1 Either (a) ‘The use of words is to be sensible marks of ideas, and
the ideas they stand for are their proper and immediate signification.’
Discuss.
Or (b) In what sense of ‘convention’, if any, is it true that
meaning is fixed by convention?
2 Can a theory of truth provide a satisfactory account of meaning?
3 Either (a) Must we quantify over a domain?
Or (b) How did Frege solve the problem of multiple generality?
4 ‘Valid arguments in English are valid in virtue of their logical form.
Similarly, invalid arguments are invalid in virtue of their logical form.’
Discuss.
5 Either (a) Are empty names such as ‘Vulcan’ a problem for a
semantic theory?
Or (b) Is Frege’s semantics committed to an infinite hierarchy
of senses? Why does it matter?
6 How much must we know about something for our words to denote it?
7 What is the law of excluded middle? Is it a logical truth?
8 Attempt all parts of this question.
(a) Describe a language for propositional modal logic.
(b) Expound a Kripke semantics for the language using the idea of
truth at a world in a Kripke frame, under a valuation. Define the
notions of logical truth and logical consequence.
(c) Describe a Kripke frame and a valuation according to which
□A→□□A is false at some world in the frame, under the
valuation.
9 ‘A theory of possible worlds cannot do without primitive modality, since
possible world is itself a modal notion. But the theory is none the
worse for that.’ Discuss.
10 How, if at all, can one prove the consistency of a mathematical theory?