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, yet is nevertheless sufficient for the truth of
, is the minimal truthmaker of
. Returning now to our apple, what then would be the minimal truthmaker for ? It seems we have already decided that it is not just the apple, which would contain lots that is extraneous to this truth. Similarly, it is not just redness, the property, as that is instantiated in lots of things other than this apple. The truthmaker will then have to be the fact that this apple possesses redness. We should be able to see straight away that this is a state of affairs – the worldly fact of this apple-having-redness. It can be noted, however, that there are occasional exceptions where objects alone stand as truthmakers. This happens in the case of necessary truths, as will be described below, and plausibly also with statements such as . The bearers of truth are propositions and the makers of truths are usually states of affairs. How do states of affairs make certain propositions true? According to Armstrong, they do so by necessitating the truth of those propositions. There is a truthmaking relation that can hold between states of affairs and certain propositions. Between most states of affairs and propositions this relation does not hold but between the apple-having-redness and it does hold. The truthmaking relation is described as an “absolute necessitation” (T&T: 5). Armstrong offers a reductio argument for this view (T&T: 6, 7). If T is the suggested truthmaker for
but does not necessitate the truth of
, then T could exist 168
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being true. But this would suggest that something more than T is needed for
to be true and this other thing, call it T+U, would be a better candidate for the truthmaker of
than is T. This is also the case for any subsequent candidate for the truthmaker of
until we reach something where it is not possible for it to exist and
not be true. This is the same as saying, however, that this thing is the truthmaker for
and necessitates the truth of
. The thesis that truthmakers necessitate the truth of certain propositions is known as truthmaker necessitarianism and the claim is one of the distinctive features of Armstrong’s theory. That any relation holds between states or affairs and propositions is problematic but this is perhaps even more so the case with a relation of necessitation. As Armstrong accepts, the relation of necessitation is a cross-categorial one. One relatum is a concrete, worldly state of affairs; the other is abstract, as propositions are abstractions from actual beliefs, speech acts and so on. This is a necessitation, therefore, that runs across two categories. The standard cases of necessitation, with which philosophers are most familiar, have relata of the same category. We are familiar with necessitation as entailment but where entailment is a relation that holds between propositions. Hence, <John is in the room> entails or necessitates that <someone is in the room>. Here, both relata of the entailment relation are abstract but Armstrong explicitly rules that such entailment will not suffice for truthmaking (T&T: 5, 6). We are interested not just in truths that are entailed by other truths but, at the fundamental level, by truths that are necessitated by the things that exist in the concrete world. Logico-linguistic entailment is not, therefore, what we are looking for. The other model we have of necessity – causal necessity – is also inappropriate for truthmaking. By making truth, we do not mean a causal making (T&T: 5). The causal relation, for those philosophers who think it something real, something like natural necessity, holds only between concrete objects, whether these are understood as events, facts, properties or substances. For the type of truthmaking relation Armstrong seeks, one relatum is concrete – the state of affairs – the other is a proposition, therefore abstract, so the relation must be cross-categorial. Although the available models of necessitation – entailment and causation – are inappropriate for truthmaking, we cannot say that Armstrong’s cross-categorial necessitation is a non-starter. But if some posit of philosophy is of its own kind, sui generis, then 169
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that often makes it an object of suspicion. Armstrong has responded to this issue by arguing that there clearly are some cross-categorial relations (2005: 275). Indeed, any realist theory of truth seems committed to truth consisting in an appropriate relation holding between non-linguistic reality and linguistic reality. It is then a separate matter whether this cross-categorial relation is one of necessitation, for which Armstrong has his reductio argument. If there are separate reasons for finding truthmaker necessitation to be plausible and for finding cross-categorial relations plausible, then why not find cross-categorial necessitation plausible? What happens when Armstrong’s theory of propositions is coupled with his truthmaker necessitarianism? The existence of a particular state of affairs will necessitate the truth of a certain proposition. Presumably, however, there are some states of affairs that we do not know about and have not yet even conceived. This tells us, what we ought already to realize, there are can be truths that we do not know. How, though, can Armstrong allow this if a proposition is an abstraction from actual beliefs and utterances? If no one has ever uttered or thought about a proposition, it seems that it does not exist. And if a proposition does not exist, how can it be true? Armstrong’s problem here is his familiar instantiation requirement. Were Armstrong to hold a Platonist view of propositions he would not have this problem. We could hardly expect Armstrong to give up his immanent realism at this stage, but he must find some way of reconciling the view with his truthmaker necessitarianism. Armstrong’s way out of the difficulty is to modify his theory of propositions slightly (T&T: 15–16). To begin with, he had said that propositions were the intentional objects of beliefs, statements, thoughts, and so on. But the world of states of affairs cannot necessitate that some particular belief is actually thought. Armstrong needs an account of the existence of propositions that will suffice whether or not they are actually expressed. His move is to say that unexpressed propositions are merely possible objects of belief, speech, and so on. All propositions will be possible objects of belief but the unexpressed ones will be merely possible. Again, this is not a comfortable position for Armstrong. What we have is the mere possibility of the instantiation of such a proposition and what we really need, therefore, is an account of the truthmakers for modal truths, which will show how it can be true that such a proposition is (merely) possible. An account of modal truths is offered later in Truth and Truthmakers. 170
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Further claims in Armstrong’s theory So far we have considered only the basic mechanism of truthmaking, as described in Armstrong’s version. We should now be able to understand how a state of affairs may necessitate the truth of a proposition through cross-categorial necessitation (and it is the truth of a proposition that is necessitated, not the proposition itself, as Armstrong has made clear, 2005: 275). There is much more to be said, however, for all we have here is a model of how truth can be made by a worldly fact. But we may wonder, straight away, whether this model can apply to every case of truth, in all its diverse instances. What about negative truths, modal truths, truths in mathematics, and general truths? Can there be worldly truthmakers for all these types of truth? Armstrong’s view is that there can be and, indeed, every truth has a truthmaker in virtue of which it is true. This is a position widely referred to as truthmaker maximalism and subscription to the view is the second main distinctive feature of Armstrong’s version of truthmaker theory. Truthmaker maximalism is a very bold position to take. Armstrong used to say (in talks) that he was “going for the jackpot”. It is bold because just one case of truth for which there is no truthmaker would render it false. How are we really to know that there is no such case of truth? Armstrong would have to produce a credible theory of truthmakers for any awkward case we throw at him. Armstrong offers no direct argument for maximalism although he does offer weaker considerations in its favour. He thinks he has a quasi-inductive argument for it. If we see the success of the theory in dealing with a host of difficult cases, we may well become optimistic that the theory will be able to deal with any further case (T&T: 7). While there is no direct argument for maximalism, therefore, the work as a whole may be considered an argument. In addition, however, there are a number of other suggestions that make maximalism seem plausible. First, Armstrong supports what he calls the entailment principle. If T is a truthmaker for
entails , then T is also a truthmaker for (T&T: 10). Given that Armstrong is searching for relevant truthmakers, however, the entailment in the entailment principle cannot be classical. In classical entailment, any contingent truth entails any necessary truth. We cannot say, however, that <John Howard is Prime Minister> is a relevant truthmaker for <Jersey is not both an island and not an island>. The entailment 171
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principle must, therefore, concern some notion such as relevant entailment. The way Armstrong expresses this is to say that it is an entailment relation that holds only between purely contingent truths. A truth is purely contingent when it has only contingent truths as components so that it is contingent through and through (T&T: 11). A conjunction that has a necessary truth as a conjunct is not purely contingent in this sense, though it would be contingent in the normal sense. The entailment principle reveals a very important thesis of Armstrong’s truthmaker maximalism. The truthmaking relation is not necessarily, indeed is seldom, a one-to-one relation. Where the entailment principle comes into play, a single truthmaker can make many truths true. For instance, T can make
true and all that
relevantly entails. Not every truth, therefore, requires a unique truthmaker that makes it true and nothing else. We can see how this aids the case for maximalism when we consider the regress of truth. If
is true, then it is true that
is true. In other words, when
is true, <
is true> is true, and < <
is true> is true> is true, and so on forever. We see from the regress of truth that there are an infinite number of truths. Were there to be a unique truthmaker for every truth, there would have to be an infinite number of facts. The world would have to be infinitely large. But we cannot say for certain that the world is infinitely large. The regress of truth is only a problematic regress, however, if we assume the relation between truths and truthmakers is oneto-one. The entailment principle shows us, however, that if T is the truthmaker for
, then it is also the truthmaker for < <
is true> is true> because <
is true> entails < <
is true> is true>. This seems a perfectly acceptable result because there are, after all, independent reasons why a single truthmaker can make many truths true and why a single truth can have many truthmakers. Suppose David Armstrong were to be in the room with me now. His presence in the room would make true but also that , , <someone is in the room>, and so on, are true. A single fact, David Armstrong being in the room, can therefore be a truthmaker for many truths. But it is easy to see that it goes the other way too. is made true by David Armstrong being in the room but it is also made true by me being in the room. Here we have two distinct facts both of which are sufficient for, or necessitate, 172
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the truth of . We can have, therefore, relations between truths and truthmakers that are many–one and one –many, as well as one–one (if a truth happens to have a unique minimal truthmaker). Because there is no demand for a one –one relation in every case, the plausibility of truthmaker maximalism is greatly improved.
Negative and general truths Most of Armstrong’s general theory of truthmaking has now been explained. As he said, however, the argument for maximalism is in the work as a whole. To accept maximalism, we would have to be convinced that there are truthmakers for all truths, including those for which it has so far been difficult to find truthmakers. Armstrong moves on, therefore, to consider some of these difficult cases of truth in detail. He starts with the related subjects of negative and general truths. The so-called negative truths are the apparent truths such as , , and <my pockets are empty>. It is very difficult to offer a firm criterion that distinguishes negative truths from the ordinary, positive truths. Stated in a general way, however, the problem concerns how we can truthfully say that something is not the case. As the above examples show, this is not done simply by using the word not because I can use words such as absent or empty to signify much the same thing. The problem of saying what is not is an ancient one and can be found in Plato’s Theaetetus, but we can see that the problem is particularly pressing for truthmaker maximalists. Many propositions state that something is not the case. If they do so truly then the truthmaker maximalist has to find something that is the case and can be a truthmaker for a statement that something is not the case. What, then, among all the things that exist, can make true (Russell’s example, 1918: 189)? The proposition is about something that is not but to be true it must have a truthmaker, which is something that is. The late George Molnar, sometime associate of Armstrong, stated the problem of negative truth succinctly. There are four theses, each of which seems attractive. They are (Molnar 2000: 84–5): 173
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(i) (ii) (iii) (iv)
The world is everything that exists Everything that exists is positive Some negative claims about the world are true Every true claim about the world is made true by something that exists
Taken together, (i)–(iv) entail that there are positive truthmakers for negative truths. Truthmaker theorists, it now seems, have a duty to either name the positive truthmakers for negative truths or, if they cannot, reject (at least) one of theses (i)–(iv). The problem of finding truthmakers for general truths amounts to much the same. The truthmaker for must include at some stage that there are no more men than the mortal ones. That there are no more men seems to be a negative truth for which, again, we require a positive truthmaker. Hence, Armstrong identifies two kinds of negative truth. There are absences, such as when I say some thing is not (a unicorn) or some property is absent from a thing (I am not tall) and there are limits, when I say that these things are all there are. Philosophers have not had much success in finding positive existents that can be truthmakers for negative truths. There is one initially attractive line of thought, but it is not regarded as being ultimately successful. Russell attributes this strategy to Demos (1917). This room contains a number of positive existents, such as tables and chairs, a man and a sofa. Being a sofa is incompatible with being a hippopotamus, as is being a man or a table or a chair. Let us then take the sum of everything that is in the room. Given that these things are all incompatible with being a hippopotamus, then perhaps, as a sum, they can be the positive truthmaker for the negative truth that . There is, however, what seems to be a fatal problem with this line of thought. It relies essentially on a notion of incompatibility. The solution “works” by accounting for the truth of <not-p> in terms of some other positive truth where
is incompatible with . That p is incompatible with q, however, seems to mean that it is not (perhaps cannot be) both p and q together. For instance, nothing can be both a table and a hippopotamus. This seems quite clearly to be invoking another negative truth: not both p and q. And what is the positive truthmaker for this negative truth? We do not know. In short, this so-called incompatibility solution merely displaces the problem. Initially it offers an apparent positive truthmaker for a negative truth but it turns out to require a further negative truth 174
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to work and at no point do we genuinely get a positive truthmaker for a negative truth. At this point, assuming we cannot salvage the incompatibility solution, we can either search for some other positive truthmakers for negative truths or we can instead reject one of the four motivating theses. This is what Armstrong chooses to do in developing his totality solution. To understand Armstrong’s solution, however, it will help if we consider Russell’s solution, upon which Armstrong is aiming to improve. Russell’s move is basically to reject Molnar’s thesis (ii). Russell argues, perhaps astonishingly, that there are negative facts. Like Armstrong, Russell has an ontology of facts, rather than of things. Some of them can be negative facts that are fit to be truthmakers for negative truths. Hence, when is true, there is a truthmaker for this truth that is a negative fact. A negative fact is a fact that something is not the case, such as that the apple is not red or that there are no unicorns. It is an admittedly negative existent. Philosophers are immediately repulsed and puzzled by such things, as Russell conceded (Russell 1919: 287) but he saw no better solution. Let us just consider a little further what is so ontologically repugnant about negative facts. This issue is seldom taken seriously so I am venturing into the unknown at this point. We have seen that a fact can be understood as a particular having a property. How would such a fact be negative? There seem to be at least two ways. First, a particular could have a negative property. So when it is true that <my pen is not blue>, my pen may have a negative property of being not-blue. We have already seen what Armstrong thinks of negative properties in Chapter 2 (p. 33). Another way is for the particular to be a negative, so that it may be true that when the room contains a non-hippopotamus, this negative existent bearing the property of being in the room. (Of course, the truthmaker might also be understood as the room having the property of non-hippopotamus-containment, which is a negative property of the kind previously mentioned.) Neither negative properties nor negative particulars are the sorts of things we usually would want in a naturalistic ontology. I may be providing the wrong analysis of a negative fact here but, even if I am, its advocates already concede its nature as a negative kind of existent. Now let us move to Armstrong’s solution. The truthmaker for a negative truth is a complex consisting of a number of positive, 175
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first-order facts plus a higher-order fact about those facts. According to Armstrong, is true for the following reason. Let us imagine that we could gather before our minds every simple, positive fact about the room: that there is a sofa in it; that there is a chair, that the walls are white, and so on. Unlike the number of truths about the room, the number of facts about the room will be finite. Let us underestimate grotesquely and assume that there are 1,000 such facts. That there is a hippopotamus in this room is not among the 1,000 facts about the room. This, alone, would still not necessitate that , for reasons we have already encountered when truthmakers for general truths were considered. To get the necessitation, we would need to add to our list a 1,001st fact, which is the higher-order fact (a fact about the other facts) that facts 1 to 1,000 are all the first-order facts there are about the room. If there being a hippo in the room is not among our 1,000 facts, and we add to those the higher-order fact that these are all the facts about the room, then we do get the necessitation of . There is a conspicuous difficulty with this solution, however, namely that this higher-order fact is itself a negative fact. It is a totality fact that “totals” the first-order facts. We have already encountered these. But the totality fact means that these are all the facts: there are no more facts than these (T&T: 58). Armstrong admits that this is a negative fact. It is a limiting fact, of the same kind that we need for general truths. In a way, therefore, Armstrong’s solution is the same as Russell’s: they both reject Molnar’s (ii), that everything is positive, so they then do not need (solely) positive truthmakers for negative truths. Nevertheless, Armstrong can claim plausibly that his account is an advance over Russell’s, albeit only an advance in economy. Russell, it seems, was prepared to countenance many negative facts. As well being true, let us assume also the truth of , and . Russell would require four different negative facts to stand as truthmakers for these four different negative truths. We can see, however, that Armstrong’s single negative, totality fact will be enough to make all negative truths about the room true. There are undoubtedly many negative truths about the room, perhaps infinitely many, and if we need invoke only a single negative fact to account for them, then that is certainly more ontologically economical than invoking countless many. 176
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Furthermore, Armstrong argues, such totality facts are needed anyway in order to make general truths true (see Chapter 6, p. 106), so “let them really earn their keep!” (T&T: 58). Indeed, the problem of negative truth has been reduced, through the totality facts, to the problem of limits. It may be recalled that Armstrong began with two kinds of negative truths: absences and limits. The absence case, like the hippopotamus being absent from the room, now has a negative truthmaker that is a limit – a totality fact that “totals” the first-order facts about the room. Absences do not, therefore, have to be admitted into our most austere ontology but, we will be somewhat startled to discover, limits do. Limits are ontological realities. Is there any alternative solution to the problem of negative truth? Armstrong claims that while this is not a palatable solution, it is better than all the other options: it is “the least evil” (T&T: 82). It does, nevertheless, clash with the naturalistic view that existence is univocal. The admission of some negative existents seems to threaten Armstrong’s most fundamental commitment, in which case the naturalistic programme may falter at the final hurdle. I have already mentioned that we may continue the search for the positive truthmakers of negative truths but with the passage of time, and the great minds that have been exercised on the search, there are few current grounds for optimism in this direction. Molnar seems to be suggesting that this is the only way forward because it seems to him out of the question that any of (i) to (iv) should be rejected. We have seen how (ii) can be rejected, but what about (i), (iii) and (iv)? As far as I know, no one has ever seriously maintained that (i) should be rejected, that the world is everything that exists. This is sometimes referred to as the Tractarian thesis. Thesis (iv) has indeed been rejected and other truthmaker theorists, such as Peter Simons (2005), now see this is the least costly option. Thesis (iv) is the maximalist thesis – to reject it is to reject truthmaker maximalism – but many truthmaker theorists are prepared to do this. Negative truths, and perhaps some other classes of truth, may be true primitively or true by default. When we say that something is not the case, why should we need anything in the world corresponding to it or making it true? Armstrong’s opponent may also point out that his maximalism is so far only weakly motivated: Armstrong could offer only a quasi-inductive argument in its favour. Maximalism was, therefore, motivated by the success of truthmaker theory in accounting for problems like that of negative truth. But Armstrong’s solution to the problem of negative truth now seems 177
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motivated by a desire to preserve maximalism. Why else would one prefer the ontologically daring rejection of thesis (ii) to the ontologically conservative rejection of thesis (iv)? There is a kind of circularity, therefore, in Armstrong’s strategy. Nevertheless, it would have to be admitted that the rejection of (iv) creates its own problems. If a truthmaker theorist rejects (iv), then they are admitting that a proposition can be true without having a truthmaker. And if there can be truth without truthmakers, then what is the motivation for any kind of truthmaker theory at all? On the other hand, were the truthmaker theorist to say that there are special reasons why we do not need truthmakers in just this case, of negative truth, then they at least owe us a principled account of why some sorts of truth need truthmakers and others, such as these, do not. The final option is one that I do not think has been taken seriously until fairly recently. This would be to reject Molnar’s (iii), that some negative claims about the world are true. One would assume that few have considered this because it just seems so obvious that there are negative truths. If one were to be a convinced truthmaker maximalist, however, one would think a proposition true if and only if it has a truthmaker. Many truthmaker theorists now seem to concede that there are no truthmakers for negative truths. Perhaps the obvious conclusion should be that these propositions are just not true. If they lack truthmakers, should these propositions instead be thought of as falsehoods (Mumford 2007a)? A putative negative truth could, on this solution, be understood instead as a disguised falsehood. For example, the apparent truth of has, let us assume, no truthmaker. It is not, therefore, true. Instead, however, we can say that it is false that . Being a falsehood, this proposition requires no truthmaker. We do not have to find any positive existent that makes it so. Rather, it is false because there is no truthmaker making it true. There are many potential objections to such a view though it may be possible to answer enough of them that such a line carries at least some hope. There is much more that can be said about this whole issue, which is perhaps now the most hotly contested area of truthmaker theory. But now I will consider Armstrong’s approach to other problem areas of the theory.
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Modality, numbers and time Modal claims present a problem. How are they made true by the facts of our world? How can a truth about what is merely possible be made true only by what is actually the case? Similarly, how can truths about what is necessary be made true by just the facts there happen to be in our world? These two issues have to be addressed separately. The mere possibilities, it will be recalled, are those which are possible without being necessary or actual. Mere possibilities appear to be capable of truth and only if one thinks there are no contingent falsehoods is one likely to claim otherwise. How then can we provide a naturalistic account of truths of possibility? Armstrong offers the following proposal (T&T: 84). First, let us assume that T crosscategorially necessitates
, that is, makes
true. Assume also that
is contingent. If
is contingent then it is a necessary truth that it is contingent. If that is so, then
necessitates . T is therefore, by the entailment principle, the truthmaker for . We have found, therefore, an actual state of affairs that is also a truthmaker for a mere possibility. The case where it is not-p, but <possibly-p> is true, is slightly more complicated. The truthmaker for not-p, as we saw above, is a complex of first-order facts plus a totality fact. These are all contingent, so could be otherwise. If they are contingent then they are necessarily so. Therefore, they necessitate <possibly-p>. So where there is no fact that there is a hippopotamus in the room, among the first-order facts about this room, and there is a totality fact that these are all the first-order facts, the totality fact could have been otherwise. This means that there could have been more facts about the room, such as that it contains a hippopotamus. We now move to truthmakers of necessary truths. Here Armstrong feels he needs a separate account to that of possibility. To understand the truthmakers for necessary truths, he offers two main claims. First, he says, the truthmakers are the objects alone, rather than states of affairs involving those objects. The necessary truths of mathematics, for instance, are made true by mathematical objects, such as numbers. The truthmakers for are the numbers 7, 5 and 12. The proposition asserts a relation between those numbers and all that is needed for the relation to hold is the numbers themselves. They bear internal relations to one another. As
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we have already seen, it is sufficient for an internal relation to hold just if the relata exist. To be 12 is, among other things, to be equal to 7 + 5. Second, Armstrong opts for a possibilist account of such objects and the truths in which they partake. This means that necessary truths are hypothetical in nature (T&T: 100). When we are asserting such a truth, we are asserting a conditional such as “(necessarily) if there are seven things and five further things, then the sum of all these things is twelve”. Possibilism is especially attractive in the case of truths about large numbers, where there may not be that number of things in the whole universe. One concern there might be about Armstrong’s account of possibility and necessity is that it does not appear to be a unified account. A reason one might want a unified account is the purely logical consideration that the two modal operators that express possibility and necessity are interdefinable (given the non-modal operator of negation). If we have an account of possibility, then we also have an account of necessity because necessarily-p can be defined as notpossibly-not-p. Armstrong accounts for truths of possibility in terms of actual states of affairs and then truths of necessity in terms of relations between hypothetical objects. With a proposition such as <not possibly not-p>, which of these two accounts should we invoke? Is it a truth about necessity or a truth about possibility? Armstrong moves on to consider mathematics and set theory in more detail (T&T: ch. 9). What, if anything, is the truthmaker for the claim that the number 4 exists? As would be expected, Armstrong rejects the Platonic view that the number four is an eternal existent or Form. He also rejects the extensionalist view of Russell, which has it that the number 4 is the class of all four-membered classes. Armstrong prefers the intensionalist response to such a view: it is because these classes have four members that they form a class of classes; they do not have four members because they belong to this class of classes. That a particular class has four members is an intrinsic matter, quite apart from what goes on in other classes. Armstrong’s naturalistic theory requires, following Forrest and Armstrong (1987), only the notion of a mereological whole. The mereological whole, comprised of four men, is the truthmaker for there being four men. There is a relation holding between the property being a man and the whole that the four men constitute. The mereological whole “fours” the property of being a man, as Armstrong says (T&T: 114). The property serves the function of determining the unit of which, in this case, there are four. Classes 180
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serve the same function. What, then, is the number 4 itself? On this account it is a universal – a dyadic universal or four-relation – instantiated by a mereological whole and some unit-determining property. Effectively, this means that the four men themselves instantiate the number four. In the case of very large numbers, they have only possible instantiations. Truth and Truthmakers ends with a discussion of time, in which Armstrong argues for omnitemporalism or four-dimensionalism, which we already encountered in his work on universals. It is accepted, certainly by Armstrong, that there are truths about the past. He also accepts that there are truths about the future, though admits this to be slightly more controversial. What are the truthmakers for these truths? An omnitemporal view provides them at a stroke. Past, present and future are equally real, as are the states of affairs within them. Consider the proposition . The presentist thinks that only the present is real. What do they have, in all existence, that could make such a proposition true? It cannot be Caesar himself, whom the presentist thinks is non-existent. Nor can the presentist say < was once true> because this itself would have to be a truth and, again, it seems to have no truthmaker in the present. The omnitemporalist will admit Caesar to be a real existent, even though he is in the past relative to our experience. Past existents can be truthmakers for truths about the past and future existents can be truthmakers for truths about the future. It is, again, most satisfying to see that truthmaker considerations support an earlier commitment in Armstrong’s metaphysics. This completes Armstrong’s survey of difficult cases of truth. Truthmaker theory works for them, he contends, and we should be encouraged enough to think it will work for any future difficult case. Hence we should be maximalists. Whether Armstrong really has considered enough cases is a decision I leave to readers.
The programme completed? Armstrong said (in conversation), just before the publication of Truth and Truthmakers, that it would be his final book. This was not because he expected an imminent demise but because he had said everything he had wanted to say. Unlike some philosophers, cut down before their work is complete, Armstrong has lived a long 181
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enough life to see his programme of naturalistic metaphysics completed and presented to the world. Despite a few minor changes of view along the way, Armstrong’s books present a beautifully integrated and systematic view of the world, with numerous interconnections between the topics of properties, laws, causation, facts, truth, powers and minds. Armstrong is pleased he does not have followers. There are no Armstrongians. If this is thought to be because there is not an Armstrongian philosophy, that would be a mistake. The books from Perception and The Physical World through to Truth and Truthmakers present a unified and coherent account of the world. It does offer a philosophy: a naturalistic, immanentist one. Perhaps, instead, there are no Armstrongians because his interest has not been in attracting followers but in the philosophy itself. Those who have been taught or informed by Armstrong’s work are happily not likely to become disciples. Rather, they are likely to want to investigate these or other philosophical issues further. Armstrong has offered a model of clear enquiry, where a position is exposed nakedly to our understanding. The effect has been to enthuse readers, make them see that philosophy need not be confusing or esoteric. That there are no Armstrongians is indeed a tribute to the man and his work. In Chapter 11, however, I shall consider one additional aspect of Truth and Truthmakers, about which I have remained deliberately silent until this point. Armstrong puts forward a new view of instantiation, inspired by the work of Don Baxter. Despite previously offering us a singular vision of the world, this new direction in his thinking threatens to overturn much of what he has argued hitherto.
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In Chapters 1 to 10 we have seen Armstrong’s naturalist programme develop. It forms a remarkably integrated and exceptionally consistent body of work covering the entire operations of the natural world, with some detailed attention paid to the operation of minds within that world. We might think of this body of work as the official Armstrong philosophy. It is at least the view that he has spent the majority of his career developing and extending with thorough and detailed argument. One distinguishing feature of the entire programme is the all-pervading presence of contingency. Things could have been different. Everything could have been otherwise. Even the fundamental elements of the world are contingent existents. Any necessity, such as it is, is usually classed as analytic necessity, grounded in the meaning of words rather than the nature of things, or concerns merely the internal relations of objects such as numbers. Let us take stock and recapitulate this contingentist position. We can start with the particulars and universals. Every particular thing is a contingent existent. No particular exists of necessity. Only God, Platonic Forms and transcendent numbers were ever seriously proposed as necessary existents, but Armstrong’s naturalism already rules these out. But while the idea of necessarily existing particulars has never had great intuitive appeal, many have thought that universals are necessary existents. Redness, for instance, was thought to be an eternal existent because it cannot be created or destroyed. It was not thought to be dependent on the existence of red things. But Armstrong argued, to the satisfaction of many, that the attraction of this view does not bear detailed scrutiny. Universals are best thought 183
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of as immanent rather than transcendent phenomena and therefore, qua second-order particulars, also contingent existents. That does not exhaust the basic components of the world. The world is a world of states of affairs and these are something additional to the particulars and universals that make them up. The particular a can exist and the universal F exist without there being a state of affairs that a is F. Even where a being F is a state of affairs, its existence is not necessitated by its constituents. States of affairs are, therefore, also contingent beings. We then move on to some of the higher-level features of our world. There are laws of nature, existing as relations of natural necessitation between universals. But as relations, laws are themselves universals: higher-order universals. And like all other universals, they are also contingent existents. Even if there is a law that N(F,G), F and G do not themselves ensure the existence of the law N(F,G). That has to be some further universal in addition to F and G. Once the law exists, it necessitates that anything which is F is also G. But this is a contingent, natural necessitation. It is not as strong as logical necessity. Laws, like all universals, exist only in their instances. But the instances of nomological relations are to be found in particular causal sequences. As it is contingent what laws exist, it is therefore contingent what causal relations there are. Laws and causes could have been different. But we can take this even further. The dispositions of things are not fundamental parts of reality and do not show that properties necessitate other properties or have essential features. All properties are categorical. Dispositions come about simply when something has a property that is, with some stimulus, nomologically related to something else (Armstrong 2005a). What a property is disposed to do, depending on the applicable laws of nature, is thus also contingent. This features large in Armstrong’s theory of mind because many mental phenomena are dispositional in nature. Which properties or states are responsible for such dispositions is a contingent matter as it will depend on what the laws of nature are. If one is to identify mental states with the physical states that cause mental behaviour, it will have to be, therefore, a contingent identification only. Other physical states could have been the causal bases of mental dispositions, had the world been different. The last major subject where we find contingency is in the topic of modality itself. Armstrong sees that the world allows free, unrestricted recombination of all the existents that are wholly distinct. 184
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All and only the recombinations of these existents are possible. His combinatorial theory of modality was limited to a theory of possibility. Little was said of necessity. A distinction between necessary and contingent truths was nevertheless maintained (for example, WSA: 183). But necessary truths were to be found in the restricted domains of logic and mathematics and, along with traditional empiricists, Armstrong saw them typically as analytic truths. Some truths of mathematics required a slightly more complicated account. Some such truths may be about particulars, such as numbers, but truths about them will be truths about their internal relations, such as 7 + 5 being internally related to 12. Internal relations are no additions of being over and above the existence of the numbers themselves. Because of this, we can have necessary truths without adding de re necessity to the world. The Armstrong who developed the core programme of metaphysics was thus not a believer of necessity in re, as a real, additional feature of the world. For a long time, that was Armstrong’s official view. But Truth and Truthmakers saw a radical shift of view and admission of a major new kind of necessity in the world. The rest of this chapter is concerned with that new view and the implications it would have for the contingentist view just summarized.
Instantiation as partial identity Armstrong’s change of mind came about through a reconsideration of the issue of instantiation prompted by a reading of Baxter (2001). It may be recalled that instantiation cannot be regarded as a relation, on pain of Bradley’s regress. Relations are themselves universals, which would have to be instantiated by their relata, so no progress would be made. We wonder how it can be that Fa; for instance, an apple being red (which is by no means a fundamental state of affairs). If we think that the apple, a, bears a relation of instantiation to redness, F, we face exactly the same question again: how can it be that I(a,F), where I is a relation of instantiation? Instantiation would have to be instantiated and the regress is under way. Hence one of Lewis’s chief criticisms of Armstrong’s view is that the instantiation invoked in his theory of universals cannot be analysed (Lewis 1983: 23). Yet Armstrong had criticized forms of nominalism and transcendent realism for failing to fully analyse their key notions, such as falling under a predicate, being a member of a class, resembling, 185
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participating in, and so on. All these views were accused of producing regresses (Chapter 2, pp. 21–2) but the charge is that the same would be true of instantiation. A particular and a universal, united in a state of affairs, cannot therefore stand in a relation of instantiation. But we need an account of how a state of affairs is composed: “We have somehow got to get particulars and their properties together” (T&T: 48). Instead, Armstrong spoke of the “fundamental tie” between a and F (U: 94, for example). He argues that there is no regress involved in instantiation understood as the fundamental tie (U: 111–12). No extra state of affairs is required over and above a instantiating F – being fundamentally tied to F – because that same state of affairs is also the truthmaker for any further instantiation claim (such as that a’s instantiating F instantiates instantiation). But this is hardly completely satisfactory, consisting as it does in the pretty loose metaphor of a “tie”. He also offered “nexus” (U: 108), which is little more illuminating. It is no surprise, then, to see that Armstrong revisited this issue, clearly unimpressed with his own earlier dismissal of the problem, where he had said “I do no think that the problem of characterizing the nature of the tie should detain us” (U: 108). One may be able to pursue the line of the tie or nexus further, and spend time characterizing it in detail, but after reconsideration Armstrong opts for a brand new theory instead: I have had a change of heart about the instantiation of universals. In previous work I conceived of the instantiation as a matter of contingent connection of particulars and universals. New work by Donald Baxter . . . has made me think that the link is necessary. . . . I have been convinced by him that what is involved in a particular instantiating a property-universal is a partial identity of the particular and universal involved. It is not a mere mereological overlap, as when two streets intersect, but it is a partial identity. This in turn has led me to hold that instantiation is not contingent but necessary. (T&T: 46–7) Let us first get clear on how this new account of instantiation is to be understood before we go on to consider its implications and viability. We shall see that while Armstrong accepts that the basics are taken from Baxter, he makes of it something quite different from the original author. For Baxter, a universal is a strict identity running through many particulars and, likewise, a particular can be thought of as a strict 186
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identity running through many universals. Where we have a particular instantiating a universal, Armstrong says we have “an intersection of the two sorts of oneness, a point of partial identity” (2004: 141). This is not simply a mereological relation. As we have seen, Armstrong’s states of affairs were supposed to have a nonmereological mode of composition. However, the attraction of the partial identity view is that no additional mode of composition is required: “Because the suggested link between the two is partial identity, any need for a fundamental tie, a copula, or what have you, seems to be eliminated” (ibid.: 142). Clearly this is a big attraction for Armstrong. The problems that he had in explaining the nature of the fundamental tie or nexus vanishes. There is no tie or nexus whose nature is to be explained. Armstrong has likened the new view to the early account of instantiation found in Plato’s Parmenides. Socrates was asked how particulars stand to the Forms. His answer was that they participated in the Forms. While Armstrong cannot see that this could be the case if the Forms are transcendent universals, where we are instead immanent realists this might be the best way to understand instantiation. Particulars can be said to participate in the universal in the sense that they are partially identical with the universal. The first theory of instantiation might have been the right one after all. A difficulty this leaves us with, however, is how to distinguish universals and particulars. Both are now depicted as Ones running through Manys. Previously, universals alone had this distinguishing feature. Now the same is being said of particulars. But there remain key differences, Armstrong alleges. In the first place, a universal has a fixed number of terms. It is either monadic, dyadic, triadic, and so on, and never varies from what it is. Particulars can instantiate any number of universals, in alleged contrast (2004: 147). And, second, universals are repeatable with no logical limit on them getting instantiated at any time and place (ibid.). We will return to these “differences” in a short while.
The necessity of instantiation The new view of instantiation has major implications for Armstrong’s philosophy. I will go on to argue that instantiation is not for him just some local problem that permits a local solution. In changing his 187
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mind on instantiation, Armstrong has to change his mind on virtually everything. The key point to this change is that instantiation as partial identity means that instantiation is necessary. As Armstrong remarks, “Particulars and universals are, on this theory, an inseparable package deal because they each help to constitute the other” (2004: 143). This produces a major consequence of the theory. Contingency has to be jettisoned. Referring to instantiation as intersection, instead of partial identity, he asks: Is it not a central idea in classical logical atomism – in the Tractatus in particular – that any state of affairs (fact) might not have existed, yet everything else remain exactly the same? The trouble is, though, that in the intersection theory neither the row that is the universal, nor the column that is the particular, would be exactly the same. Is the theory forced to say that, given the actual universals and the actual particulars, each intersection, each state of affairs, is then necessary? . . . We are indeed forced to say this. (2004: 144) Let us reconsider the red apple again, as an example state of affairs though not a fundamental one. The apple and redness are partially identical or intersect. This means that redness is constituted (at least in part) by the particulars it runs through. The apple is constituted (at least in part) by the universals it runs through (or run through it). Were the apple not red, then it would not be the particular that it is. Similarly, were the apple not red, then redness would not be the universal that it is. The upshot is that if redness exists, this very redness of our world, and if this apple exists, this very one, then it is necessary that this apple is red. This universal and this particular might not have existed, perhaps, but given that they do, it is necessary that they intersect. Being instantiated in this apple is part of what makes redness what it is. And being red is part of what makes this particular apple the apple that it is. The new view that Armstrong offers, he once criticized in strong terms. He was criticizing a certain view of trope theory for having the sort of consequences his theory now has. A heavy price is paid . . . The price is the huge amount of necessity in re that this . . . has to postulate. Every property and (it would seem) every relation that exists must be instantiated where it is actually instantiated . . . the arrangement of the world is fixed. (WSA: 117) 188
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With instantiation as partial identity, the arrangement of the world does indeed look fixed. Just how fixed it would be is the next matter to which we turn.
Consequences for Armstrong’s programme Let us consider once more the grid-like representation of the world from Chapter 2. We could consider this to be a complete description of the world at a time or, more in keeping with Armstrong’s fourdimensionalism, we could consider it as a complete account of the whole world at all times. For the latter, certain states of affairs would have to be, in some way, indexed to certain times. We can see that a is F; for example, our apple is red. a being F was originally understood as a state of affairs, something additional to the existence of a and of F. It is, of course, no longer clear that this is an additional entity because its existence has a kind of necessity, albeit with a conditional character. If a and F exist, then the state of affairs, a being F, also exists. Let us put that aside, for the moment, as the point to be considered here is how little is left of contingency
Figure 11.1 Grid for instantiation of properties
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once we accept the partial identity view. Suppose that a is indeed F and we tried to imagine a world just like ours but in which a is not F. We shall try to subtract this state of affairs from our world. We might begin by thinking that we can imagine such a world. This certainly seems to respect our pre-theoretic modal intuitions. After all, it is just a world like ours but in which this apple is not red. We see quickly, however, that by eliminating just this one state of affairs from our world, we would almost certainly eliminate the whole of the world. If it were no longer the case that a is F, then a would no longer be a and F would no longer be F. a and F would have ceased to exist. One still might not take this to be too high a price to pay, if one thinks that the partial identity view is appealing, but we can see that it does not end there. We are not just talking about a world lacking one individual and one universal. F is also instantiated, in our grid, by b, e and g. If F no longer exists, then the state of affairs b being F can no longer exist. And because instantiation is partial identity, this means that b no longer exists. By the same argument, e and g no longer exist. That only leaves us with the individuals c, d and f. They will not survive long, however. We have also said that a no longer exists. But a also instantiated A, C and E, as well as F. Because instantiation is partial identity, and a no longer exists, that means that A, C and E no longer exist. That leaves us only with universals B, D and G. But these will not survive long either. One of our few remaining individuals, c, instantiated universal C, which no longer exists. So c no longer exists. c instantiated G, however, so G no longer exists. And if G does not exist, then nor does f, and so on. We can now see that every particular and every universal would cease to exist just because the state of affairs, a being F, ceased to exist. Take away the one small fact – that this apple is red – and most likely the whole universe ceases to exist. This is because all particulars and universals are interrelated in some way, as we have just seen. To take away one state of affairs is to take away every particular that instantiates the same universal and every universal that is instantiated in that particular. And then we have to take away every particular that instantiates any of those universals that have been taken away and any universal that is instantiated by any of those particulars. We set in motion a domino effect at the end of which nothing is likely to be left standing. We have seen the importance of naturalism in Armstrong’s philosophy. There is but a single world of spacetime. Everything is 190
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therefore spatiotemporally related to everything else. But only if there are unrelated “island-universes” could anything survive once we try to remove but one state of affairs. And such an escape route is surely not open to Armstrong unless he throws off the naturalism that is his chief commitment. This has led one critic to liken Armstrong’s new philosophy to Leibnizian rationalism and describe the new position as “disastrous” (Simons 2005: 259): “everything in the world necessarily coexists with everything else” (ibid.: 260). A world would then come as a complete package, consisting of every single state of affairs, or not at all. The only other possible worlds would be completely alien worlds, containing none of our particulars and none of our universals, in clear violation of Armstrong’s commitment to naturalism. Armstrong has, after reflection, tried to prevent this domino effect: I now think that the situation does not spread to the properties. “Partial identity”, I now think, is a somewhat misleading phrase. Particulars enfold their universals – and that is a sort of partial identity – but universals do not enfold their particulars. In the envisaged “deleting”, the universal continues to exist identically in other particulars, unless, indeed, a is the only particular to instantiate that universal. (2005: 274) But this response looks ad hoc and an unconvincing retreat to a halfway position that will satisfy no one. Partial identity seemed like a way of treating particulars and universals equally. Partial identity looks symmetrical. There seems little reasoned justification for now saying that universals are exempt from the constraints of partial identity. All we have is this notion of “enfolding”, which is supposed to apply to particulars and universals asymmetrically. But it is not clear what this is, nor how it exempts universals from the domino effect. The position looks a mish-mash: half-Leibnizian and halfempiricist. Some further implications of the new position should by now be all too apparent. But here are some of the main points. First, it is clear that Armstrong no longer has a theory of possibility. The blanks on the combinatorial grid are no longer possibilities at all (2004: 148). One might think that this is all well and good. We have seen that various things that seem intuitively possible no longer are on the new view of instantiation (notwithstanding the fact that we saw in Chapter 10, p. 179 how to provide truthmakers for modal truths). But the combinatorial theory of possibility, as outlined in Chapter 4, 191
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had at least something going for it. Everything, or almost everything, is in the new theory either actual or necessary. Should we not have a modal theory that allows mere possibilities: things that are neither necessary nor actual? Are we really willing to give up our modal intuitions, and a modal theory, just on the basis of a theory of instantiation? Laws of nature would also now be necessary (2004: 153 and 2006: 246). Laws are higher-order universals that will run through the second-order particulars – the first-order universals – that they relate. These, in turn, are instantiated in particular causal sequences. All these will become necessary in a very strong sense. The universal F would not be the universal it is unless it partakes in the law N(F,G). If F exists, so does the law, and also all the particular causal transactions that are the instantiations of the law. Again, take any of these away and the whole universe ceases to exist. And if we do away with this contingency then it becomes obvious that the dispositional properties, which are endowed by a categorical property together with a law of nature, are also a matter of necessity. Given a certain categorical property, it would then be necessary what dispositions would follow. This has clear implications for Armstrong’s philosophy of mind. Which categorical properties formed the causal bases of mental dispositions would now be a matter of necessity. The notion of contingent identity, that Armstrong fought at length to defend, would also be sacrificed. It is clear that adoption of the new theory of instantiation would be a serious business. But are there any advantages to it, other than it being a putative solution to the general question of instantiation? On the plus side, general facts need no longer be posited to account for general truths. Each instantiation of F is necessary and no other instantiation is possible. The truthmaker for the universal statement that every F is a G can now just be all the Fs (2004: 148). We will not need an additional fact that these are all the Fs because there could be no more Fs than the actual Fs. It should also be conceded that at least some contingency does remain. The universals are themselves contingent existents in a sense. Assuming that a is F, then had a not been F, F would not exist. But there could be some other property very like F that exists. Suppose that F* is just like F except that it is not instantiated by a. This allows some contingency still in the world, though F* is not identical with F. But it is just like F except for the fact that it is not instantiated by apple a. The alleged domino effect might then 192
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be just a scare story. Take away the Fa state of affairs and it is not as if the world would cease to exist. All the particulars and all the universals would merely be different particulars and universals, a* to n* and A* to N*. We would not even notice the difference because a* is so like a and A* is so like A. What we have, therefore, is “a necessary connection between contingent entities, the particular and the universal” (2006: 243). The case for the new theory may be understated but, if we come to the balance sheet, it looks like we have, in the credit column, a solution to Bradley’s regress, no need for general facts, and now a surrogate for the world’s contingency. But on the debit column, we have the considerable minus that most of our ordinary modal intuitions will have to be rejected as almost everything comes out, strictly speaking, as necessary. Even parts of the new theory itself look endangered by this allconsuming necessity. On p. 187 we described how Armstrong tried to maintain a difference between universals and particulars even though both were now Ones running through Manys. But the necessity of instantiation seems even to undermine this claim. Universals were said to have fixed adicities: they always had to be instantiated by the same number of particulars. Armstrong had called this his Principle of Instantial Invariance (ToU: 94). But, taken as a four-dimensional whole, necessity would entail that each particular instantiated (or was partially identical with) a fixed number of universals. It could not have instantiated one fewer, or one more, universal and remained the particular that it is. Instantial Invariance seems, therefore, to apply also to particulars. That criterion of difference is left hard to uphold and so is the second, for similar reasons. Universals could be instantiated at any number of places and times, it was argued, while, standardly, particulars are seen as restricted. But has Armstrong not now imposed a modal limit on a universal’s instantiations? It may well exist in various places and times but could it be at any more places and times than it actually is and still be the universal it is? We must recall that Armstrong has now effectively rejected his combinatorial theory of possibility. He no longer has any ground, therefore, for invoking the possibility that a universal have a further, additional instantiation to the one it has, nor that a particular could instantiate one further universal over and above the ones that it does. The difference between particulars and universals now looks to be a very uncertain matter. 193
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Afterword There has been a twist in the tale of Armstrong’s philosophical career. So often the proponent of Humean distinctness and unrestricted combinatorial freedom, he now presents us with a radical alternative in which almost everything is connected and necessary. We are faced with a choice where we cannot accept both the contingentist programme, outlined in Chapters 1–10 below, and the necessitarian view that has just been introduced. We may, of course, choose to accept neither. The contingentist view has much going for it. Armstrong demonstrated how it could generate a systematic and integrated view of the world. That it is able to do so surely counts in favour of its truth. The alternative, though it has been branded Leibnizian, may yet be developed in an equally systematic way. The necessity involved, throughout the intersection view, is also something from which philosophers no longer shy away (see Bird 2007 and Mumford 2004). It is by no means clear-cut, therefore, which of these directions, if either, we should take. In particular, I would urge that the new view of the later Armstrong be considered seriously, for it is by no means as far-fetched as it could seem at first sight.
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Books by Armstrong 1960. Berkeley’s Theory of Vision: A Critical Examination of Bishop Berkeley’s Essay Towards a New Theory of Vision. Melbourne: Melbourne University Press. 1961. Perception and the Physical World. London: Routledge & Kegan Paul. 1962. Bodily Sensations. London: Routledge & Kegan Paul. 1968. A Materialist Theory of The Mind. Revised edition (London: Routledge, 1993). 1973. Belief, Truth and Knowledge. Cambridge: Cambridge University Press. 1978. Nominalism and Realism (Universals and Scientific Realism, Volume 1). Cambridge: Cambridge University Press. 1978. A Theory of Universals (Universals and Scientific Realism, Volume 2). Cambridge: Cambridge University Press. 1981. The Nature of Mind and Other Essays. Brighton: Harvester Press. 1983. What is a Law of Nature? Cambridge: Cambridge University Press. 1984. Consciousness and Causality (with Norman Malcolm). Oxford: Blackwell. 1989. Universals: An Opinionated Introduction. Boulder, CO: Westview Press. 1989. A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press. 1996. Dispositions: A Debate (with C. B. Martin and U. T. Place), T. Crane (ed.). London: Routledge. 1997. A World of States of Affairs. Cambridge: Cambridge University Press. 1999. The Mind–Body Problem: An Opinionated Introduction. Boulder, CO: Westview Press. 2004. Truth and Truthmakers. Cambridge: Cambridge University Press.
Other works by Armstrong 1958. “Educating Sydney?”. Observer 19/4/58: 152. 1968. “The Headless Woman Illusion and the Defence of Materialism”. Analysis 29: 48–9. 1969. “Dispositions are Causes”. Analysis 30: 23–6.
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David Armstrong 1980. “Against ‘Ostrich’ Nominalism: A Reply to Michael Devitt”. Pacific Philosophical Quarterly 61: 440–9. 1982. “A Search for Values”. Quadrant 26 (6): 65–70. 1984. “Self Profile”. In David Armstrong, R. Bogdan (ed.). Dordrecht: Reidel, 3–51. 1987. (with P. Forrest) “The Nature of Number”. Philosophical Papers 16: 165–86. 1988. “Can a Naturalist Believe in Universals?”. In Science in Reflection, U. Ullmann-Margalit (ed.). Dordrecht: Kluwer, 103–15. 1989. “C. B. Martin, Counterfactuals, Causality and Conditionals”. In Cause, Mind, and Reality: Essays Honouring C. B. Martin, J. Heil (ed.). Dordrecht: Kluwer, 7–15. 1991. (with A. Heathcote) “Causes and Laws”. Noûs 25: 63–73. 1992. “Properties”. In Properties, D. H. Mellor and A. Oliver (eds). Oxford: Oxford University Press, 1997: 160–72. 2003. “Review of Rodriguez-Pereyra’s Resemblance Nominalism”. Australasian Journal of Philosophy 81: 285–6. 2004. “How Do Particulars Stand to Universals?”. In Oxford Studies in Metaphysics 1, D. Zimmerman (ed.). Oxford: Oxford University Press: 139–54. 2005. “Reply to Simons and Mumford”. Australasian Journal of Philosophy 83: 271–6. 2005a. “Four Disputes About Properties”. Synthese 144: 309–20. 2005b. “Review of Mumford, Laws in Nature”. Australasian Journal of Philosophy 83: 607–10. 2006. “Particulars Have Their Properties of Necessity”. In Universals, Concepts and Qualities: New Essays on the Meaning of Predicates, P. F Strawson and A. Chakrabarti (eds). Aldershot: Ashgate, 237–47.
Works by other authors Adams, R. 1974. “Theories of Actuality”. Noûs 8: 211–31. Anderson, J. 1962. Studies in Empirical Philosophy. Sydney: Angus and Robertson. Anscombe, G. E. M.  1981. “Causality and Determinism”. In Metaphysics and the Philosophy of Mind, Oxford: Blackwell, 133–47. Ayer, A. J. 1954. Philosophical Essays. London: Macmillan. Baxter, D. 2001. “Instantiation as Partial Identity”. Australasian Journal of Philosophy 79: 449–64. Bird, A. 2005. “The Ultimate Argument Against Armstrong’s Contingent Necessitation View of Laws”. Analysis 65: 147–55. Bird, A. 2007. Nature’s Metaphysics: Dispositions, Laws and Properties. Oxford: Oxford University Press. Black, R. 2000. “Against Quidditism”. Australasian Journal of Philosophy 78: 87–104. Brentano, F.  1973. Psychology From an Empirical Standpoint, L. L. McAlister (ed.). Atlantic Highlands, NJ: Humanities Press. Campbell, K. 1990. Abstract Particulars. Oxford: Blackwell. Crane, T. (ed.). 1996. Dispositions: A Debate. London: Routledge. David, M. 2004. “Don’t Forget About the Correspondence Theory of Truth”. Australasian Journal of Philosophy 82: 42–7.
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Bibliography Davidson, D. 1963. “Actions, Reasons and Causes”. Journal of Philosophy 60: 685–700. Demos, R. 1917. “A Discussion of Certain Types of Negative Proposition”. Mind 26: 188–96. Devitt, M. 1980. “ ‘Ostrich Nominalism’ or ‘Mirage Realism’ ”. Pacific Philosophical Quarterly 61: 433–9. Dretske, F. 1977. “Laws of Nature”. Philosophy of Science 44: 248–68. Ellis, B. 2001. Scientific Essentialism. Cambridge: Cambridge University Press. Ellis, B. 2002. The Philosophy of Nature. Chesham: Acumen. Ellis, B. 2006. “Looking for Laws”. Metascience 15: 437–41. Engel, P. 2002. Truth. Chesham: Acumen. Franklin, J. 2003. Corrupting the Youth: A History of Philosophy in Australia. Sydney: Macleay Press. Gettier, E. L. 1963. “Is Justified True Belief Knowledge?”. Analysis 23: 121–3. Goodman, N.  1983. Fact, Fiction, and Forecast, 4th edn. Cambridge, MA: Harvard University Press. Goodman, N. 1966. The Structure of Appearance, 2nd edn. Indianapolis, IN: Bobbs-Merrill. Handfield, T. 2005. “Armstrong and the Modal Inversion of Dispositions”. Philosophical Quarterly 55: 452–61. Heil, J. 1998. Philosophy of Mind: A Contemporary Introduction. London: Routledge. Heil, J. 2003. From an Ontological Point of View. Oxford: Oxford University Press. Hempel, C. G. and Oppenheim, P. 1948. “The Logic of Explanation”. In Readings in the Philosophy of Science, H. Feigl and M. Brodbeck (eds). New York: Appleton Century Crofts, 319–52. Holton, R. 1999. “Dispositions all the Way Round” Analysis 59: 9–14. Hume, D.  1888. A Treatise of Human Nature, L. A. Selby-Bigge (ed.). Oxford: Clarendon Press. Hume, D.  1975. Enquiry Concerning Human Understanding, in Enquiries Concerning Human Understanding and Concerning the Principles of Morals, L. A. Selby-Bigge (ed.), 3rd edn rev. P. H. Nidditch. Oxford: Clarendon Press. Jackson, F. 1977. “Statements about Universals”. Mind 86: 427–9. Kripke, S. 1980. Naming and Necessity. Cambridge, MA: Harvard University Press. Lewis, D. 1966. “An Argument for the Identity Theory”. Journal of Philosophy 63: 17–25. Lewis, D. 1973. Counterfactuals. Oxford: Blackwell. Lewis, D.  1999. “New Work for a Theory of Universals”. In Papers in Metaphysics and Epistemology, Cambridge: Cambridge University Press, 8–55. Lewis, D. 1986. On the Plurality of Worlds. Oxford: Blackwell. Lewis, D. 1986a. Philosophical Papers II. Oxford: Oxford University Press. Lewis, D.  1999. “Reduction of Mind”. In Papers in Metaphysics and Epistemology, Cambridge: Cambridge University Press, 291–324. Lewis, D. 2001. “Forget About the ‘Correspondence Theory of Truth’ ”. Analysis 61: 275–80. Lewis, D. Forthcoming. “Ramseyan Humility”. In Naturalism and Analysis, D. Braddon-Mitchell and R. Nola (eds). Cambridge, MA: MIT Press.
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David Armstrong Mackie, J. L. 1962. “The Philosophy of John Anderson”. Australasian Journal of Philosophy 40: 265–82. Martin, C. B. 1984. “Anti-Realism and the World’s Undoing”. Pacific Philosophical Quarterly 65: 3–20. Martin, C. B. 1997. “On The Need for Properties: the Road to Pythagoreanism and Back”. Synthese 112: 193–231. Maurin, A.-S. 2002. If Tropes. Dordrecht: Kluwer. Melia, J. 2003. Modality. Chesham: Acumen Mellor, D. H. 1974. “In Defense of Dispositions”. Philosophical Review 83: 157–81. Mellor, D. H. 1991. Matters of Metaphysics. Cambridge: Cambridge University Press. Mellor, D. H. 2000. “The Semantics and Ontology of Dispositions”. Mind 109: 757–80. Michotte, A. 1963. The Perception of Causality. London: Methuen. Mill, J. S. 1843. A System of Logic. London: Parker. Molnar, G. 1969. “Kneale’s Argument Revisited”. Philosophical Review 78: 79–89. Molnar, G. 2000. “Truthmakers for Negative Truths”. Australasian Journal of Philosophy 78: 72–86. Molnar, G. 2003. Powers, a Study in Metaphysics, S. Mumford (ed.). Oxford: Oxford University Press. Moore, G. E.  1993. “A Defence of Common Sense”. In Selected Writings, T. Baldwin (ed.). London: Routledge, 106–33. Mumford, S. 1998. Dispositions. Oxford: Oxford University Press. Mumford, S. 2004. Laws in Nature. London: Routledge. Mumford, S. 2005. “Kinds, Essences, Powers”. Ratio 18: 420–36. Mumford, S. 2007. “Powers, Dispositions, Properties”. In Revitalizing Causality: Realism About Causality in Philosophy and Social Science, R. Groff (ed.). London: Routledge. Mumford, S. 2007a. “Negative Truth and Falsehood”. Proceedings of the Aristotelian Society, 107: 45–71. Musgrave, A. 1981. “Wittgensteinian Instrumentalism”. Theoria 46: 65–105. Nagel, T. 1974. “What Is It Like to Be a Bat?”. Philosophical Review 83: 435–50. Place, U. T. 1956. “Is Consciousness a Brain Process?”. British Journal of Psychology 47: 44–50. Plantinga, A. 1974. The Nature of Necessity. Oxford: Oxford University Press. Plato, Theaetetus. In The Collected Dialogues, E. Hamilton and H. Cairns (eds). Princeton, NJ: Princeton University Press. Plato, The Republic. In The Collected Dialogues, E. Hamilton and H. Cairns (eds). Princeton, NJ: Princeton University Press. Plato, The Sophist. In The Collected Dialogues, E. Hamilton and H. Cairns (eds). Princeton, NJ: Princeton University Press. Plato, Parmenides. In The Collected Dialogues, E. Hamilton and H. Cairns (eds). Princeton, NJ: Princeton University Press. Popper, K. R. 1959. The Logic of Scientific Discovery. London: Hutchinson. Price, H. H. 1953. Thinking and Experience. London: Hutchinson. Quine, W. V. O.  1953. “On What There Is”, in From a Logical Point of View, Cambridge, MA: Harvard University Press, 1–19. Quinton, A. 1957. “Properties and Classes”. Proceedings of the Aristotelian Society 48: 33–58.
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a posteriori realism 11–13, 31–3, 102 absences 174, 177 abstract entities 5 accidental uniformity 44, 49 act 87 action 151 actual world 64 actualism 89 actuality 88–90 Adams, R. 67 aesthetics 5 aliens 71–3, 109 analysis, paradox of 14 Anderson, J. 3–5, 10, 14, 15, 29, 105 Anscombe, G. E. M. 54 Aquinas, T. 57 argument from illusion 120, 123, 124 argument from meaning 31, 32, 47 Aristotle 2, 29, 141 Armstrongianism 15, 16, 182 atomism 106, 108–10 attitudes 118 Austin, J. L. 16 Australian philosophy 3, 130 Ayer, A. J. 122, 125 Baxter, D. 182, 185, 186 behaviour 136, 139, 146, 147 behaviourism 90, 131, 133–5, 138 Being 4, 5
belief 124, 125, 133, 137, 149–64; see also inclination to believe abstract 154 action guiding 153 contradictory 155 expression 151, 152 false 124 general 161, 162 maps 153, 161, 162 non-linguistic 152 structures 153 Berkeley, G. 13, 81, 112–14, 119, 120–22, 127, 130, 131 best systems 46, 47 biological species 75 biology 132 Bird, A. 55, 59, 194 Black, R. 57 bodily sensations 54, 114–19 intransitive 116–19 location 118, 119 transitive 116, 117 Bradley, F. H. 8 Bradley’s regress 29, 101, 185, 193 Brentano, F. 136, 145, 147 bundles of sensations 123 Campbell, K. 27 categorical base 85, 90, 91, 135, 139, 140, 141, 151 categoricalism 89–94 causal net 109 causal power see powers
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David Armstrong causal theory of mind 134, 136, 138–47 causation 1, 53, 54, 87, 91, 92, 139, 159, 169 covering-law model 54 direct bodily awareness 54, 116 immanent 104 like causing like 107 centaurs 44 central nervous system 135, 136 central-state materialism 90, 131, 134–43 certainty 154, 155 classes 103 coherence theory 46, 47 colour 36, 74, 127 combinatorialism 15, 62, 67–76, 108, 109, 191, 192 compossibility 69, 73 compresence 103 concepts 153 conceptual analysis 16, 136 consciousness 129, 133, 143–5 conditionals 80–82, 90, 94, 135 contingency 183–5, 188–93 contingent beings 108 contingent identity 85, 90, 91, 140–43, 192 contingent necessitation 50, 56 cost-benefit analysis 13 counterfactuals 7, 42, 43, 45, 47, 49, 52, 63, 64; see also conditionals counterpart theory 66 David, M. 165 Demos, R. 174 Dennett, D. 37 Descartes, R. 9, 128, 130, 133, 149, 156 Devitt, M. 24, 25 direct realism 5, 116, 123–6, 145 discrimination 36, 153 disembodied existence 132, 141, 142 dispositional essentialism 58, 59 dispositions 4, 79–94, 133, 135, 139, 146, 150, 151, 161 as causes 91 über-disposition 93 distance 113 Dretske, F. 48
dualism 8, 130–33 attribute 132 bundle 131 interactionist 9 substance 131 Duns Scotus 29 duplicate worlds 66 echo-location 144 Eleatic principle 9–11, 32, 65, 87, 93 elementarism 47 Ellis, B. 58, 59, 74, 75, 83, 103 emotion 134 empiricism 8, 11–13, 41, 42, 128 Engel, P. 165 entailment 169 relevant 172 entailment principle 171, 172, 179 epiphenomena 83 epiphenomenalism 9, 93 epistemology 11, 12 error theory 127 ersatz realism 67, 69 essentialism 57–9, 74–6, 103, 104 ethics 5 extension 128 externalism 156–64 facts see states of affairs factualism 1, 2, 96–9 global 97 fallibilism 14 first philosophy 2 Forrest, P. 77, 180 four-dimensionalism 30, 31, 181 functionalism 136, 137 Gettier, E. 158 God 5, 7, 9, 41, 122 Goodman, N. 38, 39 haecceities 57, 72, 73, 104 hallucination 120, 123, 124 headless woman illusion 140 Heathcote, A. 54 Hegel, G. 8 Heil, J. 84, 86 Handfield, T. 93 Hempel, C. 42 Holton, R. 88
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Index Hume, D. 13, 26, 41, 42, 45, 54, 109, 149 Hume-independence 68 Hume-worlds 64 Humean distinctness 108, 109 Humean supervenience 47
Irish principle 31, 34 irrational believer 154, 155
ideal limits 26 idealism 7, 8, 10, 130, 131 identity 62, 77, 85–7, 91, 142; see also contingent identity numerical 132 identity of indiscernibles 57 identity theory of mind 135–8 token–token 137, 138 type–type 137 imagination 144 imitation 26, 27 immanent realism 15, 20, 28–31, 53 immanentism 7, 20 impenetrability 128 imperfect community 38 impotence 91 inclination to believe 124, 125, 145 incompatibility 35, 73–6 indeterminacy of experience 122, 125, 126 indexicality 64 indirect realism see representationalism induction 45, 52 inference to the best explanation 58 infinite complexity 70 inner connection 45, 51 inner theatre 133–5, 138 instantial invariance 193 instantiation 2, 28, 29, 96, 101, 170, 185–93 enfolding 191 fundamental tie 186, 187 necessary 186–9 nexus 186, 187 instrumentalism 10, 48 intention 139, 140, 146, 151 intentional inexistence 146 intentional object 136, 145, 146 intentionality 10, 11, 129, 130, 136, 143, 145–7 physical 147 intersection 188
KK-principle 155 knowledge 1, 12, 125, 126, 149–64 general 162 inferential 161–3 non-inferential 156–63 Kripke, S. 62, 85, 91, 142, 143
Jackson, F. 25 justification 126, 154–6, 160, 161 regress of 156, 162, 163
language 152 law of nature 1, 10–12, 32, 41–59, 91, 92, 105–7, 110, 159, 192 contingent 50, 51, 58, 61 contraposed 51 exclusion 51 functional 45, 52, 107 governing 51, 56, 58, 93 probabilistic 45, 52, 53 spatiotemporally limited 51 uninstantiated 53 law statement 48 Leibniz, G. 8, 63 Leibnizianism 191 Lewis, D. 7, 15, 24, 37, 38, 46, 47, 55, 57, 62–7, 71–3, 76, 99, 113, 136, 137, 143, 165, 185 limits 174, 176, 177 local regularities 43 Locke, J. 13, 104, 128 logic 5 logical positivism 16 Mackie, J. 4 manifestation 80, 84, 88, 90, 133, 139, 146, 151 Martin, C. B. 4, 81, 84–6, 88, 165, 166 material implication 42, 43 materialism 130, 134, 135; see also central-state materialism mathematics 76, 77, 180 matter 11, 128 Maurin, A.-S. 27 meaning 130 Melia, J. 63 Mellor, D. H. 55, 84, 93
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David Armstrong mental images 144, 145 mereology 99, 100, 180, 187 metaphysical necessity 142 metaphysics 13–17 Michotte, A. 54 microstructure 83–5, 90, 91 Mill, J. S. 46 mind 1, 9, 79, 89, 90, 129–47 moa 44, 51 modal logic 62, 63 modal realism 7, 37–40, 63–7, 71–3, 76, 113 modalism 62, 63 modality 1, 61, 62, 179 Molnar, G. 46, 83, 86, 88, 147, 173, 175–8 Moore, G. E. 8, 14 Mumford, S. 58, 75, 80, 83, 84, 88, 178, 194 Musgrave, A. 48 Nagel, T. 143 natural kinds 58, 75, 103 naturalism 1–17, 40–42, 65, 92, 128, 147, 163, 166, 177, 182, 183, 191 naturalness 33 necessities 73–6 necessity 41, 61, 76, 85, 185–94 Necker cube 86 negative truths 69, 106, 164, 173–8 incompatibility solution 174, 175 neutral monism 84–6 no-case uniformities 44 nomic necessitation 48–53, 55 exclusion 48 probabilification 48 nomic role 56, 57 nominalism 14, 20–24, 64, 105–6 class 23, 24 ostrich 24 predicate 21–3 resemblance 22, 23, 37–40 aristocratic 23 non-mereological composition 99–101 numbers 7, 9, 26, 77, 179, 180 omniscience 160 One over Many 20, 24, 33, 39 ontology 2
operationalism 10 Oppenheim, P. 42 order 41 ordinary-language philosophy
pain 134, 137, 143 pan-dispositionalism 87–9 Parmenides 8 partial consideration 104 partial identity 35, 36, 186, 187–93 participation 26, 27, 187 particularity 30, 31 particulars 1–3, 19, 20, 26–8, 95, 98, 103–5, 187–93 abstract 27 negative 175 thick 75, 104 thin 26, 29, 30, 69, 75, 96, 101, 104 perception 1, 5, 111, 120–25, 144–7, 157, 158 as belief acquisition 144–6, 152 idle 144 infallibility 36 object of 111–14, 120, 123 organ of 114 phenomenalism 81, 82, 90, 117, 120–23, 127 philosophy 6, 13–17, 153, 154 physical world 122 physicalism 2, 10, 11, 130, 134, 144, 145 physics 1, 10, 11, 126 Place, U. T. 83, 130 Plantinga, A. 67 Plato 9, 20, 25, 26, 32, 126, 173, 187 Platonic Forms 5, 7, 9, 20, 26, 27, 53, 180, 187 Popper, K. 44 possibilia 65, 89 possibilism 180 possibility 61–77 doxastic 70 possible worlds 9, 37–40, 63–7, 76, 108 contracted 72, 109 deflationism 108, 109 empty 72 expanded 72, 109 fictionalism 65, 69, 109 potency 87, 88
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Index potential 88 powers 4, 9–11, 32–5, 58, 59, 74, 76, 88, 127; see also dispositions predictability 41 presentism 181 Price, H. H. 4, 23, 83 primary qualities 127, 128 primitive identity 56, 57 principle of instantiation 29 properties 1, 26, 28 bundles of 103 categorical 59, 80, 83, 85, 88, 91–4 coextensive 38 conjunctive 33 disjunctive 33 essential 58, 62 geometrical 90 identity conditions 32, 57, 58 natural 33 negative 33 non-relational 34 relational 34 single-instance 38 spatiotemporal 83 propositions 7, 9, 26, 67, 153, 166–8, 170 purpose 146, 147, 151 quiddities 57, 58, 72, 73, 93 Quine, W. 24 Quinton, A. 24 Ramsey, F. 46, 153 realism 5 reasons 161 regularity theory 42–6, 49 rejection of bare particulars 29, 30 relations 5, 21, 34, 35, 102 causal 109 external 5, 34, 102, 109 higher-order 48, 53 internal 34, 38, 39, 58, 66, 71, 77, 102, 179, 180 part-whole 35, 36 polyadic 35 reflexive 34 relative atoms 70, 71 reliabilism 157–64 repeatables 31 representation 153
representationalism 116, 117, 120, 121, 127, 145 resemblance 34–9, 66 rigid designation 142, 143 Rodriguez-Pereyra, G. 20, 24, 37–40 Russell, B. 69, 104, 126, 166, 173–6, 180 Russell’s regress 22, 28, 38 Ryle, G. 80, 81, 89, 90, 125, 133–5, 144, 149–51, 165 scepticism 156 science 6, 11–13, 126–8 scientific realism 11 Searle, J. 130 secondary qualities 10, 11, 127, 128 sensations, see bodily sensations sense data 119–25 sensible qualities 119, 120 sets 180 shape 83 Shoemaker, S. 32, 87 sight 112–14 Simons, P. 177, 191 simple constituents 68 simplicity 46 Skyrms, B. 68, 70 Smart, J. 10, 127, 130 single-case uniformities 44 singularism 54 solidity 128 spacetime 4, 5 spatiotemporal system 1, 6, 8–10 Squires, R. 91 states of affairs 1–3, 5, 29, 30, 55, 95–110, 167, 168; see also totality facts atomic 69, 97, 108 composition 99–101 conjunctive 71 counterfactual 82 general 164 higher-order 69, 70, 105–7, 176 molecular 69, 108 negative 106, 164, 175, 176 non-symmetric 100 types 102 stimulus 80, 92, 136, 151 Strawson, P. 101 strength 46
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David Armstrong structure 83 subjunctives 42 substance 26, 31 bundle theory 26, 31 substrata 29 supernatural 7 supervenience 71, 97, 98 Swinburne, R. 87 Swoyer, C. 50, 57 tangible space 112 temporal parts 104 theism 8 thermometer view 157–60 three-dimensional knowledge 113–14 time 181 Tooley, M. 48, 53 totality facts 69, 105, 106, 109, 176, 177 transcendent realism 25–7, 37 transparency 140, 149 tropes 27, 28, 49 truth 77, 160, 161, 163–6; see also negative truth a priori 77 correspondence theory of 164, 165 general 174, 192 mathematical 179 modal 170, 179, 180 necessary 179, 180 necessary a posteriori 142 regress of 172 unknown 170 truth-bearer 166 truthmaker principle 4, 81, 82, 90, 101 an internal relation 101
truthmakers 77, 90, 94, 157, 158 minimal 168 of modal truths 108 truthmaking 165–82 cross-categorial 169 maximalism 171–3, 177, 178, 181 necessitarianism 169 relevant 171 touch 112–16 two-sided view 84, 85 unconfident examinee 155 uninstantiated values 45, 107 unity 109–10 universally quantified conditionals 42 universals 2, 5, 19–40, 49, 91, 92, 95, 98, 102, 104–5, 187–93; see also properties, relations determinable 35–7, 74, 75, 107 determinate 35–7, 107 higher-order 11, 12, 47, 48 immanent 14 instances 26 propositions 167 qualitative 74 transcendent 9, 14, 25–7 uninstantiated 26, 69, 72, 96 victory of particularity visual space 112
Warnock, G. 113 will 146 Williams, D. C. 27 Wittgenstein, L. 2, 56, 62, 68, 70, 95, 96, 105, 106, 133, 152 world-boundedness 65, 66