Do I contradict myself?
Very well then I contradict myself
(I am large, I contain multitudes).
In his 1988 review of On the Plurality of Worlds (Lycan ), William Lycan argued that what he called Lewis's 'mad-dog modal realism' (also 'rape-and-loot modal realism' and 'nuclear-holocaust modal realism' - I suspect that some reference to the supposed extremity of Lewis's position is intended) rested upon an unanalysed modal notion. Lycan accepted that actualists all seemed to be stuck with such unanalysed notions (adding that his own was the notion of compatibility as applied to pairs of properties), but argued that Lewis's notion of worlds was also a modal primitive:
'World' for him has to mean 'possible world', since the very flesh-and-bloodiness [which relieves him of the sort of abstraction indulged in by actualists] prevents him from admitting impossibilia. (Lycan , p.46)Lycan's main concerns in this review go back to his earlier paper 'The Trouble with Possible Worlds' (Lycan ), and are taken up again in his PAS paper:
The ruling out of impossible worlds is a serious liability [...] For semantics needs impossible worlds. Though standard modal logics may trade just in possible states of affairs, the semantics of conditionals must deal with inconsistent beliefs. (Lycan , p.224)He goes on to claim that the actualist
has no problem with impossible worlds. An impossible world is just - e.g. - a set of propositions (one of which happens to be inconsistent). (loc.cit.)Whatever the truth of this in principle, most actualists have either explicitly or implicitly excluded possible worlds from their theories.* It is true, nevertheless, that Lewis has a clear problem with the very idea of worlds at which logically incompatible propositions are true. Lycan attempts to exploit this as follows.
Lewis reads a statement like:
L1 It is merely possible [that is, possible but not actual] that there have been talking donkeysin terms of possible worlds:
L2 There are talking donkeys in at least one possible world, but not in the actual world.This can be translated as:
L3 There are things which are donkeys and which talk, and which aren't spatiotemporally connected with us.Lycan argues that Lewis, faced with the Meinongian claim that there are things which not only do not but could not exist, such as round squares, must read it as:
M3 There are things which are round and which are square, and which aren't spatiotemporally connected with us.In this, at least, Lycan is clearly wrong for, as we've seen, M3 is how Lewis would read the statement:
M1 It is merely possible that there be round squaresand the Meinongian isn't claiming this. She accepts that round squares do not and could not exist; her claim is that round squares, though nonexistent and impossible, are (in some sense). Thus there is no parallel here for Lycan to exploit; Lewis is under no pressure to read a claim about what there is (in some odd Meinongian sense of 'is') as if it were a claim about what there might be.
That is all pretty straightforward, I think. However, Lycan goes on to try to make more of the supposed link between Lewisian and Meinongian metaphysics with regard to quantification over possibilia, and this requires rather more care. On the face of it, Lewis may seem rather vulnerable with regard to impossible worlds. His argument in Chapter 4 of Counterfactuals has been quoted to death, but I'll exhume it once more:
I believe, and so do you that things could have been different in countless ways. But what does this mean? Ordinary language permits the paraphrase: there are many ways things could have been besides the way they actually are. On the face of it, this sentence is an existential quantification. It says that there exist many entities of a certain description, to wit 'ways things could have been'. I believe that things could have been different in countless ways; I believe permissible paraphrases of what I believe; taking the paraphrase at its face value, I therefore believe in the existence of entities that might be called 'ways things could have been'. I prefer to call them 'possible worlds'. (Lewis , p.84)Overlooking the various problems this argument faces, it is surely as applicable to impossible as to possible worlds (via the statement 'There are many ways things could not have been'). How, then, can Lewis exclude impossible worlds from his ontology? We might argue that Lewis's main reasoning in favour of his possible worlds rests upon their usefulness, and claim that this is a factor absent in the case of impossible worlds. This, though, would be countered by the claim that impossible worlds may indeed be useful for epistemic purposes; as we have seen, Lycan adds that they are needed for the semantics of conditionals, but I'm not clear as to how they would be used for this purpose, and he offers no details. (David Armstrong's combinatorialist theory allows for impossible worlds only because it treats all worlds other than this one as mere fictions:
Impossible worlds are a conception, a conception which, like ideal gasses and frictionless planes, turns out to be useful in analysing actual phenomena. (Armstrong , p.75)A first response to Lycan's argument might be that, whatever usefulness they might have elsewhere, the inclusion in our ontology of impossible worlds would seriously reduce the usefulness of possible world theory for Lewis's purposes. I shall not be concerned with this line of argument here, as Lycan makes little of it. I am more concerned with Lewis's discussion in On the Plurality of Worlds, which uses the notion of a 'restricting modifier'.
'There is no milk' is, as it stands and out of context, true if and only if there is no milk anywhere. 'There is no milk in the refrigerator' is true if and only if there is no milk in that particular place, regardless of what's the case in the rest of the world. Thus 'in the refrigerator' is a restricting modifier - it restricts the domain of the quantifier in 'There is no milk' to a certain part of all that there is. Sometimes we make the restriction explicit, sometimes the context of utterance is enough. A restricting modifier doesn't affect any truth-functional connective in what it modifies; 'There is cheese but no milk in the refrigerator' is equivalent to 'There is cheese in the refrigerator, but there is no milk in the refrigerator', which in turn is equivalent to 'There is cheese in the refrigerator, but not: there is milk in the refrigerator'.
Lewis's claim is that 'In (possible world) Wx' is a restricting modifier. That is, 'In Wx I am tall and handsome' is true if and only if I am (or my counterpart is) tall and handsome in a certain part of all that there is - in that certain part we've labelled 'Wx'. Now, if we posit a world Wimp in which 'P & -P' holds, then we admit truths of the form 'In Wimp both P and not P'. However, as we have seen, this obliges us to admit truths of the form 'In Wimp P, and in Wimp not P', and therefore to admit truths of the form 'In Wimp P, and not: in Wimp P', which is overtly contradictory. In other words:
there is no difference between a contradiction within the scope of the modifier and a plain contradiction that has the modifier within it. So to tell the alleged truth about the marvellously contradictory things that happen on the mountain is no different from contradicting yourself. But there is no subject matter, however marvellous, about which you can tell the truth by contradicting yourself. (Lewis , p.7n)Of course, if 'In Wimp' were not a restricting modifier, but functioned like 'According to the Holmes stories' or 'Conan Doyle wrote', then Lewis's argument would fail to go through, for non-restricting modifiers do have an effect on truth-functional connectives (compare 'Conan Doyle wrote that Watson's wound was on the right, and that it was not on the right' with 'Conan Doyle wrote that Watson's wound was on the right, and Conan Doyle didn't write that it was on the right'):
But worlds, as I understand them, are not like stories or story-tellers. They are like this world; and this world is no story, not even a true story. (loc.cit.)
Lycan is unhappy with this defence. Lewis, he argues, has a single quantifier of wide scope, which runs "well past the actual, through the bizarre and into the physically impossible"(Lycan , p.227), which sometimes occurs within the scope of restricting modifiers such as 'In such- and-such a possible world ...'. Meinong also has a quantifier, 'There is ...', of unlimited scope, ranging beyond Lewis's into the logically impossible (this is similarly sometimes modified by 'exist' and 'subsist', though Lycan doesn't describe Meinong's position like this):
If Meinong is right, then there is a subject matter about which you can tell the truth by contradicting yourself, if to put a contradiction within the scope of a restricted quantifier is indeed to 'contradict yourself'; Lewis's premise to the contrary begs the question (loc. cit.).Admittedly, this isn't put very clearly, but Lycan presumably wants to say that Meinong doesn't allow us to tell the truth by contradicting ourselves - only the addition of Lewis's 'question-begging premise' leads to such a conclusion. But a number of questions arise. First, does Lewis have a question-begging premise or an argument? Secondly, if he has such a premise, what exactly is it? I suspect, in fact, that Lycan doesn't really want to disagree with Lewis's account of the logic of restricting modifiers (he doesn't need to, as far as I can see), so perhaps the first question doesn't matter so much. Where Lycan wants to disagree with Lewis is in the claim that 'in possible world Wx' is a restricting modifier. His argument rests upon his claim that Meinong's theory shows the need to treat 'in impossible world Wy' in exactly the same way as we treat 'in possible world Wx'. He must then claim that 'in impossible world Wy' isn't a restricting modifier, before concluding that 'in possible world Wx' isn't one either. I shall argue that Lycan's reasoning rests upon a misunderstanding of Meinong's aims and methods; a brief excursus into the steaming jungles of Meinongian metaphysics is therefore required.
Meinong split the world into three categories of thing; it varies throughout his writings, but this seems to be the basic version (note that most philosophers who have cause to refer to Meinong's theory - usually dismissively - ignore the third category, lumping it in with the second). First, there are those things, such as chairs, mountains, people, which are part of the world in a concrete way - they exist (or are real). Secondly, there are those things, such as classes, relations, facts, which do not exist, but which are nevertheless clearly parts of the world, though in some sort of abstract way - they subsist (or are ideal). "Whatever exists also subsists; what does not subsist, does not exist either" (Meinong 'Zur Gegenstandstheorie', translated as Appendix 1 in Grossmann , p.228). Finally, there are those things, such as the philosopher's stone, the golden mountain, Sherlock Holmes, which are not part of the world either concretely or abstractly, but about which we can talk and think - these things have neither existence nor subsistence, they just are. They have no being, as existent and subsistent things have, but they are there, somehow. This isn't, as Orayen points out, a merely linguistic claim; Meninong doesn't mean to say only that an expression like 'the round square' is meaningful, that it refers to my idea of the round square:
Meinong made explicitly clear that words 'express' ideas and are not used to refer to them but to transcendent objects which differ from those ideas and are the denotations of the words in question. (Orayen , p.118)And as Findlay comments:
Though it is not a fact that the golden mountain or the round square exists, [Meinong] thinks that it is unquestionably a fact that the golden mountain is golden and mountainous, and that the round square is both round and square. (Findlay , p.43)Furthermore:
Even if some one were to doubt whether a golden mountain was really golden, he might be led to see that it was a genuine object by another route. It is a fact that the golden mountain does not exist, and this fact is as 'hard' as any other fact, yet it is about an object which has no existence. It follows that, even in the case of a non-existent entity, there are definite facts which concern it, and that it is out of the question to treat it as a mere nothing. (Findlay , p.44)Thus for Meinong the non-fictional name 'Conan Doyle' and the fictional name 'Conan the Barbarian' both do the same sort of job - they both refer to individuals. The difference is not in the names, but in the things to which they refer: in one case the thing exists, in the other it doesn't (whereas the positions of, for example, Frege and Russell grew out of their theories of names, Meinong's grew out of his theory of things). We might express this by saying that for Meinong, the quantifier 'There are ...' has unlimited scope (a pre-echo of Quine's answer to the question 'What is there?'), and that this can be narrowed by the modifiers 'exist' and 'subsist'. As regards the truth values of sentences containing names of these kinds, we should note that 'Conan Doyle' refers to a wholly determinate individual, while 'Conan the Barbarian' does not, so that although every (well, nearly every) sentence with 'Conan Doyle' as its subject is either true or false, most sentences with 'Conan the Barbarian' as their subject are neither true nor false:
It is clear that in dealing with some non-existent objects we must completely alter our ordinary habits of thought and, after a certain point, relinquish all desire for further information. (Findlay , p.57)So there is no point in asking whether Conan the Barbarian had dandruff; there is no fact about him which any answer could express.
These non-existent, non-subsistent entities are objects of consciousness, but that they are does not arise simply from their actually being thought about. This point is made clear by the early Russell in The Principles of Mathematics. There he distinguishes in a Meinongian way between being and existence; being, he says belongs to everything - to every possible object of thought:
Numbers, the Homeric gods, relations, chimeras, and four- dimensional spaces all have being, for if they were not entities of a kind, we could make no propositions about them. Thus being is a general attribute of everything, and to mention anything is to say that it is. (Russell , p.449)Meinong and Russell may have disagreed over what can be a 'possible object of thought', but their agreement on the main point is clear (see Findlay , p.47); there is an infinite number of things which do not exist, which 'are' because they can be referred to, and of which some are referred to.
Note that in none of this does modality figure. Numbers, the Homeric gods, the golden mountain, and Conan the Barbarian are, for the Meinongian, in this world. It's true that a Lewisian Meinongian would simply hold that possible worlds exist - would simply be a Lewisian realist. But a non- Lewisian Meinongian (one who doesn't hold that possible worlds exist) would either allow them subsistence (this would fit in with various sorts of actualism), or say that there are possible worlds in much the same way that there are Homeric gods (this would fit in with fictionalism). The Lewisian Meinongian would presumably go on to say that in some or all (I'm not sure which) of these worlds, there are round squares and so on. The non-Lewisian Meinongian would place both possible worlds and round squares in this world: the actualist will talk of there being possible worlds which subsist and round squares which don't; the fictionalist will talk of there being possible worlds and round squares, none of which either subsist or exist. If the Lewisian Meinongian wants to refer to impossible worlds, she'll include them with round squares as being in some (or all) possible worlds as non-existent, non-subsistent (potential) subjects of thought. There seems to me to be no problem for Lewis in any of this. Of course, not being a Meinongian, Lewis doesn't think that there are round squares at this (or, presumably, at any) possible world, but the discussion of Meinong's theory can surely be conducted within possible worlds discourse - there's no need to drag in impossible worlds.
The question of impossible worlds remains for Lewis, but only because of the claim that they're useful. I suspect that the problem is soluble; though I'm in no position at the moment to solve it, I'm tempted to start looking at the possibility of a fictionalist account of impossible worlds, along the lines of Armstrong . On the other hand, perhaps some might find attractive a notion such as that argued for by Nicholas Rescher and Robert Brandom:
It is necessary to insist [...] that one should avoid speaking of inconsistent worlds as impossible worlds. This would be question-begging, for it is a prime aim of the present analysis to show that they can be considered as genuinely possible cases. (Rescher & Brandom , p.4)Be that as it may, I hope that I have succeeded in showing that, insofar as Lewis has a problem concerning impossibilia, it does not involve Meinongian metaphysics.
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