tom

Your msunderstanding of QM is not evidence for infinite continuous fields, which by-the-way can't be continuous if they are quantized.

Sorry to break it to you, but entanglement has nothing to do with continuous fields that extend to infinity.

No. I showed that the ASSUMPTION that there is a totality of facts leads to a CONTRADICTION. The argument works whatever Aleph number you assign to th...

What has entanglement got to do with the existence of continuous fields of infinite extent?

You don't understand Cantor's theorem then. The powerset is always strictly bigger than the set, as Cantor proved. This is how the various Aleph numbe...

Could you point me towards the empirical evidence for these fields which are continuous and stretch forever?

Nothing to do with Zeno's paradox. It's taking the power set and Cantor's theorem, as I explained. And, if supertasks exist, then the CTD-principle is...

But I've just proved there is no such thing as the totality of facts, and while doing so I have respected the CDT-Principle.

Does Cantor's theorem not work for finite sets? I thought there was a well known relation between the cardinalities of a set and its power set? As for...

Inspired by the recent thread on Zeno's paradox, I shall prove that no "totality of facts" can exist: Let T be the set of all facts T={t1, t2, t3, ......

Why is motion a supertask rather than a hypertask?

I may have been responding to you, but I thought it obvious I was not referring to you!

I think it is a bigger mistake to write off the great works of Georg Cantor and Nicolas Bourbaki (that makes at least 8 geniuses) on the basis of your...

The set {1,2,3,4,5} has the same cardinality as {6,7,8,9,10}, so we should call it foozable? How do you calculate the cardinality? Do you fooze the se...

It might be worth noting that Cantor proved that any interval of the Reals cannot be placed in one-to-one correspondence with the Naturals, before he ...

A one-to-one relationship between sets e.g. from the natural numbers onto itself (i.e. a permutation) is not a one-to-one function, but a one-to-one a...

Not that it matters one jot due to the level of willful ignorance on display, but I think you were quite correct to use the term "bijection" = one-to-...

Wow! I'm out!

The values ARE equal. There is NO difference between them. You cannot create a new number by adding an infinitesimal quantity.

It's you. And by the way, which real number is bigger: 1 or 0.999... According to you, or Peirce?

Which real number is bigger? 1 or 0.999...

Breaking sand "infinitely" yields tiny bits of sand? Please! Breaking the real numbers "infinitely" yields what?

The real continuum of the real numbers. You know parameters like "t" and "x" are real numbers, unless they are complex numbers.

I don't understand how a property dualist could argue that p-zombies are possible, even logically. If they are, then p-minds are also possible. What d...

Then I guess Chalmers would claim that a computer would continue to play chess after the deletion of the chess-playing program? If one computer is phy...

Our fundamental theories are based on the continuum of space-time. What more do you want? Quantum mechanics may be a theory that yields discrete obser...

There is no a priori way of determining anything about reality: hence Zeno's paradox is solved. There are some conjectures in physics about a granular...

It's a very important result in mathematics. The continuum has the cardinality of the power set or the natural numbers. It's a much bigger infinity. Y...

Science is perfectly capable of explaining Life. It does not do so in terms of the Standard Model or General Relativity because that is not possible.

So, you agree you can't count any interval of the real numbers. So, you agree you can count any (not too big or you'll get bored) interval of the natu...

Yet nothing physically infinite happens, and what motion is possible is determined by the laws of physics alone, and not by the necessary truths about...

The scientific explanation of life is fundamentally a theory of replicators undergoing variation and selection. Life could exist under any physics tha...

How many are there? Can you count them? Or is it impossible to count the real numbers, making them uncountable? Contrast that with the Naturals, which...

Can you count the number of real numbers between 0 and 0.1? If so, how many are there? Can you count the number of naturals between 1 and 50,000,000, ...

But we've already solved the paradox: it is merely a confusion between an abstract attribute and a physical attribute of the same name. Since it is po...

Given the Naturals, I can count some of them, in order e.g. 999 1000 1001 Given the reals, please count the three members that come after 0.999... and...

When the science of the mind reaches the level of sophistication where it can explain what you do and think, what do you think the fundamental object ...

That's not right. Everyone who is not being deliberately obtuse understands what countable means - it means you can count elements of the set. No one,...

If the reals can be disordered, just do it. Can't be more than a few lines? Take any real number, leave a gap, state where the gap is, and place it be...

No, you claimed the reals can be disordered and made discrete. You are wrong on both counts, but of course if you would like do demonstrate? Take the ...

Just keep counting. Now list the natural numbers between 0 and 0.00000000000000000001 so we can count them.

Pierce was wrong. Simple! The real numbers have been proved to for a continuum, even in the Peirceian sense.

No one claimed that. You can count as many members as you like. Given an uncountable set, you can't count any members. I recall doing this at school a...

I made the mistake of stating, way back in the thread, that the DEFINITION of a countable set is that it can be put in one-to-one relation with the In...

If I give you a natural number, you can count it, and the next ... Try 999 for size. If I give you a real number, 0.999... where do you go next?

If you think you can disorder the reals, then pleas indicate the number following this one, and suggest between which two numbers you might place it: ...

Really? Cantor proved the reals constitute a continuum. Whatever they are, they are certainly not discrete.

Our current best theory of life is Neo-Dawinism. It is a theory of replicators subject to variation and selection. Where's the physics in that? We als...

I think you might be wrong. I don't think it is possible to explain life in terms of the laws of physics(+chemistry). In order to explain life you nee...

Fair enough, but the fact is that you can count members of a countably infinite set. You can take a subset of a countably infinite set of any number y...