ABSTRACT
Since my days as an undergraduate and then a graduate student in England in the period 1968-1974 I have been an appreciative consumer of Timothy Smiley’s work, though the fi rst time I heard him referred to as Tim (or had a chance to meet him personally) was on the occasion of an Australasian Association for Logic conference organized by Graham Priest at the University of Western Australia in 1983. At that conference, I presented a version of the paper abstracted as Humberstone (1984), on the subject of the unique characterization of connectives, which is intimately connected to a theme of Smiley (1962), pursued also from a somewhat different angle in another classic paper of the same vintage, Belnap (1962). For a BPhil thesis at the University of York, I worked on a theme from Smiley (1963), trying to see how far his idea could be taken, of reducing the number of modal operators (broadly understood) to one-which we could loosely think of as expressing a kind of absolute necessity-in terms of which other modal notions could be processed as forms of relative necessity (absolute necessity given this or that statement, formally represented by a sentential constant). A descendant of this work appeared as Humberstone (1981), fi xing a problem (pointed out by Kit Fine) in my early efforts with the aid of a suggestion from Dana Scott (my supervisor for yet another BPhil thesis, this time at Oxford); related and subsequent developments are surveyed in Humberstone (2004). Some ideas from Smiley (1996) on negation and rejection are taken up in Humberstone (2000b). Footnote 1 of Smiley (1962), concerning substitution and replacement, inspired much of Humberstone (in preparation).
