15 ideas
5035 | The two basics of reasoning are contradiction and sufficient reason [Leibniz] |
13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |
13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward] |
13850 | In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward] |
13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward] |
18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
13344 | X follows from sentences K iff every model of K also models X [Tarski] |
13851 | Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward] |
13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |
5038 | Assume that mind and body follow their own laws, but God has harmonised them [Leibniz] |
13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
5037 | God doesn't decide that Adam will sin, but that sinful Adam's existence is to be preferred [Leibniz] |