Natural Deduction Systems in Logic - Stanford Encyclopedia of Philosophy ‘Natural deduction’ also designates the type of reasoning that these logical systems embody, and it is the intuition of very many writers on the notion of meaning—meaning generally, but including in particular the meaning of the connectives behind active reasoning—that it is defined by the use of the expression And for logical expressions like connectives, a salient aspect of their
The Disjunctive Theory of Perception - Stanford Encyclopedia of Philosophy For in certain places he says that his Perception-Illusion disjunctions permit a description of what is seen in terms of how the thing looks, thereby allowing the following kind of Perception-Illusion disjunction: ‘ S sees something which looks blue or is having that illusion’ (1973, 61)
Supplement to The Development of Intuitionistic Logic 2 Mathematical interpretations and model-theoretic semantics Various mathematical interpretations (in the sense explained in section 1 2) of formalized intuitionistic logic and arithmetic have been proposed Above we saw Gödel’s translation of intuitionistic propositional logic into the classical modal logic S4 from 1933; further examples are Kleene’s realizability (Kleene 1945), and
Propositional Logic - Stanford Encyclopedia of Philosophy Propositional logic is the study of the meanings of, and the inferential relationships that hold among, sentences based on the role that a specific class of logical operators called the propositional connectives have in determining those sentences’ truth or assertability conditions As early as Aristotle it was observed that propositional connectives have a logical significance, and over
The Logic of Conditionals - Stanford Encyclopedia of Philosophy A related one is that it makes the conditional interdefinable with Boolean negation, disjunction, and conjunction A third, among the driving motivations for Frege, Russell and Whitehead, is that it appears adequate to regiment mathematical proofs involving conditional sentences