On Frege's theory of natural numbers and necessity of intuitions in mathematics

This thesis attempts to argue against Frege?s theory of arithmetic and points out the logical andmathematical discrepancies of his system according to which arithmetic could be built on purelylogical grounds and hence could have foundations devoid of intuitions. It concentrates mainly on the?definite article premise? as one of the faults of Frege?s theory of arithmetic where the definite articleserves to classify something as an object. Although Frege?s formulation had failed, it is so alluring tobuild arithmetic on logical grounds with the new rules introduced by him and again so tempting toascribe numbers to concepts, that appearance of these discrepancies did not stop pursuing logiciststrying to find better formulations still for similar purposes. They have taken the problem in Frege?ssystem as his assumption on ?extensions of concepts are objects?. Although that was one of thereasons that his system of arithmetic is undermined Frege did not use this as one of the main premiseswhile building his theory in his Grundlagen. The ?definite article premise? is one of the mainpremises along with the ?context principle? and definite article premise provided a tool for Frege todefine numbers as logical objects. By this tool he could distinguish linguistically concept of cardinalnumber and cardinal number as an object so that they could have different terms which denotedifferent things. I will discuss that the ?definite article premise? itself is ineffectual. Frege?s logicistsystem is undermined for one of the premises in his argumentation is problematic. Particularly, the?definite article premise? cannot classify the concept words for numbers as objects words (propernames). Since his logicist project fails to be completed, it is not possible to secure the referent ofnumber terms as logical objects. And this brings back the possibility of intuitions for cognizing thebasic mathematical objects in arithm