1. READING #4 “DEDUCTIVE ARGUMENTS” By Robert FitzGibbons from Making educational decisions: an introduction to Philosophy of Education (New York & London: Harcourt, Brace Jonanovich, Inc., 1991)

2. Logic: (See earlier definition provided on handout) The branch of philosophy that is concerned with identifying how well certain reasons function as evidence for particular beliefs. P. 53 “[A]n argument is a set of propositions, in which some of the propositions, the premises, are offered in evidential support of another of the propositions, the conclusion.” ┌ l P 1 ╗ l P 2 ║ l. ► premises = reasons = evidence l. ║ l P n ╝ ------ l C } Conclusion ∟

3. - P. 54 “The conclusion of an argument is that proposition whose truth the argument is intended to prove or confirm. And the premises of an argument are the reasons that are offered in evidential support of the conclusion.” -“In any argument, the number of premises is finite … However, while an argument may have any number of premises, it can have only one conclusion.” -The schema (how premises and conclusion are arranged) is useful in analyzing arguments. Note: → not all arguments are arranged in such a neat and orderly way → conclusion can come 1 st, or midway through premises - P.55A proposition is a premise in an argument when it serves as a reason for some other proposition, the conclusion. Likewise, a proposition is a conclusion only when other propositions, the premises, function as reasons for it.

4. Deductive vs. Inductive Arguments Deductive arguments: -process of reasoning by which we arrive at the necessary consequences (conclusions), starting from admitted or established premises -only relative to a particular system of axioms and rules of inference -they prove or guarantee the truth of a conclusion, when (a.) all premises are true, and (b.) its form is valid. Inductive arguments: -inferences whereby the the claim made by the conclusion goes beyond the claim jointly made by the premises (ex. Arguments by analogy, predictive inferences, inferences to causes by signs and symptoms, confirmation of scientific laws and theories, etc.) -at best, they confirm conclusions to a high degree; never guarantee with certainty

5. Note the two common misconceptions about the difference between deductive and inductive arguments. (P. 57) -both argument types depend on the premises to establish the conclusion -the generality or specificity of the premises or conclusions are irrelevant Two conditions necessary for an argument's successful disclosure of the truth of its conclusion: 1.conclusion must actually be true 2.premises must be related to the conclusion in a way that proves its truth (P. 56)

6. FORM Content:the particular propositions that comprise the premises and the conclusion of an argument Form:the logical relationship between the premises and the conclusion Argument 1 P 1 :If Deb wants to become a physicist, then she must learn calculus. P 2 :Deb wants to become a physicist. ________________________________ C :She must learn calculus. Argument Form A if p, then q. p _________ q Propositional variables

7. VALIDITY VS. INVALIDITY P. 59- 60“In deductive arguments the premises are related to the conclusion in such a way that if the premises are true, the conclusion must necessarily be true. In other words, the forms of these arguments absolutely guarantee that their conclusions are true. For this reason, deductive arguments are often called valid arguments. A valid argument is any argument that has a valid form. An argument has a valid form if and only if it is impossible, given that form, to have all true premises and a false conclusion. In other words, if it has all true premises and a valid form, an argument proves with absolute conclusiveness the truth of its conclusion” The previous Argument Form A is a valid argument form, called 'Affirming the Antecedent'. If – clause : antecedent (p) then – clause:consequent (q)

8. Argument 2 P 1 :If I live in Paradise, then I live in Newfoundland. P 2 :I live in Newfoundland. ________________________________ C :I live in Paradise. Argument Form B if p, then q. q _________ p This argument form is called 'Affirming the Consequent', and it is an invalid form – all premises and conclusions may in fact be true, but the form is invalid, as the ordering does not imply the conclusion. P. 62 “One way to show that an argument is invalid is to first identify the form of the argument and then identify another argument having the same form and also having obviously true premises and an obviously false conclusion. Such an argument is called a “counter-example”. If you can identify one counter-example for a given argument form, you will have shown that form [and any argument having that form] to be invalid.”

9. Argument 3 P 1 :If I live in Paradise, then I live in Newfoundland. P 2 :I do not live in Newfoundland. ________________________________ C :I do not live in Paradise. Argument Form C if p, then q. not ~ q _________ not ~ p This argument form is called 'Denying the Consequent', and it is an valid form. Therefore, any argument having this form, and true premises, must have (guarantees) a true conclusion.

10. Argument 4 P 1 :If Einstein was a biologist, then he was a scientist. P 2 :Einstein was not a biologist. ________________________________ C :He was not a scientist. Argument Form D if p, then q. not ~ p _________ not ~ q This argument form is called 'Denying the Antecedent', and it is an invalid form. P. 63-64 “Any argument, then, is either valid or invalid. And whether it is valid or not depends exclusively upon its form. If the form … is such that it is impossible for any argument having that form to have all true premises and a false conclusion, then the argument is a valid argument. [However,] if the form … is such that it is possible for even one argument having that form to have all true premises and a false conclusion, then the argument is an invalid argument.”

11. VALIDITY & FORM Argument 5 All teachers are intelligent people. All intelligent people are logical. --------------------------------------------- All teachers are logical. (class variables) All X is Y. All Y is Z. -------------- All X is Z. X → Y Y → Z --------- (transitive X → Z property) Premises All logical people All intelligent people All teachers Conclusion All teachers All logical people

12. If the premises are true, then the conclusion must necessarily be true – thus, it is a valid argument. “The validity of this argument does not depend upon whether all teachers are actually intelligent or upon whether all intelligent people are logical. The truth of the premises is inconsequential. Rather, the validity of the argument … depends only on the logical relationship between its premises and conclusion, that is, on its form.” (P. 67)