Frege did not waste time responding to Russell, his letter dated 22 June 1902 appears, with van Heijenoort's commentary in Heijenoort 1967: 126 – 127.

* June 16-Bertrand Russell writes to Gottlob Frege informing him of the mathematical problem that will become known as Russell's paradox.

* June 16-Bertrand Russell writes to Gottlob Frege informing him of the problem in naive set theory that will become known as Russell's paradox.

Russell's awareness of the problem originated in June 1901 with his reading of Frege's treatise of mathematical logic, his 1879 Begriffsschrift ; the offending sentence in Frege is the following:

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.

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.

Frege, Dedekind, and Peano on the foundations of arithmetic.

The main influences on the early logical positivists were the positivist Ernst Mach, Gottlob Frege, Bertrand Russell and the young Ludwig Wittgenstein.

* the philosopher as geometer: centers on formal inquiry ; thinkers from Plato to Frege.

Owing to the gigantic simultaneous efforts of Frege, Dedekind and Cantor, the infinite was set on a throne and revelled in its total triumph.

( Many of the philosophical doctrines of the mature Frege have parallels in Lotze ; it has been the subject of scholarly debate whether or not there was a direct influence on Frege's views arising from his attending Lotze's lectures.

From Frege to Gödel: A Source Book on Mathematical Logic.

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

Husserl had reacted strongly to Gottlob Frege's criticism of his first work on the philosophy of arithmetic and was investigating the sense of mathematical and other structures, which Frege had distinguished from empirical reference.

Bertrand Russell famously rejected Frege's sense-reference distinction, though there is some possibility that the two were misinterpreting and arguing past one another: Frege talks about ( for example ) sentences, which have both a sense ( a proposition ) and a reference ( a truth value ); Russell on the other hand deals directly with propositions, but construes these not as abstract para-linguistic items but as tuples, or sets, of objects and concepts.

So in fact if Frege's view was " descriptivist ", then he effectively agrees with Russell on most of the apparent " proper names " of ordinary language: Frege thinks that " Aristotle " is a name, with a sense, which is equivalent to some description.

* 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 ' '

They co-authored the 1961 book Three Philosophers, with Anscombe contributing a section on Aristotle and Geach one each on Aquinas and Gottlob Frege.

But Frege criticized Cantor on the ground that Cantor defines cardinal numbers in terms of ordinal numbers, whereas Frege wanted to give a characterization of cardinals that was independent of the ordinals.

This is clearly awkward, and is a weakness exploited by Frege in his devastating attack on the system ( from which, ultimately, it never recovered ).

Boolos was an authority on the 19th-century German mathematician and philosopher Gottlob Frege.

This book reprints much of Boolos's work on the rehabilitation of Frege, as well as a number of his papers on set theory, second-order logic and nonfirstorderizability, plural quantification, proof theory, and three short insightful papers on Gödel's Incompleteness Theorem.

Yes, says Frege, and on that account the concept is a horse is not a concept at all.

Includes Frege's 1879 Begriffsschrift with commentary by van Heijenoort, Russell's 1908 Mathematical logic as based on the theory of types with commentary by Willard V. Quine, Zermelo's 1908 A new proof of the possibility of a well-ordering with commentary by van Heijenoort, letters to Frege from Russell and from Russel to Frege, etc.

After Carl's death, the school was led by Frege's mother Auguste Wilhelmine Sophie Frege ( née Bialloblotzky of Polish descent, 12 January 1815 – 14 October 1898 ).

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.

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.