Study Guide for 80-150 Midterm

1. Plato
1. knowledge
2. form of Plato’s answers
3. recollection theory
4. forms
2. Aristotle
1. substance
2. attributes
3. prime matter
4. causes

i. formal

ii. efficient

iii. final

iv. material

v. examples

5. scientific explanation
6. accidental versus essential properties
7. syllogisms

i. validity of argument

ii. soundness of argument

iii. validity of argument form

iv. figures

v. rules of conversion

vi. proof of validity of some syllogisms

vii. proof of invalidity of other syllogisms

viii. limitations

ix. syllogisms we would call invalid

3. stoic logic
1. modus ponens
2. modus tollens
3. conditional sentences
4. AI
1. is-a hierarchy
2. non-monotonic reasoning
5. Cantor
1. larger cardinality
2. same cardinality
3. infinity
4. Cantor’s first theorem
5. Cantor’s second theorem
6. one-to-one function
7. diaganol argument
6. St. Anselm’s first proof of the existence of God
1. perfect island objection
2. uniqueness objection
7. St. Thomas Acquinas proof of the existence of God
1. argument
2. counterexample
8. Euclid
1. definitions, common notions, postulates, propositions
9. combinatorics
1. number of ways of choosing ordered m-tuple from n objects
2. number of ways of choosing unordered m-tuple from n objects
3. Raymond Lull

i. reasoning mechanically

ii. reasoning proceeds combinatorically

10. method of synthesis and analysis
1. reasoning as psychological process
2. reasoning is a theory of appropriate combinations
11. Descartes
1. structure of Discourse
2. method of doubt
3. goals of inquiry
4. fundamental operations of mind

i. intuition

ii. deduction

iii. induction

iv. clear and distinct ideas

12. Binomial theorem
13. Leibniz
1. Leibniz on truth and proof
2. limitations of Leibniz’ logic
3. monads
4. contributions to logic

i. decision procedure

ii. incomplete axiomatic theory

iii. coding language by abstract symbols

iv. logical relations have algebraic strucutre

v. univeral subject-predicate propositions do not presuppose the existence of things satisfying their predicate or subject terms

14. Boole
1. logic is a set of laws
2. laws have algebraic form
3. laws have to do with correct operation of the mind
4. universe of discourse
5. field of sets
6. lattice
7. union
8. intersection
9. complement
10. three interpretations of Booles’ logic

i. sets

ii. propositions

iii. numbers 0, 1

11. Boolean algebra axioms
12. limitations
13. normative versus descriptive theories
14. Boolean representation of quantifiers
14. Hume
1. matters of fact versus relations among ideas
2. a priori versus a posteriori
3. Hume’s theory of mathematical knowledge and its problems
4. impressions
5. ideas
6. laws of combination of ideas
7. Hume’s requirements for knowledge
8. Hume’s argument against induction
9. Hume’s theory of inductive inference
10. Hume on cause and effect
15. Kant
1. synthetic versus analytic judgements
2. Kant’s theory of mathematical knowledge
16. Frege
1. logicism
2. axioms
3. rules of inference
4. proof
5. Frege’s logic

i. relations

ii. quantifiers

iii. sentence connectives

6. virtues

i. can reconstruct valid deductive arguments in mathematics and science

ii. rules of formal proof are explicit

iii. completeness

iv. correctness

7. interpretation – truth and validity
8. sense versus reference
9. logical truth
10. impossibility of mechanical method for determining whether a given set of premisses entails a given conclusion, or for determining if a formula is a logical truth
11. limitations of Frege’s logic

i. non-monotonic reasoning

ii. causal reasoning

iii. counterfactual reasoning

12. problem of meaning and reference
17. Bacon
1. Bacon’s inductive methods
2. Bacon’s goals
18. Newton
1. Newton’s laws of motion
2. Newton’s argument for universal gravitation
3. evidence for Newton’s laws
19. scepticism
1. inductive
2. metaphysical