Truthmaking

Gonzalo Rodriguez-Pereyrainterviewed by Richard Marshall.

Gonzalo Rodriguez-Pereyrais the de Chirico mannequin of philosophy. He thinks all the time about the mysteries of truthmakers, the indiscernability of identicals, resemblance nominalism, universals and metaphysical slingshots. There's a kind of weird pristine beauty to this that makes him a surreal chillin' jive.

3:AM:What made you become a philosopher? Were you a philosophical boy or was it something that you changed into?

Gonzalo Rodriguez-Pereyra:I suppose it was interest in philosophical problems. When I was eleven or twelve years old, I became for a while fixated on the question whether there could be two ‘identical’ stones. This is, of course, the question whether the principle of identity of indiscernibles is true and, as I formulated it then, I was bound to fall into confusion about it. But, although I was not aware I was philosophising, I was. So I would say I was a philosophical boy. Those thoughts about ‘identical stones’ are the earliest philosophical thoughts I remember. But when I was a teenager I also thought about the more typical philosophical problems teenagers think about: the existence of god, the objectivity of morality, whether one can know that the external world exists. At one point I took a copy of Berkeley’s Principlesfrom my father’s library. That was the first philosophy book I read. I found it fascinating and wanted to read more philosophy. So I picked up Karl Jaspers’ Philosophy. Then I read Descartes’ Meditations. No doubt I understood very little about them. But by the time I had read those books, I knew I wanted to be a philosopher. So I decided to do philosophy at university, with a view to becoming a professional philosopher. Being a rather unstable character, at some points I had doubts about becoming a professional philosopher, but the example of two of my teachers, Ezequiel de Olaso and Juan Rodriguez Larreta, made me confirm my original decision.

3:AM:You’re a metaphysician and a Descartes and Leibnizexpert. When you were asked about the role of metaphysics in relation to other areas of philosophy and the natural sciences you cited Descartes in his preface to the French edition of the Principleswhen he compared philosophy to a tree whose whole roots are metaphysics. You went on to say that ‘… the totality of knowledge forms a tree whose roots are Metaphysics.’ That’ll shock quite a few people who think that knowledge is now a whole zoo of sub-disciplines, each able to answer the ultimate questions of its own domain e.g. physics by the physicists, neuro-science by the neuro-scientists and so on. It’ll shock the Wittgensteinians who’ll say metaphysics is just misunderstood grammar. So why should they believe you and Descartes?

GRP:I suppose those groups of people will be shocked by different features of my assertion. Those who take knowledge to be a whole zoo of sub-disciplines will react to my giving metaphysics a privileged position in that zoo or to my thinking of knowledge as a tree, with more and less fundamental parts. Those who think that metaphysics is just misunderstood grammar will react to my giving metaphysics some place or another in the system of knowledge. But I don’t think that those with a ‘zoo’ view of knowledge must necessarily reject my ‘tree’ view. Whether they must or not depends on what, exactly, the ‘zoo’ view amounts to. For my view is not that the theoretical disciplines do not have autonomy to decide their own questions, but that the concepts of physics, chemistry, neuro-science, etc. presuppose the concepts of metaphysics. Metaphysics is the study of the most general nature and basic structure of reality, and therefore the concepts of metaphysics, concepts like time, space, identity, resemblance, substance, property, fact, event, composition, possibility, etc., are the most fundamental concepts. Thus metaphysics is the most fundamental theoretical discipline.

This does not mean that metaphysics is about concepts; metaphysics is about reality, but those concepts are supposed to apply to the most basic features of reality. In one way or another all other disciplines (whether philosophical or not) employ these concepts and/or others derived from them and so metaphysics contains the conceptual foundations of the rest of knowledge.

The role of metaphysics in relation to other disciplines, whether philosophical or not and including the natural sciences, is thus a foundational role. Lack of clarity in the concepts of metaphysics implies lack of clarity in other disciplines – both theoretical and practical disciplines – employing those concepts or employing concepts that depend on those of metaphysics. Since there are relations of priority between the other disciplines too, knowledge has the form of a tree, and since metaphysics is the most fundamental one of the theoretical disciplines, it represents the roots of the tree. But nothing here means that the other theoretical disciplines – whether they are natural or social sciences, humanities, or other branches of philosophy – cannot decide their own questions using their own methods.

To say that metaphysics is justmisunderstood grammar is to misunderstand a large portion of what goes on in metaphysics – now and in the past. No doubt there are examples of metaphysical reasoning that betray a misunderstanding of grammar. A famous example is Heideggeron nothing, famously criticised by Carnap. Some of Walter Burley’s arguments for universals seem also to be guilty of misunderstanding grammar. But Ockhamcriticised those and he did that to put forward his own favoured metaphysical position on the issue. Nor must one suppose that all realists about universals misunderstand grammar. David Armstrong, for instance, has argued for the existence of universals; but his argument for the existence of universals cannot be accused of being an expression of misunderstood grammar. Indeed he has explicitly rejected any kind of argument for universals based on the assumption that to every meaningful word there must correspond an entity. These are just examples, and what they show is that not all metaphysics is misunderstood grammar.

3:AM:You co-edited a book Real Metaphysicswhich was a collection in honour of Hugh Mellor. Outside of philosophy perhaps few people will have heard of Mellor. Why was he significant for you and why should he be better known?

GRP:Hugh Mellor was my PhD supervisor. As such he was very demanding but also very supportive and generous with his time. There were times at which I would meet him every week to discuss my work. My PhD thesis was a defense of, and a case for, resemblance nominalism. On my first meeting with him in Cambridge, one or two days after I arrived there as a graduate student, I told him that I had a defect, which was that although I felt I was quite good at criticising a philosophical position, I was not very good at defending and making a case for a philosophical position. He said that that was not an uncommon situation for people at my stage, and that I should try developing a position in my thesis. He also said I should try developing a position which he rejected. I accepted the challenge and since I was interested in the problem of universals and Hugh was a believer in universals, I decided to defend and argue for resemblance nominalism. He was a great supervisor, and was supportive when I was going through a difficult time, and so I have a huge personal debt to him.

Hughis, of course, very well known in the areas of philosophy where he has been active. But he is a philosophers’ philosopher, and so I do not see why he should be better known, ‘as a philosopher’, outside philosophy. But Hugh is also an actor, and so some people outside philosophy will have heard of him in this capacity.

3:AM:One big contemporary topic is about the relation of the mind and the body. It’s often discussed in a way that doesn’t seem like metaphysics. The mind-body problem can sound just like a scientific issue in many of the contemporary presentations. But you’ve written about this in terms of Leibniz’s theory of pre-established harmony. So what has a Leibnizean metaphysical approach got to offer in this area of investigation and are attempts to suppress metaphysical dimensions of the problem an added problem?

GRP:I have written on Leibniz’s pre-established harmony as a solution to the mind-body problem as he understood it. But this does not mean that I have defended Leibniz’s solution. What I have written on that is of a purely historical nature. I think there is a metaphysical problem of the relation between mind and body. Thinking that there is no metaphysical dimension to the problem is an error. This does not mean that there are no other aspects of the problem that are more amenable to a scientific treatment. Anyway, I do not think that Leibniz has a great deal to contribute to the contemporary discussion of the mind-body problem. His position is a form of parallelism (the ‘harmony’ bit of the theory), but grounded in a theory of the nature and aims of God (the ‘pre-established’ bit of the theory). The parallelism, or denial of any causation between mind and body, derives basically, and fallaciously, from a theory of substances as having complete concepts that include everything that is true of them. But sometimes he argues for the parallelism by elimination. He considers two alternative theories: interactionism and occasionalism. But his objections to interactionism are rather poor. And although I think some of his objections to occasionalism are quite sophisticated and interesting, to the best of my knowledge occasionalism is not really in the map of contemporary philosophy of mind.

3:AM:For Leibniz all truths about created individual beings are contingent, and contingency is defined in terms of infinite concepts (and proof of propositions having an infinite number of steps). It faces the challenge of the problem of lucky proof and the problem of guaranteed proof. You defend Leibniz don’t you? Can you say what these problems are and how Leibniz can be defended from them?

GRP:Leibniz believed in freedom, both divine and human, and he thought that contingency was a necessary condition of freedom. That is, if an agent A acts freely when choosing X, then A’s choosing X cannot be necessary. But there are some elements in his philosophy that seem to make contingency impossible. And so he struggled to make room for contingency in his philosophy. For instance, he believed that every truth is analytic, in the sense that in every truth the concept of the predicate is included in the concept of the subject. Take, for instance, the proposition ‘Peter denies Christ’. If being a denier of Christ is in the individual concept of Peter, it seems that it is necessary for Peter to deny Christ. Of course, this generalises and so seems to make every truth necessary.

One of the things Leibniz said in response to this was that sometimes the concept of the predicate can be found in the concept of the subject after a finite number of steps. This is what typically happens with propositions about species of things, e.g. ‘A triangle has three sides’. The concept of the subject in such a proposition is finite and so it only takes a finite number of steps in the process of analysis to find the concept of the predicate. This proposition, then, has a ‘proof’, since it can be reduced to an identity, e.g. ‘A closed three-sided figure has three sides’, in a number of finite steps by substituting definitions for the concept under analysis (in this case the concept ‘triangle’). But there are other propositions where the analysis cannot be completed in a finite number of steps. For Leibniz a proposition like ‘Peter denies Christ’ is contingent because, due to the fact that the individual concept of Peter is infinitely complex, its analysis cannot be completed in a finite number of steps, and so it does not have a proof.

Leibniz’s idea was that the distinction between necessary and contingent propositions is the distinction between true propositions that can be proved in a finite number of steps, and true propositions that cannot. The former are necessary, the latter contingent. It seems to me that this strategy to save contingency fails outright. Contingency and necessity have nothing to do with the number of steps it takes to prove or analyze a proposition. What Leibniz has done is, effectively, to change the subject. He has spotted a difference among propositions and has decided to call that difference the difference between necessary and contingent propositions. But, clearly, that difference is not such a difference.

However, that the strategy fails does not mean that it is vulnerable to all the objections that have been leveled against it. One such objection is that it faces the problem of lucky proof. This problem, first brought to the attention of scholars by Robert Adams, is that even if the individual concept of Peter is infinitely complex, we might be lucky and discover that it contains the concept ‘denier of Christ’ at the beginning of our analysis or shortly after having begun it. Indeed, under certain assumptions about the order that any proper analysis must follow, there is a guarantee that the concept of any predicate that is in the subject will be found in its concept after a finite number of steps, however large.

This is the problem of guaranteed proof. The difficulty posed by these problems is to explain why finding the concept of the predicates in that of the subject after a finite number of steps would not constitute a finite proof of the proposition ‘Peter denies Christ’. But Leibniz has an answer to this, an answer that he suggests in several texts, namely that in order to prove a proposition like ‘Peter denies Christ’ one needs to prove the consistency of the infinitely complex concept ‘Peter’. Proving the consistency of this concept requires its full decomposition and the examination and comparison of all its constituents. So, even if the concept ‘denier of Christ’ is found in the concept of Peter at some stage of the analysis, there is never a point at which one has completed the proof of ‘Peter denies Christ’.

3:AM:Leibniz is famous for his principle of the identity of indiscernibles. I guess most people told about this principle would say it was not just true but kind of obvious. But you think it’s just false. So can you tell us what we’re not understanding?

GRP:Whether the principle is trivially true or simply false depends, partly, on what one means by the principle. If it means that no two things can have all their properties in common, and one counts things like ‘being identical to Julius Caesar’ as properties, then the principle is trivially true. For no two things could share all their properties, including their identity properties. But this is not an interesting version of the principle. More interesting versions of the principle are obtained by restricting the class of properties over which the principle quantifies, i.e. by formulating the principle as the principle that there cannot be two things that share all the properties ‘of a certain kind’ (and one has to explain what kind that is).

The problem of how to characterise the properties that would trivialise the principle is one of the hardest problems concerning the principle of identity of indiscernibles and one the problems to which least attention has been paid of. I know of only two articles where that problem is discussed systematically (one by Bernard Katz and one by myself). In a nutshell, my view is that a property F trivialises the principle of identity of indiscernibles if and only if differing with respect to F ‘is’ or may ‘be’ differing numerically (where this means that merely establishing a difference with respect to such properties only establishes a numerical difference between the things in question – i.e. it does ‘not’ mean that differing with respect to them entails a numerical difference between the things in question, since, obviously, all properties are like that). So, on my view, if you exclude such properties from the domain of quantification of the principle of identity of indiscernibles, the principle is not ‘trivially’ true.

I also think that the non-trivial versions of the principle are false, at least when the principle is formulated with modal force, i.e. as saying that there cannot be two things that share all their properties. I suppose that many, if not most, philosophers nowadays will agree that the principle is false when it quantifies over so-called pure properties, i.e. intrinsic properties (e.g. ‘being green’) or relational properties whose having does not depend on the identity of the ‘relatum’ (e.g. ‘being two miles from a tall tower’).

The standard way of arguing that the principle of identity of indiscernibles understood in this way is false is by appealing to Max Black’s possible world, where there are only two iron spheres, one mile apart from each other, each having the same color, shape, diameter, temperature, etc. as the other.

Impure properties are those whose having depends on the identity of the ‘relatum’ (e.g. ‘being identical to Julius Caesar, being two miles apart from the Eiffel Tower’). But the huge majority of philosophers seem to think that including impure properties in the range of the quantifiers of the principle would make the principle trivial. I have argued that it does not: quantifying over ‘being identical to Julius Caesar’ and other such properties trivialises the principle of identity of indiscernibles, but quantifying over properties like ‘being two miles apart from the Eiffel Tower’, or ‘being the father of Aristotle’ does not trivialise the principle of identity of indiscernibles.

So I have argued that there is a non-trivial version of the principle of identity of indiscernibles that quantifies over some impure properties. The truth or falsity of such a principle is another matter, a matter for which I have not argued in print. However, I think that a principle of identity of indiscernibles that quantifies over all non-trivialising properties, including non-trivialising impure properties, may be false.

Leibniz, on the other hand, thought that even the strongest versions of the principle of identity of indiscernibles were true. That is, he thought that there cannot be two things that are even only intrinsically alike. So what he thought true was not the trivially true version of the principle, but what most philosophers think is false. Although I think his arguments for the principle do not work in the end, his arguments are really fascinating and ingenious.

3:AM:Another idea you engage with is about what exists at a basic level. You discuss the bundle theory in connection to the principle of identity of indiscernibles. So what’s the issue, how does the bundle theory deal with it and what’s your view about the fundamental basic ontology?

GRP:The bundle theory is the view that particulars are entirely constituted by universals. These universals are purely qualitative ones, i.e. what I called ‘pure properties’ above. As I said, many philosophers think that a version of the principle of identity of indiscernibles that rules out things with the same pure properties is false. And philosophers have traditionally argued that the bundle theory is committed to the truth of such a version of the principle of identity of indiscernibles. For, the thought seems to be, since particulars are entirely constituted by universals, no two distinct particulars could share all their universals. Therefore, it has been argued, the falsity of the relevant version of the principle of identity of indiscernibles shows that the bundle theory is false.

I think this is wrong. The bundle theory does not entail the principle of identity of indiscernibles. It entails it only when conjoined with a principle to the effect that no distinct particulars can be constituted by exactly the same entities. But there are no reasons to accept such a principle. We would have such reasons if particulars were sets of universals, or if they were ‘mereological sums’ of universals. But there are independent reasons why the bundle theorist will not want to account for particulars as sets or mereological sums of universals. Once it is seen that there is no reason to accept the principle that no distinct particulars can be constituted by exactly the same entities, the bundle theory ceases to be committed to the principle of identity of indiscernibles.

In my view the bundle theorist should say that when a bundle is located somewhere, there is an ‘instance’ of the bundle there. The instance is entirely constituted by the universals of the bundle. But the bundle and the instance are two distinct entities. Bundles of universals can be multiply located, but their instances cannot, and particulars are instances of a bundle of universals. Then in Black’s world what we have is a bi-located bundle instantiated by two numerically distinct particulars. This is how the bundle theory can accommodate Black’s world. Even more, this version of the bundle theory can be used to show that the principle of identity of indiscernibles is false. For bundles of universals can be in more than one place at the same time; so a bundle can have more than one instance; so there can be numerically distinct particulars sharing the same universals; so the principle of identity of indiscernibles is false.

By arguing that the bundle theory does not entail and is not committed in any way to the principle of identity of indiscernibles, I have thereby defended the bundle theory from a traditional objection to it (namely that since the principle of identity of indiscernibles is false, the bundle theory must be false too). But I do not believe in the bundle theory anyway. The bundle theory postulates universals and I do not believe in them; so I do not believe in the bundle theory.

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 Nominalismand 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 Aufbauwas 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 PhilosophyRussell 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 Aufbauproject. Does this connect up with your theory?

GRP:Not much, as far as I can see. The main idea behind Carnap’s Aufbauwas the reduction of all truths to a very limited set of truths. It is this aspect of Carnap’s Aufbauthat Chalmersis 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’sattempt to defend a correspondence theory of truth fails. The slingshotis 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 veritatesubstitution 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 veritatesubstitution 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 absurdumof 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 veritatesubstitution 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 veritatesubstitution 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 veritatesubstitution 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 veritatesubstitution 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 oneway 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 Illiadis 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:AMare! 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 Marshallis still biding his time.