Gottlob Frege

1848-1925 · German · Logic, Philosophy of Language, Philosophy of Mathematics, Philosophy of Mind

We must ask for the meaning of a word only in the context of a sentence, never in isolation.

Gottlob Frege spent his career in quiet obscurity at the University of Jena, publishing work so technically demanding that almost no one read it in his lifetime. What he was building was the foundation of modern logic — and the conceptual skeleton of analytic philosophy. Without him there is no truth-functional analysis of language, perhaps no computer science in its modern form.

Topics Gottlob Frege addresses

• sense and reference
• the cognitive significance puzzle
• thoughts as abstract objects
• the third realm
• truth-values as references of sentences
• the concept-object distinction
• the unsaturatedness of concepts
• the concept horse paradox
• the function-argument analysis
• quantifiers and bound variables
• the context principle
• anti-psychologism
• logicism
• the reduction of arithmetic to logic
• hume's principle
• basic law v
• russell's paradox
• value-ranges
• extensions of concepts
• the definition of number
• multiple generality
• the judgement-stroke
• assertion and force
• indirect reference

Questions to put to Gottlob Frege

Sense and Reference

• What do you mean by the distinction between Sinn and Bedeutung?
• How does the sense/reference distinction solve the puzzle about why 'the morning star is the evening star' is informative?
• What is the sense of a proper name, and how is it different from the object it refers to?
• Why do you think sentences refer to truth-values rather than states of affairs?
• How do you respond to the claim that proper names refer directly without going through a sense?

Concepts, Objects, and Functions

• What's the difference between a concept and an object?
• What do you mean when you say concepts are unsaturated?
• Can you explain the Concept Horse paradox — why can't 'the concept horse' refer to a concept?
• How does your function-argument analysis improve on the old subject-predicate logic?
• Why do you insist on such a strict separation between what can be said about objects versus concepts?

Thoughts and the Third Realm

• What is a Thought, and how is it different from a mental event in someone's mind?
• Why do you think Thoughts inhabit a third realm separate from physical and mental reality?
• How can multiple people grasp the same Thought if it's not in anyone's head?
• What's wrong with treating logic as a description of how people actually think?
• How do you respond to the worry that abstract objects in a third realm are mysterious or unscientific?

Logicism and the Grundgesetze Project

• What's your argument that arithmetic is reducible to logic?
• How do you define numbers as logical objects rather than psychological ideas or empirical generalizations?
• What is Basic Law V, and why did you think it was needed for the logicist program?
• How did you respond when Russell showed you the paradox in your system?
• Does Russell's paradox refute logicism itself, or only your particular formulation of it?

The Context Principle and Meaning

• What do you mean by 'only in the context of a sentence does a word have meaning'?
• How does the Context Principle guide your approach to defining numbers in the Grundlagen?
• Does the Context Principle conflict with compositionality — the idea that sentence meaning comes from word meaning?
• Did you abandon the Context Principle in your later work on sense and reference?

The Begriffsschrift and Quantification

• What was revolutionary about your concept-script compared to earlier logical systems?
• How does your treatment of quantifiers and bound variables let you express multiple generality?
• What is the judgement-stroke, and why does assertion need its own logical symbol?
• Why did you think a purely symbolic language was necessary for rigorous thought?

Converse with Gottlob Frege on Simposeum. Every reply is grounded in Gottlob Frege's own writing and cites the page it came from. The corpus is public-domain text.