Sumários
Frege
23 Outubro 2024, 14:00 • Ricardo Santos
Basic Notions: The
aim of elucidating meaning; referential theory of meaning; why meaning relates
to truth. Overview of Frege's semantic theory: functional analysis and its
applications to logical connectives, predicates and quantifiers.
Frege's semantic theory: compositionality and substitutivity; the
distinction between sense and reference; puzzles
about proper names.
Vagueness and the sorites: supervaluations
16 Outubro 2024, 14:00 • Ricardo Santos
The supervaluationist theory of vagueness. Vagueness as semantic indecision and the notion of admissible precisifications. Two semantic levels: valuations and supervaluation. Truth as supertruth. Truth-value gaps without truth-functionality. Penumbral connections. Distinction between excluded middle and bivalence. Diagnosing the sorites: a peculiar way of denying the inductive premise. Preserving classical logic. Higher-order vagueness. Introducing a ‘definitely’ operator. Adopting a vague metalanguage.
Vagueness and the sorites: fuzzy logic
9 Outubro 2024, 14:00 • Ricardo Santos
Three features
associated with vagueness: borderline cases, lack of sharp boundaries and
susceptibility to versions of the sorites paradox. Preliminary analysis of the
sorites. The implausibility of denying the inductive premise: it posits a sharp
boundary. Rejecting bivalence as a way of rejecting a proposition without accepting
its negation. Three-valued logic: a new semantics for the connectives. Options
for defining validity. Diagnosing the sorites but still positing sharp
boundaries. Degrees of truth and fuzzy logic. Generalizing the three-valued semantics.
The validity of modus ponens (as preservation of perfect truth). Diagnosing the
sorites but facing troubles with degree-functionality.
Conditionals: from the material conditional to Stalnaker’s semantics
2 Outubro 2024, 14:00 • Ricardo Santos
Paradoxes of the material conditional. Counterexamples to some classical rules of inference. The proposal of a strict conditional (by C. I. Lewis). Apparent counterexamples to forms of inference that both classical logic and the logic of strict conditionals validate: hypothetical syllogism, strengthening the antecedent and contrapositions. Stalnaker’s conditional logic. Relations of similarity and distance between worlds (allowing one to define a function ‘the nearest world to w in which p is true’) and the truth conditions for the conditional: the consequent is true in the nearest possible world in which the antecedent is true.
Modal logic
25 Setembro 2024, 14:00 • Ricardo Santos
An introduction to modal logic. Adding to modal operators (box and diamond) to the formal language. Exercises of formalization. Iteration of modal operators. Non-truth-functionality. Possible worlds semantics. Necessary truth as truth in every possible world; possible truth as truth in at least one world. Accessibility relations between worlds and the notion of relative possibility. Characteristic theorems of the main logical systems.