"Maybe the real analytic philosophy was the friends we made along the way".

"A ban on the word ‘exist’ in philosophy would be salutary"

Timothy Williamson

"It really is a nice theory. The only defect I think it has is probably common to all philosophical theories. It's wrong."

Saul Kripke

haha
n-word

haha
Trakhtenbrot

Trakhtenbrot's theorem

This point was implicit in the original critique of the denoscription theory of names. The rejection of the internalist picture was not a rejection of the idea that reference was determined by the speaker's intentions and beliefs: rather it was the rejection of the assumption that intentions and beliefs need to be explained in terms of the grasping of purely general concepts. In the sketches by direct reference theorists of an alternative account of reference, intentions played a prominent role, but it was assumed that intentions could be directed to particular individuals, and need not be explained in terms of a purely conceptual content. A causal theory of reference was not a theory that explained reference independently of intentions, but a theory that explained intentions in causal terms.
(с) Context and Content, Stalnaker

sigma set

Kohei Kishida, in Chapter 8, uses category theory to develop a model theory for modal logic by focusing on the familiar Stone duality. Specifically, he aims to bring together Kripke semantics, topological semantics, quantified modal logic, and Lewis’ counterpart theory by taking categorical principles as both mathematically and philosophically unifying.

-categories for whom?
-for the working philosopher.

For too long, philosophy has thought to constrain its interest in any current mathematical research largely to set theory, when it has long been evident that it offers little or nothing as far as many core areas of mathematics are concerned, and especially the mathematics needed for physics.

Метрическое пространство называется полным если в нем есть фундаментальная последовательность сводящаяся к элементу пространства, а иначе компактность множества R в степени n, которое как раз и является полным, можно определить как возможность определить для любой последовательности такую подпоследовательность, предел который является элементом множества. Замкнутость и ограниченность множества из R^n эквивалентно его компактности (а если для любого пространства, то необходима вполне ограниченность). При этом компактность в метрических пространствах определяется как то, что для покрытия метрического пространства из открытых множеств (шаров) существует конечное подпокрытие.