In the first section of this paper I present the measurement-theoretic fallacy of ‘over-assignment of structure’: the unwarranted assumption that every numeric relation holding among two (or more) numbers represents some empirical, physical relation among the objects to which these numbers are assigned as measures (e.g., of temperature). In the second section I argue that a generalized form of this fallacy arises in various philosophical contexts, in the form of a misguided, over-extended application of one conceptual domain to another. Three examples are given: (i) the reduction of arithmetic into set theory, (ii) the ascription of full-blown intentional states to (at least some) non-overtly intentional creatures, such as Wittgenstein's builders, and (iii) the analysis of some modal notions as involving quantification over possible worlds (or their substitutes). The discussion of the third example gives rise to a novel account of possible-worlds talk.
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- Benacerraf, P. (1983) What numbers could not be, in P. Benacerraf and H. Putnam (eds.), The Philosophy of Mathematics, Cambridge University Press, Cambridge, pp. 272-294.Google Scholar
- Baldwin, T. (1998) Modal fictionalism and the imagination, Analysis 58, 72-75.Google Scholar
- Davidson, D. (1984) Reality without reference, in D. Davidson (ed.), Inquiries into Truth and Interpretation, Clarendon, Oxford, pp. 215-255.Google Scholar
- Dennett, D. (1987) The Intentional Stance, MIT Press, Cambridge, MA.Google Scholar
- Dresner, E. (2002a) Measurement theoretic semantics and the semantics for necessity, Synthese 130, 413-440.Google Scholar
- Dresner, E. (2002b) Wittgenstein's builders and Perry's objection to sentence priority, Dialectica 56, 49-64.Google Scholar
- Krantz, D., Luce, D., Suppes, P. and Tversky, A. (1971-1989) Foundations of Measurement, Vol. 1-3, Academic Press, New York.Google Scholar
- Kripke, S. (1980) Naming and Necessity, Harvard University Press, Cambridge, MA.Google Scholar
- von Neumann, J. (1923) Zur Einfuhrung der transfiniten Zahlen, Acta literarum ac Scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae (Szeged), Sectio Scientiarum mathematicarum1, 199-208. Reprinted in van Heijenoort, J. (1967) From Frege to Godel, Harvard University Press, Cambridge, MA, pp. 346-354.Google Scholar
- Nolan, D. (1997) Three problems for "strong" modal fictionalism, Philosophical Studies 87, 259-275.Google Scholar
- Perry, J. (1994) Davidson's sentences and Wittgenstein's builders, Proceedings and Addresses of The American Philosophical Association 67, 23-37.Google Scholar
- Quine, W. V. (1960) Word and Object, MIT Press, Cambridge, MA, 26-30.Google Scholar
- Rosen, G. (1990) Modal fictionalism, Mind 99, 327-354.Google Scholar