of an extension. Generally then, an object is anything that might be designated by a proper name. There is nothing more basic to be said by way of elucidating what an object is. Similarly, first-level functions are what are designated by the expressions that result from removing names from compound proper names. Frege calls functions unsaturated or incomplete, in contrast to objects, which are saturated. Proper names and function names are not intersubstitutable so that the distinction between objects and functions is a type-theoretic, categorial distinction. No function is an object; no function name designates an object; there are no quantifiers that simultaneously generalize over both functions and concepts.
Just here Frege’s exposition of his views, if not the views themselves, encounter a difficulty. In explaining his views, he uses proper names of the form ‘the concept F’ to talk about concepts; and in contrasting unsaturated functions with saturated objects, apepars to generalize over both with a single quantifier. Benno Kerry, a contemporary of Frege, charged Frege’s views with inconsistency. Since the phrase ‘the concept horse’ is a proper name, it must designate an object. On Frege’s view, it follows that the concept ‘horse’ is not a concept, but an object, an apparent inconsistency. Frege responded to Kerry’s criticism in ‘On Concept and Object.’ He embraced Kerry’s paradox, denying that it represents a genuine inconsistency, while admitting that his remarks about the function–object distinction are, as the result of an unavoidable awkwardness of language, misleading. Frege maintained that the distinction between function and object is logically simple and so cannot be properly defined. His remarks on the distinction are informal handwaving designed to elucidate what is captured within the Begriffsschrift by the difference between proper names and function names together with their associated distinct quantifiers. Frege’s handling of the function– object distinction is a likely source for Wittgenstein’s say–show distinction in the Tractatus.
At the beginning of ‘On Sense and Meaning,’ Frege distinguishes between the reference or meaning (Bedeutung) of a proper name and its sense (Sinn). He observes that the sentence ‘The Morning Star is identical with the Morning Star’ is a trivial instance of the principle of identity. In contrast, the sentence ‘The Morning Star is identical with the Evening Star’ expresses a substantive astronomical discovery. The two sentences thus differ in what Frege called their cognitive value: someone who understood both might believe the first and doubt the second. This difference cannot be explained in terms of any difference in reference between names in these sentences. Frege explained it in terms of a difference between the senses expressed by ‘the Morning Star’ and ‘the Evening Star’. In posthumously published writings, he indicated that the sense–reference distinction extends to function names as well. In this distinction, Frege extends to names the notion of the judgeable content expressed by a sentence: the sense of a name is the contribution that the name makes to the thought expressed by sentences in which it occurs. Simultaneously, in classifying sentences as proper names of truth-values, he applies to sentences the notion of a name’s referring to something. Frege’s function-argument view of logical segmentation constrains his view of both the meaning and the sense of compound names: the substitution for any name occurring in a compound expression of a name with the same reference (sense) yields a new compound expression with the same reference (sense) as the original. Frege advances several theses about sense that individually and collectively have been a source of debate in philosophy of language. First, the sense of an expression is what is grasped by anyone who understands it. Despite the connection between understanding and sense, Frege provides no account of synonymy, no identity criteria for senses. Second, the sense of an expression is not something psychological. Senses are objective. They exist independently of anyone’s grasping them; their availability to different thinkers is a presupposition for communication in science. Third, the sense expressed by a name is a mode of presentation of the name’s reference. Here Frege’s views contrast with Russell’s. Corresponding to Frege’s thoughts are Russell’s propositions. In The Principles of Mathematics (1903), Russell maintained that the meaningful words in a sentence designate things, properties, and relations that are themselves constituents of the proposition expressed by the sentence. For Frege, our access through judgment to objects and functions is via the senses that are expressed by names that mean these items. These senses, not the items they present, occur in thoughts. Names expressing different senses may refer to the same item; and some names, while expressing a sense, refer to nothing. Any compound name containing a name that has a sense, but lacks a reference, itself lacks a meaning. A person may fully understand an expression without knowing whether it means anything and without knowing whether it designates what another understood name does. Fourth, the sense ordinarily expressed by a name is the reference of the name, when the name occurs in indirect discourse. Although the Morning Star is identical with the Evening Star, the inference from the sentence ‘Smith believes that the Morning Star is a planet’ to ‘Smith believes that the Evening Star is a planet’ is not sound. Frege, however, accepts Leibniz’s law without restriction. He accordingly takes such seeming failures of Leibniz’s law to expose a pervasive ambiguity in colloquial language: names in indirect discourse do not designate what they designate outside of indirect discourse. The fourth thesis is offered as an explanation of this ambiguity.
See also LOGICISM , MEANING, RUSSELL , SET -THEORETIC PARADOXES , SET THEOR. T.R.