Metaphysical Necessity Is Not Logical Necessity

Metaphysical Necessity Is Not Logical NecessityAuthor(s): Robert FarrellSource: Philosophical Studies: An International Journal for Philosophy in the AnalyticTradition, Vol. 39, No. 2 (Feb., 1981), pp. 141-153Published by: SpringerStable URL: http://www.jstor.org/stable/4319445 .

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ROBERT FARRELL

METAPHYSICAL NECESSITY IS NOT LOGICAL NECESSITY

(Received in revised form 28 May, 1980)

Metaphysical 1 necessity has been presented by Saul Kripke and by Hilary Putnam as being both broad in scope and metaphysical - perhaps more accu- rately, ontological - in character. Discussing the claim that water is H20, Putnam has claimed this:

Once we have discovered that water (in the actual world) is H2 0 nothing counts as a possible world in which water isn't H20. In particular, if a 'logically possible' statement is one that holds in some 'logically possible world', it isn't logically possible that water isn't H2 0.1

That is, he has claimed that if water is H20, it is logically necessarily so, it is true in all possible worlds. In this matter of scope, Kripke agrees. Dis- cussing a similar case he writes that

...such statements ...are not contingent truths but necessary truths in the strictest possible sense.2

Further, for Kripke,

a good deal of what contemporary philosophy regards as mere natural necessity is actually necessity tout court.3

It is this shared view of Kripke and Putnam that I wish to discuss, putting aside the second claim as to the metaphysical - or ontological - character of the necessity of such claims as 'Water is H2 O'. In the two sections which follow I shall argue that Kripke and Putnam are wrong in their shared view of the scope of metaphysical necessities; I shall argue that there is a possible world in which - to introduce the example I shall use for the rest of my arguments - gold fails to have atomic number 79, despite the agreement on the part of Kripke and Putnam, that it is, if true, metaphysically necessarily true that gold have atomic number 79.

It is crucial to an acceptance of the metaphysical necessity of such claims

Philosophical Studies 39 (1981) 141-153. 0031-8116/81/0392-0141$01.30 Copyright ? 1981 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston, U.S.A.



142 ROBERT FARRELL

as 'Water is H2 O' and 'Gold has atomic number 79' that substance terms such as 'gold' be taken to have a semantics analogous to that Putnam sketches for the case of 'water':

Suppose I point to a glass of water and say 'this liquid is called water' (or 'this is called water' if the marker liquid' is clear from the context). My 'ostensive definition' of water has the following empirical presuppositions: that the body of liquid I am pointing to bears a certain sameness relation (say, x is the same liquid as y, or x is the sameL as y,) to most of the stuff I and other speakers in my linguistic community have on other occa- sions called 'water'. ...the relation sameL is a theoretical relation: whether or not something is the same liquid as this may take an indeterminate amount of scientific investigation to determine. Moreover, ...future investigation might reverse even the most 'certain' example.4

It is worth remarking here that, as Putnam's last sentence indicates, scientific investigation 'determines' what is the sameL as what only in the sense of discovering what the relation sameL is, not- in the sense of constituting what the relation sameL is to be (at some stage or other of scientific development) as has sometimes been thought.

Nor is the relation sameL to be understood as relating only actual samples of liquid, according to Putnam:

...we can understand the relation sameL (same liquid as) as a cross-world relation by understanding it so that a liquid in world W, which has the same important physical properties (in W, ) that a liquid in W2 possesses (in W2) bears sameL to the latter liquid .'

My strategy will be to present a possible world in which gold fails to have atomic number 79, and thus show that, even while I take 'gold' to have the sort of semantics Putnam claims it to have, and even while I concede the truth, hence the metaphysical necessity, of 'gold has atomic number 79', it is not logically necessarily true, not true in all possible worlds that, gold have atomic number 79. The most that can be claimed for metaphysical necessity is that it is truth in all those possible worlds which share certain structural traits. Since the traits in question - I shall not discuss them - will be physical traits metaphysical necessity will be a variety of natural necessity, at least as it is specified by Karl Popper.6 Showing that will occupy Section II. In Section III I shall dicuss what happens when sameL is replaced by a weaker, similarity, relation; the results of Section II will carry over to Section III.

II

I shall argue that the necessities provided by Putnam are not, as he thinks, logically necessary, but at most physically necessary: I shall be arguing that



ON METAPHYSICAL NECESSITY 143

there are possible worlds in which such structural claims as 'Water is H2 0' and 'Gold has atomic number 79' are false, even if they are true in the actual world. I shall discuss the latter case of gold, and shall consider a possible world W.

In W there are forces at play, and particles of kinds, not to be found in the actual world. To be more specific, there are extra kinds of fundamental particles in W, and these particles find their ways into the nuclei and the shells of atoms in W. These fundamental particles have something we'll call load, analogous to, but different from, our familiar electric charge. In W there are both the familiar charged, and the unfamiliar loaded, kinds of fundamental particle.

In W the physico-chemical properties of atoms and of the substances which are composed of them depend upon the sums of the changes and the loads of the orbiting particles of atoms, and upon the equal but opposite charge plus load carried by the nucleus. Not all atoms in W contain loaded particles, though; indeed there are quite a few which contain only charged particles. In particular, there are quite a few atoms with just 79 orbiting electrons, and with 79 nuclear protons, not to mention the neutrons. These unloaded atoms can be distinguished from their loaded companions only with great difficulty, even by the advanced scientists in W. These unloaded atoms do not constitute a natural kind in W, for they are, from the point of view of W - physics, structurally identical in important physical ways with loaded atoms of load plus charge 79. They constitute only a subset of a kind.

In the actual world, we shall assume, gold has atomic number 79, and it is this fact which is responsible for the characteristic behaviour of samples of gold. If Putnam is nrght, gold has atomic number 79 necessarily. I want to argue, with W in mind, that even if gold does actually have atomic number 79, it fails to do so necessarily - that there is a possible world in which gold does not have atomic number 79, that gold has atomic number 79 only contingently. W is such a possible world.

Before W can be of positive relevance to my intended conclusion, it has to have samples of gold in it. W was specified as having in it those unloaded atoms with the 79 nuclear protons and the 79 orbiting electrons. We could further specify that there are sufficient such unloaded atoms in W and that they are so distributed that there are sizable samples of metal in W composed entirely of them. What is more, we could suppose those samples to fit our



144 ROBERT FARRELL

stereotype of gold. Clearly there is gold in W: there is a metal which fits our stereotype of gold, samples of which behave as they do because they have atomic number 79.

Is it true in W that gold has atomic number 79? In the light of what was just said, it might seem so. I shall argue against this view.

According to Putnam the question of whether or not there is gold in W is to be settled by discovering the cross-world relation sameM that holds between individuals, even if these individuals are in different possible worlds, if and only if those individuals are samples of the same metal. For Putnam the relation sameM is a structural one, relating individuals on the basis of their 'important physical properties'. An individual in W will be a sample of gold if it bears the structural relation sameM to each actual sample of gold, that is, to each sample of gold in the actual world.

The relation sameM will be, as we would expect, an equivalence relation: it will hold between any pair of samples of gold in the actual world and between any actual sample of gold and any of those special unloaded samples we specified as being in W with 79 nuclear protons and 79 orbiting electrons. Moreover sameM will hold between those pairs of samples in W, each of which has 79 orbiting particles, all charged, all loaded, or with some of each.

We thus have a chain linking any actual sample of gold with any of those samples of substance in W which are constituted of atoms with 79 orbiting particles. There are just two links in the chain: one links an actual sample of gold with a sample of the substance in W with the special property that it lacks loaded particles, and thus having 79 orbiting electrons and 79 nuclear protons; the second links that W-sample with any other W-sample which has 79 orbiting particles and 79 nuclear particles which are either charged or loaded.

Because sameM is an equivalence relation, and because of the facts just outlined, all those samples of charge plus load 79 in W bear that structural relation to all actual sample of gold. They are thus gold. But, in W, some atoms of gold fail to have atomic number 79, for atomic number takes into account only charged particles. It is rightly silent about loaded ones. It is false in W that (all) gold has atomic number 79: there is thus no necessity in the actual world to the claim that gold has atomic number 79. It is most contingently true, and metaphysical necessities are not logical necessities, or the strictest kind of necessity, but at most kind of natural necessity, in that they




are true only in possible worlds with a certain kind of basic physical structure, a structure shared with the actual world.

Does this conclusion follow? Let us consider three objections to the argument which leads up to it; the objections will centre on the relation sameM which played a crucial role in the argument, and upon the property of being loaded.

To block the conclusion, one could rule out the relation sameM and replace it with a new one same* which is the structural relation that holds between actual individuals if and only if they are samples of the same metal. Then loaded atoms of the sort that occur in W won't count as gold, and necessity will have been saved. But there are problems with this way.

The relation same* can't be a relation-in-extension (a set of ordered pairs), for then, given the way in which it has been defined, it is only actual entities that can be the same* as one another. There can never be a sample of substance in any merely possible world which bears the relation same* to any actual sample of any substance. Consequently, there can be no gold, nor any other familiar metal, in any merely possible world. Treating samem as a relation-in-extension yields the result that gold has atomic number 79 in all possible worlds in which there is gold, and hence the result that gold has atomic number 79 of necessity, only because it allows gold to occur only in the actual world. No-one defending metaphysical necessity against my arguments could welcome that as a way of restoring necessity to 'Gold has atomic number 79'.

If we insist that same* be a relation-in-extension, but allow it to be a cross-world relation, we are faced with the problem of determining which additional pairs of individuals fall within the domain of the relation. And as we have access only to pairs of actual individuals, our only way to generate new pairs of relata is to treat same* as a relation-in-intension.

Let us then treat same* as a relation-in-intension. Relations-in-intension are not the most welcome of entities; but let us

ignore that. More pressing is the question as to which of the tolerated relations-in-intension same* is to be, for there any many relations-in-intension which have as their actual extension the set of pairs of actual samples of gold.

We could, in a way parallel to the case of relations-in-extension, decide to take the minimal relation-in-intension which has as its actual extension the



146 ROBERT FARRELL

set of pairs of actual samples of gold to be same*. There are, however, four problems with that approach.

(1) The currently fashionable way of seeing a relation-in-intension as a set of pairs of possibilia will not yield us a satisfactory solution here. The minimal such relation will be our old friend the set of ordered pairs of actual samples of gold. And we've already rejected that as a candidate for the role of same* . We have to leave this neat picture of relations-in-intension if we are to get anywhere; the intensions involved in relations-in-intension have to come to more than sets of ordered pairs of possibilia.

(2) Once we've given up the neat fashionable account of relations-in-intension we are left without the accompanying neat account of minimality, and the guarantee that there will be a minimal relation-in-intension of the right kind at all. What is minimality now? We can say that R is a minimal structural relation if it is a structural relationship such that, for every structural relationship S with the correct actual extension,

(x)(y) Necessarily (If x Ry, then x Sy),

where the variables range over both actual and possible objects. To stop this version of minimality from landing us back with the twice-rejected relation we need some account of necessity other than of truth in all possible worlds. From needing an independent theory of intension we have merely moved to needing an independent theory of necessity as well. It is not clear what these independent theories could be, or that should we come up with such theories, there would be a minimal relation-in-intension to play the role of same*.

(3) And should we have such a relation-in-intension nothing so far has shown that it won't be sameM. It might seem obvious that it can't be, since we can always 'add' to sameM some additional intensional content so as to make it more minimal. But unrestricted additional of intensional content will have us trimming our allowable minimal structural relation R back to our old rejected friend. The principle that ruled out sameM will also rule out any other relation-in-intension than our previously rejected relation-in-extension.

(4) Minimality even if we can make sense of it lacks much in the way of motivation, save the motivation to rule out the original sameM which gave trouble to the proponent of metaphysical necessity.

Instead of relying on minimality alone we could try something else: we could add an epistemic or scientific constraint. The relation samem would now be the minimal structural relation needed by science to give a full and




accurate account of the nature of the actual world. Here the science in question is not science as it is now, but as it will be - or would be - in the Peircean limit. This metaphor of a limit has to be given nonmetaphorical support before it becomes usable here. It has to be shown that science has only one available candidate for a Peircean limit - otherwise a unique swnem will not be forthcoming.

This way of selecting same*, then, depends upon a commitment to relations-in-intension and, in order to get a sufficiently exclusive intension, both to a theory of intensions and necessity other than in terms of possible worlds and possible objects, and to a thesis that reality is uniquely scientifi- cally representable.

On top of these problems with this way of ruling out the loaded atoms in W as atoms of gold there is the further problem of any appeal to intensions, or to such things as stereotypes. For a scientific theory, even a limiting Peircean one, places constraints only on the extensions of its terms. It is in- different to matters of intension or stereoptype which fail to be reflected in those constraints it places upon extensions. So why should any appeal to intensions - or to other more acceptable surrogates - be thought to provide a solution here?

It seems unlikely that a proponent of the claim that metaphysical necessity is truth in all possible worlds can come up with an acceptable new relation, same*, to block the argument to the conclusion that there is a possible world in which gold fails to have atomic number 79. To the extent that this is unlikely, it is unlikely that metaphysical necessity is logical necessity; that it is, rather, as I remarked earlier no more than truth in all those possible worlds whose basic physical structure is that of our actual world, and that, if we follow Popper, is just natural, or physical necessity. We are able to say, in all likelihood, and standing Kripke on his feet: a good deal of what contemporary philosophy regards as necessity tout court is actually mere physical necessity.

Our second objection concems load. It has been suggested - by Putnam, in conversation - that load may be just a variety of charge. Insofar as that is true, gold in W continues to have atomic number 79, it continues, in actuality, to be logically necessary that gold have atomic number 79. In general, if that is so, metaphysical necessity continues to be a form of logical necessity.

This suggested objection gains its plausibility from the similarity, even the



148 ROBERT FARRELL

identity, of roles played within the atoms of W by charged and by loaded particles. If the roles are so similar, why distinguish load from charge at all? The objection loses its plausibility when we notice that the similarity or identity of roles upon which it concentrates is a local one: all that has been said of the physics of W is that within the environment of atoms loaded particles and charged particles behave identically or similarly enough for their containing chunks of stuff to conform to our stereotype of gold (to return to our example). In other environments in W charged particles and loaded particles may behave in quite different ways, in particular, the loaded particles may fail to conform to our stereotype of a charged particle: perhaps they are unaffected by magnetic fields or are affected by forces in W which leave charged particles unaffected. Two things are obvious here. One, that, given that what is at stake is logical necessity, we have enormous freedom in specifying the behaviour of loaded particles, and in specifying the other denizens of W, in such a way as to bring about one or the other of those above-mentioned possibilities in W. Two, that the mathematico-physical workings-out of such a specification of W go far beyond what can be attemp- ted here: one or another sketch will have to suffice.

Suppose our stereotype of a charged particle to be exhausted by (i) the particle's obeying, near enough, Newton's laws when it is subject to merely mechanical influence - this takes care of its particular nature; (ii) it obeys, again near enough, Maxwell's laws . We could, thus, even specify W so that most of its loaded particles violated Maxwell's laws to an extent not confor- mant with the stereotype of a charged particle. Loaded particles are not, then, charged particles in W; not all the gold in W has atomic number 79; it is not, in actuality, logically necessarily true that gold have atomic number 79, even if gold actually does have that atomic number. The claim that metaphysical necessity is a form of logical necessity remains as unlikely as ever it was in the light of the main argument of this section.

Before leaving this objection, I should comment upon the notion of atomic number, for it may be thought that the real objection here should be based on my unquestioning use of atomic numbers in such a way as to suppose them closely tied to the number of charged particles in an atom's nucleus. Granted, it may be thought worth objecting, that load is not charge, still the notion of atomic number is sufficiently commodious to accommodate both charge and load. Then, the objector may go on to




conclude, gold has atomic number 79 in W, gold is, in actuality, logically necessarily of atomic number 79.

I think the hypothetical objector wrong. Much hinges here on the stereotype we have of atomic number. Unlike charge, atomic number has no life of its own: 'charge', although originally technically used, is now a term in common use, with a fairly rich stereotype - at least when contrasted with 'atomic number'. This latter expression has, centrally, only its technical use, it is a 'one criterion' expression, and such expressions are distinctly not sufficiently commodious to take in extra referents (in such possible worlds as W) without an attendant change of stereotype. This new objection is, thus, in an even weaker position than the rejected one out of which it grew.

The third objection I wish to consider - again, it was suggested to me by Putnam, in conversation - takes up the role played by sameM in my main argument, and proceeds to weaken it from being an equivalence relation to being merely a similarity relation. Because the revision suggested threatens to be a revision of the framework of the discussion of metaphysical necessity, rather than a mre alternative suggested within the framework, I shall devote the next section to this third objection, its background, and its consequences.

III

Negatively, what distinguishes a similarity relation from a sameness relation is that it may fail to be transitive: there is no inconsistency in a's being similar to b, b's being similar to c, yet a's failing to be similar to c. We can now see the point of Putnam's suggestion: my argument in Section II relied upon the transitivity of sameM, for transitivity was needed for loaded atoms of gold in W to be linked, by way of unloaded atoms in W, with actual atoms of gold. A reading of sameM as a similarity relation invalidates the argument. I shall first briefly discuss the nature of similarity relations; then I shall discuss the consequences of treating sameM and its companions as similarity; finally, I shall return to assess the objection which gave rise to all this. By then I shall have the benefits of the two earlier discussions.

Positively, what distinguishes a similarity relation from other relations? The minimal answer is: it is a reflexive and symmetric relation. This minimal answer, if taken as the whole answer has the vice of rendering as similarity relations some which are not such at all. This vice does not constitute



150 ROBERT FARRELL

conclusive grounds for rejecting the minimal answer, and is best seen as an incitement to look elsewhere for an answer.

A good place to look for an acceptable account of similarity is Goodman's The Structure of Appearance7 . In attempting to provide the formal apparatus for an adequate phenomenal description of experience, Goodman had to develop the means to say that one phenomenal quale matches another, that it lies between two other phenomenal qualia, or that it is just discriminable from another; and in doing so he provided the substantial beginnings of an account of phenomenal similarity. The phenomenal aspect of Goodman's account is relevant to what I am concerned with here in only two ways - I shall what ways in a moment - otherwise it does not concern us. Nor will the nominalist constraints Goodman places upon an acceptable account concern us here.

The two ways in which Goodman's having provided an account of phenomenal similarity does concern us are these: (1) his account is worked out in the context of a definite body of data, a body with a specific structure; and (2) because of that structure Goodman's account is mathematically special - in short, Goodman deals only with discrete and finite collections of qualia.

The fonner way indicates that the full account of similarity is not to be provided by logic alone. This is in contrast to sameness relations which are fully characterizable using only the resources of logic. The similarity relations ultimately to arise from such an account as Goodman's will reflect, in their mathematical structure, the specific subject matter Goodman analysed. Likewise, more realistically, and more relevantly to the example of Section II, the study of matter can be seen as having given rise to similarity relations such as those between the chemical elements as are recorded in the periodic table. Whatever similarity relation it is that a proponent of Putnam's suggested objection appeals to, it will have in common with sameM an origin in the study of chemistry and physics; unlike sameM, however, it will also draw its structure from those studies.

The latter way suggests that, whereas Goodman was able to go so far in his analysis of phenomenal similarity using only algebraic techniques, other analyses of similarity may have to appeal to analytic techniques; especially in realistic analyses we would anticipate the need for topological techniques. It may even be that we need topological techniques not merely to give the mathematical details of the various similarity relations our analyses yield, but that they are needed to characterise similarity relations in general, even the ones whose details can be expressed algebraically. Both the lessons learnt




from reflecting upon Goodman's analysis will tum out to be relevant to our assessment of Putnam's suggested objection.

What, now, of the consequences for metaphysical necessity of a replace- ment of the sameness relation by a similarity relation? The problem of specifying sameM in a satisfactory way so as to allow it to be a usable cross- world relation arose in Section II; a parallel problem exists for similarityM. In the case of sameM, once we have settle upon a level of analysis we can go ahead and decide what the cross-world natural kinds are; not so with similaritym. In that case we face a further decision as to what the relevant degree of similarityM is which we take to specify natural kinds, both within the actual world, and from one world across to another: just how similarM do two atoms have to be before they are both atoms of the same metal, say gold? We find in the move from sameM to similarltyM the entry of an element of decision into the analogue of the problem discussed in Section II.

Finally, supposing the revised account of metaphysical necessity accepted, what consequence does that acceptance have for the main argument of Section II? In particular, is that argument, read now with similarity in place of sameness, a valid one; and if not, can it be adjusted so as to regain its validity? The answer to that first question has already been conceded to be: No. So we now face the task of answering the second question. I shall argue that the argument of Section II can be suitable adjusted to regain its validity, and so allow us to continue to accept the conclusion of that argument.

Suppose us to have come up with similaritym, and to have devised a means of characterizing gold, in the actual world, in terms of it. SimilarityM, to be of any interest and use to us has also to have among its relata at least some samples located in merely possible worlds: these have to be possible worlds in which there are samples of gold. The same, in consequence, will hold in W, the possible world of our example; in W, however, there are some loaded atoms which are more like standard samples - whether they be actual or in W - of gold than are the isotopes of gold. In the physico-chemical context of gold loaded particles - so the adjusted account offered late in Section II went - are virtually indistinguishable from charged particles. It is only when they are isolated from charged particles that they violate, in a noticable way, Maxwell's laws. Isotopes of gold, when present in any quantity are detectable by gross means (calculation of density) and so are distinguishable from standard gold.

Of course there are no loaded particles in actuality, so when we appeal



152 ROBERT FARRELL

to similantyM with our attention confined to actuality we have no direct need to consider loaded particles. But our actual similarityM has to be applicable, we agreed, outside actuality: if it is to be a general, theoretical, relation it has to be able to assess the degrees of similarity of, on the one hand, isotopes of gold and, on the other, atoms in W which have, say, just one loaded electron in orbit, with the other 78 charged, to standard gold atoms.

One could avoid counting the loaded atom as more similarM to standard gold than are actual atoms of isotopes of gold by having similarityM take into account only those 'important physical features' which occur in actuality. But then the relation, though still cross-world, would be inadequate to the task of picking out merely possible natural kinds - kinds of all whose samples are to be found in merely possible worlds. All the metals there are, for instan- ce, would be all the metals there could be.

Restricting similaritym unfits it for part of its task; to allow it to perform that task, we have to allow it to assess such things as loaded atoms whose only sin, from the point of view of the restricted relation, came down to their failure to be actual. And that is not failure enough to support a lack of high degree of similarityM with actual, unloaded, atoms.

What looked to be a fatal failure of transitivity in similaritym - as indeed it was, viewed formally, in terms of the logical letter - is not so. Similaritym 's failure of transitivity still allows, though it does not require, a to be similarM to c when a is similarM to b, and b to c. In consequence, our original conclusion stands: there is at least one possible world in which some gold fails to have atomic number 79; gold, even if metaphysically necessarily of atomic number 79, is not so logically.

La Trobe University

NOTES

1 P. 233 of 'The meaning of "meaning"', in Putnam's Mind, Language and Reality. Philosophical Papers Vol. 2, (Cambridge, Cambridge U.P., 1975), pp. 215-271. 2 P. 320 of S. A. Kripke's 'Naming and necessity', in D. Davidson and G. Harman (eds.), Semantics of Natural Language (D. Reidel, Dordrecht-Boston, 1972), pp. 253- 355 and pp. 761-769. 3 P. 769 of 'Naming and necessity'. 4 'the meaning of "Meaning"', p. 225.

'The meaning of "Meaning"', p. 232. 6 See Appendix *X of his Logic of Scientific Discovery (Hutchinson, London, 1959).




According to Popper a statement is naturally necessary "if, and only if, it is deducible from a statement function which is satisfied in all worlds that differ from our world, if at all, only with respect to initial conditions" (p. 433). Natural necessity is thus, for Popper, truth in all worlds having the same physical structure as the actual world has.

(D. Reidel, Dordrecht-Boston, Third Edition, 1977); see especially Part Three. 8 This paper is a reworked extract from my Harvard dissertation 'Realism and natural necessity' written with Hilary Putnam and Israel Scheffler as advisers. Discussions with them led to improvements in an earlier version of the material presented above. I thank them for their help.



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Metaphysical Necessity Is Not Logical Necessity