1. What does the compositionality of meaning explain?
2. EITHER (a) What does the liar paradox show us about truth?
OR (b) ‘The expression “…is true” is a meaningful predicate. So truth
must be a property.’ Discuss.
3. ‘It is absurd, but to some people it is also easy, to be misled by the
grammatical similarity of “Somebody came” to “Nobody came” into the
misconception that “Nobody” refers to a person just as does “Somebody”’.
Discuss.
4. Is an invalid argument invalid in virtue of its form?
5. Is Frege’s notion of the sense of a singular term coherent?
6. ‘Sin 90° = 1. Cos 90° = 0. Tan x = sin x/cos x. So tan 90° = 1/0.’ Formalize
this argument, discussing any problems that arise.
7. Answer both parts of this question.
(i) A relation R is weakly dense if ∀x∀y(xRy→∃z(xRz Λ zRy)). Show that
the formula ☐☐p → ☐p is a logical truth of the modal logic of weakly
dense Kripke models, but ☐p → ☐☐p is not.
(ii) Show that the formula ☐p → ☐☐p is a logical truth of the modal logic
of transitive Kripke models, but ☐☐p → ☐p is not.
8. Are the meanings of the logical constants given by their inference rules?
9. ‘If the arbitrarily given axioms do not contradict one another with all their
consequences, then they are true and the things defined by the axioms
exist.’ (HILBERT) Discuss.
10. Answer both parts of this question.
(i) Outline a proof of the Disjunctive Normal Form Theorem via truth
tables.
(ii) Outline a proof of the Conjunctive Normal Form Theorem via
substitution.