Realism and Underdetermination in Mathematics and the Physical Sciences

Mathematical truths are objective and independent of human activities, while scientific theories aim for a true account of the physical world. Platonism is prevalent in mathematics, with the best theories being approximately true. The underdetermination principle challenges the definitiveness of scientific and mathematical claims.

• Realism
• Mathematics
• Physical Sciences
• Platonism
• Scientific Theories

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1. REALISM AND UNDERDETERMINATION IN MATHEMATICS AND THE PHYSICAL SCIENCES James Henderson Penn State Behrend

2. The truths of mathematics are objective; they are true independently of any human activities, beliefs, or capacities. Mathematical facts are necessary and unchanging, and mathematicians discover them, not create them. A mathematical statement is true just in the case that it accurately describes these facts. Blanchette, 1998

3. The typical mathematician is a Platonist on weekdays and a formalist on Sundays (Hersh 1979, p. 34) Platonism is the natural position in the philosophy of mathematics (Blanchette 1998).

4. 1. The theoretical claims of scientific theories are to be read literally, and so read are definitively true or false. 2. Scientific theories make genuine, existential claims. 3. Science aims at a literally true account of the physical world, and its success is to be reckoned by its progress toward achieving this aim. 4. A scientific theory may be approximately true even if referentially unsuccessful. 5. The best current scientific theories are at least approximately true. Leplin 1985, pp. 1, 2

5. 1. The theoretical claims of mathematics are to be read literally, and so read are definitively true or false. 2. Mathematical theories make genuine, existential claims. 3. Mathematics aims at a literally true account of the Platonic realm, and its success is to be reckoned by its progress toward achieving this aim. 4. A mathematical theory may be approximately true even if referentially unsuccessful. 5. The best current mathematical theories are at least approximately true.

7. TH. There are seven planets in such-and-such locations BT. Newton s Laws of Motion AA1. My calculations are correct AA2. My telescope is working properly AA3. I am not dreaming AA4. I am not having a flashback from the bad acid I bought from that dumbass Darrell in college Conclusion: Uranus is located at such-and-such a position

8. Uranus isnt there!

9. Contrastive Underdetermination: For any body of evidence confirming a theory, there will be other theories that are also well confirmed by that very same body of evidence. Stanford, 2017

10. Von Neumann: 3 = ?, ? , ?, ? Zermelo: 3 = ? Frege and Russell: 3 is the collection of all sets whose cardinality is 3