A Crash Course in Logic 80-100: Introduction to Philosophy May 19, 2009 Instructor:Karin Howe Carnegie Mellon University

Some important definitions statement or proposition argument conclusion premises valid invalid sound unsound

Statement or proposition Working definition: a statement is a sentence that is either true or false. Examples: I like cats. Papa John's makes better pizza. If today is Tuesday, then tomorrow is Wednesday You may have either an apple or an orange for a snack.

Sentences that are not statements Shut the door! Is the door open? Ouch! Important Final Note! - Statements are true or false. It makes no sense to say “The statement (premise) is valid,” or “The statement (premise) is sound.” The terms valid and sound refer ONLY to arguments.

Arguments An argument is a set of statements, one of which (the conclusion) supposedly follows from the others (the premises). Arguments are attempts to prove the truth of a claim (the conclusion) on the basis of other claims (the premises). Arguments are attempts to convince you of something; namely to convince you to accept a conclusion based on your acceptance of the premises.

The Kangaroo Argument All kangaroos can fly. Jim is a kangaroo. _____________________ Therefore, Jim can fly.

Evaluating arguments All arguments have two different features that must be separately evaluated: form and content: The evaluation of the form of an FORM argument asks whether the conclusion follows from the premises. The evaluation of the content of CONTENT an argument asks whether all of the premises are true.

FORM: validity vs. invalidity A valid argument is one having the form such that it is impossible that all of its premises are true and its conclusion false. An invalid argument is one having the form such that it is possible that all of its premises are true, and yet the conclusion is false.

Recall the Kangaroo Argument All kangaroos can fly. Jim is a kangaroo. _____________________ Therefore, Jim can fly.

True Fact: 97% of all questions about validity can be answered by thinking about kangaroos. :-D

Content: soundness vs. unsoundness An argument is sound if and only if (iff): it is valid and has all true premises. An argument is unsound if and only if (iff): it is either invalid, or has one or more false premises. Quick Quiz: Kangaroo Argument -- sound or unsound?

Mapping Arguments A Quick How-to Guide

Steps 1 and 2: Finding Premise and Conclusion Indicators Premise Indicators: since however but (at the beginning of a sentence) and (at the beginning of a sentence) for Conclusion Indicators therefore thus hence so consequently it follows (that) which goes to show (that)

Identifying premises and conclusions Step 3: Identify the conclusion and subconclusion(s), if there are any Step 4: Identify the explicit premises

Step 5: Break the argument down into separate statements A word of caution: There are some statements you can, and should break, and others which you should not break! Statements you should break: Sentences that contain both a premise and a subconclusion or conclusion, joined by either a premise indicator or a conclusion indicator "And" statements (conjunctions) Statements you should never break: "Or" statements (disjunctions) "If then" statements (conditionals)

Step 6: Rewrite the statements Remove (or incorporate) parentheticals Remove any premise or conclusion indicators Standardize concepts Write statements in "standard form."

Rewriting statements in standard form If Marvin stays, then Nancy leaves The statement following the word 'if' (or its synonym 'provided that') is the antecedent; accordingly, the statement that follows the word 'if' is placed before the statement following the word 'then' (which is the consequent).

Conditionals are tricksy fellas… Necessary Conditions – P is a necessary condition for Q – Rewritten as: If Q, then P – Mnemonic: neceSSary conditions come second Sufficient Conditions P is a sufficient condition for Q Rewritten as: If P, then Q Mnemonic: suFFicient conditions come first "only if" P only if Q "unless" P unless Q Rewritten as: If not Q, then P

Some Examples 1. The Heat makes it to the playoffs only if the Hawks lose to the Cavs. 2. Your having a quiz average over 90 is a sufficient condition for being excused from the final. 3. The settlement of the west could only take place if the Indian barrier were removed. 4. Hannah could save her company if only the president would promote her. 5. Aquinas thought that the fact that the intellect is under the control of the will is a necessary condition for the existence of intellectual virtues. 6. “Now we shall have duck eggs, unless it is a drake.”

Step 7: Map the Argument Finally!! Let's practice! :-)

My Three Sons Man 1: Yes, I’m married and have three fine sons. Man 2: That’s wonderful! How old are they? Man 1: Well, the product of their ages is equal to 36. Man 2: Hmm. That doesn’t tell me enough. Give me another clue. Man 1: O.K. The sum of their ages is the number on that building across the street. Man 2: Ah ha! I’ve almost got the answer, but I still need another clue. Man 1: Very well. The oldest one has red hair. Man 2: I’ve got it!