Friday, July 25, 2008

Non-Existent Objects and Russell’s Theory of Description

Certain philosophers (e.g. Colin McGinn) defend the view that there are non-existent objects. McGinn follows Austrian philosopher, Alexius Meinong, who espoused the doctrine of the non-existent. Beginning with the philosophy of mind, particularly with Brentano’s thesis of intentionality, Meinong worked towards a theory of objects that embraces possible objects (e.g. the golden unicorn), impossible objects (e.g. the round square), and incomplete objects (e.g. something tall). Meinong argued that any subject of a true predicate is an object. So, for Meinong, “the round square is square” is true and meaningful, so there is a round square. These objects, including the round square, are mind-independent, yet are all potential objects of thought.

From the mere fact that a subject term is meaningful, and is featured in true, meaningful sentences, it does not follow that it refers to something. Russell writes:

“It is argued, e.g., by Meinong, that we can speak about ‘the golden mountain’, ‘the round square’, and so on; we can make true propositions of which these are the subjects; hence they must have some kind of logical being, since otherwise the propositions in which they occur would be meaningless. In such theories, it seems to me, there is a failure of that feeling for reality which ought to be preserved even in the most abstract studies. Logic, I should maintain, must no more admit a unicorn than zoology can; for logic is concerned with the real world just as truly as zoology, though with its more abstract and general features. To say that unicorns have an existence in heraldry, or in literature, or in imagination, is a most pitiful and paltry evasion.” Bertrand Russell, “Descriptions” in Introduction to Mathematical Philosophy (New York: Simon & Schuster, 1961), 169.

Thus, Russell rejects the view that meaning is reference. For Russell, there is a restricted range of genuine singular terms which serves as referring terms (e.g. the first person pronoun “I”). The meaningful use of these terms, also known as logical proper names, guarantees that they have reference. According to Russell, other grammatical subject terms such as ordinary proper names and definite descriptions, are impostors.

Take for example the definite description (i.e. phrases of the form “the so-and-so”):

(1) The average 18th month old child speaks 10 words.

Grammatically, this is a subject-predicate (of the form “Fa,” where “a” is the subject term and “F” the predicate). Nevertheless, the subject term “the average 18th month old child” is a dummy singular term. That is, its function is not to refer to a particular 18th month old child who speaks exactly 10 words. Here, it is apparent that the grammatical structure and logical structure come apart.

The logical structure of (1) is elucidated by:

(2) The number of words spoken by 18th month old children divided by the number of 18th month old children = 10

Thus, the logical structure of (1) is of the form “a/b = c,” and not “Fa.” (1) is just a simpler and shorter way of expressing (2). The “average 18th month old child,” although grammatically a subject term, is not a genuine referring term. Hence, meaning does not guarantee reference (contra Meinong).

Russell’s theory of description argues that descriptions are merely disguised existential quantifiers. No description, be it definite or indefinite, is a genuine referring term. The grammatical structure of sentences containing descriptions is not their logical structure.

For example, the logical structure of “An A is B” is expressed as ∃x(Ax and Bx), that is, something is both A and B. “The A is B” can likewise be expressed as ∃x(Ax and (y)(if Ay then x = y) and Bx), that is, there is an x which is A, and uniquely so, and x is B. This analysis shows that, although the descriptions appear grammatically in the sentences as Fa, the logical structure reveals that the descriptions only function as existential quantifiers (e.g. “there is”). No object corresponds to “an F” or “the F” in the analysis.

In conclusion, certain terms which appear as referring terms turn out to function logically as quantifiers, and we know that quantifiers are not referring terms. When I tell you that “there is a surgeon in the operating theatre,” I am not referring to any particular surgeon, and what I say is true only if there is indeed a surgeon in the operating theatre. If Tom is in the operating theatre, and he happens to be a surgeon, then what I said is true. But if someone else i.e. Harry is in the operating theatre, and he is likewise a surgeon, then what I said is also true. Therefore, quantified sentences are satisfied, or not, by objects. In contrast, a sentence containing a genuine singular term (i.e. a logical proper name) is made true or false only by the states and doings of the object of reference. How things are with other objects is irrelevant.

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