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 belief?

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.

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.

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.

Action and belief Spritzer (action) I am thirsty. At t 1 , I believe there is a spritzer in the fridge. So I walk to the fridge and open it at t 2 .

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 .

Action and belief My credence function at t 1 : ◮ P 1 ( Spritzer in fridge ) = 0 . 7 ◮ P 1 ( Spritzer not in fridge ) = 0 . 3 With r = 0 . 6, I may Humean-believe Spritzer in fridge . My credence function at t 2 : ◮ P 2 ( Spritzer in top of fridge ) = 0 . 35 ◮ P 2 ( Spritzer in bottom of fridge ) = 0 . 35 ◮ P 2 ( Spritzer in fridge ) = 0 . 7 ◮ P 2 ( Spritzer not in fridge ) = 0 . 3 With r = 0 . 6, I may not Humean-believe Spritzer in fridge

Action and belief ◮ If Lockean, then cannot be undermined by fine-graining possibilities. ◮ If Humean, then can be undermined by fine-graining possibilities.

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?

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.

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 E P ( u ( A )) > E P ( u ( B )) (2) for all actions A : if E P ( u ( A )) is maximal, then Bel ( Use ( A )), and for all actions B with Bel ( Use ( B )) it holds that E P ( u ( A )) − E P ( u ( B )) < (1 − r )( u max − u min )

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 E P ( u ( A )) > E P ( u ( B )) (2) for all actions A : if E P ( u ( A )) is maximal, then Bel ( Use ( A )), and for all actions B with Bel ( Use ( B )) it holds that E P ( u ( A )) − E P ( u ( B )) < (1 − r )( u max − u min )

Assertion and belief Spritzer (assertion) You are thirsty. At t 1 , 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 t 2 .

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.

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.

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 Bel t ( X ) and X is learned between t and t ′ , then Bel t = Bel t ′ . (P3) If X is learned between t and t ′ , then P t ′ ( Y ) = P t ( Y | X ). Why think (P2) is true? ◮ Going from mere belief in X to certainty in X (as a result of gaining evidence) is a substantial doxastic shift. ◮ Why think it shouldn’t affect anything else?

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...

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

Why uniqueness? ◮ So existence might fail, but not for Churchlandian reasons. ◮ 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. Poss ( Y ) and P ( Y ) > 0.

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.

Why uniqueness? The Lockean account ( LT r ) Bel ( X ) iff P ( X ) > r

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.

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: ◮ Buchakean belief supports ascriptions of moral blame.