Gottlob Frege

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Frege, Gottlob

(gôt`lōp frā`gə), 1848–1925, German philosopher and mathematician. He was professor of mathematics (1879–1918) at the Univ. of Jena. Frege was one of the founders of modern symbolic logicsymbolic logic
or mathematical logic,
formalized system of deductive logic, employing abstract symbols for the various aspects of natural language. Symbolic logic draws on the concepts and techniques of mathematics, notably set theory, and in turn has contributed to
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, and his work profoundly influenced Bertrand Russell. He claimed that all mathematics could be derived from purely logical principles and definitions. He considered verbal concepts to be expressible as symbolic functions with one or more variables. His books include Begriffsschrift (1879); Die Grundlagen der Arithmetik (1884; tr. The Foundations of Arithmetic, 1950); Grundgesetze der Arithmetik (2 vol., 1893–1903).

Bibliography

See P. T. Geach and M. Black, ed., Philosophical Writings of Gottlob Frege (1952); M. Resnik, Frege and the Philosophy of Mathematics (1980); M. Dummett, The Interpretation of Frege's Philosophy (repr. 1981).

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Frege, Gottlob

 

Born Nov. 8, 1848, in Wismar; died July 26, 1925, in Bad Kleinen. German logician.

Frege received his Ph.D. from the University of Göttingen in 1873. He was a professor at the University of Jena from 1879 to 1918. Frege’s principal work was The Fundamental Laws of Arithmetic (vols. 1–2, 1893–1903), in which he proposed a system of formalized arithmetic based on a second-order predicate calculus that he developed. His intention was to provide a substantiation of the notion of the reducibility of mathematics to logic (seeLOGICISM).

REFERENCES

Biriukov, B. V. “O rabotakh Frege po filosofskim voprosam matematiki.” In the collection Filosofskie voprosy estestvoznaniia, fasc. 2. Moscow, 1959.
Stiazhkin, N. I. Formirovanie matematicheskoi logiki. Moscow, 1967. (Contains bibliography.)
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

Gottlob Frege

(1)

Gottlob Frege

(person, history, philosophy, mathematics, logic, theory)
(1848-1925) A mathematician who put mathematics on a new and more solid foundation. He purged mathematics of mistaken, sloppy reasoning and the influence of Pythagoras. Mathematics was shown to be a subdivision of formal logic.

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References in periodicals archive ?
The latter, of course, is held by any Fregean logicist, Tennant in particular.
As Marcus notes, Russell's 'propositions' were, from our perspective, misnamed - they are rather more like states of affairs than they are like Fregean propositions.
One motivation for this move, I take it, is that to say that the individual words of a fiction 'refer to universals' is presumably to say no more than that they, and the sentences they compose, possess (Fregean) sense; which, as Frege justly observes, need not entail that they possess reference or are assessable for truth.
Five Fregean philosophical principles are presented as constituting a framework for a theory of logical or conceptual analysis, which may be called analytical explication.
(McGinn 1984, p.174) While making for a neat argument, this Fregean, formal conception of natural language semantics as being rooted in meaning identity falls foul of Wittgenstein's criticism of being dazzled by the "crystalline purity of logic".
Beaney very concisely discusses the key issues in Fregean semantics--the function-argument analysis, the distinction between subordination and subsumption, the fundamental distinction between object and concept, identity statements, types of context, compositionality, and, obviously, the sense and reference of names, sentences and concept-words.
Nor will I go into Potter's well-taken criticisms of recent attempts to salvage Fregean logicism by founding it on a version of Frege's Grundlagen argument for the analyticity of NE by appeal to the idea that the content of each side of this equivalence is a "recarving" of the content of the other.
"Transparency" includes both semantic transparency--the notion that the meaning of a word should be predictable from the meaning of its constituent morphemes ("the Fregean principle of compositionality")--and morphotactic transparency (segmentability).
Peacocke's assignments allocate standard Fregean values to expressions (or to the concepts they express): objects to terms, functions-from-objects-to-truth-values (or, less scrupulously, sets) to predicates, functions-from-truth-values-to-truth-values to propositional operators, and so on.
Indeed I am inclined to think that this is where the stress, in applying the Fregean model, should fall.
The possibility thus remains of accepting the notion of class as a logical notion and reconstruing a broadly Fregean approach within a constructivist framework.
In this essay, the author distinguishes two ways of depsychologizing psychology: "antipsychologism" and "nonpsychologism." Both positions are responses to the Fregean sharp distinction between the logical and the psychological.