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Concept
Unity of the proposition
Summary
In philosophy, the unity of the proposition is the problem of explaining how a sentence in the indicative mood expresses more than just what a list of proper names expresses.
The problem was discussed under this name by Bertrand Russell, but can be traced back to Plato. In Plato's Sophist, the simplest kind of sentence consists of just a proper name and a universal term (i.e. a predicate). The name refers to or picks out some individual object, and the predicate then says something about that individual.
The difficulty is to explain how the predicate does this. If, as Plato thinks, the predicate is the name of some universal concept or form, how do we explain how the sentence comes to be true or false? If, for example, "Socrates is wise" consists of just a name for Socrates, and a name for the universal concept of Wisdom, how could the sentence be true or false? In either case, the "Socrates" signifies Socrates, and the predicate signifies Wisdom. But the sentence asserts that Socrates is wise. The assertion of wisdom must consist in the assertion of some relation between Socrates and Wisdom. What is this relation?
The problem was discussed much later by Francis Bradley. If we assume that a sentence consists of two objects and a relation that connects them, and we represent this by three names, say John, loving, Mary, how do we express the fact that John loves Mary? For "John", "loving" and "Mary" would name the objects they do, even if this were not a fact. This is known as Bradley's regress.
The problem became significant in the early development of set theory. Set membership is a formal representation of the relation between the two parts of the proposition, and there are certain philosophical problems connected with this, as Frege realised when he investigated the distinction between concept and object. Assume that "Shergar is a horse" analyses into what "Shergar" names (an "Object", according to Frege), and what "is a horse" names (a "Concept"). Objects are fundamentally different from concepts, otherwise we get the problem of the unity of the proposition.
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