ockham’s razor without evasions, circles, or divine intervention kevin t. kelly department of...

Ockham’s Razor Without Ockham’s Razor Without Evasions, Circles, or Evasions, Circles, or Divine InterventionDivine Intervention

Kevin T. KellyKevin T. KellyDepartment of PhilosophyDepartment of Philosophy

Carnegie Mellon UniversityCarnegie Mellon Universitywww.cmu.eduwww.cmu.edu

Planetary retrograde motion

MarsEarth

Sun

Astronomy 1543Astronomy 1543

Only at solar opposition

Ptolemaic ExplanationPtolemaic Explanation

Retrograde path is due to an epicycle.Retrograde path is due to an epicycle.Can happen regardless of the position Can happen regardless of the position of the sunof the sun

epicycle

Copernican ExplanationCopernican Explanation““Lapped” competitor appears to Lapped” competitor appears to backtrack against the bleachers.backtrack against the bleachers.Lapping only happens when the center Lapping only happens when the center of the track is opposite.of the track is opposite.

lapping

epicycle

Copernicus VictoriousCopernicus VictoriousExplains the data rather than merely Explains the data rather than merely accommodating them.accommodating them.Has fewer adjustable parameters.Has fewer adjustable parameters.Is more falsifiable (failure of Is more falsifiable (failure of correlation would rule it out).correlation would rule it out).Is “simpler”.Is “simpler”.

More Victories for More Victories for SimplicitySimplicity

universal gravitation vs. divided universal gravitation vs. divided cosmoscosmoswave theory of light vs. particles and wave theory of light vs. particles and aetheraetheroxygen vs. phlogistonoxygen vs. phlogistonnatural selection vs. special creationnatural selection vs. special creationspecial relativity vs. classical special relativity vs. classical electrodynamicselectrodynamicschaos vs. infinite series of random chaos vs. infinite series of random variablesvariables

Ockham’s RazorOckham’s Razor

Which theory is true?

Ockham Says:Ockham Says:

Choose theSimplest!

Looks good.Feels good!

Skeptical ChallengeSkeptical Challenge

What about this?

PuzzlePuzzle

An indicator must be An indicator must be sensitivesensitive to to what it indicates.what it indicates.

simple

PuzzlePuzzle

An indicator must be An indicator must be sensitivesensitive to to what it indicates.what it indicates.

complex

PuzzlePuzzle

But Ockham’s razor points at But Ockham’s razor points at simplicity simplicity no matter whatno matter what..

simple

PuzzlePuzzle

But Ockham’s razor always points But Ockham’s razor always points at simplicity.at simplicity.

complex

ParadoxParadox

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

simple

ParadoxParadox

If we If we don’tdon’t know that the truth is know that the truth is simple, simple, what goodwhat good is Ockam’s razor? is Ockam’s razor?

complex

Weird ScienceWeird Science Simplicity must somehow point at Simplicity must somehow point at

the truth the truth now.now.

Weird ScienceWeird Science Hmm, how could Hmm, how could thatthat work? work?

Metaphysicians for Metaphysicians for OckhamOckham

Mysticism: Mysticism: the simple world calls to us…the simple world calls to us… Leibniz:Leibniz: God creates a simple world and God creates a simple world and

creates humans who expect it to be creates humans who expect it to be simple.simple.

Kant: Kant: simple minds create simple worlds.simple minds create simple worlds.

With friends like those….

Darwin, the New SaviorDarwin, the New SaviorIf our simplicity bias wasn’t right, we If our simplicity bias wasn’t right, we

would have been would have been squishedsquished long long ago!ago!

Darwin, the New SaviorDarwin, the New SaviorIf Darwin happens to be wrong, then If Darwin happens to be wrong, then

science should be abandoned?science should be abandoned?

Collapse of Scientific Collapse of Scientific NaturalismNaturalism

(Koons 1999)(Koons 1999)1.1. All truths are natural truths.All truths are natural truths.

2.2. Science can know all natural truths.Science can know all natural truths.

3.3. Naturalistic knowledge is belief that tracks the Naturalistic knowledge is belief that tracks the truth.truth.

4.4. Science mainly uses Ockham’s razor.Science mainly uses Ockham’s razor.

5.5. So Ockham’s razor must track the truth.So Ockham’s razor must track the truth.

6.6. The tracking relation must have some causal The tracking relation must have some causal explanation (by O.R.).explanation (by O.R.).

7.7. A truth-tracking method must work whichever A truth-tracking method must work whichever theory happens to be true. theory happens to be true.

8.8. But only some of the possible theories explain the But only some of the possible theories explain the tracking relation, unless it is known a priori.tracking relation, unless it is known a priori.

9.9. It isn’t. Contradiction.It isn’t. Contradiction.

MoralMoralKoons is onto something. Koons is onto something. Naturalists Naturalists

who expect too much from science who expect too much from science tie science to weird metaphysical tie science to weird metaphysical speculationsspeculations..

Solution: Solution: • Dump short-run tracking Dump short-run tracking as the as the

justification of scientific method.justification of scientific method.• It’s enough that Ockham’s razor be It’s enough that Ockham’s razor be

our our best possiblebest possible means for finding means for finding the hidden truth.the hidden truth.

• Maybe Maybe thatthat can be known a priori. can be known a priori.

ChallengeChallengeHow could you How could you knowknow that a fixed that a fixed

pointer helps you find something pointer helps you find something unless you unless you already know already know that it that it points at what you are looking for?points at what you are looking for?

Ummm…

simple

ResponseResponse

It happens everyday!

simple

Asking for DirectionsAsking for Directions

I’m I’m lostlost


Ask!Ask!


Where’s …Where’s …

Asking for DirectionsAsking for DirectionsTurn around. The Turn around. The freeway ramp is freeway ramp is on the left.on the left.


Goal

Best RouteBest Route

Goal

Disregarding Advice is Disregarding Advice is WorseWorse

Goal

Disregarding Advice is Disregarding Advice is WorseWorse

Extra U-turn

Goal

Is That What Ockham Is That What Ockham Does?Does?

Bean CountingBean Counting

Bean CountingBean Counting

May come at any time…May come at any time…

AnalogyAnalogy BeansBeans = “ = “empiricalempirical effectseffects”.”. CountCount = = complexitycomplexity of true model. of true model. Appearance timesAppearance times = = elusiveness of elusiveness of

effects.effects.

Polynomial ModelsPolynomial Models

Data = ever tighter open Data = ever tighter open intervals around intervals around YY at rational at rational values of values of X.X.

X

Y


0: no effect0: no effect


1: constant effect1: constant effect


2: constant + linear effect2: constant + linear effect


3: constant + linear + quadratic 3: constant + linear + quadratic effecteffect

RetractionsRetractions

U-turnU-turn = model = model retraction;retraction; FreewayFreeway = retraction-efficient = retraction-efficient

truth-finding method.truth-finding method.

HHHH

How Ockham’s Razor How Ockham’s Razor HelpsHelps

No matter which theory is true, No matter which theory is true, Ockham’s razor never retracts Ockham’s razor never retracts more than any other convergent more than any other convergent method.method.

Any non-Ockham method does Any non-Ockham method does worse.worse.

Over-counting is Over-counting is InefficientInefficient

Suppose you Suppose you over-countover-count..

3311


Where is that extra marble, anyway?Where is that extra marble, anyway?

3311


If you never say 2 you’ll never If you never say 2 you’ll never converge to the truth….converge to the truth….

3311


That’s it. You should have listened to That’s it. You should have listened to Ockham.Ockham.

33222222

11


Oops! Well, no method is infallible!Oops! Well, no method is infallible!

33222222

11


If you never say 3, you’ll never If you never say 3, you’ll never converge to the truth….converge to the truth….

33222222

11


Embarrassing to be back at that old Embarrassing to be back at that old theory, eh?theory, eh?

33222222 33

11


And so forth…And so forth…

33222222 33 44

11



33222222 33 44 55

11



33222222 33 44 55 66

11



33222222 33 44 55 6677

11

The ScoreThe Score

You: You:

33222222 33 44 55 6677

11

At moment of over-count

The ScoreThe Score

Ockham:Ockham:

222222 33 44 55 667733saved

retracation

At moment of over-count

MoralMoral

Ockham’s razor keeps one on the Ockham’s razor keeps one on the straightest pathstraightest path to the to the truth.truth.

Argument is Argument is a priori a priori and and mathematical, not mathematical, not hiddenhidden and and metaphysical.metaphysical.

Insistence on truth in the short run Insistence on truth in the short run saddles science with a priori saddles science with a priori metaphysical commitments.metaphysical commitments.

ockham’s razor without evasions, circles, or divine intervention kevin t. kelly department of...

Documents

simple slide

complex slide

simple minds

simple worlds

lapping epicycle slide

simple world calls

ockhams razor points

solar opposition slide