David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Philosophical Logic 18 (2):115 - 140 (1989)
Developing some suggestions of Ramsey (1925), elementary logic is formulated with respect to an arbitrary categorial system rather than the categorial system of Logical Atomism which is retained in standard elementary logic. Among the many types of non-standard categorial systems allowed by this formalism, it is argued that elementary logic with predicates of variable degree occupies a distinguished position, both for formal reasons and because of its potential value for application of formal logic to natural language and natural science. This is illustrated by use of such a logic to construct a theory of quantity which is argued to be scientifically superior to existing theories of quantity based on standard categorial systems, since it yields real-valued scales without the need for unrealistic existence assumptions. This provides empirical evidence for the hypothesis that the categorial structure of the physical world itself is non-standard in this sense
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References found in this work BETA
D. M. Armstrong (1983). What is a Law of Nature? Cambridge University Press.
Frank Plumpton Ramsey (1960). The Foundations of Mathematics and Other Logical Essays. Paterson, N.J.,Littlefield, Adams.
D. M. Armstrong (1978). Universals and Scientific Realism. Cambridge University Press.
J. D. Sneed (1975). The logical structure of mathematical physics. Tijdschrift Voor Filosofie 37 (1):151-152.
Alonzo Church (1944). Introduction to Mathematical Logic. London, H. Milford, Oxford University Press.
Citations of this work BETA
Maya Eddon (2013). Quantitative Properties. Philosophy Compass 8 (7):633-645.
John Forge (1995). Bigelow and Pargetter on Quantities. Australasian Journal of Philosophy 73 (4):594 – 605.
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