basic constructions:
strong axioms
further
(0,1)-category theory: logic, order theory
proset, partially ordered set (directed set, total order, linear order)
distributive lattice, completely distributive lattice, canonical extension
natural deduction metalanguage, practical foundations
type theory (dependent, intensional, observational type theory, homotopy type theory)
computational trinitarianism = propositions as types +programs as proofs +relation type theory/category theory
This page collects links related to
The Blind Spot: Lectures on Logic
European Mathematical Society 2011
on formal logic and its categorical semantics with an emphasis on linear logic and in fact on some kind of quantum logic (section 17), but emphatically not in the old sense of Birkhoff-vonNeumann.
from p. xii:
Among the magisterial mistakes of logic, one will first mention quantum logic, whose ridiculousness can only be ascribed to a feeling of superiority of the language – and ideas, even bad, as soon as they take a written form – over the physical world. Quantum logic is indeed a sort of punishment inflicted on nature, guilty of not yielding to the prejudices of logicians… just like Xerxes had the Hellespont – which had destroyed a boat bridge – whipped.
from p. xiii:
The blind spot is what one does not see and what one is not even conscious of not seeing. The most trivial blind spot is the cheap modal logic justified by an even cheaper Kripke semantics and vice versa; but one finds similar blindings in the most elaborated interpretations. The good news of these lectures is that the procedural standpoint seems to be capable of dislodging the unsaid, the unseen. Simply, while the absence of Hauptsatz is enough to show that logic S5 is nonsense, one has to work much more to imagine what could be wrong in the principles justifying – say – the function $2^n$.
Last revised on December 2, 2019 at 04:20:05. See the history of this page for a list of all contributions to it.