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Comments on the Humean thesis on belief Richard Pettigrew - - PowerPoint PPT Presentation
Comments on the Humean thesis on belief Richard Pettigrew - - PowerPoint PPT Presentation
Comments on the Humean thesis on belief Richard Pettigrew Department of Philosophy University of Bristol Ren e Descartes Lectures 2014 TiPLS Tilburg University The project How does rational (all-or-nothing) belief relate to degrees of
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The project
Humean thesis on belief (HT r)
Bel(X) iff P(X|Y ) > r for all Y s.t. Poss(Y ) and P(Y ) > 0.
◮ Humean beliefs are stable under conditioning on
doxastically possible evidence.
◮ This account is motivated by:
◮ 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.
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The project
Some concerns about the account:
◮ Even if stability is required for (extended) action and
(certain) assertions, Humean belief doesn’t provide it.
◮ Stability is not required for extended action and assertion
(but perhaps it is for suppositional reasoning).
◮ Closure of belief under conjunction is not a rational
requirement. A concern about the project:
◮ If there are any notions of belief, there are many.
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Motivating stability I
The role-based approach.
◮ Note certain roles that belief is supposed to play. ◮ Argue that they can only play these roles if they are stable.
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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.
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Action and belief
◮ If Humean, then cannot be undermined by doxastically
possible evidence.
◮ If Lockean, then can be undermined by doxastically
necessary evidence!
Lockean thesis on belief (HT r)
Bel(X) iff P(X) > r.
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Action and belief
My credence function at t1:
◮ P1(Spritzer in fridge) = 0.7 ◮ P1(Spritzer not in fridge) = 0.3
With r = 0.6, I may Humean-believe Spritzer in fridge. My credence function at t2:
◮ P2(Spritzer in top of fridge) = 0.35 ◮ P2(Spritzer in bottom of fridge) = 0.35 ◮ P2(Spritzer in fridge) = 0.7 ◮ P2(Spritzer not in fridge) = 0.3
With r = 0.6, I may not Humean-believe Spritzer in fridge
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Action and belief
◮ If Lockean, then cannot be undermined by fine-graining
possibilities.
◮ If Humean, then can be undermined by fine-graining
possibilities.
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Action and belief
Response:
◮ What is required for extended action is not that the belief
is necessarily sustained throughout the action.
◮ It is that the belief is not undermined by updating on
doxastically possible evidence. But why?
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Action and belief
◮ Why not require that belief is stable under any update?
◮ 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?
◮ 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.
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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(Use(A)) and not Bel(Use(B))) then EP (u(A)) > EP (u(B)) (2) for all actions A: if EP (u(A)) is maximal, then Bel(Use(A)), and for all actions B with Bel(Use(B)) it holds that EP (u(A)) − EP (u(B)) < (1 − r)(umax − umin)
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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(Use(A)) and not Bel(Use(B))) then EP (u(A)) > EP (u(B)) (2) for all actions A: if EP (u(A)) is maximal, then Bel(Use(A)), and for all actions B with Bel(Use(B)) it holds that EP (u(A)) − EP (u(B)) < (1 − r)(umax − umin)
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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.
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Assertion and belief
Two concerns:
◮ 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.
◮ 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.
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Motivating stability II
The norm-based approach.
◮ Note certain principles of rationality that belief is thought
to obey.
◮ Show that only Humean belief obeys them.
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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 t′, then Belt = Belt′. (P3) If X is learned between t and t′, then Pt′(Y ) = Pt(Y |X). Why think (P2) is true?
◮ Going from mere belief in X to certainty in X (as a result
- f gaining evidence) is a substantial doxastic shift.
◮ Why think it shouldn’t affect anything else?
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Why uniqueness?
Why think there is just one notion of belief?
◮ Suppose belief is an ontologically separate mental state
from credence.
◮ Its purpose is to facilitate faster and more computationally
feasible reasoning and decision-making.
◮ But then why think that there is only one such mental
state besides credence that does this?
◮ Perhaps there is:
◮ one to support action, ◮ one to license assertion, ◮ one to use in reasoning, ◮ one to justify moral blame, ◮ one that answers to accuracy considerations...
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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?
◮ Bratman on context dependence ◮ Buchak on moral blame ◮ Hempel/Easwaran/Fitelson on epistemic utility ◮ Preface Paradox
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Why uniqueness?
◮ So existence might fail, but not for Churchlandian reasons. ◮ If existence fails, perhaps there are many different belief
states.
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Why uniqueness?
The Humean account (HT r)
Bel(X) iff P(X|Y ) > r for all Y s.t. Poss(Y ) and P(Y ) > 0.
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Why uniqueness?
The Humean account
Pro:
◮ Stable under update on doxastically possible evidence. ◮ Closed under classical multiple premise consequence. ◮ Satisfies a version of the Lockean thesis. ◮ Gives a weak qualitative decision theory. ◮ Stably positive expected epistemic utility.
Contra:
◮ Not stable under fine-graining. ◮ Renders Preface Paradox beliefs irrational. ◮ Does not support ascriptions of moral blame.
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Why uniqueness?
The Lockean account (LT r)
Bel(X) iff P(X) > r
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Why uniqueness?
The Lockean account
Pro:
◮ Stable under fine-graining. ◮ Renders Preface Paradox beliefs rationally permissible ◮ Satisfies a version of the Lockean thesis. ◮ Gives a weak qualitative decision theory. ◮ Maximizes expected epistemic utility.
Contra:
◮ Not stable under update on doxastically possible evidence. ◮ Not closed under classical multiple premise consequence. ◮ Does not support ascriptions of moral blame.
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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.)
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