PHL245H1 Lecture Notes - Propositional Calculus, Finite Model Theory, Cn Tower
Document Summary
In sentential logic, we can give meaning to symbolic sentences through truth-value analysis. If we know what makes it true, then we know what it means! By taking the truth-value of an atomic component as its semantic value, we can determine the truth-value of any complex sentence from the truth-values of its components. The truth-table provides the truth-value of the sentence on every possible truth-value assignment for a sentence. Thus, given any particular truth-value assignment, we can determine the truth-value of the sentence. Some sentences (tautologies) are true on any truth-value assignment. Other sentences (contradictions) are false on any truth-value assignment. But most sentences were true on some truth-value assignments and false on others (contingent sentences). In predicate logic, we are not dealing merely with the truth-valuable relations between atomic sentences rather we are concerned with the relation of subsentential components. We need to consider whether predicates are true of the individual members of a potentially infinite universe.
