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  1. 1. september 5
  2. 2. logic <ul><li>focuses on the structure of arguments </li></ul><ul><li>made up of premises and a conclusion </li></ul><ul><ul><li>premises are propositions </li></ul></ul><ul><li>most common arguments are deductive and inductive </li></ul>
  3. 3. important terms for deductive arguments <ul><li>valid </li></ul><ul><ul><li>a valid argument is one that preserves truth </li></ul></ul><ul><ul><li>an argument is valid if it follows the correct form </li></ul></ul><ul><ul><li>if premises are true then conclusion necessarily is true </li></ul></ul><ul><ul><li>an argument need not have true premises to be valid – it is about the form of the argument, not the truth </li></ul></ul>
  4. 4. continued: <ul><li>sound </li></ul><ul><ul><li>an argument is sound if the premises are true and the argument is valid </li></ul></ul><ul><ul><li>if any premise is untrue, an argument is unsound </li></ul></ul><ul><ul><li>you cannot tell the soundness of an argument by examining the symbolic form; one must know the content of the actual propositions in order to determine soundness </li></ul></ul>
  5. 5. deductive arguments <ul><li>syllogism </li></ul><ul><ul><li>all syllogisms have three parts </li></ul></ul><ul><ul><ul><li>major premise – contains major term which is the predicate of the conclusion </li></ul></ul></ul><ul><ul><ul><li>minor premise – contains the minor term which is the subject of the conclusion </li></ul></ul></ul><ul><ul><ul><li>conclusion </li></ul></ul></ul><ul><ul><li>premises have one term in common called the “middle term” </li></ul></ul>
  6. 6. continued: <ul><li>modus ponens (affirming the antecedent) </li></ul><ul><ul><li>starts with an “if-then” statement, a conditional claim </li></ul></ul><ul><ul><li>works such that if the first proposition is true, the consequent must also be true </li></ul></ul><ul><ul><li>if P, then Q </li></ul></ul><ul><ul><li>P. </li></ul></ul><ul><ul><li>therefore, Q. </li></ul></ul>
  7. 7. continued: <ul><li>modus tollens (denying the consequent) </li></ul><ul><ul><li>starts with a conditional claim </li></ul></ul><ul><ul><li>works such that if the consequent claim is untrue, the prior claim cannot be true </li></ul></ul><ul><ul><li>if P, then Q. </li></ul></ul><ul><ul><li>not Q. </li></ul></ul><ul><ul><li>therefore, not P. </li></ul></ul>
  8. 8. continued: <ul><li>disjunctive syllogism </li></ul><ul><ul><li>we are told that one proposition or the other is true </li></ul></ul><ul><ul><li>we are then told that one of the propositions is untrue </li></ul></ul><ul><ul><li>we can then infer that the other must be true </li></ul></ul><ul><ul><li>P or Q. </li></ul></ul><ul><ul><li>not P. </li></ul></ul><ul><ul><li>therefore, Q. </li></ul></ul>
  9. 9. continued: <ul><li>reductio ad absurdum (reducing to a contradiction) </li></ul><ul><ul><li>assume A </li></ul></ul><ul><ul><li>logically deduce a contradiction from A </li></ul></ul><ul><ul><li>this shows A must be false; therefore, not-A must be true </li></ul></ul>
  10. 10. important terms for inductive reasoning <ul><li>strong/weak </li></ul><ul><ul><li>if evidence is substantial then argument is strong </li></ul></ul><ul><ul><li>if evidence is not substantial then argument is weak </li></ul></ul><ul><ul><li>determination often comes down to number of premises in the argument </li></ul></ul>
  11. 11. continued: <ul><li>cogent/implausible </li></ul><ul><ul><li>if argument is strong and the premises are true then the argument is cogent </li></ul></ul><ul><ul><li>if the argument is weak or the premises are false then the argument is implausible </li></ul></ul><ul><ul><li>just as something can be “more probable” so can there be degrees of cogency; there is no firm standard </li></ul></ul>
  12. 12. inductive arguments <ul><li>unlike deductive arguments inductive arguments do not guarantee truth; inductive arguments only deliver probability </li></ul><ul><li>inductive arguments rely on experience </li></ul><ul><li>we often have good reasons for believing inductive arguments (uniformity of nature is a good example), and, indeed, such are necessary just to get by in the world </li></ul><ul><li>inductive arguments are dangerous in that they do not guarantee truth. hence, we are subject to make mistakes and get wrong conclusions anytime we use them </li></ul>
  13. 13. abductive arguments <ul><li>reasoning to the best explanation of the facts </li></ul><ul><li>does not guarantee truth </li></ul><ul><li>unlike induction it does not rely on a building up of facts to demonstrate probability </li></ul><ul><li>offers up hypothetical explanation of the facts and attempts to discover if such holds up to deep scrutiny </li></ul><ul><li>the building of theory in science is primarily abductive </li></ul>
  14. 14. fallacies <ul><li>ad hominem (against the man) </li></ul><ul><li>argument from authority </li></ul><ul><li>begging the question </li></ul><ul><li>argument from ignorance </li></ul><ul><li>false dilemma </li></ul><ul><li>slippery slope </li></ul><ul><li>straw man </li></ul><ul><li>genetic fallacy </li></ul><ul><li>inconsistency </li></ul>
  15. 15. necessary and sufficient conditions <ul><li>a necessary condition is one that must be satisfied for the result to happen </li></ul><ul><ul><li>having your eyes open is a necessary condition for reading, but it is not sufficient; you can have your eyes open and not read </li></ul></ul><ul><li>a sufficient condition is one that, if it is satisfied, the result is certain to happen </li></ul><ul><ul><li>reading is sufficient for showing your eyes are open, but it is not necessary; you can have your eyes open and not be reading </li></ul></ul>