Thinker · TH-0197
Hartry Field
Hartry Field is an American philosopher who taught at Princeton, the University of Southern California and the CUNY Graduate Center before a long career…
b. 1946 · Los Angeles; New York
Traditions: Analytic
Hartry Field is an American philosopher who taught at Princeton, the University of Southern California and the CUNY Graduate Center before a long career at New York University. In Science Without Numbers he attacked the indispensability argument for mathematical objects by showing how Newtonian gravitational theory can be formulated without quantifying over numbers. Mathematics, on his fictionalist view, need not be true to be useful, only conservative. He has also written influentially on truth, reference and the semantic paradoxes.
Key ideas
- Mathematics need not be true to be good: it only has to be conservative over nominalistic theories.
- Physical theories can be nominalised, as he showed for Newtonian gravitation using relations among spacetime points.
- If mathematics is dispensable to science, the indispensability argument for abstract objects fails.
- Truth can be treated deflationarily, and the semantic paradoxes can be handled with a non-classical logic.
Major works
- "Tarski's Theory of Truth" (1972)
- Science Without Numbers (1980)
- Realism, Mathematics and Modality (1989)
- Saving Truth from Paradox (2008)
In the conversation
- Debate Mackie’s argument from queerness proves too much: by its standards arithmetic is queer too
- Debate Being a realist about electrons commits me to nothing about moral or mathematical facts
- Debate Gödel’s “perception” of sets explains nothing about how we actually know mathematics
- Debate The indispensability argument is the best case for numbers, and it still does not work
- Reading group Reading group: Benacerraf’s “What Numbers Could Not Be” and “Mathematical Truth”
On the map
The questions in The Coordinates of Thought where Hartry Field takes a place.
- 1.1.4 Abstract Objects Does the number seven exist?