:: Article

The Anti-Platonist Metaphysician

Interview by Richard Marshall.

I think metaphysics has two parts. One is the theory of the forms and highest categories of objects: Husserl called that formal ontology. The other is the general inventory of all that is, which I call metaphysical systematics. It’s through systematics that the formal theory reaches out to be applied to reality. That’s why I think metaphysics is the real theory of everything: nothing is off its remit. This extreme generality makes it harder to secure feedback about the truth or otherwise of its theories, so there are always many fiercely competing views, some quite extreme, and with no obvious best one even of the less extreme views.

The fact of processes being spread out has to do with how causation drives things forward: space, time and causation are intimately linked, but I am still puzzling over exactly how. Sometimes one needs to mull problems over for years or even decades before finding a congenial solution.

Tropes help to explain why simple things can be alike and different in various ways, but the objects with which we are most familiar are much more complex: they consist of parts related in various ways, often composing intermediate parts of a larger whole. Extreme mereological views, according to which there are no composite objects (mereological nihilism), or only organisms (van Inwagen’s organicism), or, at the opposite extreme, that any collection of objects compose a whole, render mereology useless in accounting for the nature of things.

In his Physical Monadology of 1756, Kant was seeking to reconcile the infinite divisibility of space with the existence of physical atoms or monads. His way to do this was to regard the monads as physically simple but spatially extended. He wrote, “A monad determines the small space of its presence not via a plurality of its substantial parts, but via a sphere of influence.” Unlike Boscovich earlier and Bolzano later, who also took monads to have zones of influence, he did not take the monad to be “in reality” a little point sitting in the midst of its sphere of influence, but as it were smeared out across it or present throughout it (maybe to different degrees). I do not normally cite Kant, because I consider his critical and post-critical philosophy to have been disastrous for philosophy, but this was the young, pre-critical Kant.

The Lvov–Warsaw School produced a host of outstanding logicians, notably Jan Łukasiewicz, Stanisław Leśniewski, and Alfred Tarski, of the last of whom one may justifiably use the word “genius”. The doyen of commentators on this tradition, Professor Jan Woleński, regards Tarski as one of the four outstanding intellectuals to have come from Poland. But there were many more excellent logicians and philosophers in the School, not a few of whom were killed in the war. The fountainhead of the School was Kazimierz Twardowski, who had studied with Franz Brentano in Vienna and who from 1895 single-handedly turned Poland into a centre for excellent philosophy.

An anti-Platonist like myself has one advantage and one disadvantage over against the Platonist. We have only one realm or domain and so do not need to worry about cross-domain magic. Ockham’s Razor tells us that if we have two equally good theories and one of them commits us to fewer kinds of entities than the other, then we should choose the one with fewer kinds. If nominalism and Platonism can account for and explain the same phenomena, then nominalism should win. The problem with Ockham’s Razor is always that it is rare for theories to be so obviously comparable. Much more often, one theory has some advantages and drawbacks, and the other has different advantages and drawbacks.

Peter Simons is a leading metaphysician. Here he discusses what he believes metaphysics to be, the relevance of logic to metaphysics,vagueness, why metaphysics isn’t philosophy of language, mereology, Leśniewski and Whitehead, temporal and modal considerations, tropes, what exists, non-existing objects, what lies between mereological atoms and continuous non-atomic gunk, the importance and brilliance of the Lvov-Warsaw School, the realism of Bolzano, Brentano and Meinong, and his anti-platonism. This is a long walk into the crucial depths…

3:AM: What made you become a philosopher?

Peter Simons: At school my favourite subjects were history, biology, music and maths. As an undergraduate I studied mathematics, and enjoyed it, but after a while I found it did not match the breadth of my interests, whereas philosophy enabled me to connect with a much broader range of topics, and deal with really deep issues. I was lucky to be able to make the transition quickly and painlessly in Manchester, where the Department of Philosophy was sympathetic to my case and broader in range than most British departments at that time. I have never regretted the decision.

3:AM: You’re a leading metaphysician. Perhaps we should start by asking you what you take metaphysics to be and how you assess its current state. After a time when it was dismissed in the early years of the twentieth century it seems to be a revitalised and important area of study. How do you account for this change?

PS: Metaphysics for me remains what it has been from the start. Aristotle said all the other sciences specialise in some part of what there is, but metaphysics deals with everything, at the most general level. Following Christian Wolff, Edmund Husserl and Donald C. Williams, I think metaphysics has two parts. One is the theory of the forms and highest categories of objects: Husserl called that formal ontology. The other is the general inventory of all that is, which I call metaphysical systematics. It’s through systematics that the formal theory reaches out to be applied to reality. That’s why I think metaphysics is the real theory of everything: nothing is off its remit. This extreme generality makes it harder to secure feedback about the truth or otherwise of its theories, so there are always many fiercely competing views, some quite extreme, and with no obvious best one even of the less extreme views. Every so often, in fact several times in the history of the subject, this has given rise to a sceptical backlash, with that of logical positivism that you mention being one of the most sustained and radical.

It turned out that the criticisms of the positivists went too far: they were self-undermining. There is a genuine place and need for metaphysics, and if it is suppressed for long, that need makes itself felt. When philosophers avoid it, others spring into the breach: philosophically interested scientists, as well as all kinds of gurus and false prophets. After several decades in the mid-part of the last century when metaphysics was criticised and largely avoided, it gradually began to revive, at first in the guise of the semantics of natural and artificial languages, what I call Metaphysics-Lite. Since semantics can be done in so many ways, eventually metaphysics was bound to be taken up again for its own sake. It was an interesting development, because a large number of philosophers moved in the same direction independently at the same time. By the 1980s it was making a strong comeback, and since then it has flourished, especially in analytic philosophy. Not so many years ago I was saying we were living in a golden age for metaphysics. Unfortunately, the rediscovered freedom has again led to some pretty extreme and crazy theories, so another wave of sceptical criticism has followed as surely as day follows night. There has been a return of concern about whether metaphysical disputes are genuine, and a new name for metaphysical reflections on the status of metaphysics: “metametaphysics”. It’s dismaying to find metaphysics through its own excesses being compelled to retrace the steps to legitimation that it so recently took. I hope the excitement about extreme views dies down and a more level-headed realism returns, but I am not betting on it. Extreme views attract comment both imitative and critical, while metametaphysics tends to undermine the drive for first-order truth. Both divert energies from the serious business of getting metaphysics right.

3:AM: So Metaphysics attempts to provide an inventory of what there is and this leads it to contact specialised disciplines investigating what there is. This doesn’t surprise us. But it also seems very involved with logic to a degree that might surprise outsiders. Why is logic so important to the metaphysicians and given that what a logical inference is falls under metaphysics itself, how can its use as a tool of metaphysics escape the charge of vicious circularity?

PS: In a discipline as abstract and general as metaphysics, which is remote from the kind of testing that goes on in science, often the only way to decisively refute a theory is to show it is inconsistent, and that is a logical matter. Because metaphysics has blossomed in analytic philosophy, which grew out of the development of powerful modern logic at the end of the nineteenth century, analytic metaphysicians embrace logic and give it a central place in their work. The development of modal logic and its semantics in the latter half of the twentieth century also stimulated investigations into the metaphysics of modality. Logic is important, but it is not everything. In the end, all it monitors is what follows logically from what. That’s why I don’t worry about the threat of circularity. Pretty well everyone agrees that a logically good (valid) inference should not take one from truth to falsehood, and it’s hard to imagine a serious metaphysical position that would undermine that. Conversely, logic should not dictate to metaphysics but should be neutral among (consistent) theories. The logic I tend to use, that of Leśniewski (of which more below) precisely respects this neutrality.

3:AM: One way of seeing how logic and ontology mix is when we consider vagueness. You ask in one paper whether the sun exists, and it’s vagueness that raises the problem isn’t it. Can you first sketch why vagueness raises an ontological question and say how you answer the question as to whether the sun really exists – and what that means in terms of metaphysics?

PS: Vagueness is endemic in language for several reasons, but as in everything in philosophy, there are several competing views about its nature and source. Most philosophers think that it comes from some kind of loose fit between language and reality, but some others hold that it arises from the limits of our knowledge. In either of these cases, it can be maintained that the world in itself is completely sharp, and it is us and our language that give rise to vagueness. The idea that objects themselves can be in some sense vague is less widely accepted. But if you hold that all vagueness resides only in language, you land in a very strange place, because you normally have to deny that there is such an object as the sun. Here is how that goes. The sun loses untold numbers of particles and huge amounts of energy by radiation, all the time, and there is in principle no way to say precisely when any such particle stops being part of the sun. If each of the many collections of particles that could make up the sun is an exact collection (something physicists tell us is not the case, but let’s put that aside), then there are massive numbers of exact objects that are equally good candidateto be the sun, and no way to select one as the sun. So, either you have to hold there are zillions of suns, all different but overlapping, or there is none at all. Now if you ask anyone except a philosopher what the largest celestial body is near the earth, they will unhesitatingly tell you it is the sun. Someone who seriously and sincerely denies the existence of the sun or who says there are many suns will be deemed ripe for psychiatric treatment. On the other hand, those who think that vagueness resides in our ignorance rather than in semantics will say that precisely one of the many exact candidates to be the sun really is the sun, and all the rest are not, but that we have no way of knowing which of them it is. Though consistent, that is even more unbelievable. It is impossible to see how our rough and ready conceptions could miraculously and unbeknown to us pick out exactly one sharp sun among all the many candidates.

The way out of all this is to deny that the sun is a sharp or exactly delimited object: it has a region where at any time many small particles are not definitely part of the sun and not definitely not part of it. There are some technical issues about how to explain the truth of such statements as that there exists exactly one sun and that it has such and such a diameter, mass and so on (these will also not be exact quantities), but one can deal with these in such a way that we can say truly and in all conviction that the sun exists and is a large object without a sharp boundary. What goes for the sun also goes in less dramatic but similar terms for all of us and other organisms, as well as other natural objects like rivers, and artefacts like aircraft. They are all to a greater or lesser extent “fuzzy”, but that doesn’t mean they don’t exist.

3:AM: Metaphysics isn’t an adjunct to semantics/applied philosophy of language, it isn’t physics, and has to give an account of everything, from consciousness to unicorns to society, modality, maths, phenomena, taxonomies and concepts etc etc – so how do you think it should be pursued? Can it avoid social and/or cultural relativism? Is everything an entity, including unicorns?

PS: That’s a very serious question, and one on which too few metaphysicians have reflected, to the detriment of the subject. Often metaphysicians will rely on what they call “intuitions” to help them work out a metaphysical theory and defend it against its rivals. Intuitions are supposed to be unchallengeable bases for assertions. The problem here is that the intuitions of different philosophers will often be in conflict, so it is not clear how to decide which, if any, are correct. The more scientifically minded will insist that metaphysics, if it has any rationale at all, should simply borrow the best confirmed theories from science and stitch them together to give an overview, leaving the hard graft to the scientists. While I am all for learning from the best science, this underestimates the importance of having a coherent overarching framework within which the sciences and other forms of knowledge about the world all have their place, which is what metaphysics is about.

So, the metaphysician has to proceed with a delicate balance of unbridled curiosity, bold conjecture, and extreme conceptual carefulness. They may start by collecting examples of things to be explained and put in their place, a hunter–gatherer quest for as many kinds of entity as possible. The next part is to sort out which of these have to be accepted at face value and which can be reduced, or explained away in terms of other things. To take one of your examples, any philosopher with what Russell called a “robust sense of reality” will deny that unicorns exist. But there are truths seemingly “about” them such as that they are horselike, have a single horn, do not fly etc., that need accounting for. Here the metaphysician will need a theory of myth and fiction that squares the fact that there are no unicorns with the fact that there is an established account of what “they” are like. Some metaphysicians will say there really are unicorns in other possible worlds, others that there are non-existent unicorns. These philosophers may lack Russell’s robust sense, but their theories cannot be just dismissed out of hand, because they are offering alternative explanations of the same phenomena. They must be argued against, and reasons given to dismiss some theories in favour of others.

This is the hard part in metaphysics: assessing and deciding between competing theories. It sometimes seems to go on for ever, or – more often – until people get tired and move on to something new. It’s also what makes many impatient with the subject and condemn it as hot air or just personal opinion. Assuming it’s not so, the third and hardest part of metaphysics is to bring the different partial accounts together into a single coherent and systematic whole. This is rarely attempted because life is short and most metaphysicians’ energies go on the fights between rival theories, but unless it is at least kept in mind as a desirable goal, there is no point in metaphysics; all we then have are an assortment of loosely collected problems and partial theories. To make this systematic enterprise work requires a universal conceptual framework of categories in terms of which any phenomenon finds its place. It also requires a metaphysician to make bold speculative conjectures that are not confirmed by evidence, but can still help to form a stable framework. For much of the history of Western philosophy, the principal speculative assumption has been the existence of a creator-God. As this example makes clear, these big hypotheses are not immune from revision and rejection. Systematic metaphysicians are rare, good ones rarer still, and good ones who get the important things right so rare there are very probably none at all. Aristotle, Aquinas, Leibniz, Bolzano and Whitehead were all good systematists but all got much wrong. When done properly, then, metaphysics should be the most difficult of disciplines: not difficult in the sense of requiring technical acuity like mathematics, physics or engineering, but in deploying that subtle blend of bravado and conscientiousness combined with a judicious sense of the plausible and sensible, and a balanced knowledge of the historical pitfalls, that requires a lifetime of learning, a rare wisdom, and yet the chastening awareness that scientific advance or hidden contradiction may overturn one’s most cherished ideas at any time.

3:AM: You’re interested in mereology – the relationship of parts to wholes – and you’ve proposed a new account that improves on previous standard accounts. So first, can you map out how mereology has been standardly handled, in particular by what the literature calls ‘the standard extensional view’?

PS: The term ‘mereologia’ was coined around 1927 by the Polish logician Stanisław Leśniewski. Before then there was no simple name for the theory of part and whole. In his early writings, he called it “theory of collections”. His motivation – as an early version of 1916 shows clearly – was to provide a consistent foundation for mathematics based on a notion of set or collection that was not subject to the paradoxes of set theory such as had been uncovered by Russell and others. His idea of a collection was that it is a whole made up of parts. Since Leśniewski did not believe in abstract sets, his wholes are concrete, spatiotemporal objects. He was dismayed to find that most others working on the foundations of mathematics preferred the much stronger (but in his view incoherent) set theory of Zermelo, and that may well have prompted him to coin the new name. To make his theory as powerful as possible for foundational purposes, Leśniewski made strong and debatable assumptions about what wholes there are. The first is that objects with the same parts are identical. This is mereological extensionality. It seems obvious, but there are apparent counterexamples, such as a bronze statue and the bronze of which it is made. The bronze existed before the statue did, for the statue was cast from the pre-existing bronze, so they are not the same. The other and much more questionable assumption is that any collection of objects compose a single whole, called their sum or fusion. I call this the General Sum Principle. This view seems absurd if we consider that collections may have as members objects from different categories and at widely different locations in space and time. For example, it would make the historical sequence of Kings and Queens of Poland together with the coastline of Norway, Napoleon’s left big toe and his last breath all compose a single individual. I think this view is crazy, but a lot of contemporary metaphysicians find it completely harmless.

Around the same time as Leśniewski, another writer was working out a formal theory of part and whole for very different reasons. Alfred North Whitehead developed what he called the ‘theory of extension’ as a basis for geometry and cosmology. His assumptions differed markedly from those of Leśniewski. For instance, Leśniewski thought there is one maximal whole, the universe, of which everything is a part: this is a consequence of the General Sum Principle. Whitehead on the other hand thought there was no maximal whole, but that every object was part of a more extensive one. Whitehead developed his ideas not as a theory in their own right but as part of his toolkit for the foundations of geometry, and what survived in print (sadly, all his unpublished writing was destroyed after his death, at his wish) is less rigorously worked out than in Leśniewski. Nevertheless, the differences between them showed that there could be more than one theory of part and whole, and it was these differences and the search for a common core of mereologies that motivated my own work, which surveyed the scattered literature and attempted to decide what to accept and what to leave. In doing so I came to the conclusion that there is a small core of principles which analyse or elucidate the concept of part, which cannot be denied without changing the subject, but that much that has been written about mereology, by Leśniewski, Whitehead and others, goes beyond that and makes substantive and often questionable additional assumptions.

3:AM: Does mereology mean that we need to have a well worked through theory of substance and accident and that this forces us to introduce modal and temporal concepts, and the notion of essence?

PS: You can have a mereology, as Leśniewski and Whitehead did, without subscribing to the classical theory of substance and accident. If you do accept something like the classical theory, then mereology is very germane to your explanations of what such a theory entails, since individual accidents are supposed to be, as Aristotle says, “in their subjects, not as a part, but as unable to exist without the subject”. So, unlike normal parts, accidents cannot be separated from their substances and make their way in the world alone, but being “in” the substance they help to make it what it is, so they are parts of it in an extended sense. Husserl called the contrast that between independent parts (“pieces”) and dependent parts (“moments”). Dependence is a modal notion. I once thought it analysable in terms of standard modal operators, but I now think it is a basic relation with modal consequences.

Now substances, in the traditional sense, come into existence, continue to exist for a time, then cease to exist, and in the meantime they undergo all kinds of change, some changes being mereological, others quantitive, qualitative and relational. A few years ago, I came to the conclusion that the only way we can account for truths of the form ‘such and such a substance exists at such and such a time’ is to look beneath substances to processes, those that sustain substances and other enduring things in existence. I now think that processes are metaphysically more basic that substances or other enduring things. That does not mean substances do not exist, but they are not basic. Unlike many so-called process metaphysicians, who think substances like you and I are processes, I am sure we need to distinguish sharply between substances and the processes sustaining them. This was incidentally also Whitehead’s opinion.

3:AM: Your new account takes into account both temporal and modal considerations. Can you first sketch for us your approach. Is it a nominalist approach, and if so, is it a Polish nominalism?

PS: The mathematical interests of the two pioneers of mereology meant that matters of time were rather sidelined in their theories, whereas in everyday life we generally come across objects whose parts change over time. In the case of organisms and their functional parts, if they stop doing so, they die. I started to develop a mereology with the notion of a part-at-a-time. Another motivation was to take account of the sketchy but suggestive ideas of the first person to come up with the idea of a formal theory of part and whole, Edmund Husserl. His views are heavily modalised: he talks of essentially dependent parts. I wanted to produce a mereology combined with modality, in which one could talk about essential parts, contingent parts, as well as essentially permanent parts, and the like.

So, I had two projects going on: one to find the conceptual core of the part concept, the other to see how that theory can be combined with related issues such as time, modality, persistence and integrity. More generally, I wanted to see how much ontology could be illuminated using mereology, as until then most ontology was little more than applied set theory or the semantics of predicate logic.

I am now a convinced nominalist, but when I wrote Parts I was more agnostic. Leśniewski and Goodman were nominalists of different sorts. Leśniewski did not believe in universals, numbers or other abstract objects, including sets. Goodman’s version of nominalism rejected sets but did not mind universals. If you are a nominalist, mereology is congenial, because unlike predication or set-membership it applies to items of the same type. You can in addition accept universals or abstract entities, but mereology alone does not force you to do so. The nominalism I think is right differs from that found among prominent Polish nominalists. Both Leśniewski and more explicitly Tadeusz Kotarbiński thought that the only entities to be taken seriously are concrete individuals. Kotarbiński believed the only things that exist are bodies. At first, he called his view ‘reism’, but to distinguish his materialistic version from the dualist reism of the later Brentano (who believed in both bodies and souls) he renamed it ‘pansomatism’.

I think any form of reism is too narrow a basis on which to account for the structure and pattern of the world, and prefer to deal in terms of concrete individuals – in the first instance processes – and their characters or features. The latter are individuals too, but dependent ones. Following Williams, I call them ‘tropes’, though initially I used Husserl’s term ‘moment’. They are common in medieval and modern ontology as individual accidents or modes. But unlike Williams, I don’t think you can get by with tropes alone: these congregate into more concrete individuals, and they in turn are related in various ways, building up the more familiar and varied items we encounter in life and science. My chief area of uncertainty concerns relations. An event like the collision of two bodies depends on two distinct things, and so is a relational trope.

Individual relational tropes are strange because they seem in many cases – unlike this one – to lack location, yet the world as we encounter it is full of things standing thus and so to one another, or in other words, related. For example, the distance between the Earth and the Moon at a certain time is so and so many kilometres, but I cannot envisage a distance trope somehow strung out between the two bodies like a long string. Their being so and so far apart must turn on other things. Nor however do I think it explains anything to say they stand in a univeral relation of being so and so far apart. I incline to think we can explain how this is without invoking a special class of relational tropes, by considering the processes in which they are involved, which are extended as they are essentially. The fact of processes being spread out has to do with how causation drives things forward: space, time and causation are intimately linked, but I am still puzzling over exactly how. Sometimes one needs to mull problems over for years or even decades before finding a congenial solution.

3:AM: Why do you think your approach is superior to previous accounts, and how does it help us understand better troubling philosophical concepts, such as similarity and equality between accidents, and the status of natural kinds and non-existing objects?

PS: It is an obvious fact that the world is both variegated and repetitive. There are many different things and kinds of things, for example dogs are not cats or trees or lakes, but there are also kinds of things with considerable similarities, even in some cases exact similarities. Leibniz thought there could be no two indistinguishable things, but I think that there are things which are exactly alike apart from their locations and relations to other things. Two carbon atoms at opposite ends of the universe may be in themselves exactly alike, but they are also different from the four oxygen atoms to which they are pairwise bound to make two molecules of carbon dioxide. Obviously these examples are remote from everyday experience, but we are familiar with less exact similarities, such as the similarities between two blades of grass, or two new coins, where any differences are so slight as to be invisible to the naked eye. The ways in which similar things may be alike or different can be factored: toy plastic bricks for example may be alike or different in shape, size and colour, for example, just as fundamental particles may be alike or different in mass, charge and spin.

These ways of being alike, that philosophers call properties, are intimately linked to the objects that have them, so intimately that it is no explanation to say two distinct objects share the identical property. The properties are very akin to parts of the object, but they aren’t detachable: they depend for their existence on the objects they qualify, so they are tropes. It is through the resemblances of tropes, exact and approximate, that things may resemble and be different from one another in criss-crossing ways. Some tropes are quantitative and measurable, such as mass. All form families giving a dimension of ways in which things may be alike or similar. In the very simplest things, like quarks, electrons and photons, there are very few tropes. Tell a physicist the mass, charge, spin and colour-charge of a particle and they will tell you what kind of particle it is. But to be simple an object does not need to be small. A photon can be smeared out over light-years during its passage from a distant galaxy to us. Nor do a simple object’s tropes need to be all together in space: so called quantum Cheshire cat experiments suggest a particle’s mass and charge can be separated in space but still belong together.

Natural kinds are then what we have when we have objects whose basic tropes come in clusters that are exactly similar to those in other instances. There may be variable properties as well. That is why I think only basic physical and chemical particles and stuffs form natural kinds. Organisms are too complex to do so, and evolution means there are no clear boundaries to kinds among organisms.

As to why the world is repetitive in its behaviour and structure, the regularities that hint at so called “laws of nature”, I am really not sure. What I find hard to take about laws of nature is how they can somehow force things to be regular. So I am rather agnostic about laws of nature, even though I concede it would be good to know why the world is so regularly repetitive.

Let me say a word about non-existing objects. One of the features of any metaphysics is that, because it is a framework discipline, it cannot simply copy its results from natural science. It has to place those results in the framework so that, as Whitehead says, everything is an instance of a general scheme. That requires metaphysicians to go beyond the data and entertain speculative hypotheses. My speculative hypotheses are naturalism and nominalism: I think everything that exists does so in the one spatio-temporal-causal cosmos, and that everything that exists is particular, either an individual, or a plurality of individuals, or a mass, or some combination of these. Non-existing objects, whether in other “possible worlds” or non-existent but in our world, as in Meinong, are outside that scheme. I strive my utmost to explain everything without bringing in non-existing objects. The reason is that they can make no difference to the world. How the world is, is determined by what is in it: non-existent objects aren’t in it, so have no say. An object which, by existing, makes a difference to the world, is a potential truth-maker, that is, could serve to render some thought true. If there is a Higgs boson out there, it and its fellows make the thought “There are Higgs bosons” true.

That is not to say that Meinong’s universe is not in many ways beguiling. For example, it gives a nice account of fictional objects, even if these are inconsistent. More importantly perhaps, a Meinongian can give a very tidy account of the nature of mathematical objects like numbers, sets, groups, topological spaces etc., which mathematicians consider determined only “up to isomorphism”. In Meinong there are so called incomplete objects, which are undetermined in many respects, but which can be “embedded” in others, in just the way mathematicians talk about. It’s a better position than platonism, which holds mathematical objects to be determinate, or structuralism, which denies that there are mathematical objects at all. It’s an attractive alternative, though I think it’s not the best we can have. The alternative is a version of formalism – but that’s a much longer story.

Tropes help to explain why simple things can be alike and different in various ways, but the objects with which we are most familiar are much more complex: they consist of parts related in various ways, often composing intermediate parts of a larger whole. Extreme mereological views, according to which there are no composite objects (mereological nihilism), or only organisms (van Inwagen’s organicism), or, at the opposite extreme, that any collection of objects compose a whole, render mereology useless in accounting for the nature of things. But saying what number and kinds of parts an object has can often contribute to the explanation as to what it is –– carbon dioxide molecules for instance, or the differences between birds and mammals. That is why I confine mereology in the first instance to telling us what the part concept is. When it comes to revealing what a certain kind of object is –– a rook, a river, a rickshaw or a rhythm –– mereology gives part of the story, but more has to be added about the configuration of the parts and what integrates them into a whole, as well as how the object typically “operates”.

Beyond this relatively modest aim for mereology and trope theory, there are two more ambitious ways in which the metaphysics to which I aspire seeks to improve on what is already out there. The first is to hunt out the features differentiating our basic ontological categories. I call these ontic factors. They are not entities in the world but distinguish the basic kinds by articulating the most intimate relationships among them: part¬–whole is one, but dependence, location, number, quantity and causation are others. Maybe there are more. There are hints of these factors in earlier metaphysicians, notably Aristotle, Whitehead and Ingarden, and a related position was taken up by the late Jonathan Lowe. An advantage of discerning factors is that if they are correctly identified, we can be much more flexible about categories than if we simply try to come up with a once-for-all list of basic kinds of object. Such lists not only spark often fruitless debates; they tend to need revising and updating because of scientific advance.

Categories are at the upper end of a classification of entities. In the twentieth century, analytic philosophers lost interest in the scientific problem of classification, mainly because it was assumed this could be left to semantics and set theory. Fortunately, advanced taxonomies were still needed in other disciplines, such as chemistry, biology and library science. In the latter two especially, there was independent but convergent evolution towards factors behind scientific taxonomies: in biology they are called ‘characters’, in library science they are called ‘facets’. Factors generalise the idea to ontology, but recognise the need for the factors to be metaphysical ultimates. Whitehead expresses the need for ultimates as follows: “In all philosophic theory there is an ultimate which is actual in virtue of its accidents. It is only then capable of characterization through its accidental embodiments, and apart from these accidents is devoid of actuality.” My only disagreement with Whitehead is over his use of the singular, ‘an ultimate’.

Factors in ontology are intended, like logical concepts, to be applicable anywhere, though unlike logical concepts, they aim to be about the world and not just regulating our cognition of it. Together, factor concepts and logic’s auxiliary concepts are the key to our aspirational metaphysical theory of everything. They also, in order to be the basis of a systematic metaphysics, need to form a coherent group, in which each one can only be properly accounted for by bringing in all the others. This requirement of coherence is not one that is commonly made in metaphysics. It is most openly stated in Whitehead: “‘Coherence’”, he writes, “means that the fundamental ideas, in terms of which the scheme is developed, presuppose each other so that in isolation they are meaningless”. In other words, the fundamental ideas form a tightly closed group rather than an assortment.

3:AM: You think that between mereological atoms or continuous non-atomic gunk there’s something else don’t you? Why do you think there are ‘extended simples’ and how is your view connected with Democritus, Kant and Whitehead amongst others?

PS: In the history of thinking about material objects on the one hand and space on the other, there have been two opposed positions. The one, atomism, holds that there are indivisible minima, whether material or spatial. Euclid called a spatial minimum a point, and defined it as “that which has no part”. A minimal material object is called an “atom”, meaning that it cannot be divided. For the Greek atomists from Leucippus and Democritus, atoms were physically indivisible but had a finite size, because they had shape. Something that has a shape cannot be pointlike, since a point has no shape, so it must have different geometric parts, even if it cannot be naturally divided. From a mereological point of view, it would seem that the only thing that could be completely without proper parts is a point, or a body which is point-sized. So Democritian (physical) atoms would not be mereological atoms. Aristotle and others thought there cannot be point-sized objects, because the world we observe is extended, and points cannot add up to extension. For such philosophers, matter cannot have pointlike parts, but must be divisible without end. So there seem to be two positions that can be adopted about things or the space they occupy: atomism (there are pointlike atoms); or atomlessness: everything is divisible without end. Standard mereology, as in Leśniewski, does not pronounce on which of these is true.

Both of the standard positions are speculative: they go beyond what we can observe. If atomism is taken seriously, it would seem that a pointlike object with a finite mass must have an infinite density, which is absurd. On the other hand, there is no guarantee that the smallest things are not so small that we are never able to observe them, even though they are not pointlike, so atomlessness is equally unsupported. We seem to be stuck. Leibniz called the problem of reconciling the indefinite divisibility of space and time with the indivisibility of atoms (he called them ‘monads’) “the labryinth of the continuum”. It’s a good rule of thumb that if Leibniz was puzzled by something, it is a genuine and serious puzzle. Modern quantum theory further indicates that there are lengths and times (so called Planck length and Planck time) which are the smallest distances and intervals that are physically meaningful, so no evidence could be given for or against atomism or atomlessness. This strongly suggests (though does not logically entail) that the smallest physical phenomena that have any effect or influence in the world cannot be pointlike but must have some finite spatial and temporal extent (though probably not a sharp boundary).

A way out of the dilemma is to give up the assumption that if a particle, event or phenomenon extends over a finite region, no matter how small, that it must have proper parts corresponding to the subregions of that region, an assumption I call the Geometric Correspondence Principle. This principle invites us to contemplate objects smaller in diameter than a Planck length and briefer in duration than a Planck time, based on the old idea that space and time are continuous. If we give up the principle, we can envisage events and objects that are without proper parts, but which extend over a finite region. They are extended simples.

The idea seems a little alien at first, but its advantages grow on one. Having toyed with the idea, I was surprised to find it in a very clear form in Kant. In his Physical Monadology of 1756, Kant was seeking to reconcile the infinite divisibility of space with the existence of physical atoms or monads. His way to do this was to regard the monads as physically simple but spatially extended. He wrote, “A monad determines the small space of its presence not via a plurality of its substantial parts, but via a sphere of influence.” Unlike Boscovich earlier and Bolzano later, who also took monads to have zones of influence, he did not take the monad to be “in reality” a little point sitting in the midst of its sphere of influence, but as it were smeared out across it or present throughout it (maybe to different degrees). I do not normally cite Kant, because I consider his critical and post-critical philosophy to have been disastrous for philosophy, but this was the young, pre-critical Kant.

In Process and Reality Whitehead – I think uninfluenced by Kant – took a similar view, except that his indivisible monads are small events rather than small substances – he called them “actual occasions”. Each actual occasion brings a small bubble of spacetime into existence with it, and unlike the occasion itself, which is atomic, the bubble is infinitely divisible. Indeed, from the mid-1920s Whitehead, who had developed his mereology for divisible events, confined it to spatiotemporal regions only.

Quantum theory strongly suggests that something along these lines is a better view than the classical ones. The main difference is that it is now thought that spacetime itself may not be a continuum separable from the events and processes that fill it. The general idea that physical indivisibles might spread out over a four-dimensional volume is much more in tune with quantum field theory, but it is quite possibly not the last word, so the “extended simples” hypothesis remains that – a hypothesis, albeit I think a promising one.

3:AM: All this is work done in the analytic tradition. Leśniewski seems to be a logician who is important in this field, but to most people outside of logic he’s probably obscure. Can you say something about this thinker and what he contributed to ontology and mereology, and why you find his contributions impressive?

PS: Leśniewski was an extremely original and fascinating figure, if not a particularly likeable one (he was fiercely, unsympathetically and often rudely critical of others, and in his later years very anti-semitic). His early work was in the philosophy of logic and language, where he was influenced by Mill, Husserl and Marty. What turned him into a logician was finding out about Russell’s Paradox of set theory. He spent years working out how best to avoid it (creating his mereology to do so), and worked on paradoxes throughout his life. He was obsessive about logical precision: Quine, who met Leśniewski in 1933, wrote, “Leśniewski was notable for the degree of prolixity which he was willing to admit in the interest of complete rigor and precision.” This prolixity stemmed in good part from Leśniewski’s nominalism: for him, a logical system is not a Platonic complex existing eternally, but a physical collection of meaningful marks which are added to by human logicians according to precise rules. Formulating these rules in a way which is self-updating as a system grew was a fearsome task, akin (before its time) to writing a self-extending grammar for a computer programming language, because the system grows not just by adding new formulas (theorems and definitions) but also by introducing new syntactical categories, which basically means that the further you extend the system, the more grammatically complex and expressively powerful it can become.

Aside from this nominalistic framework, there are two ideological features of Leśniewski’s logic with which I fully concur and which differ from standard modern predicate logic. The first is that quantification is allowed for variables of any syntactic category, and does not of itself carry any ontological commitment. An approximate rendering of how Leśniewski would understand a universal quantification ‘for all Z : …Z…’, where ‘Z’ can be of any category in the language, is “No matter how ‘Z’ may mean (of its category), …Z…”, and this neither requires that ‘Z’ be a name, nor that it range over certain entities. Leśniewski thus completely decouples logic from ontology, which in my view is exactly as it should be. The other feature is that in his logic of names, predicates and higher functors, a system he somewhat misleadingly calls ‘ontology’, Leśniewski does not restrict names to the singular, as do Frege, Russell and standard predicate logic, but allows names to be empty (as in free logic) but also plural (rediscovered as a valuable option by Boolos and others). This gives his system a much greater similarity to natural language than predicate logic has, and indeed it can be seen as a continuation and extension of both Aristotle’s syllogistic and Ernst Schröder’s algebra of logic. Because of this power and naturalness, it is my own preferred medium of logical expression. I even go beyond Leśniewski in accepting pluplurals (plurals of plurals), plupluplurals, and so on, to any level of ramification.

I already wrote about Leśniewski’s mereology, which remains in many ways the classical theory of part and whole, although – unlike many mereologists – I disagree with its General Sum Principle. There is little philosophy in Leśniewski’s later writings: he focusses exclusively on logic and the foundations of mathematics, and indeed tends to be very rude about what he calls, in scare quotes, “philosophy”. What more he may have written is unknown, because he died in 1939 and his manuscripts were destroyed in the war. I treat him as my provider of logical tools, agreeing with his generally nominalist outlook but disagreeing with his dismissal of philosophy.

3:AM: You’re working in the analytic tradition, but you seem hugely influenced and admiring of the Polish philosophers and logicians of the Lvov-Warsaw School. Can you tell us something about these philosophers and why you find them so impressive? Do you think understanding their contributions to philosophy deepens our understanding of some of the central features of analytic philosophy, and perhaps through better understanding the history of philosophical questions we get a better understanding of the problems that analytic philosophers are grappling with?

PS: The Lvov–Warsaw School produced a host of outstanding logicians, notably Jan Łukasiewicz, Stanisław Leśniewski, and Alfred Tarski, of the last of whom one may justifiably use the word “genius”. The doyen of commentators on this tradition, Professor Jan Woleński, regards Tarski as one of the four outstanding intellectuals to have come from Poland. But there were many more excellent logicians and philosophers in the School, not a few of whom were killed in the war. The fountainhead of the School was Kazimierz Twardowski, who had studied with Franz Brentano in Vienna and who from 1895 single-handedly turned Poland into a centre for excellent philosophy. His students from Lvov went on to become fine philosophers, logicians and psychologists. Twardowski valued expressive clarity, clear conceptual distinctions, awareness of the history of the subject, and the ability to work in detail at what was called “small philosophy”, which makes his School very akin in spirit to analytic philosophy. He was clearly a great teacher. It is no accident that the four life-size sculpted figures that adorn the entrance to Warsaw University Library represent Twardowski, Łukasiewicz, Leśniewski, and Tarski. I cannot imagine any other country in which philosophers – three of them logicians – would be so celebrated.

What makes the School and other Polish philosophy of the time so impressive is the balance they achieve between argumentative rigour, conceptual depth, expressive clarity, historical awareness, and down-to-earth sense. Because they knew about past philosophy, they did not fancy they were producing a unique and once-for-all “revolution in philosophy” as some other analytic philosophers did. Because they valued clarity, they were not taken in by flashy and deep-sounding gnomic utterances such as you find in Wittgenstein. Because they grew out of the Austrian rather than the German tradition, they were never tempted by Kant or German idealism. They respected good thinking where they found it, and it did not have to be all analytic: Roman Ingarden and Kazimierz Ajdukiewicz studied phenomenology with Husserl, and attempted to improve on what they had heard. Ajdukiewicz was also influenced by French conventionalism and American pragmatism. And the Polish logicians were among the first to appreciate the two greatest logicians of the 19th century, Bolzano and Frege.

For a while after 1918, Poles were concerned to build up their universities and write textbooks in Polish. They only began to be noticed elsewhere in the 1930s when they reached out to other languages and centres, by which time they had fully absorbed and integrated their several strands of influence. But that all came to a stop in 1939: many young Poles, especially Jews, were killed in the war, and after the war there was communist rule. Enough of the them survived to see off the intellectual threat of Marxism, and philosophers were also active and influential in the Solidarity movement. While contemporary Polish philosophy is not so obviously outstanding as that of the interwar generation, it remains serious and committed. Like few other nations, Poland punches well above its weight philosophically, and it retains that elusive balance and level-headedness that prevents it from veering into the wild speculative excesses of some recent analytic philosophy.

3:AM: What’s the relationship between the realism of Bolzano, Brentano and Meinong – and what’s the relationship between them and your own approach to metaphysics? Is it the Polish connection with the historically aware logicians of the Lvov-Warsaw school of whom you have engaged with over quite some considerable time?

PS: A common factor in these three great philosophers is their uncompromising rejection of Kant and idealism. Bolzano studied Kant carefully, disagreed strongly, and set out a reasoned realist alternative informed by his mathematical brilliance as well as his Catholic faith. Brentano made it his mission to rescue philosophy from the disaster of German idealism, taking his initial orientation from Aristotle. Both were persecuted for their perceived offences against church and state orthodoxy. Bolzano had to give up teaching, and celebrating mass or hearing confession, so concentrated on writing large systematic treatises. His Theory of Science completely refashioned and extended logic, but like his other large works on religion, ethics and mathematics, the forced obscurity of its publication in a small town in Bavaria meant he was not properly appreciated for generations, and his work has still to be fully evaluated and absorbed into the tradition. I rank him as the greatest of all nineteenth century philosophers, and as his work comes to be better known, especially after the publication of the English translation of Theory of Science, I expect others will come to share this (currently, extreme minority) view.

Brentano follows after him in my ranking. He continued teaching for fifteen years after losing his professorship in Vienna, and unlike Bolzano, he was unsuccessful at putting treatises together. On the other hand, his lectures and soirées were legendary, and his many inspired and brilliant students went on to become famous in their own right. His writings, the major part still unpublished, are far from easily accessible, and a settled verdict on his work and its importance is not yet at hand. For example, his famed reintroduction of the concept of the intentionality of the mental, which kick-started the phenomenological movement and much else, occurs in a book, his Psychology from an Empirical Standpoint, which he wrote basically in order to get the Vienna job, and of which only the first third appeared. He also changed his views radically over time, so that people had trouble following him, especially as he published so little. His strongly held view that philosophy aspires to be scientific in just the same way as the natural sciences is one I fully endorse, though I actually disagree strongly with his views on theism, mind–body dualism, and the rejection of tropes in his nominalism.

Meinong is an interesting contrast to both. Practically all of his work is accessible in print, and he had the fortune to become known in the Anglophone world earlier through attracting the attention of Bertrand Russell, who at one time esteemed his philosophy very highly. Russell’s later simplified and negative verdict on Meinong unfortunately misled people for decades into thinking that his work, with its acceptance of non-existent and even impossible objects, was flighty, ill-considered and easily refuted. It is anything but: it is sober and rather plodding, though it comes to startlingly original and radical conclusions. It is probably the most extreme realism there will ever be.

All three of these philosophers enjoyed little success in Germany, at that time the leading philosophical nation. Their views were simply too greatly at odds with those of Kant and neo-Kantianism, then the prevailing trend. Even today, it’s hard to find a philosopher in Germany who does not regard Kant as the supreme modern philosopher. By contrast, Edmund Husserl, Austrian by birth but German by choice, did move away from Austrian realism to German transcendental idealism. While this dismayed some of his followers, such as the brilliant Adolf Reinach and the young Roman Ingarden, it meant he fitted in better to the wider German milieu, and his extensive Nachlass spawned a veritable industry of transcription, publication and commentary, comparable only with those afforded to Heidegger and Wittgenstein.

Apart from Husserl, the most influential of Brentano’s students was Twardowski, because of the way he built up Polish philosophy. He is slowly beginning to be appreciated more widely for the quality of his own work, and I think in time he will be recognised as a key figure in twentieth-century philosophy.
Because of the way I was introduced to philosophy, I have always pursued my systematic work with one eye on the great figures of the past, particularly this Austro-German-Polish strand, which was not well known among analytic philosophers, who had been fed a one-sided diet of Frege, Russell, Wittgenstein, the Vienna Circle and ordinary language philosophy. It was not just the Polish part of the tradition that influenced me, since there are other areas of philosophy that they left rather untouched, such as the philosophy of mind. I would say it was rather the general attitude of serious but balanced realism that served as my guide in approaching the difficult issues of metaphysics. Other metaphysicians, such as Ingarden, Whitehead and Armstrong, as well as many contemporaries and friends, have also influenced my views. But I would not be in business as a metaphysician if I thought any of the philosophers I admire and from whom I have learnt got everything important right. I still think we are wanting a properly systematic analytic metaphysics, and I try to do my bit in working towards it.

3:AM: Van Inwagen proposes an ontology of just two kinds of objects: concrete objects and abstract objects and so is committed to a sort of Platonism. How would you summarise your ontology, how do you avoid any sort of Platonism and if you do can you claim that your truth bearers are absolutely true?

PS: Platonism has been around since Plato, obviously, and its critics have been around since Plato too, most notably his own star pupil, Aristotle. Many of the best philosophers have been Platonists: of those I have mentioned we can cite Bolzano, Frege, Husserl and Whitehead. Platonism is perhaps the default view if you take mathematics seriously in your philosophy, as all of these did. There have been notable anti-Platonists too after Aristotle: my own heroes are Ockham, Leibniz, and the American philosopher Donald C. Williams. I am an anti-Platonist for two reasons: I don’t think there is any way to make plausible how we could possibly have knowledge of Platonic objects, and I disapprove more generally of any metaphysics which divides the universe into such radically different subdomains as does Platonism, or, to take another example, mind–body dualism, since the connections and relations between the different subdomains all turn out to be some variety or other of magic.

So, to summarise my metaphysical credo: I believe in one world, the physical cosmos, comprising the heavens and the earth, and all the processes, things and organisms therein, including us, our mental lives, and all the products of our language and culture.

An anti-Platonist like myself has one advantage and one disadvantage over against the Platonist. We have only one realm or domain and so do not need to worry about cross-domain magic. Ockham’s Razor tells us that if we have two equally good theories and one of them commits us to fewer kinds of entities than the other, then we should choose the one with fewer kinds. If nominalism and Platonism can account for and explain the same phenomena, then nominalism should win. The problem with Ockham’s Razor is always that it is rare for theories to be so obviously comparable. Much more often, one theory has some advantages and drawbacks, and the other has different advantages and drawbacks. The drawback to nominalism is that there is much meaningful language that it cannot take at face value. There are millions of pages of pure mathematics which seem to be about timeless, abstract mathematical objects. A nominalist who does not simply turn away and lament this (as did Tarski, who was uncomfortably both a nominalist and an expert in set theory) has to find another explanation for how all these apparently timeless objects are as they are. That is the hard task for a nominalist. I am convinced it can be done, but it’s a long story. Another aspect of Platonism, the provision of universal kinds, is less problematic: that can be taken care of using tropes and a theory of abstraction as a cognitive operation. A Platonism of meanings, such as we find in Bolzano, Frege and Husserl, is another form that a nominalist has to account for. In those thinkers, the primary items that are true and false are timeless propositions, and they obviously cannot change from true to false or vice versa: their truth or falsity is absolute. But one can defend the absoluteness of truth without them. If I look out of the window and tell someone, “It’s stopped raining”, then I speak truly if and only if it is not raining outside where I am at the time I speak but was raining there shortly before. Truth characterizes my utterance, not the sentence I use and not a proposition, and it does so absolutely, even though whether it is true depends both on what I say and the local circumstances. I call it absolute truth without absolute truth-bearers. Incidentally, a very similar view was put forward in 1900 by Twardowski, and helps to explain why Polish philosophers and logicians put so much effort into trying to give us a good account of truth.

3:AM: And finally for the readers here at 3:AM, are there five books that you could recommend that would take us further into your philosophical world?

PS: My own writing is mainly in papers, which are obviously very scattered. The monograph Parts (1987, paperback 2000) is my largest piece: it took me fifteen years to write and is quite technical, but is closest to the questions answered here, and is my most cited work.

For the books from which I have taken most, I would say they are Frege’s The Foundations of Arithmetic,

Husserl’s Logical Investigations (there is a one-volume abridgement by Dermot Moran, The Shorter Logical Investigations),

and Whitehead’s Process and Reality. This last is by no means an easy read, and even professionals find it daunting, so to get an idea of what it’s about in a shorter and more accessible form I recommend my essay “Whitehead: Process and Cosmology”, in the fifth book, Robin Le Poidevin et al., eds. Routledge Companion to Metaphysics. That collection is a very comprehensive guide to metaphysics, past and present.

ABOUT THE INTERVIEWER
Richard Marshall is still biding his time.

Buy his new book here or his first book here to keep him biding!

End Times Series: the first 302

First published in 3:AM Magazine: Saturday, January 20th, 2018.