The creator of modern logic was born in the Pomeranian town of Wismar. His father was headmaster at a school for young ladies, which Frege's mother took over after her husband's early death. Frege studied mathematics at the University of Jena. His studies were encouraged by Ernst Abbe, who encouraged him to obtain a doctorate at Gottingen and then helped him secure a position as lecturer at Jena in 1874. Although trained as a mathematician, Frege also studied with Lotze at Gottingen, and his work shows the influence of both Leibniz and Kant. After the publication in 1879 of Frege's first important work, the Begriffschrift (Conceptual Notation), he was promoted to professor, and he remained at the University of Jena the rest of his life. The Begriffschrift was the basis of his new system of logic, which he then sought to apply to the task of deriving number theory entirely from logic, via the theory of classes. This he did in The Foundations of Arithmetic (1884). The next decade saw several of Frege's other important papers on the philosophy of logic and language, including "Function and Concept" (1891), "Concept and Object" (1892), and "Sense and Reference" (1892). Frege was an extreme critic of "psychologism" in logic, mathematics, and philosophy of language---that is, of any view that attempts to treat logic or other sciences pursuing necessary truth as sciences whose subject matter is the actual functioning of the human mind as it can be empirically observed. His critique of psychologism had a far-reaching impact on philosophy in the twentieth century, strongly influencing the development not only of logical positivism and analytical philosophy in English-speaking countries, but also of neo-Kantianism and the phenomenological movement on the continent. After the publication of the Foundations, Frege became aware of certain deficiencies in the logical basis of his theory, which he attempted to remedy in his two-volume Fundamental Laws of Arithmetic (1893--1903). Shortly thereafter, Frege received a letter from Bertrand Russell, which pointed out a contradiction in his theory, since it allowed classes to include themselves as members. Take the class of all classes that are not members of themselves, Russell said; if you assume it is a member of itself, then it follows that it is not, and if you assume it is not, then it follows that it is. Frege attempted to evade the Russell Paradox in a hastily composed appendix, but it was ad hoc and has generally been viewed as unsuccessful. Even apart from this, he later became convinced that the whole project of founding mathematics on logic was doomed to failure.

One aim of this volume is to make available to English readers Frege's more important logical essays, which have long been buried in various German periodicals (mostly now defunct). Besides these we have given certain extracts from his Grundgesetze der Arithmetik; these can be understood in the light of the essays, without the reader's needing to follow the chain of deduction in the Grundgesetze.

Special attention should be paid to Frege's discussion of Russell's paradox in the appendix to Vol. ii of the Grundgesetze. It is discreditable that logical works should repeat the legend of Frege's abandoning his researches in despair when faced with the paradox; in fact he indicates a line of solution, which others (e.g. Quine) have followed out farther.

The authorship of the various versions is stated in the table of contents. All versions have been revised with a view to uniform rendering of Frege's special terms; a glossary of these terms is supplied.

Footnote flags such as A, B, relate to translators' footnotes; other footnotes are Frege's own.

Acknowledgments are due to the editors of Mind and the Philosophical Review, for permission to use versions first published there. Acknowledgment is also due for use of the translations made from Vol. I of the Grundgesetze by P. E. B. Jourdain and J. Stachelroth (which were first published in the Monist, 1915-17), to the owners of the copyright, whom it has unfortunately proved impossible to trace. Professor Ryle and Lord Russell have been most helpful by lending works of Frege that were otherwise almost unobtainable.