Logic and Reason

Deductive Reasoning Reasoning that moves from the general to the particular Watchdogs bark at strangers. The watchdog did not bark at the thief The thief was not a stranger! A syllogism consists of  Two premises and a conclusion  Three terms, each which occurs twice  Quantifiers, such as “all” or “some” or “no”

Truth and Validity Truth is concerned with what is the case, validity is concerned with whether conclusions follow from premises; truth is a property of statements, validity is a property of arguments. All ostriches are teachers Mr. Valaitis is an ostrich Therefore, Mr. Valaitis is a teacher

Deductive Validity An argument is deductively valid if the truth of the reasons absolutely guarantee the truth of its conclusion; if the reasons are true, the conclusion must be true, there are no other possibilities.

The Liar Paradox Suppose Epimenides of crete says to you “Cretans” are always liars.” Is that true or false? (Epimenides by plato, c. 500 B.C.)

Inductive Reasoning Reasoning that goes from the particular to the general Inductive inferences are generalizations from observations. All arguments consist of reasons and inferences. Inferences are the “moves” we make from reasons to conclusions. When I drop a ball it will fall The sun will rise tomorrow morning

Inductive Inference Women’s brains are on average smaller than men’s, therefore women are less intelligent than men.

Judging Inferences Test 1 - Could the reasons be true and the conclusion false at the same time? If so, then the inference fails. Test 2 - Are any of the reasons untrue or otherwise unacceptable? If so, then the inference fails.

Alternative Hypotheses Good thinkers learn to consider all logically possible hypotheses. Can the theory be shown to be open to counterexamples?

Summary A theory or an argument is defective if it entails a logical contradiction (deductive reasoning that is not valid), if its reasons or conclusions are untrue (inductive reasoning), or if it can be shown to be open to counterexamples.