Organon F

Volume 27, August 2020, Issue 3, Pages 282–301

ISSN 2585-7150 (online) ISSN 1335-0668 (print)

Research Article

What We Know about Numbers and Propositions and How We Know It

Scott Soames 


The paper sketches and defends two instances of the strategy Let N’s be whatever they have to be to explain our knowledge of them—one in which N’s are natural numbers and one in which N’s are propositions. The former, which makes heavy use of Hume’s principle and plural quantification, grounds our initial knowledge of number in (a) our identification of objects as falling under various types, (b) our ability to count (i.e. to pair memorized numerals with individuated objects of one’s attention), (c) our (initially perceptual) recognition of plural properties (e.g. being three in number), and (d) our predication of those properties of pluralities that possess them (even though no individuals in the pluralities do). Given this foundation, one can use Fregean techniques to non-paradoxically generate more extensive arithmetical knowledge. The second instance of my metaphysics-in-the-service-of-epistemology identifies propositions (i.e. semantic contents of some sentences, objects of the attitudes, and bearers of truth, falsity, necessity, contingency, and apriority) with certain kinds of purely representational cognitive acts, operations, or states. In addition to providing natural solutions to traditionally un-addressed epistemic problems involving linguistic cognition and language use, I argue that this metaphysical conception of propositions expands the solution spaces of many of the most recalcitrant and long-standing problems in natural-language semantics and the philosophy of language.


Arithmetic; cognition; knowledge; natural numbers; plural properties; plural quantification; propositional attitudes; propositions; representation; semantics.

Author(s) and affiliation(s)


Scott Soames


University of Southern California


University of Southern California School of Philosophy, 3709 Trousdale Parkway, MHP 113 (223 Stonier Hall), Los Angeles, CA 90089, U.S.A.


About this article


30 December 2019


24 January 2020

Published online

29 February 2020


Institute of Philosophy of the Slovak Academy of Sciences

Institute of Philosophy of the Czech Academy of Sciences

Cite as


Soames, S. (2020). What We Know about Numbers and Propositions and How We Know It. Organon F27(3), 282–301.


Soames, Scott. 2020. "What We Know about Numbers and Propositions and How We Know It." Organon F 27 (3): 282–301.


Soames, S.  (2020). What We Know about Numbers and Propositions and How We Know It. Organon F, 27(3), pp. 282–301.

Copyright information

© Scott Soames

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