自组织多主体系统动态性的推理研究

罗捷婷 廖备水 约翰-朱尔斯·迈尔

1 Introduction

John can swim across mile-wide rivers,Jack can ride a bicycle and Jenny can solve this problem.Sentences as such,with the employment of the word“can”,state agentive abilities.As these statements describe what an agent is able to do,ability can is commonly called an agentive modal.To see more clearly why it is seen as amodalin the first place,it suffices to note that the sentence that“John can swim across mile-wide rivers”,for instance,is equivalent to“it is within John’s ability that he swims across mile-wile rivers”.The latter sentence has the form◇φ,where the diamond represents“it is within John’s ability that”,which is at least very similar to the typical modal expressions such as“it is logically possible that”,“it is permissible according to the moral principles that”and“it might be the case that”.

The notion of ability lies at the heart of many philosophical projects.The problem of power and essence in metaphysics,the problem of agency in philosophy of action,and the problem of free will and moral responsibility in moral philosophy,to name a few,all appeal in one or another to a certain assumed understanding of the notion of ability.Thus a precise account of the nature of abilities itself has wide philosophical implications.Among the various philosophical projects currently centered around the nature of abilities,one indispensable aspect of research is to develop a satisfactory logic for ability modals.

In standard modal logics,existential modals,such as alethic possibility,deontic permissibility and epistemicmight,are customarily interpreted as existential quantifications over some relevant sets of possible worlds.It is deontically permissible that John smokes in the hall,for instance,if and only if there are deontically possible worlds——worlds which comply with the relevant moral principles——where John smokes in the hall.John might be in Paris,if and only if there are epistemically possible worlds——worlds which are consistent with what the agent currently knows or justifiably believes——where John is in Paris.

One key logical feature of existential modals is that they generally distribute over disjunction.In alethic modal logic,if it is possible thatφorψ,then it logically follows that it is possible thatφor it is possible thatψ.In deontic logic,if someone is permitted toφor toψ,then it follows that she is permitted toφor she is permitted toψ.And in epistemic logic,if Jane might be in Paris or London,then it follows that Jane might be in Paris or she might be in London.These inferences are simply licensed by the standard semantics and the meaning of disjunction,and they are rarely disputable.Generally,we have the following principle of existential modals’ Distribution over Disjunction:

Distribute over Disjunction◇(φ ∨ψ)⊨◇φ ∨◇ψ

Ability modals,so the traditional wisdom has it,appear to behave as existential modals as well.To say that an agent is able toψ,according to the most prevailing account,is to say that the agent’sψ-ing is compatible with some contextually salient set of worlds.([7,11,14])“John can swim across mile-wide rivers”is true,construed in the standard way,if and only if there are some salient possible worlds,defined relative to John’s abilities,in which John swims across mile-wile rivers.That way,logics for abilities are just more applied modal logics of the standard sort.

But,as it is sometimes noted,ability modals seem to resist Distribution over Disjunction in certain cases.That casts doubt on the idea that ability modals are existential modals and the unificationist project of developing a logic for abilities within the standard framework.For if ability modals really fail to distribute over disjunction,and existential modals should comply with Distribution over Disjunction,then ability modals are not existential modals,or what’s even worse,they are notmodalsat all.Thus a new point of departure should be located before any substantial account of abilities could take shape.

This paper attempts to defend the approach of construing ability modals as existential modals,by accommodating the alleged counterexamples against it.In Section 2,we shall introduce the classical challenges philosophers leveled against construing abilities as existential modals.Also we shall briefly review the typical responses philosophers have advanced to meet the classical challenge.In Section 3,we argue that abilities fall into two varieties:the witnessable abilities and the unwitnessable abilities.Unwitnessable ability ascriptions always invoke,implicitly or explicitly,some kind of success rates,and for this reason comply with the principle of Ability Witness.Whereas witnessable ability ascriptions never invoke any kind of success rates and do comply with the principle of Ability Witness.Given the distinction,we also argue that the ability cases philosophers cite as counterexamples to construing ability modals as existential modals all involve unwitnessable abilities.In Section 4,we argue that the alleged counterexamples should be fully scrutinized in light of the distinction between witnessable and unwitnessable abilities,and the challenges can be squarely met in a principled way.We conclude the paper by drawing some of the philosophical implications this investigation may have.

2 Ability Modals and Kenny’s Challenge

The classical challenges to construing ability modals as existential modals date back to a couple of inspiring cases put forward by Kenny([8]).In one case,Kennyinvites us to consider a skilled dart player,Jerry,who is be able to hit the dartboard.Since to hit the dartboard is to hit the top half of the board or to hit the bottom half,(1)is true.

(1) Jerry is able to hit the top half of the board or to hit the bottom half of the board.But if Jerry is not skilled enough to hit any particular region of the board he wishes to hit,it would be false that

(2) Jerry is able to hit the top half of the board or Jerry is able to hit the bottom half of the board.

For(1)to be true,Jerry only needs to have control over whether he reliably hits the board as whole——any part of the board’s being hit would suffice.But for(2)to be true,Jerry needs to have control over whether he reliably hits a particular half of the board——the other half of the board’s being hit would not suffice.Obviously,(1)does not entail(2).

Another case to show the same point.In front of you is deck of regular playing cards.Given that a card is either red or black,since you have the ability to randomly pick a card from the deck,it follows that(3)is true.

(3) You are able to pick a red card or a black card from the deck.But it certainly does not follow that

(4) You are able to pick a red card from the deck or you are able to pick a black card from the deck.

For(3)to be true,you only need to have control over whether you pick a card from the deck——any card’s being picked would suffice.But for (4) to be true,you need to have control over whether you pick a card of a certain color from the deck——a card of the other color’s being picked would not suffice.Again,(3)obviously does not entail(4).

Since (1) and (3),taking ability expressions as existential modals,are of the logical from◇(φ ∨ψ),and (2) and (4) are of the form◇φ ∨◇ψ,it appears that ability modals fail to comply with Distribute over Disjunction in these cases.If so,we have to end up saying that abilities are not existential modals or Distribute over Disjunction is not a valid principle governing existential modals.Thus,we have to develop separate logics for abilities,or we have to abandon a fundamental principle of modal logic.

Most philosophers working on this issue have located the problem with the ability modals themselves.Most notably,some philosophers propose to treat ability modals instead as universal quantifiers.([1,6]) According to this proposal,agentive“can”has a universal,rather than existential,force.One key observation from this approach is that abilities are intrinsic powers or skills,which usually are stable characters or achievements of the agents.If one has a certain ability to do something,then she would do the thing she has the ability to do inallthe relevant situations,given certain background conditions.John’s ability to ride a bicycle,for instance,is an intrinsically stable achievement acquired by considerable practices and not easily defeasible under normal circumstances.Rarely exceptional situations aside,if John is able to ride a bicycle,then he would undoubtedly ride a bicycle in all relevantly conceivable situations.This seems to indicate that abilities should be construed as universal quantification over possible worlds,if the relevant situations pair with possible worlds.

One other influential suggestion is to treat abilities as some kind of conditional operators,of the form“if such and such were the case,then it would have been the case that”([3,13]).Traditionally,this idea fits well with the widely accepted account of construing powers and dispositions as counterfactual conditional expressions.For example,a bottle is breakable(i.e.,disposed to break upon being hit in certain ways),if and only if the bottle would break if it were hit with considerable power under normal conditions.Or salts are solvable (i.e.,disposed to solve into water),if and only if,they would solve if they were put into a certain amount of unsaturated water.Accordingly,one may think that ability expressions could also be treated in a similar vein.John is able to swim across mild-wide rivers,so the idea goes,if and only if John would swim across mile-wile rivers if he attempted to.On the theory under consideration here,notions such as breakability,solvability and ability are construed in the same manner is no mere coincidence,for break-abilityand solve-ability——as the ability suffix there indicate——are just more abilities of various kinds.Non-agentive abilities,though.Thus agentive abilities,the concepts we are concerned with here in this paper,and non-agentive abilities such as breakability and solvability may be treated on a par.

Another approach worth mentioning is the some what bizarre suggestion that abilities are not simply existential modals or universal modals,but some kind of operator interpretable as a combination of existential and universal force.([1,10]) And still others,such as Kenny himself ([8]),even go so far as to conclude that ability modals are notreallymodals at all.

These various accounts of abilities,though not without intuitive appeals or virtues in themselves,introduce further problems or complications,which are beyond the purpose of this paper to explore in detail.For instance,the conditional analyses of powers and dispositions face the well-known troubles of finks and maskers.1For more on the troubles of the conditional analyses of dispositions and powers,see,among others,[2,4].For instance,a bottle is breakable,but it would not break were it to be hit,for the bottle is carefully packed and protected by packing materials.The packing materials,so to speak,maskthe manifestation of its disposition.But it’s very plain that the bottle itself does have the disposition of breakability.The disposition is merely masked rather than absent.Hence the naïve conditional analysis is false.Similarly,a person may be able to swim across the river,but she would not swim across it were she attempt to,for the river is intercepted by an iron net which would stop anyone from getting across.The net,once again,masks the manifestation of her ability,but the ability itself is not impaired in the slightest.So the conditional account of abilities faces the same problems the conditional analyses of dispositions are troubled with.

Other accounts of abilities mentioned earlier may not fare better.The suggestion that abilities are universal quantification over possible worlds seems too strict to exclude many cases we would intuitively count as ability cases.For instance,the fact that John is able to swim across the river would not be captured by such an account.For there certainly are possible worlds where John fails to swim across it——the worlds where the river is intercepted by an iron net,once again,would suffice.But the account under consideration requires that John swim across the river in all possible worlds to count as having the ability in question.Also,the radical suggestion from Kenny himself,that abilities are not modals of any kind at all,seems to be riddled with severe theoretical troubles of its own as well.Most notably,it has to provide a satisfaction account of why abilities are commonly stated with locutions such as can,which is normally unproblematic to be treated as a paradigmatic modal expression.Without such an account on offer instead,the strength of the Kenny suggestion would be considerably undercut at best,or the suggestion would be essentially immaterial at worst.

But even if we lay such worries aside,these reactions to Kenny’s cases,as to be shown in what follows,are way too rash.For they all unanimously rest on the basic concession as their point of departure that sentences such as(1),for instance,is of the logical form◇(φ∨ψ)and is true.I shall argue in what follows that in making a statement such as(1),some sort ofsuccess rateis usually implicitly referred to,and the concealing of such success rates gives rise to a scope ambiguity.Making explicit such ambiguities will help illuminate the accurate representation of the logical structure of sentences such as (1),and will demonstrate that either (1) is of the form◇(φ ∨ψ)but false,or (1) is true but is not of the form◇(φ ∨ψ).As a result,cases such as Kenny’s fail to establish that ability modals resist Distribution over Disjunction,and ability modals may continue to be construed as existential quantifications.We need not to develop separate logics for abilities or abandon the principle of Distribution over Disjunction.A modal logic forcandeveloped along the standard approaches,such as those for epistemicmightand denoticmay,would be good enough to capture the logical properties of ability modals,and lay a foundation for the many philosophical projects which invoke the notion of abilities.

3 Success Rates and Ability Ascriptions

Let me begin with an observation of the relationship betweenaccidentalsuccess and ability ascriptions.In a case such as the dart game,to hit the board accidentally,due to mere luck,say,does not prove that one has the ability to hit the board.As mentioned earlier,one has to have control over whether or not she hits the board in any given shot,or to hit the boardreliably,so to speak,to count as having the ability in question.([9]) That is presumably why Jerry cannot be said to have the ability to hit a particular region(e.g.,the top half)of the board,even though he may have in fact hit that region in many of his attempts.Similarly,in a little card game,when someone is asked to pick a card from a deck of regular playing cards,she will definitely pick a card of a particular color,say red.But this does not entail that she has the ability to pick a red card——the fact that she does pick a red card in this attempt may be a mere matter of luck.

Thus,ability modals in the these cases do not obey the following rule of ability witness,a theorem of modal logics with reflexive frames:

Ability Witnessφ⊨◇φ

This rule,however,is obeyed by ability modals in many other cases.My ability to speak Finnish,for instance,is witnessed by my actually speaking Finnishat one occasion.It makes little sense to say that I spoke that language only accidentally,or merely as a matter of luck,without really having the ability to speak it.The fact that I once sangPromises don’t Come Easyis enough to establish once and for all that I can sing the song,to the same degree that my record of swimming across a mile-wide river proves my ability to swim across mile-wide rivers.The actual performances of these kinds cannot be fully accounted for without invoking the relevant abilities at some point.If not for my ability to speak Finnish,how could I actually succeed in speaking that language even once in the first place? For cases as such,no performances without abilities.

So in terms of obeying or disobeying the rule of Ability Witness,abilities come in two varieties.Abilities to hit a particular region of the dartboard,to pick cards of a particular color from a deck of regular playing cards,or to land a coin on a particular side in a fair toss,etc.,all fail to obey Ability Witness;whereas abilities to speak a particular language,to sing a particular song or to swim across a river of a particular width,etc.,all obey it.Let’s call the first class unwitnessable abilities,and the second witnessable abilities.

The distinction between unwitnessable abilities and witnessable abilities does not merely rest on our intuitive verdicts just laid out,but is also justifiable on some theoretical grounds discernible at a very general level.The theoretical justification has to do with metaphysical grounding and explanation.Suppose a layman flies a dart and it hits the board.In virtue of what does the layman succeed in hitting the board?The most likely metaphysical ground and best explanation for this,I think most would agree,is sheer luck.If we track back to what metaphysically caused the layman’s successfully hitting the board,we would most probably end up with some form of luck or coincidence,rather than any effective ability.To invoke the idea of luck provides a better explanation than to invoke the idea of ability instead.In contrast to this,the most likely metaphysical ground and best explanation for someone’s successfully speaking Finnish at a certain occasion,most would agree,is his very ability to speak that language.Tracing back to what metaphysically caused his speaking Finnish at that occasion,we are bond to end up with factors having to do with what constitutes his ability to speak that language,his mastery of the vocabulary,pronunciation and syntax,etc.,of the language.To invoke his ability provides a better explanation than to invoke anything else one may come up with.It is this difference that grounds the difference between unwitnessable abilities such as hitting the board and witnessable abilities such as speaking a language.

Since the lack of ability is generally consistent with accidental success for unwitnessable abilities,for proper ascriptions of such abilities,what matters is not the number of success but the rate of it.For a witnessable abilityA,it makes no sense to say that someone is able toAwith a success rate ofn%,even whenn100.There is no such a matter of fact concerning success rate——the problem simply does not arise.Just think about how weird it would be to say that one can speak Finnish with a success rate of,say,90%——what would stop her from speaking it in the 10%unsuccessful circumstances?

But it seems to make good sense to say that someone is able to pick a winning lottery card from a collection of many cards with a success rate of 10%.Suppose the probability of picking such a winning lottery card is 0.05%,the success rate would be very amazing,and whatever she endows to secure such an amazing success rate deserves being called an ability,literally.It’s worth noting that the ability considered here is one with explicit reference to a success rate,and it is not the ability we normally mean to attribute to someone when we say that she is able to pick a winning card,without referring to any success rate explicitly.

For sure,someone may perhaps be able to pick a winning lottery card with a success rate of 60%,and still others with that of 80%.Be that as it may,these incredible abilities are not the sort of ability we normally mean when we say“she is able to pick a winning lottery card,period”,as long as a significant chance remains for them to fail to pick a winning card.But what should be said of the situations where someone is able to pick a winning card with a success rate of 99%,or 100%? Shall we still insist that even such abilities are not the kind of ability we normally mean? I think what is more sensible to say here is that such abilities just are what we normally mean.Anyway,if those with such high success rates are not entitled to share the credit of having the ability we normally mean,who else would be? What exact success rates correspond to the unwitnessable abilities we normally mean without referring to success rates explicitly may vary from case to case,but one thing appearing to hold in common is that such success rates have to besufficiently high.And in many cases,it may simply be 100%.

To attribute an unwitnessable ability to someone in typical cases,therefore,is always committed to conferring that person a certain success rate normally associated with the ability in question.Though few would state the success rate explicitly in ordinary speech,either because it is too vague to be put in words or because it is too tedious to do so,it should not be disregarded,from a philosophical point of view,that some sort of success rates are always implicitly referred to in ascriptions of unwitnessable abilities.

Turning to the case of the dart player,when Jerry is said to be able to hit the board,a sufficiently high success rate,say 100%,isimplicitlyreferred to.And when he is said to be unable to hit the top half of the board,a similar success rate isimplicitlyreferred to as well.In contrast to the pointlessness of saying that Jerry is able to speak Finnish,or to singPromises don’t Come Easy,with a sufficiently high success rate,it makes perfectly good sense to say that he is able to hit the board with a sufficiently high success rate but unable to hit a particular region of the board with the same success rate.

Indeed,citing implicit references to success rates is pivotal for disambiguating two rather different senses of ability ascriptions,equally expressible by sentences such as(1).Apart from the sense considered above,there is a sense in which(1)doesentail(2).If the ability in question concerns howfar,instead of how accurate,Jerry can fly a dart,then Jerry’s ability to fly a dart to such an effect thatit flies far enough to hit the board does seem to entail his ability to fly a dart far enough to hit a particular region,the top half,say,of the board.To make(1)–(2)a case against ability modal Distribution over Disjunction,the ability in question has to be construed as how accurate Jerry can fly a dart.And any measure of accuracy has to refer in one way or another to certain sorts of success rates,explicitly or implicitly.

4 Meet Kenny’s Challenge

Given the observations here laid out,Kenny’s examples can be fully scrutinized and their challenges can be squarely met in a principled way.The story of dartboard,for instance,should really begin with the basic facts that Jerry is able to hit the dartboard with a sufficiently high success rate,and that to hit the dartboard is to hit the top half of the board or to hit the bottom half of it.Accordingly,writing such success rates explicitly back into their wording,(1)and(2)would turn out to be something like(1∗)and(2∗)respectively,

(1∗) Jerry is able to hit the top half of the board or to hit the bottom half of the boardwith a sufficiently high success rate.

(2∗) Jerry is able to hit the top half of the boardwith a sufficiently high success rateor Jerry is able to hit the bottom half of the boardwith a sufficiently high success rate.

Now,(1∗)may receive two interpretations,depending on the scope of the phrase“with a sufficiently high success rate”relative to the disjunction expression“or”.If it takes wide scope,(1∗)equals(Wide 1∗)

(Wide 1∗) Jerry is able[to hit the top half of the board or to hit the bottom half of the board]with a sufficiently high success rate.

And if it takes narrow scope,(1∗)boils down to(Narrow 1∗)(Narrow 1∗) Jerry is able [to hit the top half of the boardwith a sufficiently high success rate]or[to hit the bottom half of the boardwith a sufficiently high success rate].

To prove that ability modals may resist Distribution over Disjunction with this case,at least one of the two interpretations of (1∗) has to be of the form◇(φ ∨ψ)and true.That,however,is not the case.On the one hand,though(Wide 1∗)is true,it apparently is not of the logical form◇(φ∨ψ),in view of whatφandψare in(2∗).For in(1∗),bothφandψexplicitly refer to the success rate separately on their own,but in(Wide 1∗)φandψrefer to the success rate only as a disjunctive unit,not separately on their own.On the other hand,however,though(Narrow 1∗)is of the logical form◇(φ ∨ψ),in perfect accordance with whatφandψare in(2∗),(Narrow 1∗)is not true.This is because,given that Jerry is able to hit the board with a sufficiently high success rate,it only follows that the sum of the success rates of hitting the top half and that of hitting the bottom half is sufficiently high,and it does not follow that either of the two rates in the sum are themselves sufficiently high.

5 Concluding Remarks

The challenge of the playing cards case,it is easy to see,can be explained away as well in a similar fashion as above.I trust that the reader may figure this out herself.Ingenious cases such as Kenny’s,therefore,do not really establish that ability modals may resist Distribution over Disjunction or motivate any separate developments of logics for ability statements.Like typical modals associated with locutions such as‘could’(in alethic modal logic),‘may’(in deontic logic),‘might’(in epistemic logic),and the like,ability modals may continue to assume their logico-semantic status as existential quantifications after all.Within this broad outlook,we could develop with fair ease a modal logic for abilities along the lines of the epistemic or deontic logic,and inferences involving abilities can be squarely captured by such a logic.

Moreover,with such a logic at hand,many philosophical projects resting on an unaccounted notion of ability can be carried out on a better understood foundation.The notorious principle that moral responsibility presupposes that the relevant agent can do otherwise,for instance,can be more precisely understood as involving the agent’sabilityto do otherwise,rather than the weak notion of the metaphysical possibility for the agent to do otherwise.2The well-known Frankfurt Cases([5])really pose trouble for the principle that an agent is morally responsible for what she does only if it is metaphysically possible for her to do otherwise,but does not threaten the principle that an agent is morally responsible for what she does only if it is within her ability to do otherwise,if ability does not necessarily imply metaphysical possibility,as[12]persuasively argues.This,I think it fair to say,would have an enormous impact on the debates over Frankfurt Cases in particular,and many other issues in moral philosophy and metaphysics in general.