Comments on the Humean thesis on belief
Richard Pettigrew
Department of Philosophy
University of Bristol
René Descartes Lectures 2014
TiPLS
Tilburg University
The project
How does rational (all-or-nothing) belief relate to degrees of
belief?
The project
Humean thesis on belief (HT r )
Bel(X) iff P (X|Y ) > r for all Y s.t. P oss(Y ) and P (Y ) > 0.
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Humean beliefs are stable under conditioning on
doxastically possible evidence.
This account is motivated by:
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Hume’s account of belief.
The role of belief in decision-making and action.
The role of belief in assertion.
The role of belief in suppositional reasoning.
Basic intuitions about rational belief.
The project
Some concerns about the account:
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Even if stability is required for (extended) action and
(certain) assertions, Humean belief doesn’t provide it.
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Stability is not required for extended action and assertion
(but perhaps it is for suppositional reasoning).
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Closure of belief under conjunction is not a rational
requirement.
A concern about the project:
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If there are any notions of belief, there are many.
Motivating stability I
The role-based approach.
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Note certain roles that belief is supposed to play.
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Argue that they can only play these roles if they are stable.
Action and belief
Spritzer (action)
I am thirsty. At t1 , I believe there is a spritzer in the fridge. So
I walk to the fridge and open it at t2 .
Action and belief
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If Humean, then cannot be undermined by doxastically
possible evidence.
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If Lockean, then can be undermined by doxastically
necessary evidence!
Lockean thesis on belief (HT r )
Bel(X) iff P (X) > r.
Action and belief
My credence function at t1 :
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P1 (Spritzer in fridge) = 0.7
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P1 (Spritzer not in fridge) = 0.3
With r = 0.6, I may Humean-believe Spritzer in fridge.
My credence function at t2 :
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P2 (Spritzer in top of fridge) = 0.35
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P2 (Spritzer in bottom of fridge) = 0.35
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P2 (Spritzer in fridge) = 0.7
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P2 (Spritzer not in fridge) = 0.3
With r = 0.6, I may not Humean-believe Spritzer in fridge
Action and belief
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If Lockean, then cannot be undermined by fine-graining
possibilities.
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If Humean, then can be undermined by fine-graining
possibilities.
Action and belief
Response:
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What is required for extended action is not that the belief
is necessarily sustained throughout the action.
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It is that the belief is not undermined by updating on
doxastically possible evidence.
But why?
Action and belief
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Why not require that belief is stable under any update?
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What is so special about doxastic possibilities (especially
since doxastic impossibilities may well nonetheless be credal
possibilities)?
Stability ensures that you believe that the action will be
completed successfully. It doesn’t guarantee it.
This requires Certainty account (at least)
Why require any sort of stability?
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On a Lockean view, if evidence undermines the belief, then
you would lose the belief and stop.
Note: this is presumably what you would do if you were to
learn a doxastic impossibility in the Humean case.
Note: on the Lockean view, you also believe that the action
will be completed successfully.
Action and belief
Theorem 5
If P is a probability measure, if Bel satisfies the Humean thesis
HT r , and if not Bel(∅), then:
(1) for all actions A, B: if Bel(U se(A)) and not Bel(U se(B)))
then
EP (u(A)) > EP (u(B))
(2) for all actions A: if EP (u(A)) is maximal, then
Bel(U se(A)), and for all actions B with Bel(U se(B)) it
holds that
EP (u(A)) − EP (u(B)) < (1 − r)(umax − umin )
Action and belief
Theorem 5
If P is a probability measure, if Bel satisfies the Humean thesis
LT r , and if not Bel(∅), then:
(1) for all actions A, B: if Bel(U se(A)) and not Bel(U se(B)))
then
EP (u(A)) > EP (u(B))
(2) for all actions A: if EP (u(A)) is maximal, then
Bel(U se(A)), and for all actions B with Bel(U se(B)) it
holds that
EP (u(A)) − EP (u(B)) < (1 − r)(umax − umin )
Assertion and belief
Spritzer (assertion)
You are thirsty. At t1 , I believe there is a spritzer in the fridge.
I assert this and you hear. So you walk to the fridge and open
it at t2 .
Assertion and belief
Two concerns:
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Partition-dependence: without knowing my graining of the
possibilities, you cannot tell whether or not to take on my
Humean belief as your Humean belief.
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Without knowing my strongest belief, you cannot tell under
what new evidence that belief will be stable. We rarely (if
ever) state our strongest belief.
Motivating stability II
The norm-based approach.
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Note certain principles of rationality that belief is thought
to obey.
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Show that only Humean belief obeys them.
Conjunctivitus
The Rule of Conjunction
Bel(X), Bel(Y ) ⇒ Bel(X ∩ Y ).
The Review Paradox argument
(P1) If P (X) = P (Y ), then Bel(X) ⇔ Bel(Y )
(P2) If Belt (X) and X is learned between t and t0 , then
Belt = Belt0 .
(P3) If X is learned between t and t0 , then Pt0 (Y ) = Pt (Y |X).
Why think (P2) is true?
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Going from mere belief in X to certainty in X (as a result
of gaining evidence) is a substantial doxastic shift.
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Why think it shouldn’t affect anything else?
Why uniqueness?
Why think there is just one notion of belief?
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Suppose belief is an ontologically separate mental state
from credence.
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Its purpose is to facilitate faster and more computationally
feasible reasoning and decision-making.
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But then why think that there is only one such mental
state besides credence that does this?
Perhaps there is:
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one
one
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to support action,
to license assertion,
to use in reasoning,
to justify moral blame,
that answers to accuracy considerations...
Why uniqueness?
For HL, belief is a separate ontological state that is defined
functionally.
Belief is the state the function of which is to:
to reach the goal...
to satisfy the norms...
to realise the valuable state...
But what if the functional role cannot be satisfied?
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Bratman on context dependence
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Buchak on moral blame
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Hempel/Easwaran/Fitelson on epistemic utility
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Preface Paradox
Why uniqueness?
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So existence might fail, but not for Churchlandian reasons.
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If existence fails, perhaps there are many different belief
states.
Why uniqueness?
The Humean account (HT r )
Bel(X) iff P (X|Y ) > r for all Y s.t. P oss(Y ) and P (Y ) > 0.
Why uniqueness?
The Humean account
Pro:
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Stable under update on doxastically possible evidence.
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Closed under classical multiple premise consequence.
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Satisfies a version of the Lockean thesis.
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Gives a weak qualitative decision theory.
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Stably positive expected epistemic utility.
Contra:
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Not stable under fine-graining.
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Renders Preface Paradox beliefs irrational.
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Does not support ascriptions of moral blame.
Why uniqueness?
The Lockean account (LT r )
Bel(X) iff P (X) > r
Why uniqueness?
The Lockean account
Pro:
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Stable under fine-graining.
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Renders Preface Paradox beliefs rationally permissible
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Satisfies a version of the Lockean thesis.
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Gives a weak qualitative decision theory.
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Maximizes expected epistemic utility.
Contra:
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Not stable under update on doxastically possible evidence.
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Not closed under classical multiple premise consequence.
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Does not support ascriptions of moral blame.
Why uniqueness?
The Buchakean account (BT r )
Bel(X) iff
(i) P (X) > r
(ii) Attitude to X is justified by evidence E and if X were
true, then X would depend counterfactually on E.
(Cf. Buchak, L. (2014) ‘Belief, credence, and norms’,
Philosophical Studies 169(2): 285–311.)
Why uniqueness?
The Buchakean account
Pro:
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Buchakean belief supports ascriptions of moral blame.