That something so counter-intuitional can be proven shows that not all is well when it comes to our relating the continuous with the discreet.

It can be argued that only the area of a point has been proved equal to the area of any circumference. But in any case, mathematics (and logic) are separate from physical reality, that something is mathematically true doesn't imply that it's actually true, or even that it's actually meaningful.

I do think its meaningful.

How did that formal system go? Something like:
a,b
if a then bab
if b then ba
What meaning do the theorems of such a system have?

I am talking about our entire conception of the world, which is systematic.

Okay, but there's no implication from that to the effect that all statements of mathematics, logics or other formal systems are meaningful. There is a view that mathematics is almost entirely pathological, and that it's conceptual doesn't have any bearing on this.

But in any case, mathematics (and logic) are separate from physical reality, that something is mathematically true doesn't imply that it's actually true, or even that it's actually meaningful.

Okay, but there's no implication from that to the effect that all statements of mathematics, logics or other formal systems are meaningful. There is a view that mathematics is almost entirely pathological, and that it's conceptual doesn't have any bearing on this.

Take for example the proposition, "The union of a finite set whose cardinal number in 893 with a disjoint, finite set whose cardinal number is 127 is a finite set whose cardinal number is 1,020." Would you say that this proposition is (a) "mathematically true", (b) "actually true", and/or (c) "actually meaningful"?

Do you believe that mathematics is a formal system? Can you say (informally!) what you mean by the term "formal system"? And what do you mean by saying that mathematics is "almost entirely pathological"?

is the latter statement related somehow to your description of mathematics, in another thread, as being "useless" - except for those purposes for which it is useful!

Does this interview have some purpose?

I don't see how a formal system could work without at least the smallest core of intuition.

But isn't "0! = 1" counterintuitional? Or a twist on the usual method of factorilization?

I would be delight if someone saw why I find the discrete/continuous collision so fascinating.

After watching a brilliant video posted by Attano on my profile, I think the left brain / right brain issue is connected to this.

I agree, emphatically.

It's a convenient and natural convention. There are many similar instances of "null cases" in mathematics and computer science. (I'm not entirely sure that that phrase would be understood as a technical term, but any mathematician or computer scientist or programmer would know instantly what it means.)

I do. It has been a passionate, even sexual image for me for decades now. But by the same token, it is hard for me to put in words what it is or why it is important.

It could well be so. I'll try to get around to watching that video. Bit snowed under right now.

Is the ideal also "real"? Does perfection "exist" in the "real" world?

You seem to think all such concepts are merely human constructions
but
such concepts are almost universal and recurring.

5.621 The world and life are one.


5.63 I am my world. (The microcosm.)


5.631 There is no such thing as the subject that thinks or entertains
ideas. If I wrote a book called The World as l found it, I should have
to include a report on my body, and should have to say which parts were
subordinate to my will, and which were not, etc., this being a method of
isolating the subject, or rather of showing that in an important sense
there is no subject; for it alone could not be mentioned in that book.--


5.632 The subject does not belong to the world: rather, it is a limit of
the world.


5.633 Where in the world is a metaphysical subject to be found? You will
say that this is exactly like the case of the eye and the visual field.
But really you do not see the eye. And nothing in the visual field
allows you to infer that it is seen by an eye.


5.6331 For the form of the visual field is surely not like this


5.634 This is connected with the fact that no part of our experience is
at the same time a priori. Whatever we see could be other than it is.
Whatever we can describe at all could be other than it is. There is no a
priori order of things.


5.64 Here it can be seen that solipsism, when its implications are
followed out strictly, coincides with pure realism. The self of
solipsism shrinks to a point without extension, and there remains the
reality co-ordinated with it.


5.641 Thus there really is a sense in which philosophy can talk
about the self in a non-psychological way. What brings the self into
philosophy is the fact that 'the world is my world'. The philosophical
self is not the human being, not the human body, or the human soul, with
which psychology deals, but rather the metaphysical subject, the limit
of the world--not a part of it.

For the Greek rationalists the ideal, the eternal, the changeless, the perfect was more real, more being, more existent than the world of change, flux, imperfection, sense experience and temporality.

It can be argued that only the area of a point has been proved equal to the area of any circumference. But in any case, mathematics (and logic) are separate from physical reality, that something is mathematically true doesn't imply that it's actually true, or even that it's actually meaningful.

I appreciate that, because the absolute concept is a diamond in my brain.

For instance, the "self" seems like a practically necessary abstraction. But it is actually quite questionable.

That must hurt like hell.

Could you question it? I never understood how people question it =)

5.621 The world and life are one.
5.63 I am my world. (The microcosm.)
5.631 There is no such thing as the subject that thinks or entertains
ideas. If I wrote a book called The World as l found it, I should have
to include a report on my body, and should have to say which parts were
subordinate to my will, and which were not, etc., this being a method of
isolating the subject, or rather of showing that in an important sense
there is no subject; for it alone could not be mentioned in that book.--
5.632 The subject does not belong to the world: rather, it is a limit of
the world.
5.633 Where in the world is a metaphysical subject to be found? You will
say that this is exactly like the case of the eye and the visual field.
But really you do not see the eye. And nothing in the visual field
allows you to infer that it is seen by an eye.
5.6331 For the form of the visual field is surely not like this
5.634 This is connected with the fact that no part of our experience is
at the same time a priori. Whatever we see could be other than it is.
Whatever we can describe at all could be other than it is. There is no a
priori order of things.
5.64 Here it can be seen that solipsism, when its implications are
followed out strictly, coincides with pure realism. The self of
solipsism shrinks to a point without extension, and there remains the
reality co-ordinated with it.
5.641 Thus there really is a sense in which philosophy can talk
about the self in a non-psychological way. What brings the self into
philosophy is the fact that 'the world is my world'. The philosophical
self is not the human being, not the human body, or the human soul, with
which psychology deals, but rather the metaphysical subject, the limit
of the world--not a part of it.

I meant that if anything has more than one meaning - even a single sentence, it is not precise. It could go off in several directions. This can how ever be fun!!

---------- Post added 06-06-2010 at 06:20 PM ----------

To be precise - it has one meaning, one direction.