David C. Norris 🇺🇦Oct 6

Reading Feferman & Feferman 'Alfred Tarski: life and logic', I've come across this passage (p.79) that I hope a logician would explain a bit further:

"Russell had found a fundamental inconsistency in Frege's system; to avoid contradictions and repair the program, in Principia Mathematica he introduced complicated restrictions on the form of its basic principles."
[it's this next sentence that provokes my Q:]
"But mathematics could no longer be reduced to logic when restricted in that way and so, to make up for the loss, Russell added some assumptions that were not clearly logical. This step then raised the question of whether Russell's repair of Frege's system could still be counted as fulfilling the logicist program; Russell, optimistically, believed that it did."
#Tarski #Russell #PrincipiaMathematica

Doctor LogicJan 19, 2023
#logic people -- a student asked me whether #Tarski was a normativist when it comes to logic, and tbh, I am not familiar enough with Tarski to answer this. Anyone got any reading recs I can pass on?
xameerJul 9, 2021
S4 and S5 are models of interior algebra, a proper extension of Boolean algebra originally designed to capture the properties of the interior and closure operators of topology #tarski
xameerApr 18, 2021
Geometry is modular #tarski
As in you can define primitives p and define all other points P in space in terms of p. Than you can have a scheme to take a subset p' of P and connect them to obtain any shape, so it gets self-similar #recurring or #recursive at times eg #fractals
xameerFeb 2, 2021
- #Banach– #Tarski paradox is neither provable nor disprovable from ZF alone: it is impossible to construct the required decomposition of the unit ball in ZF, but also impossible to prove there is no such decomposition.
xameerJan 31, 2021
“ #deductive system” as a set of sentences closed under consequence .
One way for defining notion of consequence is Alfred #Tarski's algebraic approach
xameerJan 10, 2021
#Program semantics described w fixed points w loops or #recursive proc
Say L is a complete lattice, f be a monotonic function from L into L. Then, any x′ st f(x′) ≤ x′ is an abstraction of the least fixed-point of f, which exists, according to the Knaster– #Tarski theorem.
xameerNov 18, 2020
finitary closure operators are still studied under the name consequence operator, which was coined by #Tarski. The set S represents a set of sentences, a subset T of S a theory, and cl(T) is the set of all sentences that follow from the theory.
xameerNov 18, 2020
finitary closure operators are still studied under the name consequence operator, which was coined by #Tarski. The set S represents a set of sentences, a subset T of S a theory, and cl(T) is the set of all sentences that follow from the theory.