Re: Simple Question and the philosophy of infinity

The point is, you are doing this in your mind. What I mean to say is,
infinity has no meaning outside of your mind.

Please identify something which does have "meaning" in the
absence of a mind to consider it.

Sorry if I didn't express it exactly. Maybe it's clearer if I say that the
concept of infinity has no real-world equivalent.

what is infinity + 1? Is infinity a number that has no successor? Then
how can you call it a proper number?

Learn the math, and then you'll know the answers.

You don't seem overly confident in the power of your arguments ;-)


Mathematics is full of concepts like this. Take Pi for example. Nobody
will ever know its exact value. Yet we are using the symbol to calculate
"exactly".

So are you similarly going to claim that pi, like infinity, doesn't
"really" exist?

I find it problematic to claim that numbers "really" exist. Of course I
don't doubt that they exist as concepts (or "in your mind").
But consider the following reasonings:
"Numbers are concepts. Concepts do exist, it follows that numbers exist."
"God is, by definition, everything. Being everything includes being a
concept. Concepts do exist, it follows that God exists."
Something tells me that this line of thought is not really satisfying..

I think there is trouble with the word "existence". If you allow me - as a
non-mathematician - to take an example from maths:
Suppose you want to prove that there is no integer greater than 2 and
smaller than 1. Most probably you'll prove this by contradicting the
assumption that such a number exists. But to prove that there is a
contradiction you'll have to think and act as if such a number existed. The
statement "There is a number x greater than 2 and smaller than 1" is a
perfectly valid mathematical statement. It just happens to be false.
But how can you assume the existence of something that you later on prove
does not exist? What does that mean for the nature of your proof? When did
the concept of x come into existence? When did it cease to exist? What
exactly was the reason that it ceased to exist? Now if you say that
mathematical concepts "really" exist, what does this say about your
understanding of "reality"? Can you create and destroy objects at will just
by saying that a statement is true or false?

It's simple to avoid all these questions. In maths, "there is" means "we can
think about a certain concept in a consistent and logical way, not
contradicting our axioms". For example, "there is a number epsilon such that
bla bla" simply means "we can think of a number epsilon without getting into
logical trouble, such that bla bla". In this sense you can talk about
infinity and it's perfectly acceptable.

But: Confusing the mathematical existence quantor with "real world"
existence is a logical fallacy, a category error straight from Philosophy
101.

Strictly speaking, that's no proof at all; sure, the wall FEELS "real,"
and causes you pain when you pound it with your head - but I could
argue that it's still "all in your mind," and you'd have no way to show
that that claim is wrong.

As I mentioned earlier, I am not a constructivist. There is in fact a very
convincing argument against radical constructivism, in Rudolf Steiners
"Philosophie der Freiheit" (English title: "The Philosophy of Freedom"). I
can't repeat it here at least half as convincingly, so all I can do is refer
you to the book if you are interested.

But if we look at
it critically, it can be very important to realize that a lot of what we
believe really IS simply a convenient assumption on our parts.
See, I knew this would wind up getting more and more into
philosophy....:-)


True. It is hard to know what's "real" and what is not. But I'm quite sure
that numbers - and especially infinity - aren't :-)

Kind regards,
Leo


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