The distinction between concept and object is due to the German philosopher Gottlob Frege. Friedrich Ludwig Gottlob Frege Friedrich Ludwig Gottlob Frege (November 8, 1848 - July 26, 1925) was a German mathematician, logician, and philosopher who is regarded as a founder of both modern mathematical logic and analytic philosophy. ...

According to Frege, any sentence that expresses a singular proposition consists of an expression (a proper name or a general term plus the definite article) that signifies an Object together with a predicate (the copula "is", plus a general term accompanied by the indefinite article or an adjective) that signifies (bedeuten) a Concept. Thus "Socrates is a philosopher" consists of "Socrates", which signifies the Object Socrates, and "is a philosopher", which signifies the Concept of being a philosopher. A proper name [is] a word that answers the purpose of showing what thing it is that we are talking about writes John Stuart Mill in A System of Logic (1. ... The word copula originates from the Latin noun for a link or tie that connects two different things. ...

This was a considerable departure from the traditional term logic, in which every proposition (i.e. sentence) consisted of two general terms joined by the copula "is". Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century. ...

The distinction was of fundamental importance to the development of logic and mathematics, leading to the ideas of an element, of a set, of the membership relation between element and set, and of empty and infinite sets. Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... In mathematics, the empty set is the set with no elements. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ...

Frege's definition leads to the famous difficulty or "awkwardness of language" that any expression purporting to signify a concept - Frege's example is "the concept horse" - is grammatically an expression that by his criterion signifies an Object. Thus "the concept horse is not a concept, whereas the city of Berlin is a city".

Anthony Kenny sought to justify the distinction, other philosophers such as Hartley Slater and Crispin Wright have argued that the distinguished category of entity cannot be associated with predication in the way that individual objects are associated with the use of singular terms. Sir Anthony John Patrick Kenny (born 1931) is an important English philosopher whose interests lie in the philosophy of mind, scholastic and ancient philosophy, the philosophy of Wittgenstein and (particularly) the philosophy of religion. ... Crispin Wright is a British philosopher, who has written on neo-Fregean philosophy of mathematics, Wittgensteins later philosophy, and on issues related to truth, realism, skepticism, knowledge and objectivity. ... There is no really adequate definition of singular term. ...

References

• Buckner, E.D. review of Sainsbury, R.M., Departing from Frege: Essays in the philosophy of language (http://ndpr.icaap.org/content/archives/2003/8/buckner-sainsbury.html), Routledge, 2002, 234 pp, ISBN 0-415-27255-6
• Dummett, Michael. Frege: Philosophy of Language, chap.7, pp.211-219.
• Diamond, Cora. “What does a Concept-Script Do?” sec.II.
• Frege, G. "On Concept and Object", originally published as " Über Begriff und Gegenstand" in Vierteljahresschrift für wissenschaftliche Philosophie 16, 1892, S. 192-205, translated in Geach & Black 1952 pp. 42-55.
• Geach, P., Reference & Generality, Ithaca NY 1962.
• Geach, P. & Black M., Translations from the Philosophical writings of Gottlob Frege, Oxford 1952
• Resnik, Michael David. “Frege’s Theory of Incomplete Entities,” especially sec. 5-7.
• Russell, B. Principles of Mathematics, § 21, and § 475 - § 496.
• Slater, B.H. "Concept And Object In Frege" (http://www.ul.ie/~philos/vol4/frege.html), 2000 (Minerva)
• Wright, C. "Why Frege does not deserve his grain of salt: a Note on the Paradox of "The Concept Horse" and the Ascription of Bedeutungen to Predicates", ' 'Grazer Philosophische Studien 5' '