Word and Object, New Edition by Churchland Patricia S.; Follesdal Dagfinn; Quine Willard Van Orman

Author:Churchland, Patricia S.; Follesdal, Dagfinn; Quine, Willard Van Orman [Quine, Willard]
Language: eng
Format: epub
Publisher: MIT Press
Published: 2013-01-25T00:00:00+00:00

Now we are ready to introduce variables just as in (4):

(7) lawyer x such that x told a colleague y that [etc. as in (4)].

Note that though (5) may have been preceded in context by ‘the lawyer’ or ‘a lawyer’, it is still just to the general term ‘lawyer’ that (5) is attributive (cf. §23). Accordingly (6) and (7), like (5), are framed as general terms, to which a ‘the’ or ‘an’ may or may not be superadded to derive a singular term. The example (7) contrasts instructively with (4) in exhibiting ‘x’ in apposition not to an indefinite singular term but to a general term.

In the context of a logical or semantical discussion the phrase ‘cross-reference’ is unfortunate in a way in which its French equivalent renvoi is not. For, a pronoun or other singular term may also be said to refer, permanently or in passing, to some person or other object. Reference in the latter sense is genuinely the relation of sign to object, whereas cross-reference is only a relation of sign to coordinate sign, a harking back of pronoun to grammatical antecedent. Logicians happily have another terminology for talking of cross-reference, where variables are concerned: they speak of binding. The introductory or appositive occurrence of ‘x’ is said to bind the various recurrences of ‘x’, insofar as they hark back to that apposition and not to some independent use of the letter.

If a sentence or relative clause contains an appositive or binding occurrence of ‘x’ and sundry recurrences of ‘x’, then ordinarily it will include a component sentence that contains some of the occurrences of ‘x’ but, within itself, none to bind them. Such a component sentence, considered by itself, is called an open sentence, and its unbound occurrences of variables are said to be free in it. Examples:

x has a part smaller than x.

x thought a client z of y more critical of z than of any of z's rivals.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.