TrevTutor
This video provides an overview of propositional logic for linguists, focusing on the modeling of truth values for declarative sentences and complex propositions. Simple propositions can be combined into well-formed formulas using logical operators such as negation, conjunction, disjunction, and conditional, and each proposition can be classified as a tautology, contradiction, or contingency based on its truth value. The speaker notes that understanding propositional logic is essential for truth conditional lexical semantics in linguistics.
In this section, the concept of propositional logic and truth values are explained. Propositional logic focuses on modeling the truth of declarative sentences or complex sentences formed of declaratives. A proposition is a sentence that can be true or false, and not questions or commands. Truth values are denoted by putting double brackets around propositions - one means true, and zero means false. Simple propositions can be combined into more complex propositions called well-formed formulas (woofs). Negation is a way to negate a proposition, and conjunction requires two propositions. The truth table shows all possible combinations of truth for each proposition and their resulting truth values when combined.
In this section, the video explains three logical operators: conjunction, disjunction, and conditional. The conjunction works with two propositions and is only true if both are true. The disjunction is true if at least one proposition is true, and the conditional is true in every case but when the antecedent is true and the consequent is false. The video also explains that a well-formed formula can be classified as a tautology, contradiction, or contingency depending on its truth value.
In this section, the speaker explains the concepts of contradictions and tautologies in propositional logic, which refer to sentences that are always false and always true, respectively. These statements are often meaningless in real life, such as saying "it is what it is," or "I'm mad or I'm not mad." However, they can be used metaphorically, such as saying "I'm 20 but I have the heart of someone who's not 20." The speaker concludes by saying this quick introduction to propositional logic is enough to understand truth conditional lexical semantics, and welcomes any questions in the comment section.
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