than another, like Jakob was aiming after - that there’s gaps left in one set when you match pairs together i.e. that there’s numbers in one set that aren’t in another, therefore it’s “deeper”.

Put another way, for example, the set of the whole numbers “leave out” numbers in the set of the real numbers, and that fact is used to claim that the one with elements left out is “shallower” or smaller - with respect to Cardinality. And yet each set has a 1st element, a 10th element, a 100th, an “nth” forever. They each literally do not have an end, and the difference between how they’re constructed does not change this. This doesn’t mean they have equal or unequal cardinality, just that they both have undefined cardinality by definition of their infinite lengths as sets.

I literally do not give a shit about reputation nor politics when it comes to logic. I am quite happy to discuss any logic you have whoever you are, and whatever it is, and it won’t reflect on you, your political position or inclinations, nor what other people, including myself, thinks of you. If it’s of interest, I want to hear it. If you don’t wish to share, that is fine too.

plato.stanford.edu/entries/witt … mVsNonDenu

Gentlemen, if you please.

I really don’t think it can help to quote Wittgenstein. He uses words in such a way as to leave serious doubt as to whether he is being truly logical. I can’t verify one way or another what he truly meant. But I do sense that he is mostly exercising conscious denial without actual sound argument while casting that very accusation on transfinite believers. If we cannot examine very carefully what he meant, we cannot accept what he said as meaningful. In short, spell it out yourself like the rest of us. :slight_smile:

So you do not accept the bijection method for establishing cardinality concerning infinite sets? Like I said, you are now contending with the whole of professional mathematics. But they have been wrong before, so let’s see what we can do to come up with agreement.

All arguments are going to say that because one infinite set contains all of the other set’s items plus more, that set is greater, higher cardinality than the other. You say that if more unique items are added to only one of two infinite bijective sets (a new word I have learned), neither set is greater or of higher cardinality than the other. To me, that is an issue of language and the intelligence it allows.

You say that the cardinality for such sets is “undefined”. I would normally disagree, but I think that it would be better to just resolve that issue by giving definition to the undefined (which is exactly what James had done).

Let’s say that under President Trumps new USSPACECOM (Space Command) regulations, it is allowed that private corporations may purchase the space above many regions of Earth (being a capitalist and real estate kind of guy). But in his haste to gain the real estate taxes, a few details are overlooked in the regulations.

Spotting an opportunity, Amazon’s lawyers quickly declare ownership of “all space above” Redmond, WA. Immediately afterward, Microsoft declares ownership of “all space above” Seattle, WA. Trump is immediately thrilled as the IRS begins scooping in the new tax revenue to help build The Wall. And the corporations made a fortune by renting the space back to the US government.

For a while everything was working out great. The economy was booming and everyone (except the Democrats) were happy. But then in their bliss, something happens.

Amazon and Microsoft decided to merge.

Up until that moment, the IRS had a math formula for exactly how much to charge in taxes for “all space above” situations. Their formula had no limit for the distance into space, so they charged by the cubic mile (Americans, you know) and diminished the rate as the distance from Earth extended. To the government’s first surprise, both corporations realized that the tax formula converged such as to yield a calculable and affordable tax rate even for an infinity of space, so naturally, being faithful corporate oligarchs, they declared ownership of the entire infinity of space above their respective cities (a slight increase of the price of their goods easily paid for it all while allowing the rent to establish pure profit).

After the corporations merged, the dutiful tax man dropped by expecting to reap the same booty as always but merely from one accountant rather than from two. Then he got a surprise. The new corporate tax attorney saw that an infinity of space plus another infinity of space was still “just an infinity of space”. So he wrote a check for “an infinity of miles of space”, only half the amount that the IRS expected.

Naturally, the IRS was displeased and demanded that the new merged union had twice the amount of rentable space as each of the separate corporations had alone and so they demanded the same twice amount they had been collecting before the merge. And as always with everything associated with Trump, the lawsuits quickly emerged.

In federal court the issue came down to having to declare definitions for words that indicate a taxable property amount that reflects twice as much as an infinity of space above a city. With such new words, the IRS would be free to simply rewrite the tax code, restore the federal economy, finish The Wall, and save the US from a recession.

So now, seeing how dire the need, what words can we use to indicate a value that is twice as much as an original infinity of cubic miles?

James would have just said something like “2 * infA”, but what word(s) shall we use?