(2000). The Boundaries of Belief: territories of encounter between indigenous peoples and Western philosophies. Educational Philosophy and Theory: Vol. 32, No. 1, pp. 15-24.

The object of this paper is to study the analogy, drawn both positively and negatively, between mathematics and fiction. The analogy is more subtle and interesting than fictionalism, which was discussed in part I. Because analogy is not common coin among philosophers, this particular analogy has been discussed or mentioned for the most part just in terms of specific similarities that writers have noticed and thought worth mentioning without much attention's being paid to the larger picture. I intend with this (...) analogy (looking at others' comparisons) to shed a little light on what is going on in mathematics, how one can understand it a bit other than experientially. This intention is philosophical and the way that I am attempting to accomplish it is also philosophical. I shall conclude my attempt to explain how it is possible and even natural for mathematics and fiction to have the analogy they have, taking it for granted, as argued in part I, that they are not to be identified. To this end I shall discuss philosophers' comparisons, mainly those of Hodes, Resnik, Tharp, and Wagner, who are the writers that seem to me to have written most thoughtfully and sufficiently extensively about fiction in making the comparison and of Körner, whose comparison is different. Whether either of these comparisons or the more general analogy is of permanent philosophical interest will have to be decided by philosophers now that they have had a fuller examination. I shall mention some other writers' reference to fiction, but not all; indeed, I am sure that I have not even found all the comparisons that there are. (shrink)

Rom Harré's proposed Copernican Revolution in the philosophy of science is a very ambitious undertaking. It challenges established views, proposes a radically new model for scientific explanation, and forces a rethinking of the foundations of the field. In his treatment of the natural sciences, Harré rejects all deductivist accounts of scientific explanation basically on the grounds that such accounts seriously distort the methods of explanation actually operative in science. In the social sciences Harré, in collaboration with Secord, rejects mechanistic, positivistic, (...) and behavioristic accounts of human behavior [5]. In place of these discarded interpretations he substitutes a new realism which stresses the role that models play in supplying accounts of observed patterns of phenomena in terms of the things and processes whose interactions are responsible for the manifest phenomena. This revolution, if successfully carried out, would indeed be a valuable contribution to the philosophy of science. (shrink)

Peirce was the first logician to define three-valued logical connectives. In 1909, he defined four one-place three-valued connectives and six two-place three-valued connectives, all of which were rediscovered by later logicians. Peirce’s motivation was to accommodate within formal logic a specific, narrow range of propositions he took to be neither true nor false, viz. propositions that predicate of a breach in mathematical or temporal continuity one of the properties that is a boundary-property relative to that breach.

Philosophers have traditionally decried vagueness as an unmitigated evil, and natural scientists have consistently agreed with them. Nevertheless, as I hope to show, the vagueness of scientific terms has some important advantages for the theories in which these terms figure. In so arguing I do not mean to put the best face on some unpleasant facts or to make a virtue out of a necessity. I shall begin, however, by arguing that on some contemporary accounts of scientific language the vagueness (...) of many scientific terms is unavoidable; if it is unavoidable then lamenting it is futile, and justifying it is idle. I shall go on to argue that, independent of these accounts, the advantages of exactness attained can sometimes be substantially outweighed by the disadvantages of vagueness foregone. (shrink)

Logical structure may explain the necessity and a priori knowability of such truths as that if A is red then A is either red or green. But this explanation cannot be extended to sentences that, while necessary and knowable a priori, do not wear the appropriate logical structure on their sleeves – sentences like ''''if A is a point and A is red, then A is not green,'''' or ''''if A is a sphere, then A is not a cube.'''' The (...) real origin of these sentences'' necessity and a priori knowability is a relationship between the meanings of their component atomic sentences – a relationship which cannot be systematically reduced to logical structure by translating those atomic sentences into any kind of ''''ideal'''' language. Moreover, this kind of relationship is one to which any atomic sentences are susceptible if they have a classifying, or comparison-implying, content. Arguably, then, all atomic sentences are capable of being related to others in ways that are necessary and knowable a priori. (shrink)

THERE IS OFTEN UNCERTAINTY ABOUT WHETHER SOME PREDICATE APPLIES TO SOME PHYSICAL OBJECT OR STATE. THIS UNCERTAINTY MAY HAVE ANY OF THREE SOURCES - VAGUENESS OF A TERM, INEXACTNESS OF A CONCEPT, OR PRACTICAL DIFFICULTY IN DETERMINING ITS APPLICABILITY. VARIOUS WAYS IN WHICH CONCEPTUAL INEXACTNESS OR PRACTICAL DIFFICULTY MAY PRODUCE UNCERTAINTY ARE DISTINGUISHED. NEITHER TERMINOLOGICAL VAGUENESS, NOR PRACTICAL DIFFICULTY IN DETERMINING THE APPLICABILITY OF A CONCEPT ARE NECESSARY FEATURES OF EVERY LANGUAGE IN EVERY PHYSICAL WORLD, BUT CONCEPTUAL INEXACTNESS IS A (...) NECESSARY FEATURE OF EMPIRICAL CONCEPTS. THESE RESULTS ARE UTILIZED TO DETERMINE THE SOURCES AND NECESSITY OF IMPRECISION IN MEASUREMENT. (shrink)