We aim to expose in this research the complementary relationship The Fundamentals of Arithmetic and About Meaning and Reference. In the first writing, we have the presentation of the ontological theses related to the number and its epistemological bases. The first text dates from 1884 and seeks to answer this question: What is the number? However, to reach this goal, he ends up refuting several views, especially that of Stuart Mill, as he dialogues directly with Immanuel Kant. Frege concludes that number is not a property of things, just as it is not something subjective or psychological, constituting itself as a logical object. Thus, it appears that in the second writing of 1892, the author seeks to answer the problem of mathematical equality, presenting as a solution the concept of meaning and its existence in a third kingdom, in the latter where we would already have present logical objects - located between the materiality of things and our subjective perception. With this in mind, we postulate as a fundamental justification of this project the test of the following hypothesis: that the third kingdom Fregean concept would be complemented by its semantic theory, more precisely, by the concept of meaning, which would expose the systematic relationship between the above works.
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