Professor J.R. Cameron

Biography

ROBIN CAMERON was the Regius Professor of Logic (until 2001). He holds the degrees of MA and BPhil from the University of St Andrews, and his principal research interests are in epistemology and philosophy of logic and language. 

Research Overview

Philosophy of mathematics: a study of the nature of calculation, designed to show that it is most naturally understood, not as a telescoped form of deductive reasoning, but operating on the basis of isomorphism-based or correspondence-based representation, in which manipulable symbols (e.g., the beads on an abacus, or numerals) represent other objects: by manipulating the former we can discover (on the basis of the correspondence/isomorphism) facts about the represented objects. Pure mathematics seems to have moved decisively away from the calculatory mode of operating to the construction, more geometrico, of deductive axiomatic systems (or their uninterpreted correlates); but a grasp of the nature of calculating will help us (i) to understand better how certain parts of mathematics (perhaps most notably complex number theory) can have application to the real world, (ii) to recognise how a calculus is something more than just an axiomatic system, and hence (iii) to appreciate how logical calculi can incorporate procedures which do not correspond straightforwardly to patterns or strategies of deductive reasoning used in everyday life or in mathematics.

Philosophical logic/philosophy of language: developing the view that talk about propositions is a special kind of talk about cognate accusatives, on the level of types.

Theory of knowledge: developing the implications of the thesis of (1) above, that the infallibilist view of knowing is the result of a mistake.

Other interests: philosophy of action; causation (arguing, following Mackie, that we commonly understand causation in a non-deterministic way, and exploring the implications of this). 

Current Research

A paper on sets, aggregates and pluralities. This, following on from (2) above, argues that a set can be identified with a certain special kind of aggregate - contrary to the received view that a set is a different kind of thing from the aggregate of its members. The kind of aggregate in question is an atomic plurality; this is an aggregate taken as a plurality (see (2) above), where the constituents of which it qua plurality is composed are taken also to be its ultimate or smallest parts. This understanding of what a set is, when conjoined with the understanding of number talk as a kind of type talk (see (3) above) offers the prospect of simplifying the foundations of mathematics, by providing a simple way of avoiding the paradoxes of set theory, and simplifying the complex and unintuitive axiom systems currently accepted as needed in order to steer clear of these.