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.

However, the methods developed by Frege and Tarski for the study of mathematical language have been extended greatly by Tarski's student Richard Montague and other linguists working in formal semantics to show that the distinction between mathematical language and natural language may not be as great as it seems.

This reading of Frege has been rejected by many scholars, most strongly by Gareth Evans in The Varieties of Reference and by John McDowell in " The Sense and Reference of a Proper Name ", following lines developed by Michael Dummett.

Gottlob Frege developed a kind of two dimensional semantics: for resolving questions like those of intensional statements, he has introduced a distinction between two semantic values: sentences ( and individual terms ) have both an extension and an intension.

It was invented by Gottlob Frege, who also invented predicate calculus, in 1879 as part of his second-order predicate calculus ( although Charles Peirce was the first to use the term " second-order " and developed his own version of the predicate calculus independently of Frege ).

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 ).

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.

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 is commonly held that Frege held such a view — the description being embedded in what he called the sense ( Sinn ) of the name.

Some argue that Avicenna anticipated Frege and Bertrand Russell in " holding that existence is an accident of accidents " and also anticipated Alexius Meinong's " view about nonexistent objects.

Frege uses the following example to illustrate this view.

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.

In Saul Kripke's famous Naming and Necessity lectures, which largely turned the tide against descriptivism, he treats both Russell and Frege as opposed to Mill's view in the same way.

See also Gottlob Frege 1895 for a critique of an earlier view defended by Ernst Schroeder.

This was Russell's view, and was and is taken by many to be equivalent to Frege's view ( where the description is what Frege calls a term's " sense ").

This is very widely – though not universally – regarded as having shown the logicist program of Frege to be impossible to complete.

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.

Frege then wrote an appendix admitting to the paradox, and proposed a solution that Russell would endorse in his Principles of Mathematics, but was later considered by some unsatisfactory.

In contrast, the later logicist program of Gottlob Frege and Bertrand Russell attempted to base mathematics on logic.

The principle that cardinal number was to be characterized in terms of one-to-one correspondence had previously been used to great effect by Georg Cantor, whose writings Frege knew.

Schröder's influence on the early development of the predicate calculus, mainly by popularising C. S. Peirce's work on quantification, is at least as great as that of Frege or Peano.

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.

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

The German mathematician Gottlob Frege ( 1848 – 1925 ) presented an independent development of logic with quantifiers in his Begriffsschrift ( formula language ) published in 1879, a work generally considered as marking a turning point in the history of logic.

The group considered themselves logical positivists because they believed all knowledge is either derived through experience or arrived at through analytic statements, and they adopted the predicate logic of Frege, as well as the early work of Ludwig Wittgenstein ( 1889 – 1951 ) as foundations to their work.

Although the formalisation of logic was much advanced by the work of such figures as Gottlob Frege, Giuseppe Peano, Bertrand Russell, and Richard Dedekind, the story of modern proof theory is often seen as being established by David Hilbert, who initiated what is called Hilbert's program in the foundations of mathematics.

Serious metamathematical reflection began with the work of Gottlob Frege, especially his Begriffsschrift.

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.

In the years 1925-1926, the Thursday night group discussed recent work in the foundations of mathematics by Gottlob Frege, Bertrand Russell, and Ludwig Wittgenstein.

He made contributions to the philosophy of language, the philosophy of mathematics and science, and the philosophy of art, also publishing studies of the work of philosophers such as 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.

However, today most students of logic are more familiar with the works of Frege, who actually published his work several years prior to Peirce but whose works remained in obscurity until Bertrand Russell and Alfred North Whitehead made them famous.

The oldest definition of the cardinality of a set X ( implicit in Cantor and explicit in Frege and Principia Mathematica ) is as the set of all sets which are equinumerous with X: this does not work in ZFC or other related systems of axiomatic set theory because this collection is too large to be a set, but it does work in type theory and in New Foundations and related systems.

Frege ( 1960 ) dismissed Schröder's work, and admiration for Frege's pioneering role has dominated subsequent historical discussion.

Symbolic computational approaches to creating intelligent machines had long been the focus of AI since the days of Alan Turing, directly tracing back to the work of Gottlob Frege.

He also defends a reading of Frege, derived in part from Michael Dummett's work, according to which Frege's notion of sense is not equivalent to a description, and indeed remains essential to a theory of reference that abandoned descriptivism ( 1982, § 1. 3 ).

In most years, Kaplan teaches an upper division course on philosophy of language, focusing on the work of either Gottlob Frege, Bertrand Russell, or P. F.

Hintikka's work can be seen as a continuation of analytic tendency in philosophy founded by Brentano and Peirce, advanced by Frege and Bertrand Russell, and continued by Carnap, Quine, and by Hintikka's teacher Georg Henrik von Wright.

In the tradition of analytical philosophy, according to Michael Dummett the linguistic movement first took shape in Gottlob Frege's 1884 work The Foundations on Arithmetic, specifically paragraph 62 where Frege explores the identity of a numerical proposition.

In philosophical logic, Martin-Löf has wrestled with the philosophy of logical consequence and judgment, partly inspired by the work of Brentano, Frege, and Husserl.

In his Logical Investigations, Husserl mentions Frege only twice, once in a footnote to point out that he had retracted three pages of his criticism of Frege's The Foundations of Arithmetic, and again to question Frege's use of the word Bedeutung to designate " reference " rather than " meaning " ( sense ).

Psychologism was famously criticized by Frege in his The Foundations of Arithmetic, and many of his works and essays, including his review of Husserl's Philosophy of Arithmetic.

* Gottlob Frege, Foundations of Arithmetic.

1998, " Gottlob Frege and the Foundations of Arithmetic.

* Gottlob Frege publishes Die Grundlagen der Arithmetik (" The Foundations of Arithmetic ") presenting a theory of logicism.

Frege in particular sought to demonstrate ( see Gottlob Frege, The Foundations of Arithemetic, 1884, and Logicism in Philosophy of mathematics ) that arithmetical truths can be derived from purely logical axioms and therefore are, in the end, logical truths.

* Benacerraf, Paul ( 1981 ) Frege: The Last Logicist, The Foundations of Analytic Philosophy, Midwest Studies in Philosophy, 6: l7-35.

Psychologism was famously criticized by Frege in his The Foundations of Arithmetic, and many of his works and essays, including his review of Husserl's Philosophy of Arithmetic.