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### 17 Cards in this Set

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 What is logic? The study of the principles of reason. It’s the study of valid argumentation. What is the difference between Argument and Argument Forms? Validity is a matter of an argument’s form. An argument is valid just in case it’s an instance of a valid argument form. An argument form is valid just in case there are no instances of that form with all true premises and a false conclusion. The form of an argument is distinct from the content of the argument. How do we differentiate Truth from Validity? ‘Valid’ does not mean ‘true’! Notice that there are: Valid arguments with false premises and conclusions. Invalid arguments with true premises and conclusions. The only thing we can’t have is: A valid argument with all true premises and a false conclusion. What is a declarative sentence? Sentences that are definitely true or false. We want them to be sentences that are independent of context. We want to exclude the following: Mary is taller (taller than who?) He's bald. This is a bat. Explain the conditional sentential operator.  If ‘p’and ‘q’represent statements, we can use ‘p q’to represent the conditional with ‘p’as antecedent and ‘q’as consequent.  Example: ‘If there’s music playing, then Mary will dance’ can be represented as ‘p q’  If ‘p’and ‘q’represent statements, we can use ‘p q’to represent their biconditional  Example: ‘Mary dances if and only if John dances’ can be represented as ‘p q’ What makes a sentence compound? It is composed of at least two simple statements. What are schemata? Schemata are what we get once we replace statements and connectives with their respective symbols. Examples:  ‘p v q’  ‘p q’ What are statement operators? Our 5 operators are a species of statement operators. A statement operator is an expression containing one or more blanks such that when the blanks are filled in with sentences, the result is a sentence. Examples:  Xavier believes that p. (= Xavier believes that _______ )  It is possible that q.  If p, then q.  p and q.  Neither p nor q nor r nor s. Describe the inclusive versus exclusive instances of "or": It is important to keep in mind that the word ‘or’has two meanings.  It can mean ‘one or the other’or ‘both’, which is called the inclusivesense.  E.g. ‘You’ll lose weight, if you exercise enough or go on a strict diet.’ But ‘or’can also mean ‘either but not both’, which is called the exclusive sense of ‘or’.  E.g. ‘Steve will graduate either in 2012 or 2013.’ What are some of the words to look out for that mean "conjunction" ? Other words and phrases to look out for: however, nevertheless, still, although, even though, also, and also, not only…but also, while, despite (the fact that), moreover (see Klenk, p.56).  Some expressions can’tbe symbolized by conjunction: because, and then, and so. What are some words to look out for that signify conditional? provided that, supposing that, on the condition that, given that, in the event that. (see Klenk, p.60) What is contradiction? Contradiction: schema which is false under every interpretation of its sentence letters.  ‘p~p’  ‘The Canucks will win tonight, and the Canucks won’t win tonight.’ What is tautology? Tautology: schema which is true under every interpretation of its sentence letters.  ‘p~p’  ‘Either the Canucks will win tonight or they won’t’ What is contingency? 3. Contingency: schema which is true under some interpretations of its sentence letters, and false for others.  ‘p’  ‘the Canucks will win tonight’ What is a valid schema?  We’ll say that a schema is valid if it’s ‘true under all interpretations’  Thus, all tautologies are valid in this sense.  (but, as we’ll see later, there are valid schemata that aren’t tautologies)  Don’t confuse valid schemata with valid arguments! What is an unsatisfiable schema?  We’ll say that a schema is unsatisfiable if it’s ‘false under all interpretations’  Thus, all contradictions are unsatisifiable.  (but, as we’ll see later, there are unsatisfiable schemata that aren’t contradictions) What is a satisfiable schema?  We’ll say that a schema is satisfiable if it’s ‘true under at least one interpretation.’  Thus, all contingencies are satisfiable.  So are all tautologies!