Michael Dummett traces the linguistic turn to Frege's Grundlagen and his context principle.

It did, however, draw the attentions of Bertrand Russell and Ludwig Wittgenstein, who were both heavily influenced by Frege's philosophy.

Frege invokes his "context principle", stated at the beginning of the book, that only in the context of a proposition do words have meaning, and thus finds the solution to be in defining "the sense of a proposition in which a number word occurs."

He sees a fundamental distinction between logic (and its extension, according to Frege, math) and psychology.

Logic explains necessary facts, whereas psychology studies certain thought processes in individual minds.

Kant wrongly assumes that in a proposition containing "big" numbers we must count points or some such thing to assert their truth value.

Frege argues that without ever having any intuition toward any of the numbers in the following equation: 654,768+436,382=1,091,150 we nevertheless can assert it is true.

Asking "how many" is nonsense without the further clarification of cards or suits or what, showing numbers belong to concepts, not to objects.

Frege contends a proper theory of mathematics would explain why Julius Caesar is not a number.

He attempts to construct the content of a judgment involving numerical identity by relying on Hume's principle (which states that the number of Fs equals the number of Gs if and only if F and G are equinumerous, i.e. in one-one correspondence).

Frege goes on to give an explicit definition of number in terms of extensions of concepts, but expresses some hesitation.

[16] The book was fundamental in the development of two main disciplines, the foundations of mathematics and philosophy.

Although Bertrand Russell later found a major flaw in Frege's Basic Law V (this flaw is known as Russell's paradox, which is resolved by axiomatic set theory), the book was influential in subsequent developments, such as Principia Mathematica.

The book can also be considered the starting point in analytic philosophy, since it revolves mainly around the analysis of language, with the goal of clarifying the concept of number.