Sentence Relation and Truth

Sentence Relation and Truth

1. What is meaning?

   • A is Synonymous with B – A has the same meaning as B A. (My brother is a bachelor) B. (My brother has never been married)
     • A Entails B – We know that if A then automatically B A. (The anarchist assassinated the emperor) B. (The emperor is dead)
   • A Contradicts B – A is inconsistent with B A. (My brother Sebastian has just come from Rome) B. (My brother Sebastian has never been to Rome)
     • A Presupposes B – B is part of the assumed background against which is A is said A. (The Mayor of Manchester is a woman) B. (There is a Mayor in Manchester) A. (I regret stepping on your sandwich) B. (I stepped on your sandwich)
       • A is a Tautology – A is automatically true by virtue of its own meaning, but informationally empty A. (Ireland is Ireland) A. (Hungry people are hungry)
         • A is a Contradiction – A is inconsistent with itself, i.e. asserts and denies the same thing A. (He is a murderer but he’s never killed anyone) B. (Now is not now)

2. Modus Tollens: Aristotle’s valid argument to find logic in 3 steps A. If Natan is not in the bar, then he is in the lounge. B. Natan is not in the bar. C. Natan is in the lounge. “If A & B (called Premises) are true then C (the conclusion) is also guaranteed to be true.”

3. The truth is said to be empirical (or contingent) because we to have some access to the facts of the world to know whether a statement is true or not. My father was the first man to visit Mars (If the father did go to Mars and was the first man to do it then the sentence is true.

   • Truth Value – Is what semanticists call a sentence’s being true or false.
     • Truth Conditions – The facts that would have to be obtained in reality to the sentence true or false (Ex. If the father did go to Mars, or if he was the first man to visit Mars)
       • Logical Form – Logicians use a schema where a lower case letter (p, q, r, etc.) stands for statement and a special symbol for negation (¬). A. p B.¬p
         • Truth Effect on Negation (If A is true then B is false) A. Your car has been stolen. B. Your car has not been stolen.

4. Compound Statements A.The house is on fire B. The firefighters are on the way C. The house is on fire and the firefighters are on the way (If A and B are true, then the compound C is also true) use symbol ٨ to represent “and”

   • Propositional Logic – The study of the truth effects on connectives like ¬ and ٨. Truth Table using OR Disjunction (or alternatively inclusive or): A compound created with ˅ is true if one or both of the constituent sentences is true.  I’ll see you today or tomorrow
     • Exclusive or: only true if just one of its disjuncts is true.  You will pay the fine or you will go to jail.
       • Material Implication: Is only false when p (the antecedent) is true and q (the consequent) is false. (If…..Then)  If it rains, then I’ll go to the movies.