"For manifestly, if Socrates exists, one of the two propositions 'Socrates is ill', 'Socrates is not ill' is true, and the other false. This is likewise the case if he does not exist; for if he does not exist, to say that he is ill is false, and to say that he is not ill is true." (From Aristotle's Categories)

"That the name 'Kepler' denotes something is just as much a presupposition for the assertion 'Kepler died in misery' as for the contrary assertion." (From Frege's On Sense and Meaning)

Since Frege broke with Aristotelian tradition, a plethora of approaches to dealing with the phenomenon of presupposition have been proposed.

The approaches discussed will (as time permits) appeal to scope ambiguity (e.g. Russell), to Gricean argumentation (e.g. Atlas, Gazdar, Kempson, van der Sandt and Wilson), to partiality and trivalence (e.g. Bochvar, Burton-Roberts, Peters, Strawson, Seuren and Link), to an extra presuppositional dimension of evaluation (e.g. Herzberger and Karttunen and Peters), to a mechanism allowing presuppositions to be canceled (e.g. Gazdar, Mercer and van der Sandt), to sentence internal dynamics (e.g. Beaver, Karttunen, Heim, van der Sandt, Zeevat), and to accommodation (e.g. in theories of Beaver, Heim, van der Sandt, Fauconnier, Zeevat).

In this talk we will look at some themes which cross-cut this bewildering array. The emphasis will be on developing syntheses of ideas and theories found in the literature, and considering empirical phenomena (e.g. anaphoricity of presuppositions, dependence on world knowledge) which might yield a clear preference for one type of theory over another.