Thought Experiments

Thought Experiments Background I. A priori vs. a posteriori knowledge A priori knowledge: justification is wholly independent of sense experience (but it may be elicited or triggered by sense experience) Example: geometrical proofs A posteriori knowledge: justification relies at least partly on sense experience Examples: There are black swans. All humans are mortal. Energy is conserved in closed systems. All bodies fall at the same speed. 2. Empiricism and rationalism Empiricism: all our knowledge of the world (‘matters of fact’) is a posteriori (i.e., derives at least partly from sense experience) ⇒ reason alone cannot give us new knowledge of the world (it can only transform existing knowledge) “Knowledge of the world” = knowledge of logically contingent matters of fact. [“It’s raining or it’s not raining” does not count as knowledge about the world.] Rationalism: some knowledge of the world is a priori (derives from pure reason) ⇒ even a single case where pure reason provides such knowledge is a problem for empiricism. Such a case would “transcend” (= refute) empiricism.

3. Historical background. Prior to Hume, there was no problem with the idea that reflection (pure reason) could give knowledge of physics. Descartes: Principles of Philosophy (1644). Laws of nature are ‘derived’ from other a priori principles: for example, the existence and nature of God. Example: Conservation principles. Leibniz: Tentamen Anagogicum (1696). Laws of nature are ‘derived’ from God’s wisdom and goodness. General Principle: God’s choices cannot be arbitrary, but are always conducive to perfection. Application: Mechanical principles must maximize or minimize some quantity. Example: Snell’s Law of Refraction – light takes the ‘easiest’ path (= least time). “We should not have had this beautiful discovery so soon without the method of final causes.” 4. Two contemporary ‘problem cases’ for empiricism. • Symmetry arguments. Principle of Insufficient Reason: in the absence of any information to the contrary, assign equal probability to all cases. Examples: alien die, Buffon’s needle problem • Thought experiments. Some of them don’t appear to rely merely upon empirical knowledge, yet they give us new knowledge about the world. Do they work? Are they truly a priori? Do they transcend empiricism?

I. Jim Brown, “Why Thought Experiments Transcend Empiricism” 1.1 Galileo’s thought experiment H > L: this implies contradictory theses about the compound object. The only way out is if H = L = H+L. No actual experiment is needed. Some Questions: 1. Is H = L logically necessary? Could there be a world where H > L? What would happen if we tied the objects together? 2. What knowledge is Galileo relying upon? Would the conclusion H=L follow from that knowledge alone, without the thought experiment?

General features of TE’s: • • • • • • • •

Carried out in the mind Akin to experience (involves imagination/visualization/perception) May involve some derivation and/or manipulation May involve guesswork Idealization is sometimes required (but not essential) Fallible Usually incorporate background knowledge Sometimes feasible to perform, sometimes not

1.2 Examples of Thought Experiments (TE’s) Example 1: Galileo’s falling bodies Example 2: Lucretius’s spear and infinite space. Illustrates fallibility of TE’s: we can now conceptualize space so that it is both finite and unbounded. Example 3: chain draped over two frictionless planes. Important assumptions: uniform density on both sides; both sides of the chain have the same vertical drop. [If we had only one bead on the right, the chain would slide to the left.] Main Idea: beads added below the line add equal downward force to each end of the chain. And there is equal downward force on either end of the chain in the completed circular chain (or else we’d have perpetual motion). So there is equal downward force on either end in the original set-up – hence, no motion. Relies on background: no perpetual motion Example 4: Einstein chasing a beam of light. Impossible to find a frame in which the wave is at rest – as then, by Maxwell’s equations, there would be no wave at all. Example 5: Newton’s bucket and the two-sphere example. Newton’s bucket: Spin a bucket of water and then stop. The water keeps spinning and makes a concave shape. How do we make sense of the concavity of the rotating water? We can’t say: it’s rotating wrt bucket now, but not before – since before, when it was flat but we started the bucket spinning, the water was equally rotating wrt the bucket! The only way, for Newton, was to assume rotation wrt absolute space.

1.3 Different Roles of Thought Experiments 1. Negative: Einstein’s TE shows you can’t combine Maxwell with Galilean transformations. 2. Positive: Chain TE example reveals a static equilibrium. 3. Positive: Newton’s bucket (or two-spheres) TE reveal a new phenomenon in need of explanation.

*1.4 A priori knowledge of nature Brown’s main claim: Galileo’s TE gives us a priori knowledge of nature. A priori: No new empirical data in moving from Aristotle to Galileo. Knowledge of nature: H = E is not a logical truth. Galileo’s argument shows more generally: the rate of fall can’t be based on any extensive (additive) property. This gives extra proof that we have a priori knowledge of nature, not based on any empirical evidence.

1.5 Mathematical intuition and laws of nature Point of this section: it’s possible we could have a priori knowledge of nature. Two main ideas: 1) Intellectual intuition. Akin to sense perception, this is direct grasp of truths with the intellect, not mediated by sense. We grasp abstract entities or universals (such as mathematical relationships). Brown maintains: a) It’s possible in mathematics; b) it’s possible for matters of fact. 2) Universalist account of laws. Dretske/Armstrong/Tooley view of laws: laws of nature are contingent relationships of universals. That makes laws fit to be grasped by intellectual intuition. N(F, G)

[F-ness necessitates G-ness]

entails (x)(Fx ⊃ Gx).

Some objections: a) The N relation is mysterious, and the entailment of ordinary regularities is mysterious. b) There is no account of how the intellectual intuition takes place! Brown’s sole objective here is to clear a tiny space for the possibility of this pre-Humean epistemology.

1.6 Norton’s Arguments and Empiricism Objective: To criticize Norton’s thesis that TE’s are arguments (which sets up Brown’s account as the best alternative analysis). A. Norton’s position. 1. TE’s are arguments. 2. Empiricism: all knowledge of the world derives from sense experience. ⇒ A TE is “good” or “reliable” only if the premises are empirically justified and the conclusion follows by some sound logical rule. [SO: TE’s do not transcend experience.]

B. Contrast between Brown and Norton. Experiments vs. Arguments. Experiment: perception + background → proposition (conclusion). Argument: proposition + background → proposition (conclusion). Both Norton and Brown agree that ordinary experiments are NOT arguments. Brown sees thought experiments as having the structure of experiments. i. Replace “perception” with “intuition” in the above characterization. ii. Allow two species of experiment. Intuition = sensory perception (empirical experiment). Intuition = intellectual intuition (thought experiment).

C. Burden of proof. Norton’s position is the default: • requires no radical change to empiricist epistemology. • has managed to reconstruct all TE’s as arguments.

D. Brown’s strategy. General objection. Even if all TE’s can be reconstructed as arguments, that doesn’t prove that TE’s are actually used as arguments, or that their construal as arguments exhausts their cognitive role. [Brown does not take this point further.]

Specific objection. Find an example of a TE that is not an argument. [A single example is enough to establish the main claim that TE’s can transcend experience.] Brown gives two examples, both from mathematics. Benefit: less of a problem to argue for intellectual intuition. Cost: even if the examples work, we might think he’s only established his point for mathematics, rather than empirical science.

Example 1: a picture proof of a simple result about sums. A conventional argument exists, but it’s not suggested by the picture proof. But is this a TE at all?

Example 2: Freiling’s refutation of CH. Cardinality. Continuum Hypothesis: there is no cardinal number between the cardinality of the natural numbers and the cardinality of the real numbers. ZF set theory, the axiom of choice, well-ordering. By induction on <: {n / n < q} is enumerable, all q.

I claim: this argument does not work! But let’s try to focus on what use Brown makes of it (since it might still be a failed TE that refutes Norton’s analysis). Brown’s point: the inference is based on intuition, not argument. Norton will object: even if it’s an informal argument, it’s still an argument. Brown thinks it shows that not all TE’s need be arguments, that some rely on intellectual intuition. I think this is dubious.

1.7 Moral of the story. TE’s in mathematics need not be arguments. A small step by analogy: TE’s in science need not be arguments. Comment: This is a big jump, not a ‘small step’! From perception of mathematical abstractions to perception of laws!

Thought Experiments do not transcend empiricism: Norton 1. Introduction Question: Do thought experiments let us use pure thought to find out about the world? [Even a single case would be a problem for empiricism.] Norton’s answer: Never. A strategy, rather than an argument: #1. Every thought experiment (TE) is an argument. #2. The premises are drawn from experience. #3. If it’s a good argument (a reliable TE): the conclusion follows by some accepted principle of logic (deductive or inductive). This is only a *strategy* (or set of strategies): - Norton wants it to be true (it saves empiricism) - He has no good general argument - But he has a set of techniques to show that any putative TE is either unreliable or transformable into an argument Qualification: “Independence from empiricism” (p. 55). The thesis that every TE is an argument, without #2, is Norton’s main point. But in his conclusion (p. 64), he stresses that the “argument view” is the “natural home” for an empiricist account of thought experiments – #2 is an easy addition.

2. TE – anti-TE pairs • “Antinomies” exist: rival TE’s that support incompatible conclusions. • Test for any analysis of thought experiments: Explain why one member of each antinomy fails. Note: It’s not clear why this should be true if TE’s can be inductive arguments. (Think of Hempel’s rival I-S explanations, which are inductive arguments for opposite conclusions.) Note also: Norton’s ‘theory’ won’t automatically pass this test, despite what he says! [Only if the arguments are deductive.] Antinomy #1: The world is / is not spatially finite. Finite: in an infinite universe, uniform rotation is impossible. Infinite: Lucretius/Archytas’ spear argument. Antinomy #2: Geometry is/is not Euclidean for a rotating observer. C > πD (Einstein): more measuring rods needed on circumference C < πD (Petzold): if a ring is rotating, its diameter will not change, but its circumference will contract C = πD (Ehrenfest/Varicak): ?? Antinomy #3: An infinite rotor at rest has/does not have lift. Lift: Take limits as radius doubles, speed is halved. No lift: Take limits of a rotor at rest as radius doubles.

3. Thought Experiments as Arguments Argument thesis. Thought experiments are arguments • No knock-down defense: just “the presumption that pure thought cannot conjure up knowledge”. That is: the presumption of empiricism! [Norton does give a ‘burden of proof’ argument: everyone likes empiricism.] • To embrace empiricism but preserve the idea that TE’s show something, we must think of them as ‘transforming’ prior knowledge. That strongly suggests that they are arguments. • Empirical knowledge must enter in the premises of the argument, or as tacit knowledge employed in the argument. Two versions of the thesis: (1a) Thesis about justification. Any TE can be reconstructed as an argument, and has exactly the same justifying power as that argument. (1b) Thesis about discovery. Any actual TE consists of an argument, though it may not be obvious. Arguments for (1a): none, other than presumption of empiricism, and the record of failure to find a TE than can’t be reconstructed as an argument. Arguments for (1b): - there is nothing mystical about the persuasion of a TE - just as we can ‘reduce’ persuasive writing to arguments, we can reduce a TE to an argument Claim: the “argument” thesis solves the problem of antinomies. Two arguments with incompatible conclusions ⇒ one is unsound Problems: 1) Not for inductive arguments. 2) No ‘theory’ here, so no solution to antinomies.

4. Reliability Thesis Reliability Thesis: If TE’s can be used reliably, they must either be (good) arguments or re-constructible as (good) arguments (in some logical system). Reliable: we have justification to believe the outcomes - “more than just generators of interesting hypotheses” - Norton assumes some (but not all) TE’s are reliable Logic: - many ‘systems’ of deductive and inductive logic - some ‘systematic, identifiable’ feature must identify the good TE’s. Mark of a good TE: it either explicitly makes use of a licensed argument form, or it can be reconstructed as one. Logic again: Is a ‘new’ logic needed? Probably not, since all existing TE’s can be reconstructed using familiar logics.

5. Alternative Accounts of Thought Experiments General strategy for dealing with these alternatives: • Schematic representation of alternatives: A thought experiment = an argument + some extra factor X (where X provides additional epistemic power) • To any proposed X, Norton will apply one of four criticisms: (a) Denial. X is not present in the TE. (b) Incorporation. arguments.

X is present in the TE, but also present in

(c) Epistemic irrelevance. X is present in the TE and not in arguments – but X is irrelevant to the epistemic power of the TE. (d) Unreliability. X is present in the TE and not in arguments – but X is an unreliable guide to the epistemic power of the TE.

Platonism (Brown) • Laws are construed entities/universals)

Platonically

(as

relations

of

abstract

• Intellectual intuition allows for direct apprehension of laws by reason (unmediated by sense experience): a “radical” (non-empiricist) epistemology Here, “X” is access to the Platonic entities: the idea is that a TE delivers this kind of access (but arguments do not). Criticisms: 1. Denial. The Dretske/Armstrong view of laws is wrong (or unsupported) and we don’t need this view of laws. 2. Dilemma. Even if we grant Brown his Platonic view of laws, he faces the following dilemma: EITHER the intellectual apprehension of the laws comes by way of some accepted form of argument (which amounts to incorporation); OR it does not come by way of argument, and is unreliable (the unreliability objection) – in particular, with a purely perceptual model, we can’t adjudicate between competing pairs (antinomies).

Brown’s TE-refutation of the Continuum Hypothesis Criticisms 1. It doesn’t work at all. 2. If it works, it’s a recognizable species of argument. (Not a counterexample to the “argument thesis”.) 3. It could be formalized as a mathematical argument (not supported here). [Why not: even if it works, it’s limited to mathematics – it implies nothing broader about the empirical sciences.??]

Constructivism (Kuhn, Gendler) • TE’s reveal internal incoherence, allow scientists to reform their conceptual schemes • No violation of empiricism: TE’s provide knowledge about our models, rather than about the world

Two issues for Norton: 1. Not all TE’s are about conceptual reform. 2. The constructivist view is compatible with Norton’s thesis that all TE’s are arguments. Note: Norton’s argument here seems weak. TE’s produce changes in conceptual scheme. Arguments can produce changes in conceptual scheme. So, TE’s are arguments. If they are not arguments, they are unreliable. Question: What if science needs unreliable argument forms? Do Norton’s objections only work against TE’s that are supposed to provide strong support for a hypothesis? See his remark on p. 52: TE’s are supposed to do more than supply interesting hypotheses. Question: How does this analysis apply to Galileo?

Visualization and simulation Analogy: TE’s are experiments that we observe in a kind of “laboratory” of pure thought. Why is Norton interested? This seems to threaten the argument thesis. Experiments are not arguments; they are based on perception rather than premises. The “X” here is the perceptual component due to mental visualization/simulation. Criticism: Either these factors are included and the TE is unreliable; or they play no essential epistemic role, and are irrelevant.

Mental Models Idea: Much of our thinking (including TE’s) is accomplished with mental models; and these are distinct from arguments. Objections: 1. Mental models simply offer non-traditional “logics”, or argument schemas, for reasoning – as in the simple example involving spatial location of fork, knife and plate. (This is incorporation.) 2. Also: not all TE’s appear to be mental models. Basically, ‘arguments’ and ‘mental models’ are not all that different, on a suitably general notion of what counts as an argument.

Experimentalism [Omit] Other views 1. Mach. TE manipulates experiential data using simple schemes. Norton: This view is compatible with just about any analysis of TE’s.

2. Bishop. A single TE can correspond to two distinct arguments – so a TE cannot be identified with an argument. Norton: In fact, they are two distinct TE’s.

Conclusion The “argument thesis” is congenial to empiricism. Any information about the world was already present in the premises of the argument.