This method of inquiry is largely indebted to the work of philosophers such as Gottlob Frege, Bertrand Russell, G. E.

* Frege, G. ( 1892 ) " On Sense and Reference ", originally published as " Über Sinn und Bedeutung " in Zeitschrift für Philosophie und philosophische Kritik, vol.

* Three Philosophers: Aristotle ; Aquinas ; Frege ( with G. E. M.

** Frege, G., 1960, " A critical elucidation of some points in E. Schröder's Vorlesungen über die Algebra der Logik ", translated by Geach, in Geach & Black, Translations from the philosophical writings of Gottlob Frege.

* Frege, G. ( 1918 ) Ricerche Logiche.

Gottlob Frege did explicitly axiomatize a theory in which the formalized version of naive set theory can be interpreted, and it is this formal theory which Bertrand Russell actually addressed when he presented his paradox.

However, the term naive set theory is also used in some literature to refer to the set theories studied by Frege and Cantor, rather than to the informal counterparts of modern axiomatic set theory ; care is required to tell which sense is intended.

Gottlob Frege, founder of the analytic tradition in philosophy, famously argued for the analysis of language in terms of sense and reference.

Since many commentators view the notion of sense as identical to the notion of concept, and Frege regards senses as the linguistic representations of states of affairs in the world, it seems to follow that we may understand concepts as the manner in which we grasp the world.

From Frege to Godel: A Source Book in Mathematical Logic, 1879 – 1931.

Franz Brentano challenged this ; so also ( as is better known ) did Frege.

According to the direct-reference view, an early version of which was originally proposed by Bertrand Russell, and perhaps earlier by Gottlob Frege, a proper name strictly has no meaning when there is no object to which it refers.

It drew the adverse notice of Gottlob Frege, who criticized its psychologism.

In his professorial doctoral dissertation, On the Concept of Number ( 1886 ) and in his Philosophy of Arithmetic ( 1891 ), Husserl sought, by employing Brentano's descriptive psychology, to define the natural numbers in a way that advanced the methods and techniques of Karl Weierstrass, Richard Dedekind, Georg Cantor, Gottlob Frege, and other contemporary mathematicians.

Likewise, in his criticism of Frege in the Philosophy of Arithmetic, Husserl remarks on the distinction between the content and the extension of a concept.

Contrary to what Frege states, in Husserl's Philosophy of Arithmetic we already find two different kinds of representations: subjective and objective.

Husserl makes no mention of Frege as a decisive factor in this change.

In a letter dated May 24, 1891, Frege thanked Husserl for sending him a copy of the Philosophy of Arithmetic and Husserl's review of Ernst Schröder's Vorlesungen über die Algebra der Logik.

In the same letter, Frege used the review of Schröder's book to analyze Husserl's notion of the sense of reference of concept words.

Hence Frege recognized, as early as 1891, that Husserl distinguished between sense and reference.

Consequently, Frege and Husserl independently elaborated a theory of sense and reference before 1891.

Frege, however, did not conceive of objects as forming parts of senses: If a proper name denotes a non-existent object, it does not have a reference, hence concepts with no objects have no truth value in arguments.

According to Frege the reference of a sentence is a truth value ; for Husserl it is a " state of affairs.

" Frege's notion of " sense " is unrelated to Husserl's noema, while the latter's notions of " meaning " and " object " differ from those of Frege.

In fine, Husserl's conception of logic and mathematics differs from that of Frege, who held that arithmetic could be derived from logic.

Word and Object in Husserl, Frege, and Russell: The Roots of Twentieth-Century Philosophy.

* Mohanty, J. N., 1974, " Husserl and Frege: A New Look at Their Relationship ", Research in Phenomenology 4: 51-62.

Husserl and Frege.

Logical empiricism ( aka logical positivism or neopositivism ) was an early 20th century attempt to synthesize the essential ideas of British empiricism ( e. g. a strong emphasis on sensory experience as the basis for knowledge ) with certain insights from mathematical logic that had been developed by Gottlob Frege and Ludwig Wittgenstein.

In 1873, Frege attained his doctorate under Ernst Schering, with a dissertation under the title of " Über eine geometrische Darstellung der imaginären Gebilde in der Ebene " (" On a Geometrical Representation of Imaginary Forms in a Plane "), in which he aimed to solve such fundamental problems in geometry as the mathematical interpretation of projective geometry's infinitely distant ( imaginary ) points.

* Moses Schönfinkel, 1924, " Über die Bausteine der mathematischen Logik ," translated as " On the Building Blocks of Mathematical Logic " in From Frege to Gödel: a source book in mathematical logic, 1879 – 1931, Jean van Heijenoort, ed.

Sinn and bedeutung were introduced by German philosopher and mathematician Gottlob Frege in his 1892 paper " Über Sinn und Bedeutung " (" On sense and reference ").

* Gottlob Frege: On Sense and Reference ( English translation by Max Black )

Russell found that certain logical contradictions could be avoided if names were considered disguised definite descriptions ( a similar view is often attributed to Frege, mostly on the strength of a footnoted comment in On Sense and Reference, although many Frege scholars consider this attribution misguided ).

The syllogism was superseded by first-order predicate logic following the work of Gottlob Frege, in particular his Begriffsschrift ( Concept Script ) ( 1879 ), but syllogisms remain useful.

According to Frege, any sentence that expresses a singular thought 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 ( bedeutet ) a Concept.

" Why Frege should not have said ` the Concept Horse is not A Concept '," history of Philosophy Quarterly 3 ( 1986 ) 449-65.

" Concept And Object In Frege ", 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 ' '

Assume that " Shergar is a horse " analyses into what " Shergar " names ( an " Object ", according to Frege ), and what " is a horse " names ( a " Concept ").

( 2001 ) Bolzano, Frege, and Husserl on Reference and Object.