A Theory of Propositions

Copyright © 2000-2009 by Ronald Pisaturo. All rights reserved.
The Table of Contents and Introduction of this 9,000-word essay are shown here. The remainder of the essay is no longer available for purchase. The content of this essay may be incorporated into a future work.

May 18, 2009


1      Introduction
2      What is a Proposition?
3      Phrases, Including Subjects and Predicates
3.1       Phrases Are Like Narrowed Concepts
3.2       The Integrating Role of Phrases
3.3       A Class of Example Phrases: Definitions
3.4       Further Understanding Through Partial Exceptions
3.5       The Mathematics of Narrowing and Widening
4      The Cognitive Role of Propositions
4.1       The Purpose of Propositions
4.2       Existence and Identity in Propositions
4.3       Propositions’ Specificity as Complement to Concepts’ Open-Endedness
4.4       Polemic
5      Summary

1          Introduction

In her Introduction to Objectivist Epistemology (IOE), Ayn Rand presents her theory of concepts. In the foreword, she writes:

The issue of concepts (known as “the problem of universals”) is philosophy’s central issue. Since man’s knowledge is gained and held in conceptual form, the validity of man’s knowledge depends on the validity of concepts. But concepts are abstractions or universals, and everything that man perceives is particular, concrete. What is the relationship between abstractions and concretes? To what precisely do concepts refer in reality?[i]

The remainder of her book answers those questions and more, explaining how concepts (symbolized by words) are formed, and how they must be used to serve cognition.

As we know, however, knowledge generally is stated not as isolated concepts but in concepts organized into propositions, which are symbolized by declarative sentences. (A proposition is to a sentence what a concept is to a word. For example, “The big red book fell off the table” is a sentence denoting a proposition.) Imagine trying to read a book on American history, for example, in which there were no sentences, but rather just a series of words. Or imagine trying to write about the Civil War using only isolated concepts instead of propositions.

The questions answered by Ayn Rand for concepts should also be asked for propositions. To what precisely do propositions refer in reality? What is their role in cognition?

Ayn Rand begins Chapter 8 (“Consciousness and Identity”) of IOE with this passage:

The organization of concepts into propositions, and the wider principles of language–as well as the further problems of epistemology–are outside the scope of this work, which is concerned only with the nature of concepts. But a few aspects of these issues must be indicated.

Since concepts, in the field of cognition, perform a function similar to that of numbers in the field of mathematics, the function of a proposition is similar to that of an equation: it applies conceptual abstractions to a specific problem.[ii]

The present essay attempts to build on Ayn Rand’s theory of concepts in order to explain the meaning and cognitive function of propositions.[iii] I will explain how the specificity of propositions complements the “open-end” nature of concepts (in both senses of open-endedness described by Ayn Rand[iv]). Given a vocabulary of concepts, propositions allow more highly-differentiated and more intensively-integrated identifications than are possible merely by using each concept in isolation. One cognitive purpose thereby fulfilled by propositions is that this high degree of differentiation is achieved while preserving the unit-economy of concepts. The other purpose fulfilled by propositions is that one’s knowledge can be put into highly-specific, intensively-integrated, logical orderings.

[i] Ayn Rand, Introduction to Objectivist Epistemology (New York: Meridian, Expanded Second Edition, 1990), p. 1.

[ii] Ibid., p. 75.

[iii] Ayn Rand did not herself write a theory of propositions. Any errors I make in describing her theory of concepts and attempting to apply her theory to the issue of propositions are, of course, my own.

[iv] See IOE pp.17-18 for one sense of open-endedness, and pp. 66-68 for a second sense. (All page numbers are for the expanded, second edition.)

*     *     *

The remainder of this 9,000-word essay is no longer available for purchase. The content of this essay may be incorporated into a future work.