1 Explain what is meant by the ‘grammatical form’ and the ‘logical form’ of an
English sentence. Is one a guide to the other?
2 Expound a referential semantics for the quantifiers of classical logic. What makes
the semantics referential rather than substitutional?
3 Either (a) Expound a natural deduction system for classical propositional
logic. Is there any reason to think that one of the rules of the
system has a different status from the others? If so, what?
Or (b) What could motivate intuitionistic logic?
4 Either (a) Must a consistent axiom system have a model?
Or (b) Can we think of the natural numbers as being implicitly defined
by an axiom system?
5 Expound a semantics for the modal logic S4, showing in particular that the
characteristic S4 axiom is sound for this semantics but that the S5 axiom is not.
6 Either (a) ‘The external causal chain plays no explanatory role whatever in
Kripke’s account of personal names.’ Discuss.
Or (b) Is ‘John’ indexical?
7 ‘Russell had a one-step, Frege a two-step, semantic theory.’ What were Russell
and Frege disagreeing about? Who was right?
8 ‘The meaning of a sentence is determined by the meanings of the words of which
it is composed.’ Discuss.
9 What attitude ought I to have towards the inhabitants of other possible worlds than
my own?
10 Is a community free to adopt whatever linguistic conventions it pleases?