After introducing the conception oflaws of nature both as relations holding between universals, and as universals, in Chapter 6, we tried in the next three chapters to extend the account to functional laws, to uninstantiated laws and to probabilistic laws. It was argued that functional laws are higher-order laws: laws which dictate, or in some possible cases merely govern, lower-order laws. It was argued that uninstantiated laws are not really laws at all, but are rather counterfactuals about what laws would hold if certain conditions were realized. In the case of probabilistic laws it was argued that our original schema can be applied fairly straightforwardly. Such laws give probabilities of necessitation, probabilities less than probability 1. Deterministic laws are laws where the probability of necessitation is 1.

There are a great many other questions to be considered concerning the possible forms which a law of nature can take. In this chapter various of these issues will be taken up.

SCIENTIFIC IDENTIFICATION

We may begin from the point that, if our general account oflaws of nature is to be sustained, they must contain at least two universals. What then of theoretical identifications, such as the identification of temperature with mean kinetic energy, or laws of universal scope, that is, laws having the form: it is a law that everything is F? The present section will be devoted to theoretical identification.

Laws of nature characteristically manifest themselves or issue in regularities. It is natural, therefore, in Ockhamist spirit, to consider whether laws are anything more than these manifestations.

When philosophers hear the phrase ‘Regularity theory’ they are inclined almost automatically to think of a Regularity theory of causation. It is important, therefore, to be clear at the outset that what is being considered here is a Regularity theory of laws.

The Regularity theory of causation appears to be a conjunction of two propositions: (1) that causal connection is a species of law-like connection; (2) that laws are nothing but regularities in the behaviour of things. It is possible to deny the truth of (1), as Singularist theories of causation do, and then go on either to assert or to deny the truth of (2). Alternatively, (1) can be upheld, and either (2) asserted (yielding the Regularity theory of causation), or (2) denied. The reduction of cause to law, and the reduction of law to regularity, are two independent doctrines. They can be accepted or rejected independently.

It therefore appears that the Regularity theory of causation entails the Regularity theory of laws of nature, because the latter theory is a proper part of the former. By the same token, the Regularity theory of laws of nature fails to entail the Regularity theory of causation. Our concern is with the Regularity theory of law.

In the previous chapter we saw that there are innumerable Humean uniformities which we are unwilling to account laws of nature or manifestations of laws of nature. Being a Humean uniformity is not sufficient for being a law of nature. The Naive Regularity theory is therefore false. The Regularity theorist must find some way to distinguish between Humean uniformities which are laws and those which are not, without compromising the spirit of the Regularity theory.

In this chapter we will investigate cases, or possible cases, where laws of nature exist but Humean uniformities are lacking. Clearly, they pose a potentially still more serious threat to the Regularity theory. In the last two sections of the chapter we will consider cases where there is a failure of correspondence between the content of the law and the content of its manifestation.

SPATIO-TEMPORALLY LIMITED LAWS

From time to time it is suggested by philosophers and scientists that the laws of nature may be different in different places and times. Obviously, this is not just the suggestion that the same sort of thing may behave differently in different sorts of conditions. The latter is compatible with the laws of nature being omnitemporally uniform. The suggestion is rather that the same sorts of thing may behave differently at different places and times, although the conditions which prevail are not different except in respect of place and time.

Suppose it to be granted that laws of nature, if underived, are irreducible relations between universals. Should those relations be thought of as holding necessarily? Must they obtain ‘in every possible world’? Suppose that event a precedes event b by a certain interval of time. This is a first-order state of affairs having the form R(a,b). It would be generally conceded that this state of affairs might have been other than it is. But suppose that we ascend to a secondorder state of affairs, to a law of nature N(F,G). Here, it may be argued, we have a state of affairs which could not be other than it is.

In what follows I shall argue, on the contrary, that N(F,G) and R(a,b) are both contingent states of affairs.

The obvious objection to the view that a true statement of a law of nature, such as ‘N(F,G)’, is a necessary truth is that it is discovered to be true a posteriori, using the method of hypothesis, observation and experiment. By contrast, the necessary truths of logic and mathematics are, in general at least, established a priori, by thought, reason and calculation alone.

This argument is not conclusive. The distinction between truths known, or rationally believed, a posteriori and those known, or rationally believed, a priori, is an epistemological one. Kripke has raised the question why it should determine the logical status of the truths known, or rationally believed.

THE FORM OF PROBABILISTIC LAWS

In the last two chapters we gave an account of functional laws as higher-order laws, that is, laws governing laws. We also proposed a (non-Realist) account of uninstantiated laws. Our next task is to try to bring irreducibly probabilistic laws within our scheme.

At first sight there appears to be some difficulty in this undertaking. Suppose it to be a law that Fs are Gs, and suppose that a is F. We then have:

1. (1) (N(F,G)) (a's being F, a's being G)

where N(F,G) is a necessitation relation holding between the two states of affairs, a's being F and a's being G, a necessitation holding in virtue of the two universals involved in the two states of affairs.

Suppose, however, that the law which links F and G is irreducibly probabilistic. There is a probability P(1 > P > O) that an F is a G. Suppose, again, that a is F. It would be simple and elegant to analyse the situation in just the same way as in the case of the deterministic law:

1. (1) ((Pr:P) (F,G)) (a's being F, a's being G)

where ((Pr:P) (F,G)) gives the objective probability of an F being a G, a probability holding in virtue of the universals F and G.

But, of course, there is an obvious difficulty. Because the law is only probabilistic, the state of affairs, a's being F, may not be accompanied by the state of affairs, a's being G. The ‘relation’ ((Pr:P) (F,G)) will then lack its second term.

THE NEED FOR UNIVERSALS

It will be assumed from this point onwards that it is not possible to analyse:

1. (1) It is a law that Fs are Gs

as:

1. (2) All Fs are Gs.

Nor, it will be assumed, can the Regularity theorist improve upon (2) while still respecting the spirit of the Regularity theory of law.

It is natural, therefore, to consider whether (1) should be analysed as:

1. (3) It is physically necessary that Fs are Gs

or:

1. (4) It is logically necessary that Fs are Gs

where (3) is a contingent necessity, stronger than (2) but weaker than (4). My own preference is for (3) rather than (4), but I am not concerned to argue the point at present. But what I do want to argue in this section is that to countenance either (3) or (4), in a form which will mark any advance on (2), involves recognizing the reality of universals.

We are now saying that, for it to be a law that an F is a G, it must be necessary that an F is a G, in some sense of ‘necessary’. But what is the basis in reality, the truth-maker, the ontological ground, of such necessity? I suggest that it can only be found in what it is to be an F and what it is to be a G.

In order to see the force of this contention, consider the class of Fs: a, b, c … Fa necessitates Ga, Fb necessitates Gb … and so on.

I find myself in the position that Jerome Bruner (1976) found himself in a few years before me. I agreed to give a Herbert Spencer lecture; I planned to give a lecture on the topic of scientific explanation; I intended to discuss a particular controversy in that field, the controversy about whether scientific theories are ‘incommensurable’, about whether there is any ‘convergence’ in scientific knowledge; but I felt increasing dissatisfaction with this entire idea as the day approached. Bruner's dissatisfaction led him to some reflections about the history and present state of psychology. I intend to follow his example and ruminate on the activity itself, the activity of philosophy of science, in my own case, and on certain dissatisfactions I feel with the way that activity has been pursued, rather than discuss a particular issue within it. However, the particular issue I mentioned will come up in the course of these ruminations.

Logical positivism is self-refuting

In the late 1920s, about 1928, the Vienna Circle announced the first of what were to be a series of formulations of an empiricist meaning criterion: the meaning of a sentence is its method of verification. A. J. Ayer's Language, Truth and Logic spread the new message to the English-speaking philosophical world: untestable statements are cognitively meaningless. A statement must either be (a) analytic (logically true, or logically false to be more precise) or (b) empirically testable, or (c) nonsense, i.e., not a real statement at all, but only a pseudostatement. Notice that this was already a change from the first formulation.

I once got into an argument after dinner with my friend Zenon Pylyshyn. The argument concerned the following assertion which Pylyshyn made: ‘cognitive psychology is impossible if there is not a well-defined notion of sameness of content for mental representations’. It occurred to me later that the reasons I have for rejecting this assertion tie in closely with Donald Davidson's well-known interests in both meaning theory and the philosophy of mind. Accordingly, with Zenon's permission and (I hope) forgiveness, I have decided to make my arguments against his assertion the subject of this paper.

Mental representation

Let us consider what goes on in the mind when we think ‘there is a tree over there’, or any other common thought about ordinary physical things. On one model, the computer model of the mind, the mind has a ‘program’, or set of rules, analogous to the rules governing a computing machine, and thought involves the manipulation of words and other signs (not all of this manipulation ‘conscious’, in the sense of being able to be verbalized by the computer). This model, however, is almost vacuous as it stands (in spite of the heat it generates among those who do not like to think that a mere device, such as a computing machine, could possibly serve as a model for something as special as the human mind). It is vacuous because the program, or system of rules for mental functioning, has not been specified; and it is this program that constitutes the psychological theory.

Hegel contributed two great and formative ideas to our culture, ideas between which there is some tension. On the one hand, he taught us to see all our ideas, including above all our ideas of rationality, our images of knowledge, as historically conditioned. After Hegel it was, for example, no longer possible to see Descartes' solipsistic methodology as a pure idea, a thought anyone might have had at any time (even if that is the way we still teach Descartes); the connections between individualism in methodology and the replacement of the whole hierarchical world view of the middle ages by the individualistic and competitive world view of early capitalism have been a subject for reflection ever since Hegel (not just since Marx). On the other hand, Hegel postulated an objective notion of rationality which we (or Absolute Mind) were coming to possess with the fulfillment of the progressive social and intellectual reforms which were already taking place. In the subsequent decades many accepted this idea of a new, a modernist, conception of rationality, while refusing to identify it with Hegel's system. Hegel's system has, indeed, been regarded as something preposterous. But the positivist conception of scientific rationality as the specifically modern product which is fated to replace older notions once and for all (and to replace the sequence of ‘determinate negations’ with a steady progressive evolution, an eternal self-improvement of ‘the scientific method’) owes much to the Hegelian conception.

The thing that strikes everyone who looks at quantum mechanics is ‘superposition of states’. For example, one can have a hydrogen atom in such a condition that the probability that it is at one energy level is 25% and the probability that it is at the next higher energy level is 75%. Now, the problem is that one should not think of this as meaning that the atom is either at the first energy level or the second but we don't know which. What then does it mean? That is the question! That is what ‘interpretations’ of quantum mechanics are all about.

I shall not review the argument to show that one cannot think of it in a classical way, that one cannot think of it as meaning that the energy level is one or the other (nor can one think of it as meaning that the hydrogen atom is at an in-between energy level). Physicists gave up that way of viewing it (which is, unfortunately, the only way of viewing it that one can ‘explain to a barmaid’, in Rutherford's phrase) long before there were more-or-less formal proofs that one cannot view it that way.

Formal proofs that there are no hidden variables are not, I think, what has played a role in the thinking of physicists; what physicists are more impressed by is the fact that if one tries to think of it that way then it doesn't square with any intelligible physical picture at all.

When one reads Quine, or Carnap, or Wittgenstein one encounters virtually no references to literature, or, indeed, to the arts. Yet certain themes in literature have a striking resemblance to themes in analytical philosophy. Thus Carnap celebrates the conventional, the artificial, the planned; Wittgenstein the natural, the organic, the traditional (although Wittgenstein's celebration of the traditional has a distinctively modern quality; it is the traditional without any of the traditional premises that he wishes us to retain). A deep examination of the notion of convention is one of the great contributions of analytical philosophy. In this essay, I want to review that contribution. At the end, I shall return to the remark that themes in the discussion have echoed themes in literature, and permit myself to speculate on what that shows about philosophy itself.

The conventional versus the natural

The nature of logical and mathematical truth has been a problem for empiricism from the beginning. Hume's explanation of logical necessity, that it has to do with one idea ‘containing’ another, presupposed the atomistic and sensationalistic psychology which he helped to found. ‘All bachelors are unmarried’ is analytic (true in virtue of the relations among our ideas) because the idea of being unmarried is contained in the idea of a bachelor; but does this mean simply that my mental picture of a bachelor happens to be a picture of an unmarried person? Kant retained some of the flavor of Hume's verbal formulation while giving up the identification of ideas with mental pictures or anything like mental pictures.

In 1922 Skolem delivered an address before the Fifth Congress of Scandinavian Mathematicians in which he pointed out what he called a ‘relativity of set theoretic notions’. This ‘relativity’ has frequently been regarded as paradoxical; but today, although one hears the expression ‘The Löwenheim–Skolem paradox’, it seems to be thought of as only an apparent paradox, something the cognoscenti enjoy but are not seriously troubled by. Thus van Heijenoort writes, ‘The existence of such a “relativity” is sometimes referred to as the Löwenheim–Skolem paradox. But, of course, it is not a paradox in the sense of an antinomy; it is a novel and unexpected feature of formal systems.’ In this paper I want to take up Skolem's arguments, not with the aim of refuting them but with the aim of extending them in somewhat the direction he seemed to be indicating. It is not my claim that the ‘Löwenheim–Skolem paradox’ is an antinomy in formal logic; but I shall argue that it is an antinomy, or something close to it, in philosophy of language. Moreover, I shall argue that the resolution of the antinomy – the only resolution that I myself can see as making sense – has profound implications for the great metaphysical dispute about realism which has always been the central dispute in the philosophy of language.