Lecture 2: Language of logic, truth tables
... • On a mystical island, there are two kinds of people: knights and knaves. Knights always tell the truth. Knaves always lie. • Puzzle 1: You meet two people on the island, Arnold and Bob. Arnold says “Either I am a knave, or Bob is a knight”. Is Arnold a knight or a knave? What about Bob? ...
... • On a mystical island, there are two kinds of people: knights and knaves. Knights always tell the truth. Knaves always lie. • Puzzle 1: You meet two people on the island, Arnold and Bob. Arnold says “Either I am a knave, or Bob is a knight”. Is Arnold a knight or a knave? What about Bob? ...
Chapter 1
... Solution. We let P be the statement “we play the part”, and Q be the statement “there are four trombones.” Then P only if Q is equivalent to if P , then Q. That is, if we play, P is true, then Q must be true. However, if Q is true, then the truth value of P does not matter, the connective statement ...
... Solution. We let P be the statement “we play the part”, and Q be the statement “there are four trombones.” Then P only if Q is equivalent to if P , then Q. That is, if we play, P is true, then Q must be true. However, if Q is true, then the truth value of P does not matter, the connective statement ...
Quine. “Two Dogmas of Empiricism” - University of San Diego Home
... Ontological questions…are on a par with questions of natural science…the issue over there being classes seems more a question of convenient conceptual scheme; the issue over there being centaurs, or brick houses on Elm Street, seems more a question of fact. But I have been urging that this differenc ...
... Ontological questions…are on a par with questions of natural science…the issue over there being classes seems more a question of convenient conceptual scheme; the issue over there being centaurs, or brick houses on Elm Street, seems more a question of fact. But I have been urging that this differenc ...
Beautifying Gödel - Department of Computer Science
... We need a symbol for “antitheorem” for the same reason that boolean algebra needs symbols for both “true” and “false”, and indeed “true” and “false” are a primitive theorem and antitheorem respectively. We also need symbols for “or”, “and”, “not”, “if and only if”, and quantifiers, as seen by our ex ...
... We need a symbol for “antitheorem” for the same reason that boolean algebra needs symbols for both “true” and “false”, and indeed “true” and “false” are a primitive theorem and antitheorem respectively. We also need symbols for “or”, “and”, “not”, “if and only if”, and quantifiers, as seen by our ex ...
http://pine.kuee.kyoto-u.ac.jp/member/kaufmann/ Draft
... Aristotle (On Interpretation 1:9) noted that the past is “fixed” in a way in which the future is not. Whatever has been, cannot (now) have been otherwise. Consequently, any statement about past facts is unequivocally true or false, regardless of whether its truth value is known or not. The same is n ...
... Aristotle (On Interpretation 1:9) noted that the past is “fixed” in a way in which the future is not. Whatever has been, cannot (now) have been otherwise. Consequently, any statement about past facts is unequivocally true or false, regardless of whether its truth value is known or not. The same is n ...
Chapter 1 Elementary Number Theory
... This is false and can be shown by solving the equation x2 = 25 Implication statements are often called “if…then..” statements but the notation for this is to use the implication symbol “”. Example 1 becomes x 5 2 x 10 Example 2 becomes x 2 25 x 5 ...
... This is false and can be shown by solving the equation x2 = 25 Implication statements are often called “if…then..” statements but the notation for this is to use the implication symbol “”. Example 1 becomes x 5 2 x 10 Example 2 becomes x 2 25 x 5 ...
Ch.2 Propositional Logic
... And now we come to the great question as to why. Robbery has not been the object of the murder, for nothing was taken. Was it politics, then, or was it a woman? That is the question which confronted me. I was inclined from the first to the latter supposition. Political assassins are only too glad to ...
... And now we come to the great question as to why. Robbery has not been the object of the murder, for nothing was taken. Was it politics, then, or was it a woman? That is the question which confronted me. I was inclined from the first to the latter supposition. Political assassins are only too glad to ...
Discrete Mathematics
... A propositional variable (lowercase letters p, q, r) is a proposition. These variables model true/false statements. The negation of a proposition P, written ¬ P, is a proposition. The conjunction (and) of two propositions, written P ∧ Q, is a proposition. The disjunction (or) of two propositions, wr ...
... A propositional variable (lowercase letters p, q, r) is a proposition. These variables model true/false statements. The negation of a proposition P, written ¬ P, is a proposition. The conjunction (and) of two propositions, written P ∧ Q, is a proposition. The disjunction (or) of two propositions, wr ...
introphil_Week 4 – Morality: Objective, Relative or
... of things that can be true or false, and what makes them true or false are facts that are generally independent of who we are or what cultural groups we belong to – they are objective moral facts. ...
... of things that can be true or false, and what makes them true or false are facts that are generally independent of who we are or what cultural groups we belong to – they are objective moral facts. ...
