Is Frege and Russell’s definition of number reducible to Hilbert’s?

What is a number Bertrand Russell?

The class of all couples, however, is the number two. With this in mind, Russell defines number : ” A number (in general) is any collection which is the number of one of its members; or more simply still: A number is anything which is the number of some class ” (10).

What is a number Frege?

Frege’s definition of a number

Frege defines numbers as extensions of concepts. ‘The number of F’s’ is defined as the extension of the concept G is a concept that is equinumerous to F. The concept in question leads to an equivalence class of all concepts that have the number of F (including F).

What is a concept for Frege?

Frege’s suggestion is that “the number of Fs” means the same as “the value-range of the concept being a value-range of a concept instantiated equally many times as F.” This means that the number of Fs is a certain value-range, containing value-ranges, and in particular, all those value-ranges that have as many members …

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Who wrote Frege a letter in which he pointed out a paradox in Frege’s system thus undermining Frege entire logical program?

Frege was made aware of the inconsistency by Bertrand Russell, who sent him a letter formulating ‘Russell’s Paradox’ just as the second volume of Gg was going to press. Frege quickly added an Appendix to the second volume, describing two distinct ways of deriving a contradiction from Basic Law V.

What is Russell’s view of passions or emotions?

(It probably helped that he lived to be ninety-seven years old.) “Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind.” (The Autobiography of Bertrand Russell: Volume I, 1967).

How does Russell define knowledge?

According to Russell, knowledge is based on acquaintance with self-evident truths. True propositions which are not self-evident may have to be demonstrated to be true by self-evident propositions in order to become objects of knowledge.

What is the Frege Geach problem?

Briefly, the Frege-Geach problem is that sentences that express moral judgments can form part of semantically complex sentences in a way that an expressivist cannot easily explain.

What is Frege’s system of logic?

Frege essentially reconceived the discipline of logic by constructing a formal system which, in effect, constituted the first ‘predicate calculus‘. In this formal system, Frege developed an analysis of quantified statements and formalized the notion of a ‘proof’ in terms that are still accepted today.

Who solved Russell’s paradox?

Russell’s paradox (and similar issues) was eventually resolved by an axiomatic set theory called ZFC, after Zermelo, Franekel, and Skolem, which gained widespread acceptance after the axiom of choice was no longer controversial.

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What is an example of Russell’s paradox?

Russell’s paradox is based on examples like this: Consider a group of barbers who shave only those men who do not shave themselves. Suppose there is a barber in this collection who does not shave himself; then by the definition of the collection, he must shave himself. But no barber in the collection can shave himself.

What was Bertrand Russell’s theory?

It was Russell’s belief that by using the new logic of his day, philosophers would be able to exhibit the underlying “logical form” of natural-language statements. A statement’s logical form, in turn, would help resolve various problems of reference associated with the ambiguity and vagueness of natural language.

What is the most known paradox?

Russell’s paradox is the most famous of the logical or set-theoretical paradoxes. Also known as the Russell-Zermelo paradox, the paradox arises within naïve set theory by considering the set of all sets that are not members of themselves.

What are the three types of paradoxes?

Three types of paradoxes

  • Falsidical – Logic based on a falsehood.
  • Veridical – Truthful.
  • Antinomy – A contradiction, real or apparent, between two principles or conclusions, both of which seem equally justified.

How many different paradoxes are there?

There are four generally accepted types of paradox. The first is called a veridical paradox and describes a situation that is ultimately, logically true, but is either senseless or ridiculous.

What is the different paradox?

Knower paradox: “This sentence is not known.” Liar paradox: “This sentence is false.” This is the canonical self-referential paradox. Also “Is the answer to this question ‘no’?”, and “I’m lying.” Card paradox: “The next statement is true.

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