Ockham’s Razor Without
Evasions, Circles, or Divine
Intervention
Kevin T. Kelly
Department of Philosophy
Carnegie Mellon University
www.cmu.edu
Astronomy 1543
Planetary retrograde motion
Earth
Sun
Mars
Only at solar opposition
Ptolemaic Explanation
Retrograde
path is due to an epicycle.
Can happen regardless of the position of the sun
epicycle
q
Copernican Explanation
“Lapped”
competitor appears to backtrack against
the bleachers.
Lapping only happens when the center of the track
is opposite.
epicycle
q
lapping
Copernicus Victorious
Explains
the data rather than merely
accommodating them.
Has fewer adjustable parameters.
Is more falsifiable (failure of correlation would rule
it out).
Is “simpler”.
More Victories for Simplicity
universal
gravitation vs. divided cosmos
wave theory of light vs. particles and aether
oxygen vs. phlogiston
natural selection vs. special creation
special relativity vs. classical electrodynamics
chaos vs. infinite series of random variables
Ockham’s Razor
Which theory is true?
Ockham Says:
Choose the
Simplest!
Looks good.
Feels good!
Skeptical Challenge
What about this?
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 points at simplicity no
matter what.
simple
Puzzle

But Ockham’s razor always points at
simplicity.
complex
Paradox

If we know that the truth is simple, we don’t
need Ockham’s razor.
simple
Paradox

If we don’t know that the truth is simple,
what good is Ockam’s razor?
complex
Weird Science

Simplicity must somehow point at the truth
now.
Weird Science

Hmm, how could that work?
Metaphysicians for Ockham



Mysticism: the simple world calls to us…
Leibniz: God creates a simple world and
creates humans who expect it to be simple.
Kant: simple minds create simple worlds.
With friends like those….
Darwin, the New Savior
If our simplicity bias wasn’t right, we would have
been squished long ago!
Darwin, the New Savior
If Darwin happens to be wrong, then science
should be abandoned?
Collapse of Scientific Naturalism
1.
2.
3.
4.
5.
6.
7.
8.
9.
(Koons 1999)
All truths are natural truths.
Science can know all natural truths.
Naturalistic knowledge is belief that tracks the truth.
Science mainly uses Ockham’s razor.
So Ockham’s razor must track the truth.
The tracking relation must have some causal explanation (by O.R.).
A truth-tracking method must work whichever theory happens to be
true.
But only some of the possible theories explain the tracking relation,
unless it is known a priori.
It isn’t. Contradiction.
Moral
Koons is onto something. Naturalists who expect
too much from science tie science to weird
metaphysical speculations.
Solution:
• Dump short-run tracking as the justification of
scientific method.
• It’s enough that Ockham’s razor be our best
possible means for finding the hidden truth.
• Maybe that can be known a priori.
Challenge
How could you know that a fixed pointer helps you
find something unless you already know that it
points at what you are looking for?
simple
Ummm…
Response
simple
It happens every
day!
Asking for Directions
I’m lost
Asking for Directions
Asking for Directions
Ask!
Asking for Directions
Where’s …
Asking for Directions
Turn around. The
freeway ramp is on the
left.
Asking for Directions
Goal
Best Route
Goal
Disregarding Advice is Worse
Goal
Disregarding Advice is Worse
Extra U-turn
Goal
Disregarding Advice is Worse
Extra U-turn
Goal
Is That What Ockham Does?
Bean Counting
Bean Counting
Bean Counting
May come at any time…
Bean Counting
May come at any time…
Bean Counting
May come at any time…
Bean Counting
May come at any time…
Bean Counting
May come at any time…
Bean Counting
May come at any time…
Bean Counting
May come at any time…
Analogy



Beans = “empirical effects”.
Count = complexity of true model.
Appearance times = elusiveness of effects.
Polynomial Models

Data = ever tighter open intervals around Y
at rational values of X.
Y
X
Polynomial Models

0: no effect
Polynomial Models

1: constant effect
Polynomial Models

2: constant + linear effect
Polynomial Models

3: constant + linear + quadratic effect
Retractions


U-turn = model retraction;
Freeway = retraction-efficient truth-finding
method.
H
H
How Ockham’s Razor Helps


No matter which theory is true, Ockham’s
razor never retracts more than any other
convergent method.
Any non-Ockham method does worse.
Over-counting is Inefficient

Suppose you over-count.
1 3
Over-counting is Inefficient

Where is that extra marble, anyway?
1 3
Over-counting is Inefficient

If you never say 2 you’ll never converge to the
truth….
1 3
Over-counting is Inefficient

That’s it. You should have listened to Ockham.
1 3
2
Over-counting is Inefficient

Oops! Well, no method is infallible!
1 3
2
Over-counting is Inefficient

If you never say 3, you’ll never converge to the
truth….
1 3
2
Over-counting is Inefficient

Embarrassing to be back at that old theory, eh?
1 3
23
Over-counting is Inefficient

And so forth…
1 3
234
Over-counting is Inefficient

And so forth…
1 3
2345
Over-counting is Inefficient

And so forth…
1 3
23456
Over-counting is Inefficient

And so forth…
1 3
234567
The Score

You:
At moment of over-count
1 3
234567
The Score

Ockham:
At moment of over-count
3
saved
retracation
234567
Moral



Ockham’s razor keeps one on the straightest
path to the truth.
Argument is a priori and mathematical, not
hidden and metaphysical.
Insistence on truth in the short run saddles
science with a priori metaphysical commitments.