Space, Time and Causality: Causa4on, II David Lewis s Counterfactual Account
The New David
Prelude: What Went Wrong with Mackie? Several things, but we ll review just one: The (Just About) Any Old Fact Problem
The Any Old Fact Problem If we understand claims about necessary condilons/sufficient condilons in terms of material condilonals and/or logical entailment, too many things get counted as causes
Any Old Fact Example Suppose condilon AB is a minimal sufficient condilon for E Take any fact T, reporlng the occurrence of an event which is not a cause of E (Not T or A)B is not a minimal sufficient condilon for E But T(Not T or A)B is a minimal sufficient condilon for E, and T gets counted as an INUS condilon of E auer all
A Way Out? Mackie suggests we understand necessary condilons and sufficient condilons in terms of non material condilonals, e.g. The short occurring was a necessary condilon of the fire occurring to be understood in terms of If the the short had not occurred, then the fire would not have occurred either
An Obstacle Mackie s proposal raises the queslon of how we are to understand the relevant nonmaterial condilonals Familiar worries: Epistemology How do we have knowledge of them? Metaphysical Can we give a reduclve account of their truth?
Mackie s View of Counterfactuals Mackie suggests that the counterfactual condilonals are compressed arguments Can this work?
Mackie on Counterfactual CondiLonals If we said that a short circuit here was a necessary condilon for a fire in this house, we should be saying that there are true universal proposi8ons from which, together with true statements about the characterislcs of this house, and together with the supposilon that a short circuit did not occur here, it would follow that the house did not catch fire (Mackie 1965, p. 49 in Study Pack version; emphasis added)
The Beginnings of a Problem We need laws of nature plus facts to rule out the occurrence of a fire It s not enough that taking some laws plus some facts (supposing X not to have occurred) fails to entail the occurrence of a fire that would give us a version of AnyOldFacts
The Problem Arrives The facts and the laws will tend to entail the occurrence of the event we want to suppose not to occur (e.g. The state of the wiring in the fusebox, plus the laws of nature, may entail the occurrence of the short) So, adding the supposilon to our pool of facts and laws may simply result in contradiclon (and entail anything)
An Alterna4ve Approach: David Lewis s Account Lewis aims to provide an account of causalon in terms of counterfactual condilonals He gives an account of counterfactual condilonals different from Mackie s
Preliminary: Counterfactual CondiLonals Counterfactual claims are what ifs, e.g. If Elizabeth I had married Philip of Spain, the industrial revolulon would not have occurred in England More clearly and properly expressed as subjunc8ves: If it were the case that p, then it would have been the case that q
A Simple Counterfactual Account of CausaLon c causes e iff If it had been that c did not occur, e would not have occurred either e.g. Don s fall caused his death: If it had been that Don s fall did not occur, Don s death would not have occurred either
The Counterfactual (CF) Account and Cosmic Coincidence I will Brown s sandwich shop to have Mexicana Cheese on sale, and they do (just like every other Lme I will that) The CF account seems to avoid saying my willings cause the sandwich makings, because the following is (plausibly) false: If it had been that my willing did not occur, then the sandwich making would not have occurred either
3 Worries About Counterfactuals Can we explain how we have knowledge of counterfactual claims? Can we give a reduclve account of them (without menloning unreduced causal facts)? Are they simply too vague, woolly, and poorlyunderstood to help explain/explicate causalon?
Lewis s Account of Counterfactuals Key QuesLon: What makes a counterfactual true? Lewis gives a reduclve account of counterfactuals in terms of possible worlds
Possible Worlds Possible worlds are ways things could have been A possible world is a complete or maximal way things could have been: a way an en8re possible universe could be
A Simple Account of Truth for Counterfactuals? Is the following right? If it had been the case that p, then it would have been that q iff in every possible world in which p, it is the case that q It would seem not
A Counterexample to the Simple Account If I had placed my finger between the door and frame at the hinge side and slammed the door, I would have suffered a horrible injury True, despite the fact that there are some possible worlds in which the door behaves like foam rubber, or my hands are covered in bony hide Plausibly, these worlds just aren t close enough to ours to count
Lewis s Account of Counterfactuals If it had been that p, then it would have been that q iff In the worlds in which p closest to the actual world, it is also the case that q Closest? At a first, rough try = Most similar
A Simple Counterfactual Account of CausaLon c causes e iff in the possible worlds closest to the actual world in which c does not occur, e does not occur either e.g. The short circuit caused the fire iff in the possible worlds closest to the actual world in which the short does not occur, the fire does not occur either
Aside: Knowledge of Counterfactuals Worry: How do we know enough about possible worlds to know counterfactuals? Possible Response: We can describe possible worlds, and make informed judgements about their similarity etc., and we know what possibililes there are independently of experience of them
A Problem with Closeness? I strike a match; it ignites The simple CF theory says: The striking causes the ignilon iff In the closest worlds in which the striking does not occur, neither does the ignilon
A Problem with Closeness Actual World: Striking IgniLon World 1: No Striking IgniLon World 2: No Striking No IgniLon In one sense, World 1 seems more similar to the actual world than World 2 it differs less in terms of par8cular ma>ers of fact
Laws and Closeness Note first that intuilvely the no strike noignilon world is closer but what s driving our intuilon? Proposal: In general, laws (of nature) should be given more weight than parlcular mamers of fact in determining closeness
Dilemma OpLon 1: Say laws are all and only the true generalizalons Problem(s): We ll run into the troubles which faced simple regularity accounts OpLon 2: Say laws are not mere true generalizalons Problem: Seems to risk difficulles over epistemology or metaphysics (lack of reduclon)
Lewis s Best System Account of Laws A generaliza4on is a law iff it appears in the best systema-c account of the facts On Lewis s view, laws are generalizalons, but not all generaliza8ons are laws In Lewis s terms, laws do not, in themselves, have counterfactual force (Lewis gives a reduc8ve account of lawhood)
Best System An account of the facts is the best iff it has the best balance of simplicity and strength One account is simpler than another if it involves fewer basic rules, or kinds, or properles One account is stronger than another if it covers (predicts, entails) more of the facts
A GeneralizaLon Which Isn t a Law Every Lme Barry wills there to be Mexicana cheese sarnies in Brown s, there are Suppose this is a true generalizalon It seems it won t count as a law, because it won t figure in the best system (what will are the generalizalons of empirical science)
Interim Summary We have the beginnings of a counterfactual account of causalon c causes e iff in the possible worlds closest to the actual world in which c does not occur, neither does e Closeness is a mamer of similarity, but with more weight given to best system generalizalons
Lewis s Account: Problems and Refinements We have the basic outline of Lewis s account in view The account faces a number of problems, which force adjustments Let s see how well Lewis s account stands up to crilcism
Some Shorthand NotaLon Shorthand Read as O(a) Event a occurs ~X It is not the case that X ~O(a) It s not the case that event a occurs A B In the closest worlds in which A, it is the case that B <a, b, c, d> The things a, b, c, d considered in that order
A Problem: Pre emplon Short c Sparks d Ignition g Fire e Arsonist sees sparks and runs off Closest No Short World? Arsonist sees no sparks and ignites some fire gel f Fire e
The Problem with Pre EmpLon The account says: The short c causes the fire e iff in the closest possible worlds in which it is not the case that c occurs, e does not occur either But this seems false in the pre emplon case
Lewis s Refinement: Chains of Counterfactual Dependence c causes e iff there is a chain of counterfactual dependence running from c to e b counterfactually depends on a iff ~O(a) ~O(b) <h, i, j, k> is a chain of counterfactual dependence iff k cf depends on j, j cf depends and so on
Chains and the Arsonist c: short d: sparks g: ignilon e: fire f: arsonist lighlng gel Actual world: O(c), O(d), O(g), O(e), ~O(f) World w*: ~O(c), ~O(d), ~O(g), O(f), O(e) World w : O(c), O(d), ~O(g), ~O(e), ~O(f) In the closest world in which ~O(c), it is slll the case that e occurs, but there is a chain of CF dependence between c and e, so c gets counted as a cause of e by the revised account
The Key The closest world at which there is no ignilon (of the flammable material) there are sparks (O(d)), so the arsonist has run off (~O(f))
Something Fishy? You might think there s something dodgy about Lewis s solulon to pre emplon Actual World: Sparks IgniLon World 3: Sparks No IgniLon World 4: No Sparks No IgniLon The solulon requires World 3 to be a closer No Igni8on world than World 4. How can that be right? We ll come back to this
Two Related Problems Now we ll look at two problems related to the issue we just noted The DirecLon of CausaLon (Lewis s Problem of Effects ) The Problem of Epiphenomena
The DirecLon of CausaLon The striking caused the ignilon Lewis: In the closest worlds in which the striking (c) does not occur, neither does the ignilon (e) But what are the closest no ignilon worlds like? (Favouring retenlon of the laws of our world)???in the closest worlds in which the ignilon does not occur, neither does the striking?? If so, Lewis s account would say the effect caused its cause!
Insist on Temporal Order? We could just say that effects have to come auer their causes in Lme? But this would Rule out back over causalon a priori Block giving an account of Lme direclon in terms of the prevailing direclon of causalon Fail to deal with the next problem
The Problem of Epiphenomena Pressure Drop d Barometer Fall b Rain Shower r It would seem that ~O(b) ~O(r) If so, the Lewis s account says that b causes r!
Closeness of Worlds Lewis s proposed solulons to these problems rely on more specific views about closeness between worlds Lewis first thought that comparalve overall similarity could be taken as basic in determining closeness (1973) But later (1979) he proposed a more specific and complex account, to deal with the problems
Closeness of Worlds [To find a closer world (in importance order)] (1) Avoid big, widespread violalons of our (i.e. the actual) laws of nature (very important) (2) Maximize the spalo temporal extent of perfect match of parlcular mamers of fact (3) Avoid small, localized violalons of our laws (4) Secure approximate similarity of parlcular mamers of fact (not at all important)
Lewis s View on DirecLon Lewis: In the problemalc direclon cases we can have ~O(c) ~O(e) but deny ~O(e) ~O(c) The closest no c worlds are no e worlds The closest no e worlds are not (all) no c worlds But how can this be?
The Key to Lewis s Proposed SoluLon OverdeterminaLon is hugely more common causally upstream than it is causally downstream That is events typically have many effects which (together with laws) determine that they exist and events typically have few causes which (together with laws) determine that they exist
The Asymmetry of OverdeterminaLon A typical cause and effect pair (in a world like ours) c f1 f2 f3 f4 e f5 f6 f7 f8 Lewis s view of a normal case of cause and effect Cause c has many determining consequences, f1 to f4. A world in which e does not occur and c does not occur will have to deal with the links between c and f1 to f4.
The Asymmetry of OverdeterminaLon Example: Barry fondly strokes Chris s head (c), warming it slightly (e) You all see the stroking i.e. the pamern of light at your viewpoint is enough to determine its occurrence (given our laws)
The Fond Stroke Example In the closest worlds in which c (the fond stroke) does not occur, neither does e (the warming) for one thing, this avoids a breach of consideralon (3) In the closest worlds in which e (the warming) does not occur, c (the fond stroke) does this avoids breaches of (1) and (2)
The State of Play Lewis s asymmetry of overdeterminalon move allows him responses to: The accusalon of fishiness in his treatment of pre emplon (sparks with no ignilon) The DirecLon of CausaLon / Problem of Effects The Problem of Epiphenomena But we ain t done yet
Problem: Causal OverdeterminaLon Recall the kind of case: J is shot in the head by each of 2 assailants J dies as a result Each individual shot would have been fatal on its own (J s death is overdetermined) In the closest worlds in which one par8cular shot does not occur, the death s8ll occurs
Causal OverdeterminaLon: Lewis s Response We do not have clear intuilons about cases of overdeterminalon so, they don t provide useful data for theories of causalon (QuesLon for you: Is this salsfactory?)
Pre EmpLon Again A different kind of case: Two bullets, b 1 and b 2, are moving toward a target; b 1 reaches it first, and a holing of the target (h) occurs Had the movement of b 1 not occurred, the movement of b 2 would slll have occurred, and so h would slll have occurred also
The Armageddon Counterfactual Suppose there is an Armageddon bumon, connected to a flawlessly designed, perfectly constructed, and scrupulously maintained Armageddon system, but the bumon is never pushed, and no NH occurs (AC) If Obama were to push the Armageddon bumon, then a nuclear holocaust would follow
A Problem with Armageddon (AC) If Obama were to push the Armageddon bumon, then a nuclear holocaust would follow The condilonal (AC) seems true in the circumstances, but intuilvely the most similar bumon push world has no holocaust Why believe the very special form of similarity posited by Lewis is aclve in our thinking?
The AucLon Example At auclon, I raise my right hand (r); the aucloneer forms a belief I ve made a bid (b) IntuiLvely, the raising, r, causes the belief formalon, b Lewis s Account seems to require: Had r not occurred, b would not either
A Problem with Events Had right hand raising r not occurred, belief formalon b would not either But I could have raised my hand higher, and if I d found my right arm limp or constrained, would have raised my leu (QuesLons for you: What problem does this raise for Lewis? Can he deal with it?)
EvaluaLng Lewis s Account Are any of the problems fatal? How sa8sfying is the amended theory? (Complexity, intuilveness, independent molvalon of principles) Any doubts about components? (Counterfactuals, Account of Laws, Worlds)
DirecLons: What Have We Gained? Whether or not you believe Lewis s parlcular account, it opens up the possibility of providing a reduclve account in terms of counterfactuals CF accounts seem to be a step on from simple regularity accounts Broadened horizons: Note what forms causalon might take, if it were a mamer of CF dependence AlternaLves: ConsideraLon of the problems facing CF accounts may lead you to favour other kinds of account