Saturday, 21 April 2018

An Introduction to Tropes

Since they have cropped up in a number of discussions before and arguably form an indispensable part of the metaphysics of 'Classical Realism', Scholastic Realism very much included, I thought it would be worth doing an all-round intro post on the subject of tropes. First of all a terminological distinction: the term 'tropes' and 'property-instance' will be used synonymous throughout this post, though the former is often used in the context of a certain kind of Nominalism it is in fact neutral as to whether one also includes universals in one's ontology. The term property-instance on the other hand might imply a realist commitment with said entities being instances of something above them. The phenomenologically inclined will of course also recognize tropes/property-instances as being equivalent to Husserl's 'moments'.

Hackneyed Tropes

What are tropes? Tropes are individual accidents, particular instances of a property. They form the backdrop of our lived experience of the world: much of our everyday discourse, our referring and judging, are about tropes directly and only mediately about universal properties. When we refer to the red of a rose, the pitch of a note or the wisdom of Socrates we are intentionally directed to these categorical entities, this particular redness, this particular pitch and this particular wisdom, and not the universals redness, pitch and wisdom1. As particulars, tropes are individual and unrepeatable; they are entities which come and go out of existence as and when their bearers gain or lose that property. It is from witnessing the unperishing universal kinship between these perishable individual properties that we come to recognise the need for and existence of universals proper: as Keith Campbell puts it in his classic 'Metaphysics of Abstract Particulars':

It is the existence of resembling tropes which poses the problem of universals. The accurate expression of that problem is: What, if anything, is common to a set of resembling tropes?

Aside from being phenomenologically self-evident tropes are potentially candidates for a number of core ontological roles, such as that of truthmakers. Consider the question: what is the truthmaker for the claim 'Socrates is wise'? It cannot merely be the existence of the particular substance Socrates and the universal Wisdom for these two might well both exist without Socrates' being wise. Might it not be Socrates' wisdom trope instead though? Said entity cannot exist apart from Socrates and has the existence of Socrates qua substance and the universal Wisdom as the necessary and sufficient condition for its existence. There is room for disagreement here but it would certainly be a good option for those looking to account for truthmakers without having to add states-of-affairs to their ontology to explore.

Trope Nominalism

Most people first hear about tropes in the context of modern Nominalism. Now, the famous proposals for trope Nominalism were bound in with related proposals pertaining to the Bundle Theory of Substance, construing the world as made up of nothing but tropes, but as this is strictly speaking a separate issue, I'll put it aside and attempt to give a brief rundown on the Nominalist part.

A comparison with Resemblance Nominalism will help here. Resemblance Nominalists (at least of the old guard), on the one hand, were wont to claim that to say x entity was red was to say that x entity belonged to the set of entities which resembled one another. This lead among other things to the famous Problem of Imperfect Community since it was hard to see how one could get by with saying x entities resemble one another without clarifying as to in what manner they resemble one another (remember our Resemblance Nominalist does not want to bring in properties either particular or universal). Trope Nominalists, on the other hand, assay claims to the effect that 'x is Red' as 'x possesses trope R which is a member of an appropriate set of resembling tropes'; this avoids Imperfect Community since tropes just are their quality there is arguably only one strong determinate way in which they can resemble one another. So what is it in virtue of the members of a set of resembling tropes resemble one another? The—highly unsatisfying—answer Trope Nominalists are wont to give is: They just do, resemblance is primitive, stop asking questions', a maneuver which somewhat begs the question 'Well if you are content just to take resemblance as primitive why bother with tropes in the first place and not just go down the Ostrich Nominalist route?'. Keith Campbell is alive to this problem and admits that even if a trope-centric ontology is the correct one we might not be able to do without universals after all. There is also the perennial problem facing Nominalist theories which account for objects or properties as Sets in that Sets have their members necessarily.

The prime way in which Trope Nominalists and Realists will differ over the nature of these entities is that the former must hold them as simple whilst realists will assay them as complex being composed of an individuator, exemplification relation and universal. This notion of simplicity is crucial: to quote Moreland it's something they must do if they are to avoid assigning the individuating and qualitative aspects of the trope to non-identical internal constituents. Unfortunately, it has proved a difficult task as the various drastic modifications Campbell has made to his own account show. On his early view tropes not only have their spatial, and perhaps spatiotemporal, location essentially but are in fact identical to it, an endorsement which pushes one towards the uncomfortable conclusion that two tropes sharing a location are in fact identical; more recently he attempts to circumvent this worry by introducing spatial location as an additional ‘quasi-entity’, a ‘quasi-trope’, which is not identical to a given trope but is tied in with it by a ‘quasi-relation’ of necessity—aside from the obvious difficulty of understanding how the hell a ‘quasi-entity’ can be anything other than a real entity the philosopher does not want to include on his or her ontological tax return this comes close to making so-called nominalistic tropes into one-time abstract Platonic universals. In short Nominalism remains a chronically unattractive option.

One and Two Category Ontologies

And now we come back to the more radical proposal behind Trope Nominalism: that we can satisfactorily account for the world in terms of tropes alone, that they provide all the metaphysical resources we need for a 'One Category Ontology' (technically this moniker is inaccurate as the Nominalist still owes us an anti-realist account of the Sets to which they are also committed but we shall ignore this for now). If objects are construed as nothing but tropes and tropes properties, albeit particular ones, then this proposal is evidently a version of the Bundle Theory of Substance

Before we go any further it must be noted that by no means all Trope Nominalists are willing to take this step; some, like the late C. B. Martin and his disciple John Heil, maintain the more traditional view that properties are always properties of something, that they require a bearer to adhere in. As such, they are Substratum Theorists.

Let us compare the virtues of the Trope Bundle Theory with that of its Realist counterpart. The Realist Bundle Theory which holds that all seemingly particular entities are really clusters of universals is subject to a well-known objection which many philosophers of the last century took to be decisive: it entails that no two beings can be qualitatively identical without being numerically one and the same. If bundle a is made up of universals F, G and H, and Bundle b is also composed of these universals then a and b must be the same being. This strong variation of the Identity of Indiscernibles is considered to have been refuted and with it the Bundle Theory. Such appraisal is probably unfair: the validity of supposed counterexamples to said principle are subject to challenge (one might for instance appeal to temporal properties or argue that the inter-determinacy of the physical shows that Symmetrical Universe scenarios are impossible) and even if its falsity is granted in recent years Bundle Theorists have proposed increasingly sophisticated solutions involving higher-order universals.

The Trope Bundle Theorist does not face this problem. On his or her theory no two tropes are ever identical and, in consequence, if objects are just bundles of tropes then no two objects can ever be identical. However it is still a Nominalist Theory and as such is subject to many of the objections facing all Nominalist theories along with special ones of its own.

However there is an ace up the Bundle Theorist’s sleeve, one which few have recognised the full power of. There is in fact a simple yet radical solution to the problems outlined above, that is, to combine the two theories to give a Realist Trope/Property-Instance Bundle Theory. On this objects are conceived of as bundles of tropes; as tropes they are unrepeatable and unique, however these tropes still stand under the universals of which they are instances freeing the theorist from the worries of Nominalism and the uneasy spatial account of trope individuation. If the theorist is so minded they might also endeavour to assay mathematical entities as structural universals first grasped via their instances; this way they might be able to avoid the need to posit Sets qua Quinean perfect particulars as silent additions to their ontology. Thus far dual Universal/Trope Bundle Theories have received very little attention, which is a shame; if the problems facing all forms of Bundle Theory i.e. subject/predicate discourse and the unification problem, can be overcome then we have an account which is superior to other contenders including Aristotelian substratum theories (Jeff Brower has argued that Thomas is a Substratum Theorist albeit a sophisticated one).

To conclude: tropes form an essential part of any Constituent Ontology from at least the time of Aristotle onwards. They accord with essential aspects of our experience of the world and have great ontological versatility, though more radical proposals to assay the world in terms of nothing but tropes are suspect.


1From an axiological standpoint tropes also explain how we can value the qualities of others qua individuals, as non-fungible goods. The beauty of one's beloved might be an instance of the universal Beauty but qua instance it's an unrepeatable entity, something unique and beyond even the power of God to duplicate.

Essays and References

Elements of Being – D. C. Williams

This famous, lucidly written essay is the locus classicus of Trope Theory and Trope Nominalism. The actual arguments for Nominalism are non-existent but it contains an in-depth phenomenological analysis of tropes and the central role they play in our perceptual and intentional experience of the world. Although he only wrote a handful of essays Williams was one of the most interesting Naturalists of the 20th century and one of the few who paid a relative amount of respect and attention to Neo-Scholastic writers.

Keith Campbell’s equally famous essay on the virtue and power of Trope Theory. It starts with an accessible overview of the main arguments for tropes, the thinking behind One Category ontologies, and ends with a brief summary of Campbell’s own theory of tropes and spatial location.

Realist Bundle Theory – David Pitt

One of the few sketches for a Realist Trope Bundle Theory:

Another of the few sketches for a Realist Trope Bundle Theory:

Peter van Inwagen's Trouble with Tropes – William F. Vallicella

(Bill Vallicella’s common sense defense of Tropes against Inwagen)

(Lowe talks about the potential role of tropes as trumakers in preference to States-of-Affairs)

(Lowe gives further information on what he sees as the importance of including Tropes in one's ontology)

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