## 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 …

## 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.

## 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.