Thought Experiments

James Robert Brown

Physics, TorontoMarch 2009

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QuickTime™ and a decompressor

are needed to see this picture.

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TEs in the natural sciences

• Lucretius, De Rerum Natura

• Is space infinite?

• Typical TE: – Set things up– observe what happens– draw conclusion

• Fallible

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Steven & StaticsHow will the chain move?

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Is it obvious now?

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Newton’s Bucket

Is space absolute or relational?

Tension in cord

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A Leibniz “shift”

U U

• Why would God put the Universe in one place rather than any other?

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Galileo on free fall

Do bodies fall at different rates?

H

L

H+L

Without experiment, I am sure that the effect willhappen as I tell you, because it must happen that way.

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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.

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TEs in Philosophy

TEs are used extensively everywhere in philosophy, but especially in philosophy of mind and ethics.

Here’s an anti-abortion argument:

1. The foetus is an innocent person with a right to life2. Abortion violates the foetus’s right to lifeThus, abortion is morally wrong.

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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:

1. The violinist is an innocent person with a right to life2. Detaching violates the violinist’s right to lifeThus, detaching is morally wrong.

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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.

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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.

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• Once we make the distinction, we see that the initial argument is faulty.

1. The foetus is an innocent person with a right to life2. Abortion violates the right to lifeThus, 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.

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• 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

Qualia: Mary the brilliant scientist

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Insight & Understanding

• Some TEs provide understanding for those learning the theory.

• Newton on the orbit of the moon.

• The “aha effect”

QuickTime™ and aBMP decompressor

are needed to see this picture.

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Relativistic Car & Garage

• Will the car, moving at velocity v, fit in the garage?

• They have the same rest length.

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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.

←

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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.

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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).

←

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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:

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Theorem: 1 + 2 + 3 +…+ n = n2/2 + n/2

Proof:

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• 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?

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How to Refute the Continuum Hypothesis

Throw 2 darts at [0,1]

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• Assume ZFC and CH

• Thus, [0,1] can be well ordered and has cardinality 1א

• 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

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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?

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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)

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Three Accounts

1. A TE is an Argument (maybe disguised).– Empirical premisses– Conclusion follows by deductive/inductive logic.

2. A TE is a Mental Model– We construct a model (in our heads), based on

what we already know– Then simply observe the details.

3. Platonism– Some TEs give us a priori knowledge of nature– “seeing with the mind’s eye”– Many take such a view of math.

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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.

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