Phil 200 Exam 4 Review

Expressing Arguments in Standard Form

1) Express both of the premises and the conclusion in either A,E,I,O. 2) Form is: Major Premise(Predicate Term) Minor Premise (Subject Term)

Rules of Replacement for Ordinary Language

1) Only: "only P is Q" = "if its not P then its not Q" 2) The only: "The only P is Q" = "if its not Q then its not P" 3) Unless: "P unless Q" = "If not Q then P" 4) Sufficient: "P is sufficient for Q" = "If P then Q" 5) Necessary: "P is necessary for Q" = "If not P then not Q" 6) "The Evers" (whatever, whenever, etc.): "Whenever P is Q" = "If P then Q" 7) Negations: a) P is never Q= No P is Q; If P then not Q b) Not all P is Q = Some P is not Q c) Not none of P is Q = Some P is Q d) Not only P is Q = Some Q is not P e) Not just P is Q = Some Q is not P f) It is not true that if P then Q = Some P is not Q

Simplification

A and B. There, A (or: Therefore, B) (It is a rule of inference)( valid form of argument)

Checking for Validity Using Rules of the Syllogism

A valid syllogism does not require the conclusion to have distributed terms. Five Rules: 1) The middle term must be distributed at least once. 2)If a term is distributed in the conclusion, it must also be distributed in its corresponding premise. (illicit major/minor then invalid) 3) At least one premise must be positive. (two negative premises = invalid argument.) 4) If the syllogism has a negative premise, there must be a negative conclusion, and vice versa. 5)If both of the premises are universal, the conclusion must also be universal, and vice versa. STUDY IN BOOK STUDY IN BOOK STUDY IN BOOK

Logical Addition

A. Therefore, either A or B.

Categorical Propositions

A: All P is Q universal; positive E: No P is Q universal; negative I: Some P is Q particular; positive O: Some P is not Q particular; negative

Fallacy of Affirming the Consequent

An invalid argument form that has this pattern: If P, then Q; Q, therefore, P.

Logical Connectives (Translating a Proposition)

And : & Or: v If..then: -> If and only if: = Not: ~

Conjunction

Any proposition that can be written in the form "A and B". If A is true and if B is true, then the claim "A and B" is then true.

5 types of compound propositions

Conjunction: A and B Disjunction: Either A or B Negation: Not A Conditional Claims: If A then B; B only if A Biconditional Claims: (Equivalence) A if and only if B

Testing for Validity Knowing Only the Mood and Figure

Construct the Syllogism then test the 5 rules

Formal Rules of Replacement

DeMorgan's Laws: DeMorgan's Law #1 (Not Both): ~(P & Q) = (~P v ~Q) Demorgan's Law #2 (Neither/Not): ~(P v Q) = (~P & ~Q) Transposition:If P then Q -->If not Q then not P (P-->Q) = (~Q-->~P) Material Implication:If P then Q-->Either not P or Q (P-->Q) = (~P v Q) Exportation: If A and B, then C. --> If A then, if B then C. [(A & B)-->C] = [A-->(B-->C)] Biconditional (Equivalence): --> If P then Q, and if Q then P: (P-->Q) & (Q-->P) --> If P then Q, and if not P then not Q: (P-->Q) & (~P-->~Q)

Categorical Syllogism

Deductive argument consisting of three statements: first two are premises and last one is conclusion. Together they use only 3 terms: major, minor and middle

Variables

Do not use 2 of the same

Disjunctive Syllogism

Either A or B /// Not B /// So, A

Fallacy of Denying the Antecedent

If A then B. Not A. Therefore, not B.

Absorption

If A then B. Therefore, if A then (A and B). (Rule of inference, valid form of argument)

Modus Ponens

If A, then B. A. Therefore, B.

Hypothetical Syllogism

If A, then B. If B, then C. So, if A, then C.

Modus Tollens

If A, then B. Not B. So, not A.

Destructive Dilemma

If p, then q. If r, then s. Either not q or not s. Therefore, either not p or not r.

Constructive Dilemma

If p, then q. If r, then s. Either p or r. Therefore, either q or s.

Mood/Figure of Syllogisms

M P P M M P P M P M P M M P M P

The 3 Terms of the Syllogism

Major: Predicate of the Conclusion Minor: Subject of the Conclusion Middle: term only in the 2 premises

Distribution

Step 1: Check the location of the term. (subject or predicate?) Step 2: If term is in the subject place, and A or E, it is distributed. If term is in the predicate place, and E or O, the predicate is distributed.

Propositions:

Tautologies: always true/true by definition Contradictions: always false/false by definition Contingent Claims: true or false according to the context. They are dependent on what is going on in the world to determine the truth value. Includes claims for which the truth value is unknown.