Lewis Desire and Paradox Doug Campbell Department of
Lewis, Desire and Paradox Doug Campbell Department of Philosophy
Feedback from talk. 1. I need a principled reason up front why indicative reading is to be preferred over subjunctive reading, that doesn’t rely on later arguments. 2. Is it possible to desire something you don’t think is possible? Surely it is. 3. What is the truth table for the third truth value? 4. A lot of philosophers will complain about amending logic to save DAB. (Me: the claim is not that this is required in order to be an anti. Humean. )
Part 1 LEWIS’S ARGUMENT
Lewis in defense of Humeanism The theory Lewis is attacking
Lewis’ protagonist: “Frederic, that famous slave of duty” • “Frederic desires things just when he believes they would be good. Or better, since we must acknowledge that desire and belief admit of degree, he desires things just to the extent that he believes they would be good. To any ordinary proposition, A, there corresponds another proposition: A°, the proposition that it would be good that A. Frederic’s expected value for A, which represents the degree to which he desires that A, equals the degree to which he believes that A°. ” (Lewis, 1988, pp. 325– 326)
• “At any moment, Frederic has a credence function, C. It measures the degree to which he believes various propositions. ” (1988, p. 326) • “At any moment, Frederic also has an (evidential) expected value function V. It measures the degree to which he desires that various propositions be true. ” (Ibid. )
The equation that determines the strength of all of Frederic’s desires: • ‘Desire-As-Belief’ (DAB): V(A)=C(A )
Here Lewis is making a simplifying assumption • “Let us suppose, for now, that Frederic does not discriminate degrees of goodness. His desire that A is connected simply to his belief that A would be good—not to beliefs about just how good A would be. ” (1988, p. 325) • So, Frederic is concerned only with the likelihood of world peace and/or a nice coffee being good (as opposed to not being good), not with their respective degrees of goodness. • “It is fair to take a simple case; because if our Anti-Humean's thesis collides with Decision Theory only in simple cases, that is bad enough. ” (1988, p. 325)
C(World Peace°) V(World Peace) World Peace C(Nice Coffee°) Frederic A nice coffee V(Nice Coffee)
• Lewis proceeds to argue that Frederic cannot be rational by the lights of Bayesian decision theory. Bad Frederic!
Step 1: UPDATE • Suppose that Frederic learns that A is true. • V(A|A) denotes the strength of his desire that A in light of this new information. • C(A |A) denotes his updated credence for A° in light of this new information. • Assuming that Fredric’s desires still continue to be related to his beliefs as per DAB after he has acquired this information, then UPDATE will be true: • UPDATE: V(A|A)=C(A |A)
Step 2: INV • Should V(A|A) differ at all from V(A)? – That is, should Frederic change his valuation of A merely because he has come to believe that A obtains? – Should he be more inclined (or less inclined) to think that A is good after learning that A is true than he was before learning that A is true? • It would appear not. – If the discovery that A is true was apt to make him more (or less) inclined to think that A is good, then he should have factored this into account when he made his initial judgment as to the likelihood of A being good. (This information should have already been “baked into” his judgement. ) • Thus it would appear that INV is true: • INV: V(A|A)=V(A)
STEP 3: DACB • UPDATE: • INV: V(A|A)=C(A |A) V(A|A)=V(A) • Together UPDATE and INV entail Desire-asconditional-belief (DACB): • DACB: V(A)=C(A |A)
STEP 4: IND • DACB: • ‘Desire-As-Belief’ (DAB): V(A)=C(A |A) V(A)=C(A ) • Together DACB and DAB entail IND: • IND: C(A )=C(A |A) • So, since Frederic’s C and V functions conform to DAB, his C function must also conform to IND.
STEP 5: Why IND isn’t stable under Bayesean updating IND: C(A )=C(A |A)
1 C(A )= 3
STEP 5: Why IND isn’t stable under Bayesean updating IND: C(A )=C(A |A)
1 C(A |A)= 3
= • So far, so good. • Frederic’s credence function satisfies IND. • But…
STEP 5: Why IND isn’t stable under Bayesean updating Now Frederic Learns that A°∨A
STEP 5: Why IND isn’t stable under Bayesean updating IND: C(A )=C(A |A)
1 C(A )= 2
STEP 5: Why IND isn’t stable under Bayesean updating IND: C(A )=C(A |A)
1 C(A |A)= 3
≠ • In short, even if Frederic’s credence function satisfies IND before he learns that A∨A°, then it will not satisfy it afterwards if he adjusts his credences in the approved Bayesian manner. • Hence he cannot proportion his desires in accordance with DAB while remaining rational by the lights of Bayesian decision theory!
• “If an Anti-Humean Desire-as. Belief Thesis collides with Decision Theory, it is the Desire-as-Belief Thesis that must go. ” (1988, p. 325)
Part 2 WHAT IS AT STAKE
Lewis’ Target: anti-Humeanism about desire • Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them. • `Tis not contrary to reason to prefer the destruction of the whole world to the scratching of my finger. • In short, a passion must be accompany'd with some false judgment, in order to its being unreasonable; and even then `tis not the passion, properly speaking, which is unreasonable, but the judgment.
The Humean Picture
The anti-Humean Picture
Why I care
Extant anti-Humean Desire as belief theories • Humberstone (1987): an agent desires that iff she believes that D , where D means roughly ‘it is desirable that ’ or ‘would that it were that ’. • Mc. Naughton (1988, p. 112): an agent desires that iff she believes that ’s being true is attractive. • Gregory (2017): an agent desires to ϕ iff she believes that she has normative reason to ϕ. • Campbell (2017): an agent desires that with strength x iff she believes that D( , x), where D is a special mental predicate capable of producing motivating reasons via the operation of a version of the meansend rule, and where D( , x) means, roughly, that is valuable to degree x.
Why the stakes are high in the Humeanism / anti-Humeanism dispute Anti-Humean Desire as Belief solves Smith’s Moral Problem produces Improvements In theoretical economy helps solve The problem of naturalizing propositional attitudes supports Attitudinal Monism
The ‘moral problem’ Motivational Humeanism • MH 1: An agent can be motivated to act only by some combination of a desire and a means-end belief • MH 2: Desires and beliefs are ‘distinct existences’ in the sense that they are modally separable. Internalism: moral judgements, when combined with suitable means-end beliefs, have motivational force. Cognitivism: moral judgments are judgments about matters of fact. × Moral judgements are desires If a moral judgement is a desire, then it is not a belief, and vice versa Moral judgements are beliefs
How Attitudinal Monism helps solve the problem of naturalizing the propositional attitudes The problem decomposes into two sub-problems: • Propositional sub-problem. For any given proposition p, what are the naturalistic properties of the brain in virtue of which it mentally grasps p? • Attitudinal sub-problem. For any given attitude, A, what are the naturalistic properties of the brain in virtue of which it grasps propositions under the aegis of A instead of some other attitude?
Suppose there were five fundamental attitudes—A, B, C, D and E. • A solution to the attitudinal sub-problem would then need to include a five-way decision procedure for classifying any given grasping of p as being a token of one of the following five propositional attitudes: Ap, Bp, Cp, Dp or Ep.
Suppose instead that there were only two fundamental attitudes—belief and desire. • A solution to the attitudinal sub-problem would then only need to include a binary decision procedure, for classifying a grasping of p as being either a belief that p or a desire that p.
Finally, imagine Attitudinal Monism is true. There is only one fundamental attitude, belief • A decision procedure that must always yield the same answer—‘belief’—is no real decision procedure at all, there being no decision to be made. • So the attitudinal sub-problem is thereby reduced to triviality, and dissolved.
• This still leaves the other half of the problem of naturalizing propositional attitudes—the propositional half—intact. • But progress can be claimed even on this front. – A satisfactory solution to the propositional subproblem is liable to be much easier to find when it needn’t be compatible with a separate solution to the attitudinal sub-problem.
Part 3 POSSIBLE ANTI-HUMEAN RESPONSES TO LEWIS
The argument Informal description of Frederic Formal description of Frederic, including DAB UPDATE DABC INV IND Frederic is irrational, and so anti-Humeanism Is in trouble Contradiction
Option 1 Informal description of Frederic Formal description of Frederic, including DAB Accept that Frederic is irrational by lights of Bayesianism, but hold that more sophiisticated forms of anti-Humeanism can still be true. UPDATE DABC INV IND Frederic is irrational, and so anti-Humeanism Is in trouble Contradiction
Option 2 Informal description of Frederic Formal description of Frederic, including DAB Hold that Frederic, as both informally and formally described, is rational by the lights of Bayesian decision theory, because INV is false (which blocks the derivation of a contradiction). UPDATE DABC INV IND Frederic is irrational, and so anti-Humeanism Is in trouble Contradiction
Option 3 Informal description of Frederic Formal description of Frederic, including DAB Hold that Frederic, as informally described, is rational by the lights of Bayesian decision theory, but accept that DAB leads to a contradiction. UPDATE DABC INV IND Frederic is irrational, and so anti-Humeanism Is in trouble Contradiction
Option 4 Informal description of Frederic Formal description of Frederic, including DAB Hold that Frederic, as both informally and formally described, is rational by the lights of Bayesian decision theory, not because INV is false, but because the contradiction isn’t real. UPDATE DABC INV IND Frederic is irrational, and so anti-Humeanism Is in trouble Contradiction
Option 1 • Accept Lewis’ refutation of DAB. – I. e. , accept that Frederic cannot conform to DAB except on pain of irrationality. • But then point out that DAB is a very simple anti-Humean theory, and hold that some more sophisticated anti-Humean theory is true instead. – For example, DAB ignores the fact that goodness comes in degrees.
• Humberstone (1987): an agent desires that iff she believes that D , where D means roughly ‘it is desirable that ’ or ‘would that it were that ’. – This desire-as-belief theory fails to accommodate the idea that desirability come in degrees, so it is vulnerable to Lewis’ attack. • Mc. Naughton (1988, p. 112): an agent desires that iff she believes that ’s being true is attractive. – And ditto. • Gregory (2017): an agent desires to ϕ iff she believes that she has normative reason to ϕ. – And ditto. • Campbell (2017): an agent desires that with strength x iff she believes that D( , x), where D is a special mental predicate capable of producing motivating reasons via the operation of a version of the means-end rule, and where D( , x) means, roughly, that is valuable to degree x. – But this theory explicitly accommodates the fact that the value of an outcome is a matter of degree. – I could claim on this basis that my theory is immune to Lewis’ anti. Humean argument.
However… 1. In one of the final sections of his 1988 paper, Lewis generalizes his argument so that it will work even for multiple degrees of goodness. 2. And I can imagine an agent who desires only one thing (e. g. , that a certain button be pressed before the end of time), and for whom everything else valuable only in so far as it is a means to that end. – For such an agent, there are only two degrees of goodness—good (button pressed), and not good (button not pressed).
Why Lewis’ argument appears to be flatly paradoxical Frederic • Recall the initial informal setup: • “Frederic desires things just when he believes they would be good. Or better, since we must acknowledge that desire and belief admit of degree, he desires things just to the extent that he believes they would be good. ” • It seems we can coherently imagine an agent, Frederic, who desires things just to the extent that he believes they are conducive to the button being pressed. • Yet Lewis’ argument appears to show that this isn’t possible!
Lewis voices a similar concern himself • “You may think (as I did) that my argument against the Desire-as. Belief Thesis has to be wrong, because it proves too much. For it does not just refute the Anti. Humean's grand Desire-as-Belief Thesis; it refutes also the supposition that some modest, contingent equation of desire with belief might hold in some special case. “ (1988, p. 328)
Option 2 Informal description of Frederic Formal description of Frederic, including DAB Hold that Frederic, as both informally and formally described, is rational by the lights of Bayesian decision theory, because INV is false (which blocks the derivation of a contradiction). UPDATE DABC INV IND Frederic is irrational, and so anti-Humeanism Is in trouble Contradiction
Option 2 • Accept Lewis’ demonstration that IND is incompatible with Bayesian decision theory, but reject Lewis’ refutation of DAB on the basis that INV should be rejected.
Bradely and Stefansson • “As we will explain, [INV] is not only intuitively implausible, but inconsistent with the (standard formulation of the) version of Bayesian decision theory that Lewis assumed in his arguments against DAB. ” (2016, p. 691)
Option 3 Informal description of Frederic Formal description of Frederic, including DAB Hold that Frederic, as informally described, is rational by the lights of Bayesian decision theory, but accept that DAB leads to a contradiction. UPDATE DABC INV IND Frederic is irrational, and so anti-Humeanism Is in trouble Contradiction
Option 4 Informal description of Frederic Formal description of Frederic, including DAB Hold that Frederic, as both informally and formally described, is rational by the lights of Bayesian decision theory, not because INV is false, but because the contradiction isn’t real. UPDATE DABC INV IND Frederic is irrational, and so anti-Humeanism Is in trouble Contradiction
Part 4 A FLAW IN LEWIS’ DEMONSTRATION THAT IND IS CONTRADICTED BY BAYESEAN DECISION THEORY
The informal presentation, again… • “Frederic desires things just when he believes they would be good. Or better, since we must acknowledge that desire and belief admit of degree, he desires things just to the extent that he believes they would be good. To any ordinary proposition, A, there corresponds another proposition: A°, the proposition that it would be good that A. Frederic’s expected value for A, which represents the degree to which he desires that A, equals the degree to which he believes that A°. ” (Lewis, 1988, pp. 325– 326)
Two readings of “it would be good that A” • Indicative: “it will be good if I get promoted”, – This would be made true by me being promoted, and by that being good. • Subjunctive: “It would have been good if dirt were delicious and nutritious” – This would be made true (maybe) by there being a nearby possible world in which dirt is delicious and nutritious, and where that is good.
Which reading is operative? • “Frederic desires things just when he believes they would be good. Or better, since we must acknowledge that desire and belief admit of degree, he desires things just to the extent that he believes they would be good. To any ordinary proposition, A, there corresponds another proposition: A°, the proposition that it would be good that A. Frederic’s expected value for A, which represents the degree to which he desires that A, equals the degree to which he believes that A°. ” (Lewis, 1988, pp. 325– 326)
It would be good that A, but A is false. This demands some pretty sophisticated analysis of subjective truth-conditions A is true and it would be good that A – so the good is attained.
A problem case A° A C(A°) is very high. But should Frederic desire that A?
Another problem case A° A C(A°) is very high. But should Frederic desire that A?
My proposal • A’s being good is to be read indicatively, not subjunctively. • This is the reading under which the informal description of Frederic appears to be a description of a potentially rational person.
This is OK A A°
This isn’t A A°
Making sense of DAB: V(A)=C(A ) A A° In which case should C(A°) be the highest? That is, in which case is A more desirable?
The problem • We want C(A°) to be high when a large proportion of the A-domain is in the A°-domain, irrespective of the size of the ¬A-domain. In other words, we want the ¬Adomain to be ignored when we are calculating the credence of A°. • But that is not how credences normally work. Normally you consider the entire domain of the Venn diagram. • The worry here is that we are not going to be able to make sense of DAB—which says that V(A)=C(A ). • This would mean that we would not be able to ‘save’ the idea that Frederic, as formally described by Lewis, could potentially be rational.
A solution. De-Finetti’s (1935) three valued logic for indicative conditionals P True False Q True False P→Q True False Null
My proposal • A° is true iff A→H is true, where H is the halo of goodness, and where the arrow is De Finetti’s indicative conditional. A° is true H A A° is false A° is null C(A°)=[area where A° is true]/[area where A° is true or false] = C(H|A)
How this blocks IND from contradicting Bayesian updating IND: C(A )=C(A |A)
How this blocks IND from contradicting Bayesian updating IND: C(A )=C(A |A)
1 C(A )= 3
How this blocks IND from contradicting Bayesian updating IND: C(A )=C(A |A)
STEP 5: Why IND isn’t stable under Bayesean updating IND: C(A )=C(A |A)
1 C(A |A)= 3
How this blocks IND from contradicting Bayesian updating Now Frederic Learns that A°∨A
How this blocks IND from contradicting Bayesian updating IND: C(A )=C(A |A)
1 C(A )= 3
How this blocks IND from contradicting Bayesian updating IND: C(A )=C(A |A)
1 C(A |A)= 3
= • In short, Frederic’s credence function will keep satisfying IND when he adjusts his credences in the approved Bayesian manner. • Hence he can proportion his desires in accordance with DAB while remaining rational by the lights of Bayesian decision theory!
THE END Good Frederic!
- Slides: 84