The suggestion that there is such a ‘metaphysical necessity’ derives from the work of Kripke and Putnam, who claimed that there are necessary a posteriori truths, i.e. necessary truths, which mere conceptual reflection on concepts could not show to be such; their necessity depends on how things are in the world, and not solely on the logical properties of the concepts we use to describe the world. Kripke, for example, argued that ‘Hesperus is Phosphorus’ (at any rate as this sentence was used in the seventeenth century) is a necessary a posteriori truth—when ‘Hesperus’ is the name of the actual planet which often appears in the evening sky shortly after sunset, and ‘Phosphorus’ is the name of the actual planet which appears in the morning sky shortly before sunrise.¹ These two are the same planet, the planet Venus. And they could not be other than the same planet for they consist of the same chunks of matter. Yet that they are the same planet depends on how things are in the world—it is no truth of logic that ‘Hesperus’ names the same object as ‘Phosphorus’. Likewise Putnam argued that ‘water is H₂O’ (at any rate as this sentence was used in the nineteenth century) is a necessary truth.² ‘Water’ names the actual stuff in our rivers and seas. That actual stuff, being H₂O, could not be other than H₂O. Yet that it is H₂O depends on how things are in the world—it is no truth of logic that that's what ‘water’ means. In both of these cases it is empirical investigation, not conceptual reflection, which enables us to discover these truths. By contrast, the argument goes, the logically necessary is that whose necessity is involved in the meaning of the words used. That is ‘all squares have four sides’, or ‘2 + 2 = 4’ could not but be true, given that the words mean what they do. Mere logic will reveal that these sentences are true in all possible (i.e. coherently describable) worlds. Hence their truth is knowable a priori—i.e. without the need for empirical investigation. But ‘Hesperus is Phosphorus’ and ‘water is H₂O’ also hold in all possible worlds. Yet since that necessity has its source in how things are, we may call it by a different name—‘metaphysical necessity’; and note that it is discoverable only a posteriori.

But the contrast is misleading. For not merely is the necessity of both kinds equally hard, but it has the same nature—the necessary is that which holds in all possible worlds, where ‘possible’ means ‘coherently describable’. The difference to which Kripke and Putnam drew our attention is not a difference between two sorts of necessity, but between two kinds of sentence which express logically necessary truths—those of which we can understand fully which claim they are making merely by understanding the words used, and those whose claims can only be understood fully when we know something about the world. We do not need to know anything about the world in order to understand ‘2 + 2 = 4’ or ‘all squares have four sides’. We know by mere reflection what their claim is, and mere reflection will then show us whether it is logically necessary. But we do not know what is being claimed by ‘water is H₂O’ until we know what water is. You may think that it is enough to know that the stuff in our lakes is water. But that is not enough—for if it were water is H₂O would mean the same as ‘whatever the stuff is in our lakes, it is H₂O’, and since the latter is only contingently true, so would be the former. No, the former is a claim about the essence of the actual stuff in our lakes and unless we know what that actual stuff is, we don't understand the claim. When we do understand it (namely, understand that the claim about ‘water’ is a claim about H₂O) we see that what makes it true are the same logical considerations as make ‘2 + 2 = 4’ true. ‘Water is H₂O and ‘Hesperus is Phosphorus’ are thus like ‘what I wrote 3 lines back is true’—when we know what the referring expression picks out, we can see the necessity of the sentence.

Such ‘metaphysical necessity’ will arise only where what constitutes the identity of a substance or property is something which causes or underlies the observable characteristics—the ‘stereotype’—by which we typically pick it out. Water is water in virtue of its underlying chemical essence being the same as that of (most of) various paradigm examples of water—the actual stuff in our rivers and seas. Likewise what makes Hesperus Hesperus is not being a planet which appears in the evening sky, but being made of chunks of matter which the actual planet is made of. Only in such cases do we need to know something about the world in order to know what claim is being made by the sentence. But for reasons given in the text (p. 56) sensory properties and events are not the properties and events they are in virtue of what causes or underlies them, but in virtue of what is accessible to the subject (and the same goes for other pure mental properties and events). Even if some physical properties and events are what they are in virtue of what underlies a stereotype, that underlying thing is clearly itself physical. It follows not merely that mental events are not the same as physical events, but they do not supervene on them, they are not constituted by them, and they are not realized in them—where the terms ‘supervene’, ‘constitute’ and ‘realize’ are meant to designate a species of metaphysical necessity. For the necessary connection would have to be one in which some physical event, described intrinsically in physical terms entailed some mental event described intrinsically in mental terms. And that clearly cannot be. No description of the public physical world entails that when you shine a certain light, I will have a blue image; or when you prick me with a needle, I will feel pain.

The suggestion that the mental ‘supervenes’ on the physical took a serious position in the philosophical debate, I suspect, in consequence of the work of Donald Davidson. In ‘Mental Events’ he described the thesis that the mental is supervenient on the physical as the view ‘that there cannot be two events alike in all physical respects but differing in some mental respect, or that an object cannot alter in some mental respect without altering in some physical respect’.³ Jaegwon Kim distinguished two kinds of supervenience, weak and strong.⁴ Weak supervenience of mental properties on physical ones requires that within each world necessarily any two objects (i.e. substances) which share all their physical properties also share all their mental properties. Strong supervenience requires that any object within a world which has all the same physical properties as some object in another world also has all the same mental properties. But, for the reasons given, since there is no entailment of the mental by the physical, neither form of supervenience can hold.

Definitions of the mental being ‘constituted by’ or ‘realized in’ the physical, typically lead by similar routes to a similar consequence—that the mental is not realized in or constituted by the physical. P. F. Snowdon defined being ‘constituted’ for facts.⁵ On his definition, the fact that Q is constituted by the fact that P if and only if it is a necessary truth that ‘if P, Q’; and Q has no independent causal influence from that of P. But since facts are the facts they are (in part) in virtue of the properties which are involved in them, arguments of the previous paragraph show that the mental facts are not constituted by physical facts. There are no necessary truths of the form ‘If S has P (physical property), S has M (mental property)’, because whatever physical properties S may have, there is always a possible world in which S does have M and another one in which he does not. A similar definition in terms of properties or events constituting other properties or events would of course yield the same result.

Putnam drew philosophical attention to the evident phenomenon that mental properties, such as being-in-pain could be instantiated in organisms with very different brain structures.⁶ Philosophers came to describe this phenomenon as the phenomenon of the ‘multiple realizability’ of mental properties. The concept of ‘realizing’ was taken over by Searle, to delineate the relation of ‘higher-level’ properties such as the liquidity of a substance to ‘lower-level’ properties such as its molecular structure. This, in his view, was the relation of the mental to the physical.⁷ Searle's account has been developed by Heil.⁸ He regards realization as a relation which holds between token-events. Yet this relation is said to be constrained by the supervenience relation which holds between ‘families of properties’:

But since mental properties do not supervene on physical properties, token mental events will not be realized in physical events.

None of these suggested connections between the mental and the physical hold, I have been arguing, if they are supposed to be necessary in the logical (or metaphysical) sense. If the connection is supposed to be a causal or physically necessary one between logically distinct entities, then of course the suggestion of such a connection becomes immensely more plausible. I have argued in the text that many mental events (though not all) are caused in whole or part by physical events.