Forthcoming in Kontroversen
Dr. phil. Daniel von Wachter, Oriel College, Oxford OX1 4EW, England, daniel.wachter@oriel.ox.ac.uk,
[Length of this text: 3610 words]
‘There has been an "ontological turn"’, states Fraser MacBride at the beginning of his article ‘Could Armstrong Have Been a Universal?’ (1999). He is referring to the fact that even in circles where there once has been a ‘linguistic turn’, or where metaphysical problems have been treated as problems of semantics, now again ontological theories of things and properties are developed. (For a survey of theories of properties see Oliver 1996.) Such theories are used in philosophical analyses of, e.g., causation or modality. MacBride argues that these analyses are ‘flawed’. ‘The concepts of particular and universal such analyses presuppose are not properly understood. The ontological turn has proceeded hastily without the required proper examination of these concepts’ (MacBride 1999, p. 471). In what follows I shall argue that MacBride’s criticism is flawed. He proceeded hastily without the required proper examination of these ontological theories. My aim here is not to discuss whether Armstrong’s theory of possibility is adequate but only to clarify it and to show that MacBride’s criticism of it is inadequate. MacBride’s criticism is an example of a, to my impression, widespread failure to recognise the difference between the aims of ontology and those of semantics.
MacBride’s aim is to show that theories of modality such as David Armstrong’s (hence the use of his name in the title of MacBride’s paper), which are supposed to be reductionist, fail to be reductionist because the concepts of particular and universal which are employed by the theories are ‘suffused with modality’. I shall first describe what MacBride takes to be the aim and the content of those reductionist theories of modality. Then I shall present the core of MacBride’s criticism of these theories. Thirdly, I shall sketch Armstrong’s theory of modality. Fourthly, I shall show how MacBride’s criticism is misplaced and results from a confusion of ontology and semantics. I shall conclude with a general remark on the relationship between semantics and metaphysics. Although MacBride’s criticism is supposed to be ‘a fully general critique’ (p. 474) of a whole family of theories, to streamline my argument I shall concentrate on MacBride’s criticism as it is designed to apply to Armstrong’s theory of modality.
From how MacBride presents the theories of modality which he criticises one can see that he takes Armstrong’s theory of modality to run as follows.
There are particulars and universals. There are no merely possible entities, but only actual entities. There are not really merely possible worlds, but possible worlds can be admitted as mere representations, or as merely fictional entities. They are ‘possible worlds surrogates’. They ‘depict worlds that combine existing particulars and universals in different ways’ (MacBride 1999, p. 475). Or one can say possible worlds ‘exist according to a fiction in which genuinely existent particulars and universals are recombined to form novel instantiations’ (MacBride 1999, p. 475). So in other possible worlds—understood as mere representations or fictions—particulars and universals are combined in different combinations than in the actual world. For example, if in the actual world there is a particular a which instantiates only the properties F, G, and H, then there is another possible world where there is no particular which instantiates only these three properties. Or, if in the actual world there is a particular b which instantiates only the properties L, M, and N, and L and M are instantiated only by b, and F is instantiated by some particular, then in other possible worlds b instantiates L, M, and F.
According to MacBride, Armstrong’s theory then proceeds as follows: Modal sentences are ‘translated into a language where, roughly, necessity is expressed by universal quantification over possible worlds, possibility by existential quantification’ (MacBride 1999, pp. 476f). Now ‘a semantics is provided for the possible worlds language by treating its quantifiers as ranging over possible worlds surrogates’ (p. 476). So MacBride takes the aim of Armstrong’s theory to be to provide in this way ‘truth conditions’ for modal sentences. He takes the aim of Armstrong’s theory to be to translate modal sentences into possible worlds language, to say they are true if and only if the possible worlds are so-and-so, and to say, in general, what possible worlds are. Take the example just mentioned: Assume in the actual world there is a particular b which instantiates only the properties L, M, and N, and L and M are instantiated only by b, and F is instantiated by some particular. Take the sentence S ‘b could have been F instead of N’. According to MacBride, Armstrong’s theory translates S into S* ‘There is a possible world in which b is F but not N’. Further, the theory states that S*, and hence S, is true iff there is a fiction of a certain kind according to which b is F instead of N.
Now we come to the bit which is most important for MacBride’s criticism. Armstrong calls his theory of modality ‘reductionist’. MacBride spells this out as follows.
[A] modal reduction must, on any account, be capable of specifying non-modal truth conditions for sentences that contain modal vocabulary. [...] This means that a reductive theory of modality must satisfy (in principle) the following two constraints. First, the theory must be extensionally adequate (EA). Each specification of a truth condition that the theory associates with a modal sentence must be materially equivalent to the sentence for which it specifies a truth condition. Second, the theory must be non-circular (NC). Each specification of the truth condition of a modal sentence that the theory provides must be expressed (perhaps at infinite length) using only non-modal vocabulary. (MacBride 1999, p. 474)
So, according to MacBride, Armstrong’s theory aims to provide ‘non-modal truth conditions’ for modal sentences, that is, it aims to transform, in a certain way, sentences which express modal claims or which contain modal vocabulary into sentences which express no modal claims and which contain no modal vocabulary.
The core of MacBride’s criticism is that Armstrong’s theory, contrary to what Armstrong claims, is not reductive. ‘The concepts of particular and universal dictate that if particulars and universals exist a range of modal sentences are true [...]. Combinatorial theories cannot be reductive because they cannot provide truth conditions for these sentences that simultaneously satisfy (EA) and (NC).’ (MacBride 1999, p. 477) MacBride shows that there are modal sentences for which Armstrong does not provide non-modal truth conditions. He argues that in some cases Armstrong provides truth conditions which are prima facie non-modal but which contain concepts which have modal ingredients, and he shows that there are irreducibly modal sentences to the truth of which Armstrong is committed.
I think MacBride is right here. One will have to admit that the sentences which MacBride puts forward as examples against Armstrong are (as far as one takes them to be meaningful) irreducibly modal. Let me give three examples.
(1) Necessarily, nothing is both 5kg and 1kg in mass. (p. 478)
A defender of a combinatorial theory of modality could hold that, as any combination of properties is possible, (1) is false. This theory would be open to the objection that it fails to satisfy (EA). But Armstrong takes (1) to be true. MacBride argues that then Armstrong has to specify which fictive possible worlds contain only possible combinations of properties. This cannot be done whiteout the use of modal vocabulary. Hence Armstrong has to admit that there are true modal sentences which are either themselves irreducibly modal or for which he cannot provide truth conditions without the use of modal vocabulary. Hence Armstrong’s theory does not satisfy (NC).
Further, MacBride explains that Armstrong is committed to certain principles about particulars and universals. MacBride shows that some of these principles are irreducibly modal and that hence again (NC) is violated. Take for example:
(2) Every universal is necessarily instantiated. (p. 485)
In fact, Armstrong rejects the possibility of non-instantiated universals. Hence he holds that (2) is true. But no totally non-modal truth conditions for (2) are given. So Armstrong’s theory violates (NC). Another example is:
(3) Necessarily, particulars only instantiate universals. (p. 487)
Armstrong takes instantiation to be a non-symmetrical relation between particulars and universals. So he is committed to the truth of (2). Armstrong does not, and cannot, provide truth conditions for (2) without the use of modal vocabulary. Hence again Armstrong’s theory violates (NC).
I accept that MacBride is right in holding that ‘the concepts of particular and universal’ are ‘suffused with modality’ and that Armstrong’s theory does not satisfy (NC), i.e. it does not provide for every modal sentence ‘truth conditions’ which can be ‘expressed using only non-modal vocabulary’ (p. 474).
However, MacBride misunderstood Armstrong’s description of his theory of modality as ‘reductionist’. I shall argue that a theory which is reductionist in Armstrong’s sense does not need to satisfy (NC). Let me sketch Armstrong’s theory (cf. Armstrong 1989 and 1997, ch. 10).
There are particulars and universals. Universals, i.e. properties, are instantiated by particulars. If two particulars, a and b, have the same property F, then the F-ness of a is identical with the F-ness of b. Which universals there are is not to be discovered a priori, but only a posteriori. Universals are not meanings, and there is no one-to-one correlation between predicates and universals. A predicate may apply in virtue of one or of several universals. Different predicates may apply in virtue of the same universal. A particular together with a universal (or several universals) which it instantiates, i.e. an entity of the form a’s being G, is called a state of affairs. Every universal is instantiated at least once. Everything which there is is either a state of affairs, or composed of states of affairs, or a constituent of a state of affairs.
There are true statements about what is possible and about what is necessary, e.g. ‘Nothing can be both 1kg and 5kg in mass’ or ‘There could be a man 5m tall’. The aim of Armstrong’s theory of modality is to ‘give some account of the nature of possibility’ (Armstrong 1989, p. 3), and to answer the question ‘What truthmakers can our ontology supply for modal truths?’ (Armstrong 1997, p. 149).
Armstrong’s theory of modality is reductionist, or ‘deflationary’, in the sense that it entails that ‘necessary and merely possible states of affairs are not required. The contingent states of affairs are to provide truthmakers enough’ (Armstrong 1997, p. 172). Let us clarify this by stating what a non-reductionist view would be like. Look at the following line of thought. ‘Raising the arm entails that the arm goes up, but the arm’s going up does not entail that the arm was raised. In the same way, what is actual is possible, but what is possible need not be actual. As a result, just as we ask what must be added [...] to the arm’s going up to yield raising the arm, so we are tempted to ask what must be added to something merely possible to yield its actuality.’ Giving in to this temptation leads to a non-reductionist view, because one who asks ‘What must be added to something merely possible to yield its actuality?’ grants some ontological status to the merely possible. The non-reductionist believes ‘that there are two sorts of states of affairs: the actual ones and those that are merely possible’ (Armstrong 1997, p. 148). According to the non-reductionist view, the statement that there could be a man 5m tall is made true by a merely possible state of affairs consisting of a particular instantiating the universal ‘being 5m in length’ and all the universals which something needs to instantiate to count as a man. The reductionist resists this temptation. He claims that all the entities there are are actual. True modal claims are made true just by the actual entities.
A slightly different line of thought which might lead a philosopher to a non-reductionist view starts from the principle that for each true statement there is a state of affairs corresponding to it, which is the object of the statement and which makes the statement true, and different statements correspond to different states of affairs. If one then recognises that there are true modal statements this leads one to the recognition of merely possible states of affairs. Anyway, the creed of the reductionist is that there are no such things as merely possible entities.
Here is the rest of Armstrong’s theory of modality in a nutshell: For any two properties which are wholly distinct, any particular can instantiate both of them, one of them, or none of them. In this case they are called ‘compossible’. Any combination of properties, as long as the properties are wholly distinct from each other, is possible. So this is the nature and scope of possibility: all the combinations of particulars and properties ‘that respect the form of atomic states of affairs constitute the possibilities for [...] states of affairs’ (Armstrong 1997, p. 160).
So only wholly distinct properties are compossible. Two universals can have common parts, they can overlap. Universals which overlap cannot be instantiated by the same particular (at the same time). Also, a universal cannot be instantiated by a particular twice. (These are basic principles on whose defence Armstrong spends much time. See especially Armstrong 1989, ch. 6; cf. Armstrong 1997, p. 155 and p. 174.)
Armstrong’s conception of ‘possible worlds as fictions’ is, at least in his more recent writings, not an essential part of his theory of modality. In his A World of States of Affairs (1997) they do not play the role any more which they played in his A Combinatorial Theory of Possibility (1989). He now writes: ‘given that the theory now put forward does not go through fictional possible worlds, may they not still be admitted as useful fictions?’ (Armstrong 1997, p. 172).
True modal statements are all made true just by the actual contingent universals and particulars. No merely possible states of affairs and no necessary states of affairs are needed as truthmakers. Let us see for some examples of modal statements how this view can be upheld, on the background of the theory just stated.
A statement like ‘There is nothing which has just the properties F, G, and H, but there could be such a thing’ is true (if it is true) because F, G, and H exist and are wholly distinct (and hence compossible). It is made true by the universals F, G, and H.
A statement like ‘a, which is F, G, and H, could as well not exist, and it could be that there is nothing which is F, G, and H’ is true because a, F, G, and H, like all entities, are contingent entities. It is made true by a, F, G, and H.
A statement like ‘b, which is L, M, and N, could have been F instead of N’ is true (if it is true) because L, M, N, and F are wholly distinct (and hence compossible). It is made true by b, L, M, N, and F.
A statement like ‘Nothing can be both F and G’ is true (if it is true) because F and G are not wholly distinct universals. It is made true by F and G.
Finally, why is, according to Armstrong, ‘every universal is necessarily instantiated’ true? I think Armstrong would say that this is true because of the essential nature of universals. (He speaks about ‘the essential nature of universals’ e.g. in his 1997, p. 127.) It flows from the essential nature of universals that they are promiscuously repeatable, that they cannot exist without being instantiated, etc. We reached the bedrock here. And that is just what the theory wants to do: say how things are at the ontological bedrock.
It is of course a matter of dispute whether this theory is true, and many or most elements of it can be, and are, disputed. One can dispute Armstrong’s ontology, one can dispute the claim that wholly distinct properties are always compossible, one can dispute the claim that properties can overlap, etc. MacBride disputes that the theory achieves its objectives. But the objectives he expects the theory to achieve are not the objectives which the theory is designed to achieve.
He expects the theory to provide ‘non-modal truth conditions for sentences that contain modal vocabulary’ (p. 474) and hence to satisfy (EA) and (NC). I take it that that means that the theory should offer an algorithm how modal sentences can be somehow translated into sentences which are materially equivalent to the original sentences, but which are not modal.
Take again the example ‘Nothing can be both 1kg and 5kg in mass’. What does Armstrong’s theory have to say about this example, which Armstrong discusses extensively (see Armstrong 1989, ch. 6)? Can we see from this what the aim of Armstrong’s theory is? The theory says about this example, first, that it is true, and, secondly, that it is true because the universals to which the predicates ‘1kg’ and ‘5kg’ refer overlap. In general, the theory states that a statement of the form ‘Nothing can be both F and G (at the same time)’ is true if and only if the universals in virtue of which the predicates ‘F’ and ‘G’ apply are not wholly distinct. There is no attempt to translate a modal statement into a non-modal statement. There is no attempt to translate anything. There is no attempt to provide what MacBride calls ‘truth conditions’. Hence there is nothing to satisfy or violate (EA) and (NC). The theory makes a general claim about the ontic structure of this world and about the combinability of universals. One may argue that this whole project of describing the ontic structure of this world and of the nature of possibility is doomed to failure. But one has to recognise that this is Armstrong’s project.
There is no need to argue at length, as MacBride does, that Armstrong is committed to irreducibly modal statements, i.e. that his theory violates (NC). It is clear in everything Armstrong writes that he thinks that there are such true statements. Otherwise he would not have to be worried about what their truthmakers are. The modal statements (1), (2), and (3) mentioned above which MacBride’s presents as counter-examples to Armstrong’s theory, are statements which Armstrong would take to be examples of true irreducibly modal statements. MacBride is wrong in assuming that Armstrong wants to deny that there are such statements. Therefore MacBride’s criticism is misplaced.
We are confronted here, I believe, with an example of a misunderstanding of a very interesting type. There are philosophers who think that semantics has quite an important role in philosophy. They think that philosophers should be concerned with semantics a lot. They not only think that semantics is an interesting field, but they think that many traditional philosophical problems, e.g. problems about modality, have to do with semantics or are to be solved by providing a semantics. They think that much of philosophy is about providing ‘truth conditions’ for certain sentences.
But there are other philosophers who don’t share this enthusiasm for semantics. They are rather puzzled by the fact that some of their colleagues always ask them to specify ‘truth conditions’ for certain statements, or they are puzzled by the fact that some of their colleagues think they can solve philosophical problems by specifying truth conditions for certain sentences. They think that most traditional philosophical problems, or those problems which they think are philosophical and important, are not problems of semantics, because, at least as they understand it, semantics is concerned with meaning, and most philosophical problems are not about meaning. The theories they put forward, e.g. of causation, or of properties, or of modality, do not say much about semantics and truth conditions. These philosophers might make claims about ‘truthmakers’, but they don’t see why what their colleagues call ‘truth conditions’ is relevant for the problem. Let us call the former sort of philosophers S-philosophers and the latter sort of philosophers M-philosophers.
Of course Armstrong is more of an M-philosopher, and MacBride is more of an S-philosopher. Armstrong, for example, sees it as one of his tasks in his theory of modality to provide truthmakers for certain sentences. MacBride, however, writes in a footnote about an attempt of Armstrong to provide truthmakers for a certain type of modal statements: ‘He [Armstrong] offers a corresponding account of their truth-makers [...]. But a provision of truth-makers does not make for a specification of truth conditions.’ (1999, p. 480, note 5) So we have the S-philosopher telling the M-philosopher ‘A provision of truthmakers does not make for a provision of truth conditions’, and the M-philosopher telling the S-philosopher ‘A provision of truth conditions does not make for a provision of truthmakers’.
It is very difficult for the S-philosophers and the M-philosophers to understand each other. Those in one of the camps often either don’t understand what the aim and the method of those in the other camp is and they realise that they don’t understand it, or, although they realise that certain other philosophers put things in a way which seems a bit strange to them, they don’t realise that these other philosophers are pursuing quite a different project. I have argued, in effect, that MacBride misunderstands Armstrong in the latter way. That is why, for example, MacBride refers to Armstrong’s theory as ‘the proposed semantics’ (p. 477), although Armstrong does not propose a semantics at all.
It is clear, I suggest, that the two projects need to be disentangled. But will they both turn out to be philosophical projects in their own right? Or will one of the two perhaps turn out to be less worthwhile?
References
Armstrong, David, 1989, A Combinatorial Theory of Possibility, Cambridge University Press.
Armstrong, David, 1997, A World of States of Affairs, Cambridge University Press.
MacBride, Fraser, 1999, ‘Could Armstrong have been a Universal?’, Mind 108, pp. 471–501.
Oliver, Alex, 1996, ‘The Metaphysics of Properties’, Mind 105, pp. 1–80.