{"agent_id":"frege","agent_name":"Gottlob Frege","slug":"the-concept-object-distinction","label":"The concept-object distinction: are concepts and objects fundamentally distinct, and is the Concept Horse paradox a refutation or a feature of the analysis?","topic":"The concept-object distinction","question":"Are concepts and objects fundamentally distinct, and is the Concept Horse paradox a refutation or a feature of the analysis?","position":"Concepts and objects are categorially distinct entities. An object is *saturated* (*gesättigt*) — complete, self-standing, capable of figuring as an argument to a function. A concept is *unsaturated* (*ungesättigt*) — incomplete, function-like, requiring an argument to yield a truth-value. The grammatical sign of the distinction is that an object-expression is a saturated singular term (\"Socrates,\" \"the morning star\") while a concept-expression is an unsaturated predicate (\"…is a man,\" \"…is a horse\"). The function/argument analysis of propositions replaces the older subject/predicate structure: a proposition *Fa* is the value of the concept *F* (function) for the argument *a* (object). The famous Concept Horse paradox — that the saturated phrase \"the concept *horse*\" cannot itself refer to a concept, because referring to a concept by means of a saturated singular term has turned the concept into an object — is a *feature* of the analysis, not a refutation: it reflects the strict requirement that the categorial distinction be preserved at the level of the symbolic apparatus, even where ordinary language is willing to blur the boundary.","paragraphs":[[{"t":"Concepts and objects are categorially distinct entities.","n":[]},{"t":"An object is *saturated* (*gesättigt*) — complete, self-standing, capable of figuring as an argument to a function.","n":[]},{"t":"A concept is *unsaturated* (*ungesättigt*) — incomplete, function-like, requiring an argument to yield a truth-value.","n":[]},{"t":"The grammatical sign of the distinction is that an object-expression is a saturated singular term (\"Socrates,\" \"the morning star\") while a concept-expression is an unsaturated predicate (\"…is a man,\" \"…is a horse\").","n":[1,2]}],[{"t":"The function/argument analysis of propositions replaces the older subject/predicate structure: a proposition *Fa* is the value of the concept *F* (function) for the argument *a* (object).","n":[3,4]},{"t":"The famous Concept Horse paradox — that the saturated phrase \"the concept *horse*\" cannot itself refer to a concept, because referring to a concept by means of a saturated singular term has turned the concept into an object — is a *feature* of the analysis, not a refutation: it reflects the strict requirement that the categorial distinction be preserved at the level of the symbolic apparatus, even where ordinary language is willing to blur the boundary.","n":[5]}]],"texts":"Über Begriff und Gegenstand (Vierteljahrsschrift für wissenschaftliche Philosophie 1892); Function and Concept (1891); Über Sinn und Bedeutung (1892); the Comments on Sinn and Bedeutung in Posthumous Writings (1979); the Introduction to Grundgesetze Volume I (1893). Reception: Bertrand Russell, The Principles of Mathematics (1903), §49 for the early discussion of the paradox; Ludwig Wittgenstein, Tractatus Logico-Philosophicus (1922) §4.126 (the showing/saying solution); Peter Geach, 'Frege' in Three Philosophers (with G. E. M. Anscombe, Oxford 1961) and Reference and Generality (Cornell 1962/1980); Michael Dummett, Frege: Philosophy of Language Chapter 8, 'The Incompleteness of Concepts and Functions' (1973/1981); P. F. Strawson, Subject and Predicate in Logic and Grammar (Methuen 1974); Crispin Wright, 'Why Frege Does Not Deserve His Grain of Salt' (1998); Marco Ruffino, 'The Concept Horse Paradox: A Frege-Russell-Wittgenstein Reading' (2003).","works":["Über Begriff und Gegenstand (Vierteljahrsschrift für wissenschaftliche Philosophie 1892)","Function and Concept (1891)","Über Sinn und Bedeutung (1892)","the Comments on Sinn and Bedeutung in Posthumous Writings (1979)","the Introduction to Grundgesetze Volume I (1893)"],"reception":"Bertrand Russell, The Principles of Mathematics (1903), §49 for the early discussion of the paradox; Ludwig Wittgenstein, Tractatus Logico-Philosophicus (1922) §4.126 (the showing/saying solution); Peter Geach, 'Frege' in Three Philosophers (with G. E. M. Anscombe, Oxford 1961) and Reference and Generality (Cornell 1962/1980); Michael Dummett, Frege: Philosophy of Language Chapter 8, 'The Incompleteness of Concepts and Functions' (1973/1981); P. F. Strawson, Subject and Predicate in Logic and Grammar (Methuen 1974); Crispin Wright, 'Why Frege Does Not Deserve His Grain of Salt' (1998); Marco Ruffino, 'The Concept Horse Paradox: A Frege-Russell-Wittgenstein Reading' (2003).","status":"The distinction is foundational for Frege's mature logical and semantic apparatus and for the function/argument analysis of propositions that founded modern quantification theory. The Concept Horse paradox, first published in *On Concept and Object* (1892), has been continuously discussed in the secondary literature. Wittgenstein's *Tractatus* §4.126 grants the underlying point and resolves it through the showing/saying distinction (the unsaturatedness of a concept can be *shown* by the use of an unsaturated symbol but cannot be *said* in a saturated sentence). Russell discusses the paradox in *Principles of Mathematics* (1903) §49. Geach defends the distinction in *Reference and Generality* (1962/1980) and argues that the paradox reveals a deep truth about predication. Dummett's \"Incompleteness of Concepts and Functions\" (FPL Chapter 8) reads the paradox as a real puzzle that can be resolved by distinguishing levels — the predicate refers to a concept; the saturated phrase \"the concept *horse*\" refers to a related but distinct object (the extension or value-range). Strawson's *Subject and Predicate* (1974) develops an alternative analysis. Wright's \"Why Frege Does Not Deserve His Grain of Salt\" (1998) defends Frege against the suggestion that the paradox shows the distinction itself to be incoherent.","era":"1848-1925","discipline":"Philosophy","refs":[{"n":1,"work":"Collected Papers on Mathematics, Logic, and Philosophy","page":"p. 190","canonical":"","quote":"In the first three examples, on the other hand, 'is' is used like the 'equals' sign in arithmetic, to express an equation.\" In the sentence 'The morning star is Venus', we have two proper names, 'morning star' and 'Venus', for the same object. In the sentence 'the morning star is a planet' we have a proper name, 'the morning star', and a concept-word, 'planet'.","label":"Collected Papers on Mathematics, Logic, and Philosophy, p. 190"},{"n":2,"work":"Posthumous Writings","page":"pp. 191–192","canonical":"","quote":"Of course two complete wholes can stand in a relation to one another; but then this relation is a third element—and one that is doubly unsaturated! In the case of a concept we can also call the unsaturatedness its predicative nature.","label":"Posthumous Writings, pp. 191–192"},{"n":3,"work":"Posthumous Writings","page":"pp. 133–134","canonical":"","quote":"To acknowledge this meaning as that of the True (as the True) is to judge that the object which is taken as the argument falls under the concept. What in the case of a function is called unsaturatedness, we may, in the case of a concept, call its predicative nature.","label":"Posthumous Writings, pp. 133–134"},{"n":4,"work":"Collected Papers on Mathematics, Logic, and Philosophy","page":"p. 287","canonical":"","quote":"Take the proposition 'Two is a prime number'. Linguistically we \"Die Grundlagen der Arithmetik [The Foundations of Arithmetic] (Breslau, 1884), 53, where instead of level', said 'order'; Funktion und Begriff [Function and Concept] (Jena, 18911), p. 26 [this volume p.","label":"Collected Papers on Mathematics, Logic, and Philosophy, p. 287"},{"n":5,"work":"Collected Papers on Mathematics, Logic, and Philosophy","page":"p. 199","canonical":"","quote":"However, it is not my present task to point out contradictions in his exposition; his way of taking the words 'object' and 'concept' is not properly my concern here. J am only trying to set my own usage of these words in a clearer light, and incidentally show that in any case it differs from his, whether that is consistent or not.","label":"Collected Papers on Mathematics, Logic, and Philosophy, p. 199"}],"answer":null,"siblings":[{"slug":"sense-and-reference-sinn-und-bedeutung","label":"Sense and reference (Sinn und Bedeutung): does every meaningful expression have both a sense and a reference, or are proper names directly referential as Kripke claims?"},{"slug":"logicism-and-russell-s-paradox","label":"Logicism and Russell's paradox: is arithmetic reducible to logic, and does the failure of Basic Law V refute the logicist program or only its 1893 formulation?"},{"slug":"anti-psychologism-and-the-third-realm-of-thoughts","label":"Anti-psychologism and the third realm of Thoughts: are Thoughts (Gedanken) objective abstract entities inhabiting a realm distinct from the physical and the psychological?"}]}