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Apr
13
revised Category theory and model theory as “natural” counterparts
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Apr
13
answered Category theory and model theory as “natural” counterparts
Apr
5
revised Is there a “large powerset axiom” so extreme that it disproves the existence of strongly inaccessible cardinals?
added 2 characters in body
Apr
5
comment Is there a “large powerset axiom” so extreme that it disproves the existence of strongly inaccessible cardinals?
@ToddTrimble, yep, I find your argument utterly persuasive. Its worth pointing out that "beg the question" is no shorter than "assume the conclusion," and much more ambiguous. In any event, the statement I was nearly persuaded by, namely: "it cannot be denied that logic and philosophy stand to lose an important conceptual label should the meaning of [beg the question] become diluted" is clearly false in light of your comment.
Mar
23
accepted Good set theory in which to study ordinal-indexed sequences?
Feb
25
awarded  Nice Question
Feb
23
comment The groupoid of algebraic expressions and proofs
@SylvainJULIEN, that's an intense look question fella. What, in particular, do you think the connection might be? By the way, your previous comment made my day. :)
Feb
20
comment The groupoid of algebraic expressions and proofs
@AndrejBauer, well the path category of a quiver is associative precisely because the domain of the forgetful functor $\mathbf{Cat} \rightarrow \mathbf{Quiv}$ is $\mathbf{Cat}$. It should be the same thing here; by choosing an appropriate forgetful functor, with the correct domain, its left adjoint should build an associative structure "automatically".
Feb
16
comment How have mathematicians been raised?
Step 0. Don't force them to do math. Ever. Step 1. Tell them interesting puzzles at their current level of development. Step 2. Set up somewhere to lie outside, so they can gaze up at the heavens, and wonder. To quote Atiyah: "In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life." Step 4. Don't force them to do math. Ever.
Feb
15
comment The groupoid of algebraic expressions and proofs
@PaulTaylor, now if you can see a way of describe the construction of interest by abstracting the concept "Lawvere theory" and considering "Lawvere theory objects in a $2$-category $\mathbf{C}$ with sufficient structure", and then choosing $\mathbf{C}$ carefully to explain the construction of interest, well this would be very interesting. I cannot currently see how to do this, however, and your answer offers absolutely no hints or suggestions in this direction.
Feb
15
comment The groupoid of algebraic expressions and proofs
@PaulTaylor, you misunderstand me. I would very much like to be able to view this as a special case of a more fundamental construction, perhaps the left-adjoint to some $2$-functor or some such. Nonetheless, the point remains that this groupoid-like-object is not a Lawvere theory in the usual sense of the word, and it cannot be recovered from the Lawvere theory. The act of passing from the presentation to the Lawvere theory throws away too much information, and we can't recover the groupoid of interest.
Feb
13
comment The groupoid of algebraic expressions and proofs
Interesting. There's definitely a strong connection there.
Feb
13
comment The groupoid of algebraic expressions and proofs
@TheMaskedAvenger, do you mean absolutely free algebra?
Feb
13
accepted Has this construction, which builds a symmetric multicategory from a commutative monoid, been described or studied anywhere, and if so, where?
Feb
13
asked The groupoid of algebraic expressions and proofs
Feb
6
comment Which mathematicians have influenced you the most?
@GerryMyerson, we can be both. :)
Feb
6
comment Which mathematicians have influenced you the most?
@IgorRivin, why did s/he say that?
Jan
23
comment Proofs without words
Also, I am afraid you have misunderstood me. If I were to post a truth-tree for some logical tautology, well that would be a literal example of a "proof without words"; but, you would surely reject it as a non-example. Hence what you really mean is not "proof without words" but "proof without logic."
Jan
23
comment Proofs without words
@MarianoSuárez-Alvarez, oh the concept is well-known alright; these useless so-called "proofs without words" are all over YouTube, usually paired with a lot of downvotes, and rightly so. Its sad that so much effort went into discovering these beautiful arguments, and then producing pictures and even animations to illustrate the idea, only to have all that hard work spoilt by this proof without words nonsense. How much better those so-called "proofs" would have been with a few premises, some inferences, and a conclusion.
Jan
23
comment Proofs without words
There is no such thing as a "proof without logic," and since words are usually the best tool for conveying logical relations, I'm going to have to reject the idea of "proof without words." Sorry, -1.