I'm extremely old fashioned.

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By "empirical", in the original passage, I meant "existing as an object in the physical world".



I entirely agree; and of course, this is why physics is "useful" in the vulgar sense and mathematics is only "useful" in virtue of its applications to physics or other scientific fields. It doesn't change the fact that there is nothing we can point to in the physical world which has the property of "triangularity" as part of its nature. From what you're saying, and I think you're right, we "willingly suspend disbelief" in the "atriangularity" of the object depicted on the sheet of paper in order to derive "useful" conclusions about it. Of course, this is true, and it has its virtues, but that doesn't change the fact that the object depicted on the sheet of paper is, as it were, a shadow of the subject in question - that the triangle itself is a conceptual or mental entity.



For the sake of intellectual and linguistic rigour. You mentioned the field of logic, and this is the same reason why in logic we distinguish between words and the things they represent. For instance, a logician will tell you that the following sentence is valid:



While the next sentence is invalid:



A word, such as "London", may or may not have any given number of letters; a city cannot be said to have any number of letters as letters and cities are conceptually incompatible. Of course the practise is irrelevant for most purposes and the average man, in going about his business, will readily interchange the two without a second thought - and that's fine, because everyone knows what he means when he chooses the stricly incorrect alternative. In science, however, greater rigour is called for.



Yes, though I don't claim to know what it is on most subjects.

RE Richard Smullyan, I know very roughly who he is and have been meaning since seeing his obituary to read some of his books, but haven't had time so far.

As far as piracy is concerned, I reject it as unethical, though as far as unethical acts go, it seems to me a moderately trivial one.

In that case, you can borrow the book in electronic form (I am assuming legally) from Open Library

You might find some of the first few puzzles trivial but there are varying levels of complexity, with puzzles most would find difficult in the later pages of the book.

To Prometheus18: I am curious about your username. If you feel inclined to tell us about it, what does the ancient Greek Titan Prometheus mean to you personally?

I offer people knowledge in the form of disabusing them of their illusions about the world - and am shunned for it. I'm also fascinated by the number nine and multiples thereof.

I was curious because, even before I came to Wrong Planet, I had come to see the Prometheus myths as a metaphor for the more highly talented autistic people generally: able to give a lot of new knowledge to the world, but, all too often, prevented from doing so by living in a world that is not autistic-friendly.

You sound like a legitimately cool guy.

I don't believe in the notion of absolute truth, though. I believe in absolute truth and sew with notions.