Outline of Lecture Basic Conceptual Tools We Need Sets Possible worldspossible situations Some basic notions of set theory Intuitively, a set is a collection of objects We wont give a precise definition of a set, though, but well assume the notion of a set to be a primitive, as we do with numbers You know how to use 1, 2, 3, etc., though it is hard to define them or define what a number is in general Core Semantic Data We want our theory to account for Truthconditionsvalues Truth values == truth conditions Synonymy Contradiction Contrariety: Ivano neither likes nor hates pasta, neither is true Entailment Goes in one direction All entailments must be true if the first sentence is true Set Theory Three ways of representing a set By defining the properties that all and only the members of that set shares: Example: {x: x is a natural number smaller or equal to 10} To be read: the set of individualsobjects x that are natural numbers smaller or equal to 10 By listing all the members of the set separated by comas and between curly brackets Example: {1, 2, 3, 4, 5, 6, 7, 8, 9 ,10} To be read: the set containing the individuals objects 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 By listening all the members of the set separated inside a closed line (Venn Diagram)

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