What is a concept for Frege?

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 a …

What did Gottlob Frege discover?

In effect, Frege invented axiomatic predicate logic, in large part thanks to his invention of quantified variables, which eventually became ubiquitous in mathematics and logic, and which solved the problem of multiple generality.

What is Gottlob Frege known for?

Friedrich Ludwig Gottlob Frege (b. 1848, d. 1925) was a German mathematician, logician, and philosopher who worked at the University of Jena. Frege essentially reconceived the discipline of logic by constructing a formal system which, in effect, constituted the first ‘predicate calculus’.

What is the sense of a sentence Frege?

The reference of a sentence is its truth value, whereas its sense is the thought that it expresses. Frege justified the distinction in a number of ways. Sense is something possessed by a name, whether or not it has a reference.

What is concept give an example?

In the simplest terms, a concept is a name or label that regards or treats an abstraction as if it had concrete or material existence, such as a person, a place, or a thing. For example, the word “moon” (a concept) is not the large, bright, shape-changing object up in the sky, but only represents that celestial object.

Why is Frege important?

Gottlob Frege was a German logician, mathematician and philosopher who played a crucial role in the emergence of modern logic and analytic philosophy. Frege’s logical works were revolutionary, and are often taken to represent the fundamental break between contemporary approaches and the older, Aristotelian tradition.

What is a thought Frege?

Frege, 1918, p.302) “When one apprehends or thinks a thought one does not create it but only comes to stand in a certain relation, which is different from seeing a thing or having an idea, to what already existed beforehand.” ( ibid, fn)

What’s a word that has a sense but no referent?

Thus, there are words that have a sense, but no referents in the real world. The term denotation (that is also frequently used in the sense of an extensional reference) refers to the constant, abstract, and basic meaning of a linguistic expression.

What is a number Frege?

Frege argues that numbers are objects and assert something about a concept. Frege defines numbers as extensions of concepts. So, the number of this concept is the extension of the concept of all concepts that have no objects falling under them. The number 1 is the extension of being identical with 0.

What is a natural concept?

A natural concept is a mental representation of events or objects drawn from personal experience, because of this ability to create a mental representation, kind of like a mental blueprint, we are able to perform previously learned tasks (like tying shoes) without needing instructions each time.

What was the inconsistency in Frege’s Grundgesetze?

The inconsistency in Frege’s Grundgesetze overshadowed Frege’s achievement: according to Edward Zalta, the Grundgesetze “contains all the essential steps of a valid proof (in second-order logic) of the fundamental propositions of arithmetic from a single consistent principle.” This achievement has become known as Frege’s theorem.

Is the Grundgesetze a valid proof of arithmetic?

Until late in the 20th century, the inconsistency in Frege’s Grundgesetze overshadowed a deep theoretical accomplishment that can be extracted from his work. The Grundgesetze contains all the essential steps of a valid proof (in second-order logic) of the fundamental propositions of arithmetic from a single consistent principle.

What did Friedrich Frege do in the Grundlagen?

More generally, Frege provides in the Grundlagen a non-technical philosophical justification and outline of the ideas that he was to develop technically in his two-volume work Grundgesetze der Arithmetik (1893/1903). In the years 1891–1892, Frege published three of his most well-known papers]

What is the meaning of Frege’s theorem?

Frege’s theorem. In metalogic and metamathematics, Frege’s theorem is a metatheorem that states that the Peano axioms of arithmetic can be derived in second-order logic from Hume’s principle.