jgill

Metaphysical Actuality: The philosophical position that thought becomes actual by becoming concrete. Subjectivity, the "I" has constitutive validity, ...

Interesting links. Thanks. I've dabbled in mathematical vector fields for years, particularly time-dependent fields. If it were possible I would post ...

I got carried away by your comment that physics doesn't investigate reality, which is the domain of philosophy. I cited the "x=x" thread because, to a...

About the moon which is not there breaking into pieces which aren't there either? :nerd:

An extreme version of reincarnation? Or is it?

And what of the word "being" ? Quite a bit of philosophy seems to revolve around that concept, and it has always been suspect for me. A Manhattan towe...

The square root of two just won a Golden Globe award! :gasp:

x=x thread? :lol:

"I submit that 5 is prime and the square root of 2 both exists and is rational. . . . But they are true." The square root of two is rational? Am I mis...

I know it has no bearing on modern science, but sixty years ago, as a young USAF officer, I took a post-graduate curriculum in meteorology at the Univ...

It's been mentioned before, but many of those who toil in the depths of reality, the physicists, don't seem to worry about this issue. It seems to be ...

A thing? I give up. What's the answer? :worry:

K-theory, Category theory, etc. might enforce this view. I remember years ago hearing a well-known algebraist joke that, "K-theorists will tell you, "...

What am I missing here? :chin:

I don't know what this means. Matrix factorization? That's all there is to mathematics research these days? Surely you jest. :cry:

:roll: Oh oh. It sure isn't. :cool:

What about inverses? It's not immediately obvious, but in fact if a+b\sqrt{2}\ne 0 then \frac{1}{a+b\sqrt{2}}=\frac{a}{{{a}^{2}}-2{{b}^{2}}}+\frac{-b}...

Looks like an error in your truth table for implication. F => F is T. But I haven't been following the discussion and you may be into something else.

Comment: The identity \sqrt{x} = 1+\frac{x-1}{1+\sqrt{x}} generates a periodic continued fraction \sqrt{x}=1+\cfrac{x-1}{2 + \cfrac{x-1}{2 + \cfrac{x-...

. . . "Two dimensional objects have a fundamental problem which demonstrates that space cannot actually be represented in this way . . . We see a very...

My very first course in abstract algebra (taken in my first semester in grad school) did something like this. Not being conversant with the various co...

Good luck with this project. :roll:

True enough. In computations involving non-infinitesimal calculus higher order terms can be ignored depending on the settings. Hmmm. I keep learning t...

Some years ago the New Math was in vogue. As a mere instructor at the time I was given a text on College Algebra having a lengthy first chapter devote...

You can learn something on this forum. A number of years ago I bought Robinson's book on NSA and got excited about it for a while, even contemplated t...

I think physicists resort to complex (or imaginary) variables when it is convenient to do so and by doing so can predict phenomena. There's no magic o...

The movie, The Time Machine, taken from Wells' novel, shows the moon that is not there breaking apart in a catastrophic sequence, which, apparently, i...

Good explanation. I seem to recall from long ago a study by Piaget on the ability of young people to understand calculus. I may be mistaken but it see...

Since MUs is such a mind-blowing concept I don't think "more likely" has any bearing. But have a good new year! :cool:

It's mostly a metaphysical problem. Most mathematicians and physicists do quite well without contemplating such issues. But that's not to say that "in...

How can you possibly know this? Have you traversed the spectrum? But, interesting thread. :chin:

And then there is determinism. Wiki: "Confusion of causality and determinism is particularly acute in quantum mechanics, this theory being acausal in ...

:lol: Not likely. I thought the thread needed some comic relief.

And this is true of entities that defy the winds of time, like 2=2. But introducing a time gap when speaking of physical objects is different. X(t1)=X...

Must we pick at the bones of this troubled man? Wiki: Cantor retired in 1913, living in poverty and suffering from malnourishment during World War I. ...

Is a line segment a "thing?" As opposed to a wooden rod, say? Does a line segment actually exist as a physical thing?

Not only do the foundations shift, but mathematics rolls along like a giant intellectual snowball, gathering layer after layer of new concepts and the...

Perhaps Peter Lynds' essay on the impossibility of "points" in time has appeared in this forum. If not, some might be interested in his discussion of ...

Assuming God has laid forth unto us the Axiom of Choice. This is quite entertaining. :smile:

Political correctness is something I do not miss since retirement. :brow:

Interesting. Thanks. Nice exposition. I only took one course in set theory almost sixty years ago and it was Halmos' Naive book. When he started discu...

Your book is very impressive. And your posts are excellent. :cool:

This seems a bit harsh and I do not agree. However, I will admit that working in an area may clarify and solidify the knowledge gained as an undergrad...

Yes. However, he implied that anyone beginning a study of a particular philosopher should read not only those works, but other's critiques as well.

Nice exposition. A few additional comments: There are various kinds of fields. A mathematical field is more an algebraic structure with operations, li...

I think the notion of an orange being divided infinitely is ap-peeling. :smirk: I'm so happy that Cauchy, Weierstrass, and others settled this issue f...

Well, you have to start somewhere, I suppose. What do you think of X=X+1 ? :gasp:

My knowledge of philosophy is limited, but I recall my prof giving the opposite advice after I tried reading several of the well-known philosophers li...

This is distantly connected with wave/particle duality in physics. But when an electron, for example, is detected, it is detected as a particle. Where...

Once again, I can't argue with this. :brow: