# How does Frege’s definition of number solve the Julius Caesar problem?

## What is Frege’s Julius Caesar problem?

The Julius Caesar Problem

A neo-Fregean argument to the effect that every object belongs to a unique category is criticized and an alternative, more pragmatic argument to the same effect is developed. The handling of such mixed identity statements often needs conceptual decisions, not just factual discoveries.

## 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 did Frege do?

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 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 …

## 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.