Taking a page from Hume and Spinoza

[JuanFlorencio]

I can give you a math function Y=Y(X) (read it X cause Y). I can define a set produced by this function S={S0,S1…} where S1=Y(S0) etc. Now I define an amplitude a=A (for example the sum of a geometric series) which exists and it is finite. Hence there is no problem with infinite regress if the function and the norm are defined properly.

Just define the function, the set, the amplitude, and the procedure to relate them, and let’s see.

Regards
JuanFlorencio

 

[Bahman]

Just define the function, the set, the amplitude, and the procedure to relate them, and let’s see.

Regards
JuanFlorencio

I can define them in many different ways. But lets stick to the one which is the simplest: Y being law of nature, X being state of universe and the amplitude being the knowledge within.

 

[JuanFlorencio]

I can define them in many different ways. But lets stick to the one which is the simplest: Y being law of nature, X being state of universe and the amplitude being the knowledge within.

Fine. Define them mathematically.

 

[Bahman]

Fine. Define them mathematically.

The point is that weather we could agree that such a thing in principle exist. Hence there is no problem with infinite regress. I have a PhD degree in Physics and to be honest it is very difficult to define a set of mathematical equation to define reality. From philosophical point of view, I however believe that this set does not exist unless it is manifestation of an infinite regress. How you could be free in a pure mathematical framework?

 

[JuanFlorencio]

The point is that weather we could agree that such a thing in principle exist. Hence there is no problem with infinite regress. I have a PhD degree in Physics and to be honest it is very difficult to define a set of mathematical equation to define reality. From philosophical point of view, I however believe that this set does not exist unless it is manifestation of an infinite regress. How you could be free in a pure mathematical framework?

Dear Bahman,

Yes, to define reality through a mathematical model must be extremely complex. It is even unimaginable to me. I thought you had something when you said it was the simpler case, and naturally I wanted to see it. Anyway…

I don’t think that philosophy can make things simpler to you, because it is no less rigorous than physics (I think it is even more demanding). You should not think that a set of statements are philosophical just because they sound very strange, or because they are impossible to decipher.

If you wish, state any other mathematical example that can illustrate what you wanted to show, and let’s see.

Kind regards
JuanFlorencio

 

[Bahman]

Dear Bahman,

Yes, to define reality through a mathematical model must be extremely complex. It is even unimaginable to me. I thought you had something when you said it was the simpler case, and naturally I wanted to see it. Anyway…

I don’t think that philosophy can make things simpler to you, because it is no less rigorous than physics (I think it is even more demanding). You should not think that a set of statements are philosophical just because they sound very strange, or because they are impossible to decipher.

If you wish, state any other mathematical example that can illustrate what you wanted to show, and let’s see.

Kind regards
JuanFlorencio

That is how I understand it in simple term: Consider a geometric series for example. Now assume that each term in this series is caused by another term. The sum of series is finite although the number of terms are infinite. Hence there is no problem with infinite regress if the casual chain is appropriate.

 

[JuanFlorencio]

That is how I understand it in simple term: Consider a geometric series for example. Now assume that each term in this series is caused by another term. The sum of series is finite although the number of terms are infinite. Hence there is no problem with infinite regress if the casual chain is appropriate.

Well, Bahman, I don’t know why you need to stress that we must assume causality in the series. There is no causality in it at all.

However, if the geometric series is convergent, the sum of their elements is finite. If it is divergent, it is not. I don’t see any relation to “infinite regress” here.

Best regards
JuanFlorencio

 

[Bahman]

Well, Bahman, I don’t know why you need to stress that we must assume causality in the series. There is no causality in it at all.

However, if the geometric series is convergent, the sum of their elements is finite. If it is divergent, it is not. I don’t see any relation to “infinite regress” here.

Best regards
JuanFlorencio

Oh well. Infinite regress claim that the set S={s0,s1,…} where s1=L(s0) etc. cannot be exist since the number of terms is infinite. I am arguing that number of terms is not a good measure for refuting an infinite causal chain.

 

[JuanFlorencio]

Oh well. Infinite regress claim that the set S={s0,s1,…} where s1=L(s0) etc. cannot be exist since the number of terms is infinite. I am arguing that number of terms is not a good measure for refuting an infinite causal chain.

Dear Bahman:

Even though your question deals with infinity, it is very different from the problem stated by Thinkandmull.

Thinkandmull’s problem was this: Assuming that a segment of length L is made up of infinite parts, is L finite or infinite?

The mathematical representation of this problem is a geometrical convergent series, and I said it can be demonstrated that the sum of its elements is finite, and it is not necessary to add them one by one. So, I said “L is finite”.

Now, you are mixing causality with mathematical series. I insist that they have nothing to do with each other. There is no causality at all in mathematics. Now, if you ask me if I can conceive all the elements that belong to an infinite mathematical series, my answer is “no, I can’t”. If you ask me, “do you feel compelled to stop counting the elements of the series?” My answer is again "no, there is nothing intrinsic in the series that can prevent me from going on counting its elements”.

On the other hand, in a causal series you need to think differently: Given the fact that something is changing now, there must be a cause. There might be a causal chain. But if you pretend that there is no first cause, the change that you are observing is left without explanation.

This is analogous to demonstration in general: To explain something you need a number of premises. If your premises are questioned, then you need to demonstrate them based on other set of premises. Then, you will have an argumentative chain. But if you think that every premise needs demonstration, you will be unable to demonstrate anything at all. So, you will need a set of premises that allows you to demonstrate other propositions but that do not need demonstration themselves. Those are the axioms; the analogous of the first cause that is not caused.

Best regards
JuanFlorencio

 

[thinkandmull]

What does it **mean **to say that the sum of an infinite length is finite? There is infinite length, so it goes on infinitely… We can name the series finite, chocalate, a Big Mac, or whatever. But how does it add anything to our knowledge? Sure there are larger infinities. By finite, do you mean simply “not the largest of infinities”?

 

[JuanFlorencio]

What does it **mean **to say that the sum of an infinite length is finite? There is infinite length, so it goes on infinitely… We can name the series finite, chocalate, a Big Mac, or whatever. But how does it add anything to our knowledge? Sure there are larger infinities. By finite, do you mean simply “not the largest of infinities”?

Hi Thinkandmull!,

Finite is a technical word which means limited. So it is opposed to infinite.

By the way, did you do the excercise that I recommended you (the sum in Excel)?

Best regards
JuanFlorencio

 

[JuanFlorencio]

Hi again Thinkandmull:

I am sorry, I did not read your reply well. I did not say that the sum of an infinite length is finite, but that the sum of the infinite parts of a finite length is finite.

Good night!
JuanFlorencio

 

[thinkandmull]

I read what you wrote but I didn’t do the exercise. I’ll check it out next time I get on the computer, I got to leave in a minute

Finite does mean limited, but if the parts in what you call “finite” is infinite, than it is an infinite set. It’s only limited by something larger, a larger infinity. That’s why I titled this thread as I did. Thinking that a pen has no limit is counter-intuitive, but I have found that I can reject the idea of limit in space without getting into a contradiction.

“I did not say that the sum of an infinite length is finite, but that the sum of the infinite parts of a finite length is finite.”

If there are infinite parts (lengths), than there is an infinite length, and finite would just be the title

Good night!

 

[JuanFlorencio]

I read what you wrote but I didn’t do the exercise. I’ll check it out next time I get on the computer, I got to leave in a minute

Finite does mean limited, but if the parts in what you call “finite” is infinite, than it is an infinite set. It’s only limited by something larger, a larger infinity. That’s why I titled this thread as I did. Thinking that a pen has no limit is counter-intuitive, but I have found that I can reject the idea of limit in space without getting into a contradiction.

“I did not say that the sum of an infinite length is finite, but that the sum of the infinite parts of a finite length is finite.”

If there are infinite parts (lengths), than there is an infinite length, and finite would just be the title

Good night!

Try to do the excercise, Thinkandmull. Let’s talk then.

Good night
JuanFlorencio

 

[thinkandmull]

I’m not sure I get the Excel thing… it approaches a limit but never gets there. If the limit doesn’t move, how is that possible?

 

[JuanFlorencio]

I’m not sure I get the Excel thing… it approaches a limit but never gets there. If the limit doesn’t move, how is that possible?

Dear Thinkandmull:

I think you are prepared now. This is what happens: you start with 1/2. If you sum another 1/2, you will get 1 right away; but instead of that you sum half 1/2, that is to say, 1/4. You come close to 1, but the sum is still less than 1.

If you sum another 1/4, you will get 1; but instead of that you sum half 1/4, that is to say, 1/8. You come closer to 1, but the sum is still less than 1.

If you sum another 1/8, you will get 1; but instead of that you sum half 1/8, that is to say, 1/16. You come closer to 1, but the sum is still less than 1.

If you sum another 1/16, you will get 1; but instead of that you sum half 1/16, that is to say, 1/32. You come closer to 1, but the sum is still less than 1.

And you can proceed forever, but the sum will never be 1, because you always sum half of what is needed to reach 1.

That is why, Thinkandmull.

Good night!
JuanFlorencio

 

[thinkandmull]

If we apply this to a line, what will the final step to 1 be? Will it cover a length? Than it is divisible. And you go another half. This goes on forever so the line can’t even lay there. That is what I am referring too

 

[JuanFlorencio]

If we apply this to a line, what will the final step to 1 be? Will it cover a length? Than it is divisible. And you go another half. This goes on forever so the line can’t even lay there. That is what I am referring too

Yes, Thinkandmull! All the succesive parts are still divisible, and if you continue dividing the last one, you will never reach 1. That is true. However it does not mean that 1 is infinite. Naturally, when we travel a length L and we do it by foot, we never shorten our steps; we keep a uniform pace and we cover the total length with a finite number of steps, and within a finite time. Do you agree?

Best regards
JuanFlorencio

 

[thinkandmull]

Have you read about supertasks?

plato.stanford.edu/entries/spacetime-supertasks/

en.wikipedia.org/wiki/Supertask

Last month I realized that time is divisible to infinity just as easily as motion, and than read that very argument 10 minutes latter in Aristotle’s Physics!

 

[thinkandmull]

Hmm… if it get’s infinitely smaller, than it would be finite and seem to stay infinite. Ok, that makes sense.