You raised a lot of really good points in this post and it's late so I only want to respond to this one point and I'll aspire to get back to the rest ...
I did acknowledge that people are doing this research and that they're serious people. And I simply stated that if I met one of them I'd offer up the ...
Ah ... a while back you objected that I misquoted you saying that incompleteness was on point here. But in fact I believe I was originally correct. Yo...
Ok herewith my response to the deferred post. But no, you're just restating your bias, not explaining it. "Q: Why is primes a simple proof by contradi...
I plead tragic ignorance of Aristotelian logic. Perhaps I over-identify the word logic with the standard predicate logic used in mathematics. The para...
Ahhhh, very interesting article. I learned something. I do feel a tiny bit sandbagged in the sense that you've had this somewhat obscure topic in mind...
Sorry, I overstepped my knowledge. I don't know anything about Aristotle. Poor Frege, such a brilliant and original thinker, forever remembered for hi...
Well that's the conventional wisdom, pretty much universally accepted. But I wouldn't say that we don't need unrestricted comprehension (I don't know ...
This is exactly how I got in trouble last time. Conversating back and forth while deferring responding to the important earlier post. But a few though...
Ok. Just wanted to make sure you accept law of excluded middle and proof by contradiction. Will do. I got in trouble once around here when I deferred ...
That didn't even make sense. I do remember reading it now. I don't follow your point at all. We assume there's a largest prime and derive a contradict...
Link please, I didn't see it. But it wasn't an argument, since I'm merely stating what every single mathematician agrees with. I'm asking you a questi...
Uh ... LOL. That made me chuckle. It's because the form of the two proofs is identical: * Assume there's a largest prime. * Derive a contradiction. * ...
Do you regard the proof by contradiction that there's no largest prime a conundrum or paradox? Why or why not? In other words: The assumption that the...
I addressed that point in my earlier response to @MindForged. Naming is generally a matter of historical accident. Is the Axiom of Choice an axiom, Zo...
You raised a number of interesting points. Before I respond in detail, it would help me to understand your point of view if you could tell me in clear...
MindForged, you are completely misunderstanding the difference between a veridical paradox and a plain old proof by contraction. Moreover, Russell's p...
LOL. I ask again: Why is it that in one case, you invoke the standard mathematical formalism to explain or ignore the underlying philosophical issues;...
Yes, that is the mathematical formalism. So in this case you fall back on the mathematical formalism to ignore the philosophical paradox; but in the c...
Which has what to do with anything I wrote? Let me tl;dr this for you. Why are you so focussed on a particular paradox of Riemann integration, when it...
I have a question for you. Gabriel's horn is a paradox of Riemann integration, accessible to students of freshman calculus. As others have noted it's ...
In the synagogue one day the Rabbi kneels and puts his forehead to the floor and says, "Before you oh Lord, I am nothing." The Cantor puts his forehea...
I don't know your background so I can't say. But here is a free pdf of Shoenfeld's classic text on Mathematical Logic. It's one of the standard grad-l...
That's right. I noted that there is no general definition of number in mathematics. A well-known and true observation. For whatever reason, this simpl...
No. It's not. That's the point. i is a number but it's not a quantity. That's a counterexample to your idea that a number is something that is a quant...
My remark was intended as lighthearted. What the meaning of "is" is was very big in American popular culture during that particular scandal. This is t...
Your complete misunderstanding and lack of comprehension of category theory and mathematical structuralism was evident to several other posters the la...
I did not write the quote you attributed to me. What is your attitude problem? I stated originally that there is no general definition of number in ma...
I certainly can't understand how you would have gotten that impression. Many specific types of numbers are defined within set theory. But there is no ...
The quaternions are numbers whose multiplication is not commutative. The transfinite ordinals are numbers whose addition is not commutative. How weird...
There's no definition of number in ZFC. In ZFC we have a definition of natural numbers, and we can make definitions of the integers, rationals, reals,...
Bill Clinton made that very same argument to try to wiggle out of a sex scandal. In the end he lost his license to practice law and was impeached (but...
Yes that's an interesting point. Philosophers and logicians have struggled to define what a number is. Mathematicians don't really care that they have...
The list of posts I need to respond to is growing faster than my available time to respond. I'm plugging along though. Like the guy writing his autobi...
Saying that a number is anything that's number-like is a circular definition. No better than the poster above who said that a quantity is anything tha...
Ok I'll play. Four questions. * What is quantity? * The imaginary unit i with i^2 = -1 ... what quantity does it represent? * Do you regard i as a num...
It's a philosophical curiosity that there is no definition of number in mathematics. In other words if you major in math, get a Ph.D. spend a career a...
The rightness or wrongness of Tegmark's idea doesn't matter so much as the fact that I can add, "and Tegmark agrees with me!" when I argue the same po...
That fits nicely with some thoughts I have. The risk isn't computers acting like people. The risk is people acting like computers. Every time you're t...
What a wonderful thought. In the old days people had phone numbers like MUrray Hill 5-9975. You'd dial the MU characters on your dial phone. In the 19...
It it intellectual rebuttal that's important here? Or the emotions stirred up by family dynamics? Perhaps this is more of a psychological problem than...
That was in the old days of sound monetary policy. As David Stockman notes, that was the time of President Dwight Eisenhower and Fed Chairman William ...
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