Friedrich Ludwig Gottlob Frege

Gottlob Frege (b. 1848, d. 1925) was a German mathematician, logician, and philosopher who worked at the University of Jena. He wrote philosophical works about logic, mathematics, and language.

Principal Works:

Begriffsschrift (`Concept Notation'), eine der arithmetischen nachgebildete Formelsprache des reinen Denkens , Halle a. S., 1879
Die Grundlagen der Arithmetik (`The Foundations of Arithmetic'): eine logisch-mathematische Untersuchung über den Begriff der Zahl, Breslau, 1884
Funktion und Begriff (`Function and Concept'): Vortrag, gehalten in der Sitzung vom 9. Januar 1891 der Jenaischen Gesellschaft für Medizin und Naturwissenschaft, Jena, 1891
`Über Sinn und Bedeutung' (`On Sense and Denotation'), in Zeitschrift für Philosophie und philosophische Kritik, C (1892): 25-50
`Über Begriff und Gegenstand' (`On Concept and Object'), in Vierteljahresschrift für wissenschaftliche Philosophie, XVI (1892): 192-205
Grundgesetze der Arithmetik (`Basic Laws of Arithmetic'), Jena: Verlag Hermann Pohle, Band I (1893), Band II (1903)
`Was ist eine Funktion?' (`What is a Function?'), in Festschrift Ludwig Boltzmann gewidmet zum sechzigsten Geburtstage, 20. Februar 1904, S. Meyer (ed.), Leipzig, 1904, pp. 656-666
`Der Gedanke' (`The Thought'). Eine logische Untersuchung', in Beiträge zur Philosophie des deutschen Idealismus I (1918): 58-77

Frege's Life:

Born, November 8, 1848, in Wismar (Mecklenburg-Schwerin)
1869, entered the University of Jena
1871, entered the University of Göttingen
1873, Ph. D. in Mathematics (Geometry), University of Göttingen
1874, Habilitation in Mathematics, University of Jena
1874, Privatdozent, University of Jena
1879, Professor Extraordinarius, University of Jena
1896-1917, ordenlicher Honorarprofessor, University of Jena
Died, July 26, 1925, in Bad Kleinen (now in Mecklenburg-Vorpommern)

Frege's Advances in Logic:

Frege virtually founded the modern discipline of mathematical logic. He developed a system of conceptual notation (inspired by Leibniz's conception of a rational calculus), and though we no longer use his notation, his system constituted the first predicate calculus. Frege's second-order predicate calculus was based on the `function-argument' analysis of propositions and it freed logicians from the limitations of the `subject-predicate' analysis of Aristotelian logic. Frege's formal system made it possible for logicians to develop a strict definition of a proof. Unfortunately, Frege employed a principle (Basic Law V) in his later system (Grundgesetze) which turned out to be inconsistent. Despite the fact that a contradiction invalidated his system, Frege validly derived the Peano Axioms governing the natural numbers from a powerful and consistent principle now known as Hume's Principle (some philosophers have proposed that the derivation of the Peano Axioms from Hume's Principle should be called `Frege's Theorem'). Frege is most well-known among philosophers, however, for suggesting that the expressions of language have both a sense and a denotation (i.e., that at least two semantic relations are required to explain the significance of linguistic expressions). This seminal idea in the philosophy of language has inspired research in the field for over a century.

Further Reading:

General:

Currie, G., Frege: An Introduction to His Philosophy, Sussex, The Harvester Press (Totowa, NJ: Barnes and Noble), 1982
Dummett, M., `Gottlob Frege', in Encyclopedia of Philosophy (Volume 3), New York: MacMillan, 1967
Zalta, E., `Gottlob Frege', in Stanford Encyclopedia of Philosophy, Philosophy Department.
Zalta, E., `Frege's Logic, Theorem, and Foundations for Arithmetic', in Stanford Encyclopedia of Philosophy, Philosophy Department

Specific:

Anderson, David, and E. Zalta, "Frege, Boolos, and Logical Objects", Journal of Philosophical Logic, 33/1 (February 2004): 1-26
Boolos, G., "Saving Frege From Contradiction", Proceedings of the Aristotelian Society, 87 (1986/87): 137-151
Boolos, G., "The Consistency of Frege's Foundations of Arithmetic", in J. Thomson (ed.), On Being and Saying, Cambridge, MA: The MIT Press, 1987, pp. 3-20
Demopoulos, W., (ed.), Frege's Philosophy of Mathematics, Cambridge, MA: Harvard University Press, 1995
Heck, R., "The Development of Arithmetic in Frege's Grundgesetze Der Arithmetik", Journal of Symbolic Logic, 58/2 (June 1993): 579-601
Parsons, T., "On the Consistency of the the First-Order Portion of Frege's Logical System", Notre Dame Journal of Formal Logic 28/1 (January 1987): 161-168
Resnik, M., Frege and the Philosophy of Mathematics, Ithaca, NY: Cornell University Press, 1980
Sluga, H., Gottlob Frege, London: Routledge and Kegan Paul, 1980
Wright, C., Frege's Conception of Numbers as Objects, Aberdeen: Aberdeen University Press, 1983
Zalta, E., "Natural Numbers and Natural Cardinals as Abstract Objects: A Partial Reconstruction of Frege's Grundgesetze in Object Theory", Journal of Philosophical Logic, 28/6 (1999): 619-660