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Truthmaking

3:AM: You’re a defender of resemblance nominalism as a solution to the problem of universals. So before you give us your solution, can you set up the problem that it is addressing?

GRP: There are different interpretations of the problem of universals. I understand it as the problem of giving the truthmakers of propositions to the effect that a certain particular is such and such, e.g. propositions like ‘this rose is red’. Others have interpreted it as a problem about the ontological commitments of such propositions or a problem about what those propositions mean.

A truthmaker is an entity in virtue of which the proposition it makes true is true. And it is a necessary condition of being a truthmaker (though not a sufficient one) that a truthmaker necessitates the proposition it makes true. Thus the truthmaker (assuming there is one and only one) for ‘this rose is red’ will be that entity in virtue of which ‘this rose is red’ is true; and that entity will necessitate the truth of ‘this rose is red’.

A traditional solution to this problem has been to postulate universals. On this view, what makes true that ‘this rose is red’ is that the rose instantiates the universal redness, where a universal is an entity that can have multiple instances. So, to continue with our example, the rose and the cloud, being both red, instantiate the same universal. There are many different theories postulating universals, and universals are conceived by some of these theories in very different ways, but however they are conceived, universals tend to be seen as rather controversial entities, for a variety of reasons.

Thus there are many theories that reject universals and that can be grouped under the generic name of ‘nominalism’. One nominalist theory is trope theory, according to which what makes true that this rose is red is that the rose has a certain redness, a redness which is not had by anything other than the rose but that may perfectly resemble other rednesses, like the redness of that cloud. These individual rednesses are tropes. There are many versions of trope theory. And then there are many other theories that reject both universals and tropes. Resemblance nominalism is one of these.

3:AM: So what is Resemblance Nominalism and how does it solve the problem?

GRP: According to resemblance nominalism there are no universals, and there are no tropes either. There are only things like roses, people, atoms, planets, dolphins, rocks, trees, and cars. What makes it true that this rose is red is that this rose resembles all the other red things. What makes it true that that plate is round is that it resembles all the round things. Resemblance is a primitive relation, i.e. it is not understood in terms of shared universals, for instance. And it is a primitive relation between things like roses, people and trees, i.e. it is not a primitive relation holding between tropes, since resemblance nominalism does not postulate any tropes.

So the ontology of resemblance nominalism is very different from the ontology of theories of universals and tropes. Since resemblance nominalism is committed to classes, its ontology is shared by class nominalism, the theory which in its canonical form identifies properties with classes of particulars and which, to give an answer to the problem of universals as I understand it, would say that what makes it true that this rose is red is that it belongs to the class of red things. The difference between resemblance nominalism and class nominalism is that the former, but not the latter, brings in resemblance to account for the truthmakers of the propositions in question.

Now, there is an obvious problem. What if, say, all green things are round and vice versa? Does the resemblance nominalist, in that case, say that what makes this plate round is what makes it green? I don’t think that’s the right thing to say. When I developed resemblance nominalism I thought that the solution to this consisted in committing to an ontology of concrete possible worlds and ‘possibilia’, à la Lewis. Thus what makes this plate round is not simply that it resembles all round things in this world but that it resembles all ‘possible’ round things, all round things in every possible world. Since there are possible worlds where some round things are not green and vice versa, then what makes this plate round is not what makes it green.

This problem is a version of the famous problem of coextensive properties. And my solution faces a variant of the problem of necessarily coextensive properties: what if, say, it is necessary that green things are round and ‘vice versa’? My thought was that in this case we should say that what makes this plate round is what makes it green. In that case the difference between green and round would be, in fact, a difference between the predicates ‘green’ and ‘round’, a semantic difference with no ontological correlate.

Although an ontology of concrete possible worlds is consistent with the ontology of resemblance nominalism, since those worlds and ‘possibilia’ are concrete particulars, most people dislike this commitment of the theory. But it is important to note that what resemblance nominalism is committed to is just the ontology of concrete possible worlds and ‘possibilia’, not the full Lewisian modal realism. For instance, resemblance nominalism is not committed to counterpart theory, or the reduction of propositions to possible worlds or many other elements of Lewis’ modal realism. Even so, many philosophers would still reject a theory on the basis of its commitment to an ontology of concrete possible worlds.

When I first developed resemblance nominalism I was not concerned about this. But now I think that it would be best to try to develop resemblance nominalism without committing it to concrete possible worlds and ‘possibilia’ and I am currently thinking about this. I think there might be different ways of developing the theory without committing it to concrete possible worlds; but this is very much thought in progress at the moment.

3:AM: You note that Carnap in his Aufbau was an early proponent of this position. Carnap is supposed to have failed thanks to arguments from Goodman. How does your approach see off Goodman?

RGP: Carnap tried to define properties, or qualities, in terms of similarity circles and, to this extent, his position can be thought of as a version of resemblance nominalism. But there are many differences of many kinds between Carnap’s position and resemblance nominalism as I have developed it.

Anyway, for Carnap a property is a class of particulars such that (a) all the particulars in the class resemble each other and (b) nothing outside the class resembles everything inside it. Thus a property is a maximal resemblance class. Goodman presented two formidable difficulties to this proposal: the imperfect community and the companionship difficulties. Suppose a is red, round and hot, b is red, square and cold, and c is green, square and hot (and they have no other properties). These three things resemble each other; so they satisfy (a). And if they satisfy (b), they form a maximal resemblance class.

But what is the property to be identified with it? Neither the property of ‘being red’ (because c is green), nor the property of ‘being green’ (because a and b are red), nor the property of ‘being round’ (because b and c are square), nor the property of ‘being square’ (because a is round), nor the property of ‘being hot’ (because b is cold), nor the property of ‘being cold’ (because a and c are hot). These three things form an imperfect community, i.e. a class such that every two of them have a property in common but there is no property common to all of them.

Imperfect communities show that being a maximal resemblance class is not sufficient for being a property. (You might worry that the class of a, b and c need not be maximal, since many other things might resemble all three of them – fair enough, but every maximal resemblance class having a, b and c as members will be an imperfect community: since there is no property common to a, b and c there cannot be any property common to all the members of a class of which they are members; so the assumption that the class of a, b and c is maximal is innocuous).

But being a maximal resemblance class is not a necessary condition for being a property either. Imagine that every red thing is square, but some square things are not red. This is a case of companionship, since the property of ‘being square’ ‘accompanies’ the property of ‘being red’. In that case, each square thing, even green square things, resembles every red thing. But then there is no maximal resemblance class that is the property of ‘being red’. For the maximal resemblance class containing all red things will also contain some green ones.

These two problems made Carnap’s proposal collapse. One might think these problems do not affect resemblance nominalism as I have presented it, since I did not say that for resemblance nominalism properties are classes of resembling things. All I said was that for resemblance nominalism what makes true a proposition like ‘this rose is red’ is that the rose in question resembles the red things. And what makes it, say, light, is that the rose resembles the light things. So resembling some things makes the rose red and resembling certain other things makes it light. But resembling some things does not endow the rose with any property. In fact, resembling b and c, in the example above, does not make a any way, it does not give a any property.

So what are the groups of things such that resembling them gives something a property? This is the problem posed to resemblance nominalism by the imperfect community difficulty. Companionship cases show that resembling all the red things cannot be what makes something red, since in the example above all square things, including green ones, resemble all red things. But then how can resembling all red things make a red thing red?

Lewis suggested solving these problems by using a polyadic and contrastive resemblance relation. But I have solved these problem using a dyadic resemblance relation that comes in degrees and that applies not only to things but also to pairs of things, pairs of pairs of things, pairs of pairs of pairs of things, and so on. The solutions to these difficulties are too technical for me to present them in detail here (the solutions to these difficulties, together with a solution to a different problem I have dubbed the ‘mere intersections difficulty’, are presented in the final chapters of Resemblance Nominalism).

But the basic idea is the following. The difference between a perfect community (a class all of whose members share a property, like the class of all red things) and an imperfect community (a class such that every two of its members share a property but there is no property common to all of them) is that not only do all the members of a perfect community resemble each other, but so do all the pairs of those members, and all the pairs of those pairs, and all the pairs of the pairs of those pairs, and so on; while in an imperfect community, although all its members resemble each other, either some pairs of those members do not resemble each other, or some pairs of those pairs do not resemble each other, or some pairs of pairs of those pairs do not resemble each other, and so on.

The idea behind the solution to the companionship difficulty is that when a property F accompanies a property G (i.e. when all Gs are F but not vice versa), the lowest degree of resemblance to which any two Fs (or any two pairs of Fs, or any two pairs of pairs of Fs, etc.) resemble each other will be lower than the lowest degree of resemblance to which any two Gs (or any two pairs of Gs, or any two pairs of pairs of Gs, etc.) resemble each other.

3:AM: D.M Armstrong also attacked the Carnapian idea of resemblance mominalism and developed his own theory of universals. So what did he say, and again, how does your theory survive?

GRP: Armstrong has a battery of arguments against resemblance nominalism, but the two main objections he raises against resemblance nominalism are the problem of coextensive properties, a problem I discussed above, and Russell’s regress. In his book The Problems of Philosophy Russell objected that one cannot avoid universals since the relation of resemblance is a universal. But why not think that resemblances are as particular as the things that resemble each other?

Russell is usually represented as having suggested that the problem with this is that it leads to an infinite regress. For suppose there are no universals and there are three white objects, call them a, b and c. Since they are white, they resemble each other. But then there are three resemblances, the resemblance between a and b (r1), the resemblance between b and c (r2), and the resemblance between a and c (r3). Since these resemblances are resemblances between white things, they resemble each other, and thus we have three further resemblances, the resemblance between r1 and r2 (r4), the resemblance between r1 and r3 (r5), and the resemblance between r2 and r3 (r6). Since r4, r5 and r6 are resemblances between resemblances between white things, they resemble each other, and thus we have three further resemblances, and so on ad infinitum.

It is not immediately clear what is supposed to make this regress vicious or problematic, and different philosophers have said different things about this. But I suppose the most interesting idea is that the regress is vicious because it prevents the resemblance nominalist from finishing his explanation of what makes things white.

The resemblance nominalist wants to explain what makes a, b and c white without appealing to universals. Instead he appeals to resemblances, but then he has to explain what makes these resemblances resemblances between white things. And he can only appeal to higher order resemblances, resemblances which he will have to account for in terms of yet higher order resemblances, and so on. But since this goes on ad infinitum, the resemblance nominalist explanation cannot be completed, or so the thought seems to be.

But, in fact, that the regress is infinite does not mean that the explanation cannot be completed. Anyhow, there is a more fundamental problem with the regress: it is illusory – so the question whether it is vicious or not should not even arise. What the resemblance nominalist says is that a and b are both white because they resemble each other. This resemblance between them is primitive, and is not explained in terms of shared universals or resembling tropes. Indeed it is not explained on the basis of any facts about any entities other than a and b.

Therefore, resemblances are not reified by the resemblance nominalist; that is, the ontology of the resemblance nominalist consists only of things like a and b, but not of things like resemblances between things like a and b. But if resemblances are not entities, then they do not resemble each other, and so there is no regress of resemblances. The regress is stopped at the first step: there are the three things a, b and c, which resemble each other, but there are no further entities that are the resemblances between them.

3:AM: Dave Chalmers has recently resurrected Carnap’s Aufbau project. Does this connect up with your theory?

GRP: Not much, as far as I can see. The main idea behind Carnap’s Aufbau was the reduction of all truths to a very limited set of truths. It is this aspect of Carnap’s Aufbau that Chalmers is interested in. Chalmers wants to show that all truths are a priori entailed by a limited class of truths. But this is not part of my project in defending of resemblance nominalism. First, my project is not about ‘all’ truths, but about truths that the opposition would account for in terms of universals or tropes. Second, my project is not concerned with a priori entailment, but with the ontological grounds of truths, or truthmakers.

So this difference between my project and Chalmers’ points to a difference between my project and Carnap’s. And there are other differences too between my project and Carnap’s. Carnap attempted to ‘construct’ qualities or properties on the basis of resemblance relations between particular ‘phenomenal’ entities, the so-called ‘Erlebs’, i.e. momentary cross-sections of experience. And the most basic relation obtaining between these ‘Erlebs’ is not resemblance or similarity but what he calls ‘recollection of similarity’, which obtains between any two Erlebs x and y if and only if x and y are recognised as similar.

So, my resemblance nominalism is less restrictive than Carnap’s since it says nothing about the nature of its particulars, except that they are concrete, and this permits them to be physical or mental, experiential or not. Furthermore, my basic relation is one of resemblance or similarity, not Carnap’s relation of ‘recollection’ of similarity. Also, my theory is meant as a solution to the problem of jniversals, a problem Carnap was not concerned with.

3:AM: You engage with the metaphysics of truth and defend the view that truths have truthmakers. You also show that Searle’s attempt to defend a correspondence theory of truth fails. The slingshot is a crucial element in the argument. So can you say what this is, why it kills Searle’s argument and whether it affects your own view that truths have truthmakers?

GRP: The slingshot is an argument that tries to show that no connective having certain features can be non-extensional. In one of the versions of the slingshot, the argument tries to show that no connective that permits salva veritate substitution of both co-referring singular terms and logically equivalent sentences can be non-extensional. Now, it is thought that the connective ‘— corresponds to the fact that …’ is non-extensional. For ‘snow is white’ and ‘grass is green’ have the same truth-value.

But replacing ‘snow is white’ by ‘grass is green’ in the true ‘“Snow is white” corresponds to the fact that snow is white’ produces the false ‘“Snow is white” corresponds to the fact that grass green’. But if (a) the connective ‘— corresponds to the fact that …’ permits salva veritate substitution of both co-referring singular terms and logically equivalent sentences and (b) the slingshot is right that such connectives must be extensional, then it follows that replacing ‘snow is white’ by any other true sentence in ‘“Snow is white” corresponds to the fact that snow is white’ produces another true sentence.

The result is absurd, since it means that “Snow is white” corresponds to the fact that grass is green, and to the fact that elephants are big, and to the fact that the Moon orbits the Earth – indeed it corresponds to all the facts. That is a reductio ad absurdum of the correspondence theory of truth.

Searle attempted a defense of the correspondence theory of truth arguing, basically, that the connective ‘— corresponds to the fact that …’ does not allow salva veritate substitution of logically equivalent sentences. For Searle our intuitive notion of fact is such that the fact that snow is white is not the same fact as the fact that ‘snow is white and 2 + 2 = 4’.

But I think that our intuitive notion of fact (if there is any such thing) is a weak foundation for the correspondence theory of truth. Furthermore, any reply to the slingshot that presupposes that there is a multiplicity of facts, as Searle’s does, is subject to the objection that it begs the question against a more basic slingshot, a slingshot trying to show that there is only one fact. According to this slingshot the connective ‘— is the same fact as the fact that …’ permits salva veritate substitution of both co-referring singular terms and logically equivalent sentences and so it must be extensional. But then the fact that Socrates is Greek is the same as the fact that Aristotle taught Alexander, and the fact that Aristotle taught Alexander is the same as the fact that snow is white. In short, there is only one fact.

The correct way to block this slingshot, I think, is by having an adequate criterion of identity for facts, based on an adequate conception of facts. In my view Searle, for different reasons, cannot use any such criteria. Since I believe in truthmakers, and I take some of these truthmakers to be facts, I need an answer to this slingshot.

My answer is based on a structuralist conception of facts according to which facts are identical if and only if they have the same constituents combined in the same way. Thus the facts that ‘Socrates is wise’ and ‘Socrates is wise and 2 + 2 = 4’ are not identical because they do not have the same constituents combined in the same way: the fact that 2 + 2 = 4, and therefore the numbers 2 and 4, are constituents of one of these facts but not the other. Since they are not the same fact, then the connective ‘— is the same fact as the fact that …’ does not permit salva veritate substitution of logically equivalents.

But if facts stated by logically equivalent truthbearers need not be the same, then there is no reason to think that logically equivalent truthberarers have the same truthmakers, i.e. there is no reason to think that the connective ‘— is made true by the fact that …’ permits salva veritate substitution of logically equivalents.

Some may worry that a commitment to facts conflicts with resemblance nominalism, for aren’t facts entities composed of particulars and universals? This is one way of understanding facts. But the resemblance nominalist has another way of understanding them. For the resemblance nominalist the fact that a is F is a conjunctive facts whose conjuncts are resemblance facts between a and every other F thing. Thus the fact that ‘Socrates is wise’ is a conjunctive fact whose conjuncts are facts like ‘Socrates resembles Plato, Socrates resembles Aristotle’, and so on. And the constituents of such facts of resemblance are the resembling particulars themselves, that is, the constituents of the fact that ‘Socrates resembles Plato’ are Socrates and Plato, and the constituents of the fact that ‘Socrates resembles Aristotle’ are Socrates and Aristotle. So this is a conception of facts without universals.

There is a lot more to say about what are the truthmakers of basic resemblance sentences or propositions according to resemblance nominalism, and there is also a lot more to say about this conception of facts I have just sketched – indeed at the moment my views on these issues are in flux, and I am re-thinking them. But the point I wanted to make is that a commitment to facts, even if they are conceived of as structured entities, is not incompatible with resemblance nominalism.

3:AM: So when you’re not philosophising, are there books, music, art that you have found enlightening?

GRP: Some of the things I like I find enlightening, others I simply like. Here is a list of things I like, some of which I have found enlightening too. As you will see, I am rather eclectic in my tastes.

My favourite music is electronic music: Paul Oakenfold, Hernan Cattaneo, and many others. But Handel and Bach are also good.

As for art (painting), I tend to prefer Italian Renaissance, in particular Mantegna, Botticelli, Uccello and Titian (in that order). But I also enjoy Monet and De Chirico.

Books: The Illiad, Antigone, Middlemarch, Decline and Fall, Narcissus and Goldmund, and many more, but these are the ones that come to mind right now (The Illiad is possibly the one that always comes to mind).

3:AM: And finally, for the metaphysical readers here at 3:AM, are there five books (other than your own of course which we’ll be going out to read straight after this) that you’d recommend?

GRP: It is very difficult to recommend only five metaphysical books. This is for two reasons. One is that there are so many excellent metaphysical books. So it is difficult to recommend ‘only’ five metaphysical books. And I am sure I will want to change any list of five metaphysical books almost as soon as I have completed it. The other reason is that one recommends something on the basis of the interests and needs of the person for whom one is making the recommendation. But I don’t know what the interests and needs of the metaphysical readers at 3:AM are! So it is difficult for me to recommend any metaphysical books at all. Anyway, here is a try:

1. Aristotle. Categories. Although officially classified as one of Aristotle’s ‘logical treatises’, this is a beautiful and concise treatise on basic ontology. It has been very influential in the history of metaphysics.

2. Descartes. Meditations on First Philosophy. A wonderful book that has something for everyone. This is a classic in the history of metaphysics. And it is also, of course, a classic in the history of philosophy. But it is more than that: it is one of the great works of human thought.

3. Leibniz. Discours on Metaphysics. You can’t get more metaphysical than this. It is a concise and tightly argued presentation of a fascinating metaphysical system.

4. Kripke. Naming and Necessity. A brilliant book; it might be impossible to combine its degrees of penetration and clarity again. It was greatly influential and played a major part in the resurgence of interest in metaphysics in the 1970s.

5. Armstrong. A World of States of Affairs. A presentation of a comprehensive metaphysical system by one of the preeminent metaphysicians of our time. Armstrong’s system is based on the reality of universals, so this is a system that I do not accept, but it is one I admire.




ABOUT THE INTERVIEWER
Richard Marshall is still biding his time.

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First published in 3:AM Magazine: Friday, September 7th, 2012.