Is free-will an illusion?

@tomr,

tomr wrote:

The natural numbers are unbounded. So you must be able to write them as endless strings.

False, wrong and incorrect.

tomr wrote:

End of story.

I agree. You don't understand this or pretty much anything else about this matter, even after looking it up. I conclude that you're a hopeless case.

1 Reply

@ughaibu,

Quote:

False, wrong and incorrect.

Answer the question. Which 9 must I stop at then?

999999999999999999999999999999999999999......

If the natural numbers are unbounded then there is not a position I must stop at. If it is bounded then there is one.

1 Reply

@tomr,

I agree with your analogy. That's what I was saying about its "result" to be practical for human use. Most issues that go beyond infinity that humans fail to comprehend has no meaning whether they are "rational" or anything else.

1 Reply

@cicerone imposter,

Quote:

I agree with your analogy. That's what I was saying about its "result" to be practical for human use. Most issues that go beyond infinity that humans fail to comprehend has no meaning whether they are "rational" or anything else.

It is a very simple matter to show a natural number can be expressed as an endless string. But there are so many garbage theorems and proofs out there that someone like Ughaibu is going to take out of context to support his argument at any cost.

Once you admit that infinity means endless. The concept is very understandable. You don't need extravagent theorems to show something like the natural numbers can be represented as endless strings. It follows directly from the definition of infinity (which in math terms means unbounded). I hate it when something so simple can be so confused by people who can't think for themselves and just follow anything they hear or read. But when you ask them to pick the digit in the sequence to show us where the natural numbers must end they won't do it. They cry foul and make reference to the entirety of the internet. Either the natural numbers end at some placeholder or they go on forever.

Anyway to your point on extra infinities. That has always been troubling to me too. Either the numbers are endless or they are not. In the end there is no way to quantify endlessness except for trick proofs like the diagonal argument that can be shown to be false.

Why is it that these arguments for freewill take us to the foggy boundaries of mathematical concepts like uncountable numbers anyway. That more than anything says something about the lack of support for free will here in reality.

0 Replies

@Fil Albuquerque,

Fil Albuquerque wrote:

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/

From the above link, posted by Fil Albuquerque, for Tomr's benefit; "The basic error, though, is the same as above: he’s got an enumeration of all
finite length paths. Everything that he says is talking about the set of
finite-length paths. Because natural numbers are all finite-length."
There is nothing to dispute about the matter, Tomr is wrong, that's all.

1 Reply

@ughaibu,

Quote:

An infinite-length string of digits isn’t a natural number, or an integer. And so everything else in that “proof” breaks down.

And I would ask this person the same question I ask you. If a natural number cannot be an endless string of digits then at what point do I need to stop:

989898999898998989898963667803......

The 100th element or the 1000000th element in the sequence? Please Ughaibu pick the finite number where the natural numbers end. I beg you. Do this thing for me and show everyone how stupid you really are. Until you can do it, we will have to assume you can't because it is an endless or "infinite-length string of digits".

1 Reply

@tomr,

tomr wrote:

And I would ask this person the same question I ask you. If a natural number cannot be an endless string of digits then at what point do I need to stop:

989898999898998989898963667803......

The 100th element or the 1000000th element in the sequence?

Your question doesn't even make sense and demonstrates your incorrigible ignorance, even after the matter has been spelled out for you, several times. It is the set of natural numbers which is infinite, not the numbers themselves. If your "logic" were valid, then an infinite number of penguins would imply a penguin of infinite size. There is no such implication.

tomr wrote:

Do this thing for me and show everyone how stupid you really are.

You have failed to understand the role of essential principles of science, that freely willed actions are observable, the argument against determinism and that rejecting uncountability entails rejecting science. In fact, you have failed to understand almost everything I've posted on this thread, though very little of it requires even a high school level of technical background.

tomr wrote:

Until you can do it, we will have to assume you can't because it is an endless or "infinite-length string of digits".

You really should stop insulting the other members by using "we", and concentrate on getting your head out of your arse.

1 Reply

@ughaibu,

Quote:

Your question doesn't even make sense and demonstrates...

Sure it doesn't Wink

1 Reply

@tomr,

Here is proof that the the number of digits in a natural number is infinite. All that I assume is what Ughaibu just said:

Quote:

It is the set of natural numbers which is infinite

Here is a mathematical function that will give the length of a natural numbers digit string. The length function is a function of some natural number n denoted by the symbol "l(n)". The "l" is for length. The function is:

l(n) = 1 + log10(n)

You can try this function out on any calculator with log base 10 functionality. So for n= 2222, the length of the digits in the string is 1 + log10(2222) = 4.3467444. Always discount the remainder of the function. So the length of n=2222 is 4. Try out different values it is kind of neat I think.

Anyway the proof is simple. But you do need to know how to do limits which is done in elementary calculus.

Proof:
We are given that the set of natural numbers is infinite.

So we can take the limit of the length function as the natural number n approaches infinity.

lim n->∞ (1 + log10(n))

= 1 + lim n->∞ log10(n)
= 1 + ∞
= ∞

All I have done in the step to get infinity is use a known property of the limit of a log10(n) function: http://www.rapidtables.com/math/algebra/logarithm/Logarithm_of_Infinity.htm

Therefore the number of digits, in some natural number n, becomes infinite as n becomes infinite. I am sorry for the excessive math but Ughaibu doesn't know what he is talking about.

1 Reply

@tomr,

tomr wrote:

Therefore the number of digits, in some natural number n, becomes infinite as n becomes infinite.

What is the first thing that I read at your link? "Since infinity is not a number, we should use limits" In short, what you have proved is the larger the number, the more digits it has and that there is no largest number of digits.
But, look on the bright side, if you really believe this nonsense, then your question has a framework within which it makes sense. As we know that small natural numbers have finite numbers of digits and if, as you claim, large natural numbers have infinite numbers of digits, what is the largest natural number that has a finite number of digits?
As I hope is obvious to everyone but you, whatever number you name is succeeded by another natural number, and as all natural numbers in base ten end in one of the following digits 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9, whatever number you name will be succeeded by another number with a finite number of digits and ending with the successor of its final digit.

tomr wrote:

I am sorry for the excessive math but Ughaibu doesn't know what he is talking about.

Okay, you are hereby publicly challenged to post both your proofs on a respectable maths forum and link to the threads.

2 Replies

@ughaibu,

Quote:

tomr wrote:
I am sorry for the excessive math but Ughaibu doesn't know what he is talking about.

I'm quite sure Ugh you're onto something but to save the Average Clod (me) hours of reviewing 489 postings above could you please explain in short sentences using common words how math bears at all upon the subject of freewill

Thanks again

1 Reply

@dalehileman,

He only dances around on that subject without any direct answers.

1 Reply

@cicerone imposter,

Quote:

He only dances around on that subject

Cis that's why I was hoping someone might explain his position

….but it would have to be CWISSAC [Common Words in Short Sentences for an Average Clod (me)]

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His argument is actually quite easy to refute justified in the uncertainty that surrounds human knowledge on any matter when it comes to absolutes or ontological claims, and while some arguments may at best be convincing they are far from certain, thus whether true randomness is or is not the case whatever we speculate about it is not final...mathematics as it is expressed by human beings is a work in progress, and since Cantor pretty much without solid foundations...confirming randomness would require the unfolding of the whole of reality itself through space time, once that's precisely what it means when we say randomness it is not computable...

Quote:

...a string of bits is random if and only if it is shorter than any computer program that can produce that string (Kolmogorov randomness)—this means that random strings are those that cannot be compressed.

It is thus quite obvious that final knowledge about true randomness cannot be asserted by human beings...bottom line what that means is that complex patterns that may appear random to us may well be just highly complex numbers...

2 Replies

@Fil Albuquerque,

Okay Fil and again thank you. I am still wondering however how randomness can possibly enter into the discussion of the freewill/determinism impasse

2 Replies

@dalehileman,

Well it can't at least not in favor of free will...in fact if anything randomness as a result of chance clearly opposes the naive idea that an agent is in charge of any causal agency...

1 Reply

@Fil Albuquerque,

I believe randomness is much simpler than that! It's because humans decide on what they will do next based on their own biology, experiences, environment, education, culture, and perceptions. The multitude of those individual experiences are "all different" by degrees and how they impact any individual.

How any individual decides to do one thing over another is not predictable when given different options at any one point in time. They are all different, and cannot be measured. No math formula can be developed to measure it.

In other words, we are all "different."

It's beyond what we call "habit." Nobody can predict what I will do as an individual based on any math formula tomorrow, next week, next month, or next year.

The only math formula that can accurately predict anything about me might be how long I'll live based on my current age and health.

2 Replies

@cicerone imposter,

Quote:

How any individual decides to do one thing over another is not predictable…and cannot be measured. No math formula can be developed to measure it.

I hope this reply doesn’t cause much anger. If you really accept this you may want to start with John Von Neumann and John Nash (The movie A Beautiful Mind was based on his life). You will eventually be lead to a huge area of mathematics called Game Theory. It is purported to do just that thing noted impossible in the above quote. Of course that is said by people like leading mathematicians (read: ignorant trouble-makers).I wouldn’t want to put mathematicians at the same level of A2K regulars, of course, but some non-inteelectual (sic) “sheeple” types might want to look into the people and math area noted for themselves.

1 Reply

@Zarathustra,

Okay, develop a math formula for what I will do tomorrow, next week, next month, and next year - and the rest of my short life.

You're so smart, you could probably produce it by next month.

1 Reply

@cicerone imposter,

I am not saying nor defending that such math formula predicting behavior can or can't be done...I am just saying whether true randomness is or is not the case we can't know for sure...equally I presented a reason on why I think that even if it was the case true randomness existed true randomness does not make a case for free agency, as agency imply precisely the opposite, that is, that I am the causal agent beyond the willing and not chance...what you were referring regarding the predictability of human behavior does not make a case neither in favor of randomness nor against it, but makes a very good example on how complexity makes prediction very hard...you seamed to be implying that people take decisions and make choices out of good reasons, I also think so, that if anything meaning, that reasons are causes for action that even if complex and hard or even eventually almost impossible to predict imply a deterministic explanation on the process of will...

1 Reply

Is free-will an illusion?

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