Elementary categorial logic, predicates of variable degree, and theory of quantity

Journal of Philosophical Logic 18 (2):115 - 140 (1989)
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Abstract

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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Citations of this work

Properties.Francesco Orilia & Michele Paolini Paoletti - 2020 - Stanford Encyclopedia of Philosophy.
Quantitative Properties.M. Eddon - 2013 - Philosophy Compass 8 (7):633-645.
Emergence for Nihilists.Richard L. J. Caves - 2018 - Pacific Philosophical Quarterly 99 (1):2-28.
Bigelow and Pargetter on quantities.John Forge - 1995 - Australasian Journal of Philosophy 73 (4):594 – 605.

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References found in this work

What is a Law of Nature?D. M. Armstrong - 1983 - New York: Cambridge University Press. Edited by Sydney Shoemaker.
The Foundations of Mathematics and Other Logical Essays.Frank Plumpton Ramsey - 1925 - London, England: Routledge & Kegan Paul. Edited by R. B. Braithwaite.
Universals and scientific realism.David Malet Armstrong - 1978 - New York: Cambridge University Press.
Introduction to mathematical logic.Alonzo Church - 1944 - Princeton,: Princeton University Press. Edited by C. Truesdell.
Introduction to mathematical logic..Alonzo Church - 1944 - Princeton,: Princeton university press: London, H. Milford, Oxford university press. Edited by C. Truesdell.

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