By Otavio Bueno, Oystein Linnebo (Editors)
During this ebook, 13 promising younger researchers write on what they take to be the proper philosophical account of arithmetic and talk about the place the philosophy of arithmetic must be going. New developments are printed, comparable to an expanding realization to mathematical perform, a reassessment of the canon, and concept from philosophical common sense.
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Example text
They assert not connexions between phenomena, but connexions between judgements; and among judgements are included the laws of nature. (Frege 1980, 87) This is all well and good, of course, as reconstruction of what Frege was up to. But as noted, the project depends crucially on BLV. ). In addition, the reduction of first-level concepts to their object-level proxies provided by BLV is central to Frege’s identification of the cardinal numbers. Thus, the central question facing us, which I shall attempt to answer in the next section, is how the neo-Fregean can retain the promising logicist epistemological story while simultaneously rejecting BLV.
13. It is worth noting that late in his life, after the discovery of Russell’s paradox, Frege clung to the view that there are three sources of knowledge: empirical, logical, and geometrical/temporal. See Frege (1979a). 14. g. Hale (2000), Wright (2000) for two options). The present reading is a relatively weak interpretation of Frege’s intentions. 15. The translation of this passage is taken from Wright (2000). 16. It is important to understand the appropriate force of Frege’s Constraint: The claim is that we can apply arithmetic (or analysis) to any collection of objects, not that we should.
Frege, of course, famously believed that extensions are immune to the Caesar Problem, but it is unclear why. For a detailed discussion of this issue, see Heck (2005). 18. It should be noted that the level of satisfaction one receives from this explanation of the epistemology of arithmetic will depend on one’s views about concepts, and in particular, on whether or not one views concepts as something shared and accessible in a manner in which abstract objects such as cardinal numbers are not. 32 Roy T.