Truth-conduciveness Without Reliability: A Skeptical Derivation of Ockham’s Razor

Truth-conduciveness Without Reliability: A Skeptical Derivation of Ockham’s Razor Kevin T. Kelly Department of Philosophy Carnegie Mellon University www.cmu.edu

Naivete Lo! An apple.

Skeptical Hypothesis Lo! An apple. Maybe you are a brain in a vat. Everything would look the same.

Skeptical Hypothesis poof Maybe you are a brain in a vat. Everything would look the same.

Retrenchment That’s not a serious possibility You have the burden of proof. It’s remote. It’s implausible. It’s distant from the actual world. You’re not in my community. Who cares about the worst case?

Unsatisfying • Possibilities delimited a priori: circular account. • Possibilities delimited a posteriori: how do we seek knowledge? So there!

Zen Approach • Don’t rush to defeat the demon. Grrrr!

Zen Approach • Don’t rush to defeat the demon. • Get to know him extremely well. • Justification may be located in the demon’s power rather than in his weakness.

The Zen of Computation • Algorithms are justified by efficiency. • Efficiency means you couldn’t do better. • You couldn’t do better due to a demonic argument (the halting problem, etc).

Scientific Theory Choice Which theory is true?

Ockham Says: Choose the Simplest!

Skeptical Hypothesis Maybe a complex theory is true but the data are simple

Puzzle • An indicator must be sensitive to what it indicates. simple

Puzzle • An indicator must be sensitive to what it indicates. complex

Puzzle • But Ockham’s razor always points at simplicity. simple

Puzzle • But Ockham’s razor always points at simplicity. complex

Meno • If we know that the truth is simple, we don’t need Ockham’s razor. simple

Meno • If we don’t know that the truth is simple, what good is Ockam’s razor? complex

Some Standard Responses

Simple Theories are Virtuous • Testable (Popper, Glymour) • Unified (Friedman, Kitcher) • Explanatory (Harman) • Symmetrical (Malament) • Compress data (Rissanen) • Interesting (Vitanyi)

But the Truth Might Not be Virtuous • To conclude that a theory is true because it is virtuous is wishful thinking (van Fraassen).

Overfitting (Akaike, Sober, Forster) • Empirical estimates based on complex models have greater mean squared distance from the truth Truth

Overfitting (Akaike, Sober, Forster) • Empirical estimates based on complex models have greater mean squared distance from the truth. Pop! Pop! Pop! Pop!

Overfitting (Akaike, Sober, Forster) • Empirical estimates based on complex models have greater mean squared distance from the truth. Truth clamp

Overfitting (Akaike, Sober, Forster) • Empirical estimates based on complex models have greater mean squared distance from the truth. Pop! Pop! Pop! Pop! Truth clamp

Does Not Aim at True Theory • ...even if the simple theory is known to be false… Four eyes! clamp

Miracle Argument (Putnam, Rosenkrantz) • Simple data would be a miracle in a complex world. • Simple data would be expected in a simple world.

Miracle Argument Planetary retrograde motion Mars Earth Sun

Miracle Argument • Simple data would be a miracle in a complex world. • Simple data would be expected in a simple world. epicycle q lapping Complex theory Simple theory

Miracle Argument • Simple data would be a miracle in a complex world. • Simple data would be expected in a simple world. epicycle lapping q’ Complex theory Simple theory

However… • Simple data would not be a miracle if the complex theory’s parameter were set nearq; epicycle q lapping Complex theory Simple theory

C P q q q q q q q q The Real Miracle Ignoranceabout model: p(S) p(C); +Ignoranceabout parameter settings within theories: p(C(q) | C) p(C(q’ ) | C). =Knowledgeabout parameter settings across theories p(C(q)) << p(S). Is it knognorance or Ignoredge?

1/3 ? ? Urn The Ellsberg Paradox 3 ball colors with these frequencies

1/3 ? ? The Ellsberg Paradox p q r Human betting preferences p q >

1/3 ? ? The Ellsberg Paradox p q r Human betting preferences ! p q > p r < q r

1/3 ? ? Diagnosis p q r knowledge ignorance

1/3 0 2/3 Robust Bayesianism (Levi, Kadane, Seidenfeld) knowledge ignorance 1/3 p ? q r ? . . . Credence is range of probs. 1/3 1/3 1/3 . . . 1/3 2/3 0 Choose the act with highest worst-case expected value.

p q r Worst-case Expected Values 1/3 ? ? 1/3 ? ? 1/3 0 > > 1/3 0 < 2/3

Whither Ockham? Since you don’t really know that complex worlds won’t produce simple data, shouldn’t your ignorance include distributions concentrated on such possibilities? I prefer ignoredge.

In Any Event The coherentist foundations of Bayesianism have nothing to do with short-run truth-conduciveness.

Temptation If only the probabilities p(C(q’ ) | C) were chances rather than opinions. Then the alleged miracle would be a proper miracle.

Proof of God (R. Koons 1999) Natural chance is determined by the fundamental theory of natural chance. If Ockham’s razor reliably infers the theory of natural chance, the chance that a complex theory of natural chance would have its parameters set to produce simple data must be low. But since natural chance is determined by the free parameters of the fundamental theory of natural chance, the parameter setting is not governed by natural chance. Hence, it must be governed by non-natural chance. Holy water is available at the exit.

Moral The basic point is right. Solution: • Keep naturalism • Keep fundamental scientific knowledge • Dump short-run reliability as explication of truth-conduciveness.

Leibniz, evolution Simple B(Simple) Kant Simple B(Simple) Ouija board Simple B(Simple) Externalist Magic • Simplicity informs via hidden causes or tracking mechanisms. G

Metaphysicians for Ockham With Friends Like Those… • Practice and data are the same. • Knowledge vs. non-knowledge depends on hidden causes. • By Ockham’s razor, better to explain Ockham’s razor without the hidden causes. ?

The Last Gasp: Convergence Bayes (washing out of the prior) BIC (Schwarz) Structural Risk Minimization (Vapnik, Harman) TETRAD (Spirtes, Glymour, Scheines) truth Complexity

The Last Gasp: Convergence truth Plink! Blam! Complexity

Truth-conduciveness Without Reliability: A Skeptical Derivation of Ockham’s Razor