Thought Experiments James Robert Brown Physics, Toronto March 2009

1. Thought ExperimentsJames Robert BrownPhysics, TorontoMarch 2009

3. TEs in the natural sciences • Lucretius, De Rerum Natura • Is space infinite? • Typical TE: • Set things up • observe what happens • draw conclusion • Fallible

4. Steven & StaticsHow will the chain move?

5. Is it obvious now?

6. Newton’s Bucket Is space absolute or relational? Tension in cord

7. A Leibniz “shift” U U • Why would God put the Universe in one place rather than any other?

8. Without experiment, I am sure that the effect will happen as I tell you, because it must happen that way. L H H+L Galileo on free fall Do bodies fall at different rates?

9. Galileo’s Reasoning • Aristotle and common sense claim: H > L. • Thus, H+L > H • But, H > H+L • This is a contradiction. • Galileo’s resolution: H = L = H+L. • In other words, all bodies fall at the same rate, regardless of their weight.

10. TEs in Philosophy TEs are used extensively everywhere in philosophy, but especially in philosophy of mind and ethics. Here’s an anti-abortion argument: • The foetus is an innocent person with a right to life • Abortion violates the foetus’s right to life Thus, abortion is morally wrong.

11. Thompson’s Violinist • Assume (for the sake of the argument) that a foetus is an innocent person with a right to life. Is the above argument a good one? • A sick violinist (who is innocent and has a right to life) is hooked up to YOU for 9 months. • You face the following argument: • The violinist is an innocent person with a right to life • Detaching violates the violinist’s right to life Thus, detaching is morally wrong.

12. Moral judgement in this case • You are not morally obliged to remain attached, even though the violinist is an innocent person with a right to life. • You may stay hooked up (and be a hero), but you are not morally obliged to do so. • Thus, the argument involving the violinist is flawed. • The abortion argument is analogous, so, it is also flawed. • Thus, abortion is morally permissible.

13. What Did the TE Achieve ? • Thompson’s TE forced a conceptual distinction on us: right to life ≠ right to what is need to sustain life • We need the artificial situation of the TE to see the difference.

14. Once we make the distinction, we see that the initial argument is faulty. The foetus is an innocent person with a right to life Abortion violates the right to life Thus, abortion is morally wrong. The foetus has a right to life, but not a right to the mother’s body. Abortion, even if it results in the death of an innocent foetus, is not morally wrong unless the foetus also has the right to use the mother’s body.

15. Qualia: Mary the brilliant scientist • Frank Jackson’s TE for “qualia” • Qualia are subjective aspects of experience • If physicalism is right, qualia do not exist • Mary learns all physical facts in a black and white environment • When she steps out of the laboratory for the first time she comes to know something new — ie, what it’s like to experience red, etc. • Thus, there is something to be known in addition to the physical facts • Thus, physicalism is wrong

16. Insight & Understanding • Some TEs provide understanding for those learning the theory. • Newton on the orbit of the moon. • The “aha effect”

17. Relativistic Car & Garage • Will the car, moving at velocity v, fit in the garage? • They have the same rest length. ←

18. Yes, according to garage frame, since the car will be Lorentz contracted. ← No, according to the car frame, since the garage will be Lorentz contracted. ←

19. Resolution • The two frames disagree on the simultaneity of events. • In the garage frame, the car front bumper was still in the garage after the rear bumper entered. • In the car frame, the front bumper went through the garage wall before the rear bumper entered.

20. What do we see in a TE ? • Normally we try to visualize things realistically in a TE. • But this would not work here. • The visual appearance of a rapidly moving object in SR is not contracted • It is rotated (degree of rotation depends on velocity). • In the garage frame things would appear like this: ← • Our intuition would be confused and we would not see the paradox. • Somehow, we manage to see the right thing (ie, Lorentz contraction).

21. Visualization in Mathematics • Standard view in math and logic: We establish theorems by proving them. • A proof is a series of propositions, starting from given axioms (or previously proven theorems), concluding with the theorem. • A proof is a verbal/symbolic entity. • Pictures are psychologically useful, but they are not proofs. • But, consider this example:

22. Theorem: 1 + 2 + 3 +…+ n = n2/2 + n/2 Proof:

23. How does such a picture work? Common claim: picture and reality have same structure, hence we can make the inference from one to the other. But this picture has only finitely many numbers represented, whereas the theorem is about infinitely many. Could the picture be a stimulus for an intellectual grasping, a perception into Plato’s heaven by the mind’s eye?

24. How to Refute the Continuum Hypothesis Throw 2 darts at [0,1]

25. Assume ZFC and CH • Thus, [0,1] can be well ordered and has cardinality א1 • Let first dart hit p and second hit q • First thrower says: Set of points that precede p in the well ordering is countable, so second dart won’t land in that set (a measure zero set, hence zero probability). • Second thrower says: Set of points that precede q in the well ordering is countable, so first dart won’t land in it. • But one will. Absurd. Blame CH. • Thus, ~CH

26. Some Big Questions • Epistemic problem: How is it possible that just by thinking we can learn something new about the world? • Classification problem: What are the different ways in which TEs work? • Subject matter problem: Why are there so many TEs in physics and philosophy, but very few in anthropology or chemistry? • Literature problem: Are novels (and other works of fiction) a kind of TE ? • Background knowledge problem: Training matters, but to what extent (if any) does culture matter?

27. The Epistemic Problem • We normally evaluate theories by means of observation and experiment, taking into account unification, novel predictions, etc. • All of this is part of liberal empiricism, the doctrine that all knowledge is based on sensory experience. • A majority of current philosophers are naturalists and embrace empiricism as part of their general outlook. • How do TEs fit into this? (Maybe they don’t)

28. Three Accounts • A TE is an Argument (maybe disguised). • Empirical premisses • Conclusion follows by deductive/inductive logic. • A TE is a Mental Model • We construct a model (in our heads), based on what we already know • Then simply observe the details. • Platonism • Some TEs give us a priori knowledge of nature • “seeing with the mind’s eye” • Many take such a view of math.

29. Is the Galileo example empirical or a priori knowledge? • No new empirical data • Not a logical truth • Not derived from previously accepted empirical truths • This is a candidate for genuine a priori knowledge of nature.