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

    1. scientific explanation
    2. accidental versus essential properties
    3. 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

  1. stoic logic
    1. modus ponens
    2. modus tollens
    3. conditional sentences
  2. AI
    1. is-a hierarchy
    2. non-monotonic reasoning
  3. 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
  4. St. Anselm’s first proof of the existence of God
    1. perfect island objection
    2. uniqueness objection
  5. St. Thomas Acquinas proof of the existence of God
    1. argument
    2. counterexample
  6. Euclid
    1. definitions, common notions, postulates, propositions
  7. 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

  1. method of synthesis and analysis
    1. reasoning as psychological process
    2. reasoning is a theory of appropriate combinations
  2. 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

  1. Binomial theorem
  2. 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

  1. 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

    1. Boolean algebra axioms
    2. limitations
    3. normative versus descriptive theories
    4. Boolean representation of quantifiers
  1. 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
  2. Kant
    1. synthetic versus analytic judgements
    2.  Kant’s theory of mathematical knowledge
  3. Frege
    1. logicism
    2. axioms
    3. rules of inference
    4. proof
    5. Frege’s logic

                                                               i.      relations

                                                             ii.      quantifiers

                                                            iii.      sentence connectives

    1. virtues

                                                               i.      can reconstruct valid deductive arguments in mathematics and science

                                                             ii.      rules of formal proof are explicit

                                                            iii.      completeness

                                                           iv.      correctness

    1. interpretation – truth and validity
    2. sense versus reference
    3. logical truth
    4. 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
    5. limitations of Frege’s logic

                                                               i.      non-monotonic reasoning

                                                             ii.      causal reasoning

                                                            iii.      counterfactual reasoning

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