This paper argues against Logical Realism, in particular against the view that there are facts of matters of logic that obtain independently of us, our linguistic conventions and inferential practices. The paper challenges logical realists to provide a non-intuition based epistemology, one which would be compatible with the empiricist and naturalist convictions motivating much recent anti-realist philosophy of mathematics.
This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics of mathematics--the view that mathematics (...) is about things that really exist. (shrink)
Nothing has been more central to philosophy of mathematics than the distinction between mathematical and physical objects. Yet consideration of quantum particles shows the inadequacy of the popular spacetime and causal characterizations of the distinction. It also raises problems for an assumption used recently by Field, Hellman and Horgan, namely, that the mathematical realm is metaphysically independent of the physical one.
We argue that Horgan's program for nominalizing science fails, because its translation of quantitative statements destroys the inferential structures of explanations, predictions and retrodictions of nonquantitative scientific facts.
This paper examines some work in welfare economics based upon generalized social welfare function (GSWFs). Impartial welfarism consists in a set of apparently quite weak moral axioms concerning GSWFs. Using that framework, welfare economists have derived both utilitarian and Rawlsian doctrines. These results would seem to be of great importance to moral philosophy. I argue, however, that applying them presupposes a view of persons as mere place holders for preferences, thereby limiting the theorems' appeal for moral philosophers. I propose a (...) more satisfactory view of impartial welfarism by replacing the term person by the more general welfare recipient, but this still fails to make the doctrine available to all moral philosophers. (shrink)
In Science without numbers Hartry Field attempted to formulate a nominalist version of Newtonian physics?one free of ontic commitment to numbers, functions or sets?sufficiently strong to have the standard platonist version as a conservative extension. However, when uses for abstract entities kept popping up like hydra heads, Field enriched his logic to avoid them. This paper reviews some of Field's attempts to deflate his ontology by inflating his logic.
By a logical theory I mean a formal system together with its semantics, meta-theory, and rules for translating ordinary language into its notation. Logical theories can be used descriptively (for example, to represent particular arguments or to depict the logical form of certain sentences). Here the logician uses the usual methods of empirical science to assess the correctness of his descriptions. However, the most important applications of logical theories are normative, and here, I argue, the epistemology is that of wide (...) reflective equilibrium. The result is that logic not only assesses our inferential practice but also changes it. I tie my discussion to Thagard's views concerning the relationship between psychology and logic, arguing against him that psychology has and should have only a peripheral role in normative (and most descriptive) applications of logic. (shrink)
Michael Dummett argued that Frege was a realist while Hans Sluga countered that he was an objective idealist in the rationalist tradition of Kant and Lotze. Sluga ties Frege's idealism to the context principle which he argues Frege never gave up. It is argued that Sluga has correctly interpreted the pre?1891 Frege while Dummett is correct concerning the later period. It is also claimed that the context principle was dropped prior to 1891 to be replaced by the doctrine of unsaturated (...) entities. (shrink)
This paper examines four arguments in support of Frege's theory of incomplete entities, the heart of his semantics and ontology. Two of these arguments are based upon Frege's contributions to the foundations of mathematics. These are shown to be question-begging. Two are based upon Frege's solution to the problem of the relation of language to thought and reality. They are metaphysical in nature and they force Frege to maintain a theory of types. The latter puts his theory of incomplete entities (...) in the paradoxical position of maintaining that it is no theory at all. Moreover, his metaphysics rules out well-known suggestions for avoiding this difficulty. (shrink)