Well put. It seems that science is founded on logic and ontology. For me, ontology and logic are one. For beings are logical structures. Science uses math, hugely, of course, and yet what is number? What is the number one, just to start with an "easy" one?

That is way too deep !:bigsmile:

I said " numbers don` t exist". I said it is a "refutation" of mathematical realism, since mathematical realism claims that "numbers do exist"!

Easy, right?

At least I put forward a sequence of arguments, instead of an exclamation or a single sentence. If you can't recognise them, that is not my problem.

At least I put forward a sequence of arguments, instead of an exclamation or a single sentence. If you can't recognise them, that is not my problem.

I think you are referring to me.

Not a refutation, but a denial. A refutation has to show what is refuted is false. A denial (or rebuttal) does not show that. I cannot refute what you say simply by denying it is true. You are confusing, "refute" with "deny" or, "rebut".

Godel was a mathematical realist. I think mathematical realism is a very hard position to refute. Most people don't refute it, they simply fail to grasp it.

I was indeed referring to you. I shall await further responses, thank you.

I was trying to be ironic in reply to:




A failure to grasp a joke, ken.

I hope so. (If it was a joke, then the word you want is, "sarcastic", not "ironic"). If it was a joke, then I suppose that Jeeprs did not grasp it too, since he asked for arguments, and not just statements.

That would be like saying " when i am talking about 2+2=4, i am really talking about sets, and operations that act on those sets". This is not intuitive! The second thing is that it does not do away with ontology, since you would be committed to sets, rather than numbers.

OK, I am not trying to come across 'with attitude'. I don't intend to write a summary of Platonism. It is a very large area of study. The particular argument that interests me here is the one about mathematical realism. It could quite possibly be a fallacious argument, but so far has not been addressed, and requesting a discourse on the pros and cons of Platonism is not relevant, in my view.

I can't recall the details of that talk, as I said, but it did demonstrate very convincingly how to derive all of the numbers from 1-9 (what others count?) in terms of sets. But it took 45 minutes to go through it, and I was not a mathematically-literate audience member. I will go back to the site and see if I can find the lecturer's name.

Godel was a mathematical realist. I think mathematical realism is a very hard position to refute. Most people don't refute it, they simply fail to grasp it.

I feel myself moving toward that position. Of course this is not far at all from the real as rational. In fact, the move from transcendental to absolute idealism would seem to imply mathematical realism. It seems to me that Hegel fused Plato and Aristotle. He's a realist as far as ideas go, but asserts that these ideas must be engendered in time. This explains why we seem to invent numbers. And yet a number like pi starts to seem found. It just is the constant in the volume of a sphere, for instance.

If we drop the transcendental distinction, the invention/discovery distinction is questionable. And also the word "concept" becomes questionable, as concept has this idealism association. There's just the form of what is, and this form exist systematically. Russian dolls. (Great chain of being.) Maybe the trans idealist would say we twist the thing-in-itself into that shape. But his dialectical successor, the absolute(undiluted) "idealist" would say that the "thing-in-itself" is part of this supposed twist, which is therefore not a twist. It's feeling like a moebius striptease. Total idealism reverts/inverts into total realism. union of opposites.

Anyway, great subject.

Anyone else?

I am sure we don't invent number. Numbers must be independent of particular minds because they are common to all who think. In coming to grasp them, consciousness cannot convert them into its possessions or alter them. Also the mind discovers rather than forming or constructing them, and its grasp of them can be more or less adequate. For this reason, numbers cannot be part of consciousness' own nature or produced by consciousness out of itself. They must exist independently of individual human minds.

Yet numbers are not material objects. They are eternal and immutable. They cannot be perceived by means of the senses, but only by reason. In these respects, they are quite different to material objects of any kind.

So in this sense, they are real, but they don't exist.

I am sure we don't invent number. Numbers must be independent of particular minds because they are common to all who think.

In coming to grasp them, consciousness cannot convert them into its possessions or alter them. Also the mind discovers rather than forming or constructing them, and its grasp of them can be more or less adequate. For this reason, numbers cannot be part of consciousness' own nature or produced by consciousness out of itself. They must exist independently of individual human minds.

For this reason, numbers cannot be part of consciousness' own nature or produced by consciousness out of itself. They must exist independently of individual human minds.

Yet numbers are not material objects. They are eternal and immutable. They cannot be perceived by means of the senses, but only by reason. In these respects, they are quite different to material objects of any kind.

So in this sense, they are real, but they don't exist.

.Again, how are numbers any different from supercalifragilisticexpialidocious?

The value of number or numerical relationship correlates with observable phenomena which is not culturally determined or defined.

Well, Reconstructo, I am sure there is a formula somewhere for the percentage of that post which I understand, but it is perishingly close to zero.

I just wanted to quickly rehearse an idea that the reason Platonism appeals to the logic of mathematical law as a demonstration of a non-material reality, is not because maths is all that philosophically significant in its own right, but because of the principle that an idea can be real while not being material. Plato as we know said that the level of noesis was higher than the level of pistis which is the level of perception of mathematics and scientific observation. But it is similar, because in order to grasp a mathematical truth, we must be mathematically capable, that is, capable of perceiving numbers. In order to grasp the Ideas, we must be noetically capable, which by definition the non-philosophers are not. So in this respect the platonist argument on number is really an analogical argument. It is saying, just as the mathematician understands numbers by reason, so to the philosopher understands the Forms via noesis. In so doing, the Philosopher is understanding something which is real in the same way numbers are real, but of much greater ontological status.

Now I am not saying whether I think this is true or not, but I think it is a valid interpretation of Platonism.

---------- Post added 04-20-2010 at 12:26 PM ----------

Incidentally, I just noticed your signature line. There is a frequently-repeated maxim in Eckhardt: 'Creatures are mere nothings'. By 'creatures', of course, he doesn't mean cats and dogs, but all created things.

Not at all, as I have just pointed out, the Greek geometers entirely avoided numbers. And the inhabitants of the UK need only cross the channel to find that numerical relationships are culturally determined.

And didn't Plato have a sign forbidding those ignorant of geometry to keep out? (Those simple shapes are absolute form).