Special research Centres to be funded in the humanities. The new Centre was a joint project between CSu and the University of melbourne, with CSu being the host institution and the director, Professor Miller, being a CSu employee.
in 2004 the australian national university (anu) also became part of CaPPE after the CSu node of CaPPE had been based on the anu campus from 2001.
With the establishment of CaPPE more philosophers, particularly in applied ethics, were employed at CSu, and it quickly gained a significant international reputation in this field. in recent years a number of important appointments have been made jointly by CSu-CaPPE with overseas universities, currently oxford university, John Jay College of City university, new york, and Washington university in St. Louis. recent significant appointments include Professor John Kleinig, the leading international expert on criminal justice ethics, and Professor Larry May, one of the foremost international researchers in global justice. as of 2008, CSu employs eighteen philosophers full-time or part-time, seven at professorial level and all at level b or above. Most of the appointments are, or include, half time research positions with CSu-CaPPE.
a notable feature of philosophy at CSu has been the emphasis on applied ethics and the number of consultancies and australian research Council Link-age Grants gained by CSu philosophers.
The postgraduate program is growing, both in the coursework Masters area and in the number of Ph.d. students. Currently six Ph.d. students are enrolled and three have graduated in the last few years.
Classical Logic
Greg Restall
Philosophical logic in australasia is much more famous for innovation in modal logic and other areas of non-classical logic than in core, traditional classical logic.
For accounts of those themes in research in australasian philosophy, the reader is referred to the entries on modal logic, nonclassical logic and relevant logic.
There is some work in philosophical logic that remains to be covered, and that is the subject for this article. it is fitting that in a region most famous for non-class-ical logic, the entry on classnon-class-ical logic should focus on work that is not non-classnon-class-ical.
Classical logic here is understood as traditional two-valued propositional logic and its extensions with quantifiers, as introduced by Frege, russell and White-head, and which became dominant in logic teaching and research throughout the world from the middle of the twentieth century to this day. Classical pro-positional logic can be taught in many ways, with truth-tables, or with a proof technique such as ‘natural deduction’, and in most philosophy departments
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through out australia and new Zealand logic teaching forms a part of the first or second year program for philosophy students, whether as a compulsory unit or as one of a few options. The teaching of classical logic in australasia has been a distinctive feature of the philosophy curriculum there, and so it is with this topic that we will start. From there, we will look at two prominent issues in research in philosophical logic in australasia that also count as not non-classical logic.
Logic Teaching in Australasia
Logic teaching throughout australia and new Zealand has played an important part in the activities of researchers in philosophy departments. For a significant number, it has not been an adjunct to research, but a core activity. From the Masters Program in Logic established by Malcolm rennie, Len Goddard and richard routley (later richard sylvan) at the University of New England in the 1960s, to new textbooks replacing the teaching of aristotelian logic with classical logic, by Charles hamblin at the University of New south Wales, and Malcolm rennie and roderic Girle at the University of Queensland, logic teaching modernised significantly through the 1960s and ’70s (see hamblin 1967, and rennie and Girle 1973). Girle’s work, in particular, saw logic become a part of the high school curriculum in Queensland, and through his work, the Australian Logic Teachers’ Journal was founded in 1976, and lasted through ten years of publication—a vital resource for logic teachers in secondary and tertiary education throughout australia and beyond.
Girle’s pedagogy was radical: he taught logic using raymond Smullyan’s tableaux (tree) technique, a proof system which is mechanical enough for students of many levels to be able to master, yet also with pleasing formal properties that make techni-cal results in logic (soundness and completeness, decidability, etc.) straightforward to explain (Girle 2002). This technique has seen broad adoption throughout the region, and Girle has made use of it in teaching classical logic to many generations of students, at the university of Queensland and now uni versity of auckland.
introducing logic by way of tableaux has moved beyond australia, to be adop-ted in many centres around the world, and the technique has been extended far beyond classical logic to be the centrepiece of Graham priest’s widely used Introduction to Non-Classical Logic (2001) as well.
Classical Logic and Language
Charles hamblin, mentioned above, was a logician, trained at the University of melbourne and the London School of Economics, and returned to australia, becoming the professor of philosophy at the university of new South Wales, where he worked until his death in 1985. his research in logic was instrumental in the development of research in computer science in australia: in the 1950s he developed a programming language (based on ‘Polish’ notation, familiar from work in logic in this period) for the third computer available in australia. he also worked on the logic of imperatives, the categorisation of fallacies, and on formal treatments of the rules of dialogue (hamblin 1971), where the formal rules of
Classical Logic
classical logic play just one part in a larger system of rules for asking questions, giving answers, etc. This work has been taken up by other australasians, such as Jim Mackenzie and rod Girle. hamblin, furthermore, provided a close analysis of classical logic itself: for example, his under-appreciated paper on a fragment of classical logic (hamblin 1973) presages more recent work on tractable languages, and translations between natural and formal languages.
Type Theory
another strand of work in classical logic in australasia is found in a tradition of work on type theory. type theory, which dates back at least to russell and Whitehead’s Principia Mathematica, goes beyond classical predicate logic by adding higher domains of quantification: not only can we talk about all things (the domain at level 1), but also all collections of things (the domain at level 2) and collections of collections of things (the domain at level 3), etc. russell and Whitehead’s original theory was a ‘simple’ type theory of this kind. russell’s later work showed that one might need to complicate the picture: perhaps talk of higher categories of things facilitated the description of more things lower down in the hierarchy, and if we think of these stages as stages of construction, then perhaps we need to keep track of this. Perhaps the hierarchy has to be ‘ramified’
and when we talk of all of the many different collections of things, we need to be aware of whether we need to specify in advance which collections we mean before we can construct things based on them: a definition or construction satisfying this kind of restriction is said to be predicative. allen hazen (of the university of Melbourne) has done a great deal of research on predicative logic (hazen 1983) and russell’s ramified type theory (hazen 2004).
Work in type theory has not merely been of historical or purely theoretical interest in studies in formal logic itself. Work in classical type theory has been applied to other areas of logic, most prominently in australasian work on the logic of adverbs.
Adverbial Modification: With Types and without
Malcolm rennie, also mentioned above, wrote a short monograph on applicat-ions of type theory in natural languages (rennie 1974). one of those applicatapplicat-ions is in the logic of adverbs. We may say that Sam sliced a bagel, and when we do this, we use the name ‘Sam’ and the predicates ‘bagel’ (to distinguish those things that are bagels and those things that are not) and ‘sliced’ (to distinguish those pairs of things where the first sliced the second from those where the first didn’t slice the second). to say that Sam sliced a bagel is to say that there is some thing that is both a bagel, and is such that Sam sliced it. We can also say that Sam carefully sliced the bagel. here ‘carefully’ is not a predicate in the same way:
neither Sam was carefully (though, he perhaps was careful), nor was the bagel.
‘Carefully’ in that sentence modifies the predicate ‘sliced’. it is one thing to slice, and another to carefully slice. rennie’s work on type theory classified the logic of different kinds of adverbs. Merely finding a place in a hierarchy of types is not
Classical Logic
the end of the story: different kinds of adverbs combine in different kinds of ways.
Gunsynd is a champion and a miler and a racehorse: it follows, for example, that he is a champion racehorse, but it does not follow that he is a champion miler. (Perhaps he is a champion over another distance.) in rennie’s work these kinds of differences are classified and an account is given of how we are to understand them.
This type theoretical account of adverbs is taken up in a larger setting in the work of maxwell J. Cresswell, chief among many (see, e.g. Cresswell 1985a). in this expanded context of work in logic and linguistics, the resulting typed logic is richer than rennie’s original setting, as modal and contextual features play a vital role. not only are there types for objects at level 0, and truth values, and constructions out of them at different levels, but also for possible worlds and other indices of evaluation such as speakers and times. in this work, type theory meets modal logic to form a mainstream tradition in formal semantics in the work of Montague, Cresswell, Partee and others.
This approach to the logic of adverbs and other predicate modifiers was not the only one pursued in australasian logic in the second-half of the twentieth century. barry taylor’s work took things in another direction, in which the towering conceptual structure of a never-ending hierarchy of types is traded in for a slight increase in ontology (taylor 1985). instead of thinking of the pred-icate modifier ‘carefully’ as a predpred-icate of a higher type, we can think of it as an everyday predicate describing items in the world in the same manner as do the predicates ‘bagel’ or ‘sliced’. The trick is to admit that the items are different.
What is careful is not the bagel, or perhaps not even Sam, but the event of the slicing. taylor argues that one should follow the work of donald davidson, and hold that when we say that Sam carefully sliced a bagel, we say that there is an event which is a slicing of a bagel by Sam, and which is careful. in this way, the adverb becomes a predicate describing an item, where the item is now a concrete event. taylor’s work extends davidson’s logic of adverbs by giving a rich account of the structure of events as a species of the wider genus of states of affairs. The result is a picture of adverbial modification that allows one to avoid a hierarchy of types to stay within the realm of first-order classical logic, at the modest cost of an ontology of events and states of affairs.
australasian work on predicate modifiers in a rich logical setting has not ended with the work of rennie, Cresswell and taylor. recent approaches to the topic by Lloyd humberstone (of Monash university) have shown that there are many insights remaining to be mined in this area (humberstone 2008).
Into the Future
There is no doubt that classical logic will play an important role in philosophy teaching and research in philosophy in australasia into the future. it is hard to say what shape that might take. one hint of where this may go is in some recent work of the author (restall 2005), which presents a new defence of classical logic, connecting it to other themes in the norms and pragmatics of assertion and denial.