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First published in 1985, D. M. Armstrong's original work on what laws of nature are has continued to be influential in the areas of metaphysics and philosophy of science. Presenting a definitive attack on the sceptical Humean view, that laws are no more than a regularity of coincidence between stances of properties, Armstrong establishes his own theory and defends it concisely and systematically against objections. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Marc Lange, illuminating its continuing importance and relevance to philosophical enquiry, this influential work is available for a new generation of readers.

Preliminary The strength of the case against the Naive Regularity theory of laws in particular, and the Regularity theory of laws in general, should now be evident. Some of the difficulties which have been rehearsed have been appreciated by Regularity theorists themselves. It is rather generally recognized that the class of Humean uniformities includes members which we do not wish to include among the laws of nature. A number of Regularity theorists have also recognized that it is not even easy to say what a uniformity is. The trouble here is provided by strange predicates such as ‘grue’. Suppose that all Fs are Gs, but that the predicates ‘F’ and ‘G’ pick out what we would naturally think of as a heterogeneous miscellany. Is this a Humean uniformity? Intuitively, no. But the unsupplemented Naive Regularity theory seems to lack the resources to eliminate such ‘uniformities’. More recently, Regularity theorists have faced up to the difficulties posed for their view by the apparent existence in nature of irreducibly probabilistic laws. There is no simple emendation of the Naive theory available for dealing with such laws. For instance, it is no good substituting relative frequencies for uniformities, because certain relative frequencies are only the most probable , not the inevitable, manifestations of probabilistic laws. The only way to preserve a Regularity theory seems to be to introduce objective single-case chances or propensities, and then assert that probabilistic laws are uniformities linking more ordinary properties with these new sorts of property. Against this background, let us consider various attempts to produce sophisticated versions of the Regularity theory. (For an account of the earlier literature, see Suchting, 1974.) The attempts fall under two heads in the first place. First, there are those who look for an external criterion to mark off ‘good’ from ‘bad’ uniformities. The criterion given is always, in a broad sense, epistemic. It is a matter of our cognitive attitudes to the uniformities – what evidence we have for them, and so forth. Second, there are those who look for an internal criterion, something about the uniformities themselves. There are, in turn, two types of view here. First, there is Brian Skyrms’ recent attempt (1980) to mark off the good uniformities as the resilient ones.

Truths are determined not by what we believe, but by the way the world is. Or so realists about truth believe. Philosophers call such theories correspondence theories of truth. Truthmaking theory, which now has many adherents among contemporary philosophers, is a recent development of a realist theory of truth, and in this book, first published in 2004, D. M. Armstrong offers the first full-length study of this theory. He examines its applications to different sorts of truth, including contingent truths, modal truths, truths about the past and the future, and mathematical truths. In a clear, even-handed and non-technical discussion he makes a compelling case for truthmaking and its importance in philosophy. His book marks a significant contribution to the debate and will be of interest to a wide range of readers working in analytical philosophy.

So much for truthmakers for truths of possibility. Our task now is to tackle the more difficult problem of necessary truths. AGAINST EXTENSIONAL ACCOUNTS OF NECESSITY We will begin, however, by criticizing extensional accounts of necessity. Let us temporarily assume modal realism, the real existence of the Lewisian pluriverse which contains all possible worlds. If one tries to combine this assumption with the acceptance of truthmaker theory, then presumably one must say that necessary truths are those that have truthmakers in every world. For certain necessary truths we might wish to limit the worlds to ones that contain the entities that are involved in this truth. Thus, for the truth that 7 + 5 = 12, we might restrict the worlds to those that contain at least twelve entities because smaller worlds, if there are such possible worlds, seem to furnish no truthmakers for this truth. But this restriction seems not particularly important here. We pose once again that wonderful dilemma: the Euthyphro question. In the dialogue of that name, Socrates asks whether the piety of certain actions is constituted by the fact that the gods love these actions, or whether instead the acts are independently pious and therefore are loved by the gods. In the same sort of way, we can ask whether the necessity of a particular necessary truth is constituted by the fact that it has a truthmaker in all possible worlds, or whether instead the truth is independently necessary and therefore it has a truthmaker in all these worlds.

INTRODUCTORY Given properties and relations in our ontology, one great issue is whether they are repeatables (universals) or unrepeatables (tropes). We have opted for universals. But another large question in the theory of properties and relations demands our attention, an issue in great degree independent of the dispute between universals and tropes. It is an issue of equal importance, though perhaps less well canvassed. Concentrating, for convenience, on properties as opposed to relations, we think of them as bestowing powers upon the particulars that have them. A property that bestows no power will not be easy to detect! Conversely, if a particular has a power, either to act or be acted upon, then that is a property of the particular. The question arises, therefore, whether a property's nature is exhausted by the powers that it bestows, or whether instead the property, in itself, is to be distinguished from those powers. To discuss and come to a position on this issue is the main business of this chapter. Properties (and relations) are thought of by some philosophers as having a nature that is self-contained, distinct from the powers that they bestow. We shall call this position Categoricalism . Others think of them as having a nature that essentially looks beyond the particulars they qualify, outward to potential interactions with further particulars, and where this nature is exhausted by these potential interactions. This view may be called Dispositionalism .

In this important study D. M. Armstrong offers a comprehensive system of analytical metaphysics that synthesises but also develops his thinking over the last twenty years. Armstrong's analysis, which acknowledges the 'logical atomism' of Russell and Wittgenstein, makes facts (or states of affairs, as the author calls them) the fundamental constituents of the world, examining properties, relations, numbers, classes, possibility and necessity, dispositions, causes and laws. All these, it is argued, find their place and can be understood inside a scheme of states of affairs. This is a comprehensive and rigorously this-worldly account of the most general features of reality, argued from a distinctive philosophical perspective, and it will appeal to a wide readership in analytical philosophy.

This is a study of a crucial and controversial topic in metaphysics and the philosophy of science: the status of the laws of nature. D. M. Armstrong works out clearly and in comprehensive detail a largely original view that laws are relations between properties or universals. The theory is continuous with the views on universals and more generally with the scientific realism that Professor Armstrong has advanced in earlier publications. He begins here by mounting an attack on the orthodox and sceptical view deriving from Hume that laws assert no more than a regularity of coincidence between instances of properties. In doing so he presents what may become the definitive statement of the case against this position. Professor Armstrong then goes on to establish his own theory in a systematic manner defending it against the most likely objections, and extending both it and the related theory of universals to cover functional and statistical laws. This treatment of the subject is refreshingly concise and vivid: it will both stimulate vigorous professional debate and make an excellent student text.

David Armstrong's book is a contribution to the philosophical discussion about possible worlds. Taking Wittgenstein's Tractatus as his point of departure, Professor Armstrong argues that nonactual possibilities and possible worlds are recombinations of actually existing elements, and as such are useful fictions. There is an extended criticism of the alternative-possible-worlds approach championed by the American philosopher David Lewis. This major work will be read with interest by a wide range of philosophers.

The Distinction between Concepts and Ideas Propositions have an inner complexity. If a proposition is believed (restricting ourselves to beliefs for the present) then the belief-state will have to have an inner complexity which mirrors the complexity of the proposition. How is this complexity of the belief-state to be conceived? The analogy of a map seems useful. Suppose that what is believed is that Perth is to the west of Sydney. In a map, this putative state of affairs would be represented by two marks on the map, one labelled ‘Perth’, the other ‘Sydney’, the former being to the left of the latter. These marks, thus labelled and thus related, represent a state of affairs. Let us think of the belief-state as a sort of map. It will contain elements, like the map-marks labelled ‘Perth’ and ‘Sydney’, which have a certain interpretation. These elements will be related in certain ways, just as the map-marks are related in a certain way in the map, and the relations of the elements will also have a certain interpretation. Given this interpretation of the elements and the relations, the elements-in-relation to be found in a particular belief-state determine what it is that is believed . (The elements may themselves be complex, involving further elements-inrelation, but, since the human mind is finite, we must in the end come to elements whose parts do not represent.) In general, at least, the relations in the belief-state will represent relations in the world, and the elements in the belief-state the terms of relations in the world.

The Classical account of knowledge Having attempted to give an account of what it is for A to believe that p, and having said something about what it is for a belief to be true, we ask now what it is for A to know that p. There is an analysis of the concept of knowledge which has been put forward again and again in the history of philosophy. Its first recorded occurrence is in Plato's Meno (87–8). According to this analysis A knows that p if, and only if, three conditions are satisfied. Two of these conditions differ somewhat (and not merely verbally) in different formulations. But there is a common form which all the formulations satisfy. A knows that p if, and only if: The Truth-condition is satisfied : p is true The Belief-condition is satisfied : A believes that p or A is certain that p, etc . The Evidence-condition is satisfied : A has adequate evidence for p or A has good reasons for believing that p, etc . Knowledge, on this view, is true belief properly evidenced, or some similar formula. This classical analysis of knowledge seems a good place to begin our own investigations, so we will proceed by examining the three suggested conditions. The present chapter deals only with the first two: The Truth-condition and the Belief-condition. The Truth-condition We can begin with something uncontroversial. I do not think that there has ever been any serious doubt that it is a necessary condition for knowledge that what is known be true .

In this chapter various topics will be treated in a rather miscellaneous way, with the object of rounding out our account of the nature of knowledge. In the last section it will be argued that not only does the concept of knowledge presuppose the concept of belief, but that the concept of belief presupposes the concept of knowledge. Knowledge of Knowledge It is possible for A to know that p without knowing that he knows it (Kap & ∼ KaKap), and even for A to know that p and disbelieve that he knows it (Kap & Ba ∼ Kap). Nevertheless, when we know we very often know that we know and, indeed, one who says ‘I know that p’ implicitly commits himself to the claim that he knows that he knows that p. What conditions have to be satisfied for such knowledge of knowledge? ‘A knows that A knows that p’ (KaKap) is simply a substitutioninstance of ‘A knows that A 1 knows that p’ (KaKa 1 p) for the special case where a 1 = a. In what follows I give an account of the general case which can then be applied without the slightest difficulty to the special case. In the case where A knows that he himself knows something this knowledge of knowledge will often be non-inferential, a situation which seldom if ever occurs in the third person case. But we have given the same account of both inferential and non-inferential knowledge of particular states of affairs. There are two things to be noted about knowledge of knowledge.