Recent content by nomadreid

Thanks, SSequence. This was my impression as well; that was of course the whole point of Gödel's inclusion of omega consistency in his original proof. At first I thought that perhaps Artemov was trying to somehow create some kind of a Rosser sentence to justify his weaker version of consistency...

Thank you for the analysis, SSequence. This can help me in attempting to make sense of Artemov's arguments. (Your analysis also confirms my reaction that his arguments are not written in a way as to be clear to many readers.) Also, I read the Chow article, which I found very interesting (and, as...

I have come across several preprints by Prof. Sergei Artemov, for example https://arxiv.org/abs/2508.20346 https://arxiv.org/abs/2403.12272v1 (If it has appeared in a peer-reviewed journal yet, I have not found it.) I have questions about the general approach. First, my main question...

Super! Excellent and full explanation, thank you very much, Demystifier. Points I myself would not have come up with, and will follow up on. And thank you for the book recommendation: yes, I have seen the book sometime in the past, but I will dig it out and reread it.

I have just looked through https://arxiv.org/abs/2305.07331 by the physicist Prof. Dr. Claus Kiefer (Institut für Theoretische Physik; Universität zu Köln, Germany) . The reason I am putting this in the logic thread instead of a physics thread is as follows. It appears to me that the...

Thanks, Gavran. Your post explains the confusion very well and concisely, and clears up a whole lot of my confusion. Super! As well, wrobel, I have been reading the book by Halmos that you recommended, and this also clears up a lot of my previous confusion. So many thanks for the recommendation.

OK, downloaded.

Yes

Ah, I guess I mean a non-orthonormal vector space; i,e, a vector space in which not all of the basis vectors are orthogonal to one another.

I am older/less young than the poster, and have been receiving answers from the wonderful people on this forum for many years for my inexpert dabbling in various subjects, mostly physics and mathematics but also chemistry, biology, and computers. They are always very patient with my foolish...

I am a bit confused about dual space unit vectors in the case of non-orthonormal vector spaces. (Reference: A Student's Guide to Vectors and Tensors, by Daniel Fleisch, Cambridge, 2012.) I will be grateful for being corrected in the following: Suppose V is a non-orthonormal vector space, and...

One of the possible false assumptions here is that mathematics is uniform enough to have the same answer for all of it. It is possible that parts of mathematics are invented, and parts are discovered. The people claiming one side often latch on to that part of mathematics that fits their...

Huge thanks for the replies, Gavran. (The delay in my response was due to my not getting the usual email notification of a reply.) Your examples and explanations are excellent, and well answer my question. Super! Also thanks to you, Wrobel, for the warning, and for your interesting example.

Thanks for the replies, Gavran and Wrobel. First, Gavran. That is good to hear. Could you give me an example of each, and why? (That is, one in which it is better to use an inner product, on in which it is better to use a dual space operation.) That would be super. Second, Wrobel. I am more...

Thanks for answering, Hill, although it appears that either I did not state the question clearly enough, or you read the question rather hastily, as I mentioned neither which inner product was being referred to nor over what field the vector fields were; I neither mentioned nor meant the dot...