This article treats three aspects of Frege's discussions of definitions. First, I survey Frege's main criticisms of definitions in mathematics. Second, I consider Frege's apparent change of mind on the legitimacy of contextual definitions and its significance for recent neo-Fregean logicism. In the remainder of the article I discuss a critical question about the definitions on which Frege's proofs of the laws of arithmetic depend: do the logical structures of the definientia reflect the understanding of arithmetical terms prevailing prior to (...) Frege's analyses? Unless they do, it is unclear how Frege's proofs demonstrate the analyticity of the arithmetic in use before logicism. Yet, especially in late writings, Frege characterizes definitions as arbitrary stipulations of the senses or references of expressions unrelated to pre-definitional understanding. I conclude by examining some options for conceiving of the status of Frege's logicism in light of this apparent tension, and outline a suggestion for a philosophically fruitful way of resolving this tension. (shrink)

The author contends that the Objectivist epistemology has lacked a viable model of propositional knowledge for nearly fifty years, due to neglect of Rand's unit-perspective view of concepts. This pioneering insight, he says, not only is an essential building block of her concept theory, but also welds together the three levels of logical theory and provides the clearest X-ray picture of our multilayered conceptual knowledge. Using the unit-perspective to expand Rand's theory of concepts, the author then devises a theory of (...) the proposition, giving considerable attention to axioms and statements about nonexistent subjects. (shrink)