NEIL W. TENNANT

tennant.9@osu.edu

If you email me, please use the header PHIL 250: YOURNAME.

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Professor
Department of Philosophy

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Topics it would be wise to revise for the final exam

Statements of:

• truth tables for connectives
• rules of inference for the connectives "not", "and", "or", "if...then---"; the quantifiers "some" and "all"; and the identity predicate "=" (with particular attention paid to restrictions on parameters, and to possibilities of discharge of assumptions in subordinate proofs)
• what rules make up the systems of minimal, intuitionistic and classical logic

Definitions of:

• term
• well-formed formula
• truth-value assignment (in propositional logic)
• interpretation/model (in first-order logic)
• truth-value of a complex sentence under an interpretation/model
• logical consequence
• logical deducibility
• logical truth
• theoremhood
• consistency
• soundness of a logical system of proof
• completeness of a logical system of proof.

Techniques:

• translating sentences of English into logical notation, paying particular attention to (i) the quantifying expressions "everyone", "someone", "anyone" (in context), and "no one"; (ii) anaphoric and reflexive pronouns that are rendered as bound variables or as repetitions of terms; and (iii) words and phrases such as "unless" and "only if", which need to be translated with care into logical complexes
• evaluating a sentence of propositional logic as true (or as false) under a given truth-value assignment
• evaluating a first-order sentence as true (or as false) in a finite model, using the "model-relative" rules for introducing the universal quantifier and eliminating the existential quantifier
• finding a proof (of no more than around 9 or 10 steps) of a valid formal argument with 2 or 3 premises
• finding a counterexample (with no more than, say, 4 indiviuals in the finite case) to an invalid formal argument with 2 or 3 premises
• translating an English argument into logical notation, and
  
  • proving it, if it is valid, or
    
  • finding a counterexample to it, if it is invalid.
    
  [In these cases, the proofs and counterexamples involved will be a little easier to find than in the cases where you are told to find a proof, or told to find a counterexample.]

Theoretical understanding of the system:

• For propositional logic:
  • using the rules of inference of intuitionistic logic to mimick the left-right readings of the rows of the truth-tables for the connectives
  • in classical logic, using negation and one binary connective to define the other binary connectives
  • deriving any of the four classical negation rules from any other such rule, within intuitionistic logic
• For first-order logic:
  • explaining why it is necessary to obey the restrictions on parameters in applications of the rules of existential elimination and universal introduction
  • understanding why every argument has either a proof or a counterexample

[Please let me know if you think anything has been left off this list, or if you think that anything on this list has not been sufficiently covered in the lectures and is not easy to learn about from the web-pages. If you do not find any of the above material in your notes or on the web-pages for this course, please thoroughly re-read the relevant parts of the textbook Natural Logic first, before emailing me for help!]

NT 3/11/03