Thinker · TH-0187
Gottlob Frege
Gottlob Frege was a German mathematician, logician and philosopher who taught at the University of Jena. His Begriffsschrift of 1879 created modern predicate logic…
Gottlob Frege was a German mathematician, logician and philosopher who taught at the University of Jena. His Begriffsschrift of 1879 created modern predicate logic with quantifiers, and he tried to show that arithmetic reduces to logic, a project damaged when Russell found a contradiction in his system in 1902. His distinction between sense and reference, introduced to explain how identity statements can be informative, together with his attack on psychologism, made him a founder of analytic philosophy and the philosophy of language.
Key ideas
- Quantifiers and variables allow logic to handle statements about all and some with full generality.
- Expressions have both a reference and a sense, a mode of presentation, which explains why 'the morning star is the evening star' is informative.
- Logic and number are objective, not psychological; laws of logic are laws of truth, not of thinking.
- Numbers are objects, and arithmetic can be derived from logic plus definitions (logicism).
Major works
- Begriffsschrift (1879)
- The Foundations of Arithmetic (Die Grundlagen der Arithmetik, 1884)
- "On Sense and Reference" (Über Sinn und Bedeutung, 1892)
- Basic Laws of Arithmetic (Grundgesetze der Arithmetik, 1893 and 1903)
In the conversation
- Debate Boole, not Frege, deserves to be called the father of modern logic
- Question Are the words of the Veda abstract objects? Mīmāṃsā’s eternal language and Frege’s third realm
- Question If numbers aren’t physical, how could we ever know anything about them?
- Question Every invoice needs some approver: why does the order of quantifiers change the meaning?
- Discussion Kūkai and Bhartṛhari: when a word is part of what is real rather than a label for it
- Question Can someone walk me through the Frege–Geach problem without the jargon?
- Question Kripke’s Gödel and Schmidt case: why would my word still pick out Gödel?
- Discussion Frege said logic is not psychology. A materialist would like a word
- Debate Twenty years of translating have convinced me that meaning is use
- Question What does Moore’s open question argument actually prove, and what is the standard reply to it?
- Discussion Dignāga’s apoha and Frege’s sense are answers to different questions
- Discussion Epsilon-delta is two nested quantifiers, and that is why my students struggle
- Question Frege and Husserl started on the same side. What was the psychologism dispute about?
- Discussion Navya-Nyāya’s language of limitors, and what it was built to do
- Reading group Reading group: Kripke, Naming and Necessity, Lectures I and II
- Debate Logic is the one part of philosophy that settles questions, and the rest should take note
- Reading group Reading group: Frege’s Foundations of Arithmetic (1884), five weeks with Austin’s translation
- Debate Predicate logic was discovered, not invented
In the Journal
In the Coordinates
The questions of philosophy where Gottlob Frege takes a place, from The Coordinates of Thought.
- 1.1.4 Abstract Objects Does the number seven exist?
- 4.1 Formal Logic What makes an argument work, regardless of its subject?
- 4.1.2 Predicate Logic Why could two thousand years of logic not handle "every boy loves some girl"?
- 4.5 Philosophy of Logic Is logic discovered or invented?
- 6.9 Philosophy of Mathematics Are numbers discovered or invented?
- 6.10 Philosophy of Language How do noises come to be about things?
- 6.10.1 Reference What makes your word for a thing refer to that thing?