Is free-will an illusion?

@ughaibu,

Quote:

Which is what can't be done, even by an infinite number of verifications, because there is at most a countable number of verifications.
Anyway, this isn't interesting, so you're on your own again.

And you are assuming there are uncountable verifications? Every verification sequence can be included in the countable numbers... why would I need more.

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@tomr,

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@tomr,

All numbers are constrained by the formula being used; whether is has practical application for humans is another thing - IMHO.

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@Fil Albuquerque,

But what Ughaibu is saying in addition to what the video covers is that after that number is generated from the diagonal number ( the number I called S') it can be added to the list of countably infinite real numbers (the original list of decimal numbers that is paired with the integers). So that new number that wasn't in the list before can be placed in that list and then paired with positive integers. So in one instant it was shown to be incapable of being paired with positive integers and in the next it was shown to be paired. So either that diagonal number generated was an uncountable number or it was not. If you add it to the list and pair it with a positive integer then you are showing that the number generated from the diagonal number was not really an uncountable number to begin with. And there is nothing to stop us from doing just that with each consecutive number generated.

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If one wants a rational world one drops infinity ! Problem sorted...or else you may as well start to go to witches and see your sign forecast in the newspaper and stuff like that...not for me I tell ya !

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@Fil Albuquerque,

Trust me I feel your pain with infinity. But Ughaibu wants to bind his arguments to these concepts.

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@tomr,

tomr wrote:

countably infinite real numbers (the original list of decimal numbers that is paired with the integers).

There isn't a list of "countably infinite real numbers". There are two sets, the naturals and the reals. The naturals are a countable set, the reals are assumed to be countable for the proof. That is to say, it is assumed that there is a one to one correspondence between the naturals and the reals. But Cantor's argument shows that this assumption is false, so there was no one to one correspondence and the set of the reals is uncountable.

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The lack of paring is a perfect example of mechanical disconnection...precisely the reason why mechanical correspondence between an evolving agent and willing wouldn't exist with infinite many infinity's...chance is not choosing !

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This guy presents an interesting talk although I find him confused in his conclusion...its a lengthy slow talk worth seeing with close attention !

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@ughaibu,

Quote:

There isn't a list of "countably infinite real numbers". There are two sets, the naturals and the reals. The naturals are a countable set, the reals are assumed to be countable for the proof. That is to say, it is assumed that there is a one to one correspondence between the naturals and the reals. But Cantor's argument shows that this assumption is false, so there was no one to one correspondence and the set of the reals is uncountable.

I found the problem with the proof:

If we write the natural numbers in array form as we do with decimal digits we can see that the diagonal argument has no merit:

n = 1 or n = 99999999... <--> .00000000.....
n = 2 or n = 98989898.... <--> .010101010.....
n = 3 or n = 98898898... <--> .01101101....
n = 4 or n = 99988899... <--> .00011100...
.
.
.

It is just a trick that is not obvious because one set of numbers is written in array form and the other set is not. By "reversing" the order of the natural numbers that each decimal real corresponds to we can see clearly that the diagonal argument can be used for both sides. So we start n values out as infinitely long strings just as the decimals are. There is no reason we are not allowed to do this. So we can follow Cantor's argument for both sets.

n = 1 or n = 99999999... <--> . 00000000.....
n = 2 or n = 98989898... <--> .0 10101010.....
n = 3 or n = 98898898... <--> .01101101....
n = 4 or n = 99988899... <--> .00011100...
.
.
.

Now both sets of numbers can be shown to correspond one to one with each other. For every anti-diagonal in the natural numbers there is one in the decimal reals. Problem solved. The decimal reals are countable.

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So free-will is now based on numbers?

What have we come to?

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@north,

Quote:

So free-will is now based on numbers?

Not anymore.

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@tomr,

It never was - and it never will be.

Numbers is actually a late-comer in human history.

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@cicerone imposter,

Yea Cis, and another thing, Number is almost as abstract as God, the latter actually being easier to defend as real

…..while like North, Tomr, and others above I can't see how numbers have anything at all to do with freewilll

….yes, I know, review all the above

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@tomr,

tomr wrote:

By "reversing" the order of the natural numbers

So you think that there's a largest natural number? There isn't, that's exactly the point of infinity.
I'm not going to carry on addressing this stuff, it's just silly. If you claim that diagonalisation is logically invalid, then, because diagonalisation is valid in classical mathematics, you are committed to the rejection of classical mathematics. And, as science uses classical mathematics, you lose recourse to science. But even at this cost, all you have achieved is the denial of a single result. You have still not shown that willed actions would be impossible in a nondetermined world, obviously not, because by observation we perform willed actions, so, if willed actions were impossible in a nondetermined world, then the mere fact of us performing willed actions would establish that we live in a determined world. But there are many people, who are aware of the facts and the arguments, who think that we clearly do not live in a determined world.
So what have you achieved? By denying uncontroversially true statements, that freely willed actions are observable and that willed actions are possible in a nondetermined world, you have abandoned classical maths and essential principles of experimental science, you have left yourself without science. As commitment to denialism goes, that's pretty dedicated, it's probably further than most evolution deniers or global warming deniers go.

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@ughaibu,

Quote:

So you think that there's a largest natural number? There isn't, that's exactly the point of infinity.

No I don't think there is a largest natural number. I obviously never claimed that. Now I know what it feels like be given a pseudo-objection. There is no good reason I can't write the combinations of natural numbers as infinitely long sequences just as the decimal numbers are written. Do you not understand that 1010.... is an endless string of digits just as .1010... is an endless string. If you want to say the natural numbers are endless or infinite then you should be able to express its numbers as endless strings. It is extremely simple. Once you've done that my proof follows.

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So what have you achieved? By denying uncontroversially true statements...

You can only claim a statement is true until it is proven false. I have unquestionably proven it false. If you can't see that then I can't explain it any further.

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If you claim that diagonalisation is logically invalid, then, because diagonalisation is valid in classical mathematics, you are committed to the rejection of classical mathematics.

Is this your way of saying you concede to the proofs validity? Once again science never had any use for uncountable numbers before Cantor or after him. It is an irrelevant topic.

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@tomr,

Interesting comments on the objection to Cantors proof here...it seams you can't win this one Tomr...not that such makes a better case for Free Will anyways...
Link: http://scienceblogs.com/goodmath/2009/01/28/the-continuum-hypothesis-solve/

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@tomr,

tomr wrote:

No I don't think there is a largest natural number.

Then you can't reverse the ******* order, can you?

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@Fil Albuquerque,

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it seams you can't win this one Tomr...

Why can't I? Do you agree with the proof I gave?

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@tomr,

From the same link I gave you earlier in the comments section below I found this justification :

Quote:

Infinite sets are very counter-intuitive. A lot of things that seems like they should make sense don’t. The set of even numbers is the same size as the set of integers – even though it seems as if it should be smaller. The set of rational numbers is the same size as the integers – even though it seems like it should be larger.

The only way to compare infinite sets is by looking for bijections. There is a bijection between the rationals and the naturals – so they’re the same size. There’s a bijection between all naturals and even naturals (b(n) = n×2) – so they’re the same size. But there isn’t a bijection between the integers or the reals – so they’re not the same size; and in every attempt at a bijection, you can cover all of the integers, but you’ll always miss some reals – so the set of the reals is larger than the set of the integers.

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Is free-will an illusion?

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