6. Four Category
Ontology (E.J. Lowe)
7. Property-Object Ontology (M. Kistler)
8. Ontology of Physical Laws and States (R. Wasserman)
9. Summary of Modern Realist Discussion
10. Abstract and Concrete Objects
Readers already familiar with modern treatments of ontological questions may have found the discussion in Part I to be quaint or naive in its assumption that all four ontological classes ought to be taken seriously as possible representations of real entities. Most modern philosophers claim to reject one or another aspect of the ontological square, or deny category theory altogether, either on a priori or a posteriori grounds. We will set aside the critique of those who deny we can know anything about objective reality, for it belongs to a treatise on epistemology to show how this position is self-stultifying and incoherent. Instead, we will address the concerns of ontological realists, those who admit we can know things that are, yet nonetheless find problems with the classical ontological classes. I will show that modern realist treatments, despite their novel terminology, actually refer to the same conceptual entities as the classical ontological square, all four aspects of which are necessary to give a conceptually complete account of possible reality.
We should note that most contemporary philosophers treat ontological questions a posteriori, as judgments of metaphysical reality. This differs from our approach, which is confined to a priori conceptual possibilities. Nonetheless, by showing that a four-class ontology holds up well even in modern a posteriori discussions, we gain confidence that our model is not only conceptually useful, but will eventually help lay a solid foundation for metaphysics.
Four-CategoryOntology (E.J. Lowe)
A leading exponent of a four-class ontology is the English philosopher E.J. Lowe of Durham University, who has written extensively on this topic. Lowe, following the modern convention of applying the term category
to any logical or ontological fundamental, calls his theory a four-category ontology, where his categories are what we have called classes
of entities in the ontological square. Following classical usage, I usually reserve the term category
for the ten Aristotelian categories of substance and accidents. Nonetheless, in Part II, we will allow category
to take the broader meaning of any ontological fundamental, though we exclude purely formal constructs, as we are concerned with ontology, not mere formal logic. Aside from terminology, Lowe’s system has some substantive differences with the classical ontology we have expounded, but an examination of the dialogue between Lowe and his critics will show that the basic premises of classical ontology are still highly relevant to contemporary philosophy.
Lowe has astutely observed that a major flaw in the approach of many modern philosophers is the substitution of set theory or some other mathematical or logical syntax for a real ‘science of being,’ as though we could substitute a model for reality without any loss of meaning. In particular, we must dispense with the notion that set theory can provide an adequate substitute for a theory of categories of being. A set has no existence apart from the elements of which it is constituted, whereas a category or universal is conceptually independent of its individuated subjects. The concept pig
contains something other than merely the set of all individual creatures that we identify as pigs. On the contrary, we could continue to define and understand pig
even if no more pigs existed, and even if no pigs ever existed. In Lowe’s words, a universal is not exhaustively specified
by its dependence relations with particulars. When we use set theory notation to make an individual subject an element
of a species, or a species a subset
of a genus, we are being sloppy with concepts, and losing information. A species is not a subset of a genus, though we can say that, as a logical consequence of the relationship between species and genus, the set of individuals belonging to a species must be a subset of the set of individuals belonging to a genus. Set theory can be a useful shorthand, but it is never a substitute for a theory of universals. The abuse of set theory and other forms of mathematical logic can lead to an evisceration of the ontological content of philosophy, leaving only relatively barren algorithms.
In his 2001 lecture, Recent Advances in Metaphysics,
Lowe usefully shows how modern realist ontological schemes can all be related to the same hierarchy of categorical concepts, the difference among schools being only which categories are to be suppressed or reduced to other categories. The names of these modern concepts are displayed below, with their classical analogues shown parenthetically.
In this overview of modern realist ontological schemes, entities are subdivided into universals and particulars, with particulars subdivided into objects and tropes. Object
is simply another name for individual substance, while trope
is a modern term for individuated accident. Various schools of realism attempt to reduce some of these categories to others. So-called trope theorists
contend that objects are reducible to tropes. In this view, a flower consists of nothing more than a collection of localized properties such as color, mass, and smell, but there is no underlying substance
that has color, mass and smell. Trope theorists also reduce universal accidents to tropes, claiming they are nothing more than classes or sets of tropes that resemble each other. Thus the universal red
is nothing more than the arbitrary collection of all individual instances of redness. Other philosophers, such as C.B. Martin, admit the existence of objects as a fundamental category distinct from tropes. Still others, such as the Australian factualist D.M. Armstrong, admit objects but reject tropes, allowing the existence of only universal accidents or properties. Few modern ontologists regard universal substance as a category of being, so it is omitted from the diagram.
The disputes among modern ontologists at the most fundamental level of category theory reduce almost entirely to the question of which of the four classical ontological classes of entities are real. An overzealous application of Occam’s razor leads many to favor either pure trope theory or an ontology consisting solely of individuated objects and universal properties. The latter property-object
ontology is motivated by the recognition that the laws of physics are relations between universals. These laws hold not only for actual substances in existence, but also for potential substances that might someday exist. The predictive power of physical laws consists precisely in their applicability to counterfactual conditions, that is, their independence of individuated realities. Thus physical laws necessitate universals.
Trope theorists are on less solid ground, since their denial of universals is difficult to reconcile with the reality of natural laws, and their denial of individual objects strains credulity. In their view, individuated substances are merely bundles of tropes, effectively giving tropes the ontological independence that is characteristic of substance. This reduces trope theory to mere wordplay, since the trope theorist’s tropes
are effectively substances, and there is the additional difficulty that such bundles of tropes would be free to disintegrate at will. The trope theorist believes his single-category ontology to be parsimonious, yet this is achieved at the expense of the absurdly unparsimonious account of all individual entities in nature. We are to believe that redness, mass, shape, and other tropes independently sustain themselves in a cluster, rather than admit that a single substance, the rose, sustains all these different individuated properties. Trope theory has plausibility only to the extent that we confuse individuated tropes with the microscopic parts of an object. A part, of course, is a substance, not a trope.
The aversion of some modern philosophers to admitting the existence of substance comes from a fallacy similar to that advanced by Kant against the distinction between essence and existence. It is argued that substance
adds nothing to our description of an entity, for we have completely accounted for it by a summation of all its properties. Lowe has noted that this criticism presumes that properties or tropes are constituents of an entity, rather than ways of being. We recall that accidents are existentially dependent on their subject, which could not be the case if they were constituents. Thus Lowe is correct to regard substances as bearing
properties, sustaining them in their individuated existence. These properties modify the being of the substance, but it is incoherent to regard individuated accidents as constituents or parts of an entity.
At least three of the classical ontological classes can be established as real to a high degree of certainty. If there are any entities at all, logical coherence demands the existence of individuated substances (objects). Trope theorists circumvent this necessity only by making tropes effectively substances. The reality of physical laws, or the regularity of behavior in nature, is potent evidence in favor of the reality of universal properties. Lastly, Lowe argues, individuated accidents must exist since the observation of a property in a particular object does not entail my apprehension of the same property in another object.
The most difficult challenge for Lowe is to establish the reality of universal substances. He approaches this task by first showing that natural laws apply to counterfactual conditionals. His example is the law that a planet moves in an elliptical orbit, a principle whose truth implies that if an actually planetless star had a planet, that planet would move in an elliptical orbit. This counterfactual conditional does not follow from the mere fact that every actually existing planet moves in an elliptical orbit. The applicability of physical laws to counterfactual conditionals requires that they be considered as relations between universals. This necessity applies equally whether the terms of physical laws are substances or accidents, so Lowe might have left the argument there, but he proceeds to attempt a further justification for universal substances that is problematic.
Lowe contends that the four-category ontology makes a better account of dispositional (potential) and occurrent (actual, or categorical,
in unfortunate modern terminology) states of objects. He begins by showing that universal accidents are necessary, since the proposition X is water soluble
means more than simply If X were immersed in water, than X would be dissolving,
for there are any number of inhibiting conditions that might prevent it from actually dissolving. Water solubility is a real potentiality, a real attribute, independent of any instance of its actualization, so it is not to be regarded simply in its individuated manifestations. Unfortunately, Lowe does not stop with using this example as an argument for universal accidents, but proceeds to give a strange account of dispositional and occurrent states as though they depended on which sides of the ontological square we were to trace.
In Lowe’s account, an object has a disposition to a universal accident or property if it instantiates a species or kind that is characterized by that property. For example, this salt
has a disposition to be dissolved by water because it is an instance of the kind sodium chloride,
which has the property of water-solubility. According to Lowe, an object is occurrently a property when it bears an individual accident (trope or mode) that instantiates that property. Thus this salt
is occurrently being dissolved by water when it bears the relational mode of dissolving, which is an instance of the universal relation of dissolving. An object exemplifies a property dispositionally or occurrently depending on whether it is linked to that property via a species that is characterized by the property or by bearing an instance of that property, as shown in the diagram above.
This analysis demands too much of the ontological square, for it really should not matter which sides of the square we follow from an object to a universal property. If an object exemplifies a property, then, by definition, it belongs to a species that is differentiated by that property, and it has an individual instance of that property. In his desire to make universal substances more real, rather than a matter of arbitrary definition, Lowe has tried to funnel dispositional tendencies exclusively through universal substances and not through individual accidents, to make the former ontologically indispensable. However, both dispositional and occurrent states can be accounted for by both paths in the ontological square.
For example, suppose a certain leaf occurrently exemplifies the property green.
For this to be true, the leaf must both possess a localized instance of the property green
(per Lowe), and also belong to a universal species or genus differentiated by green.
If the latter were not the case, this leaf could not be green, since it would not belong to any genus differentiated by the property green,
not even the genus green objects.
Since Lowe has wedded his concept of universal substances to the notion of physical laws, rather than using such laws as but one example among many of the need for universals, he would probably not admit that there must be a real genus green objects,
but instead restricts universal substances to those entities related in dispositional laws of physics. Since Lowe contends that all natural laws are dispositional, it follows for him that universal substances only have bearing on dispositions. Anything else is just arbitrary taxonomy.
While this implied limitation on the scope of universal substances has the advantage of giving them a stronger basis for acceptance, grounded as they are in the laws of nature, the analysis still fails since dispositional states may be expressed through individual accidents or universal substances equally well. If this leaf
has a disposition to become orange in the autumn, we are saying both that it has the disposition to become a member of a genus that is characterized by orange
and that it has the disposition to instantiate the property orange.
In Lowe’s account, the leaf would be potentially orange by virtue of already belonging to a genus that is defined by the disposition to become orange. While this is a valid approach, it does not exclude our ability to account for disposition by saying this object has a tendency to instantiate this property, so the necessity of universal substances cannot be established through this contrived separation of dispositional and occurrent ontological routes.
The question of potentiality and actuality is of a different order from the distinction of essences into universal and particular, substance and accident. While it is true that we tend to identify the individual with the actual and the universal with the potential, these are different dichotomies, and it is quite possible to treat individuals both as actuality and potentiality. Although the mathematical formalism of quantum mechanics may tempt us to collapse these two dichotomies into one, we must resist this false parsimony, recognizing that a potentially existent individual is not the same thing as a universal. The individuated orange that this particular green leaf may someday have is not numerically identical with the universal orange
which already is actualized in many individuals.
In upholding the four-category ontology, Lowe holds a minority opinion among contemporary philosophers. Critics of his position, as we shall see, do not directly undermine the four-category model as such, but address subordinate issues or at most maintain that the necessity of all four categories has not been proven. While reviewing some of these criticisms, we can identify some of the stumbling-blocks to modern acceptance of a full classical ontology.
Max Kistler of the University of Paris at Nanterre has detailed some of the limitations of Lowe’s four-category ontology. (Analysis 64.2, April 2004, pp. 146-51.) First among these is Lowe’s definition of an individual, which has three conditions:
An individual object:
- bears properties
- possesses determinate identity conditions
- has the unity required for making it countable
According to Lowe, any entity meeting the first two of these criteria but lacking the third is a quasi-individual, while an entity lacking only the second criterion is a quasi-object. Kistler points out that this makes it possible for something to become or cease to be an object, a problem that arises from the third condition's requirement of countability. This criterion would make homogeneous parts of a discrete whole fail to be objects, contradicting common sense and leading to a host of paradoxes.
Lowe’s notion of countability is excessively narrow, failing to regard parts of homogeneous, continuous substances as countable. It is true that there are uncountably many such parts, but that does not preclude treating each extensive part as an individual object, at least in potentia. As Kistler notes and as I have shown in my study of intensive and extensive magnitudes, counting requires an arbitrary unity of measurement, as well as a means of distinguishing parts so they are not twice counted, this latter condition being met by regarding the parts in a common space. Space can serve as a principle of individuation
(in the sense just described, not the classical Aristotelian sense), since objects can act as landmarks distinguishing one point in space from another, and these points in turn can distinguish parts of objects from each other. A milliliter of fluid in the bottom of a flask is distinct from the milliliter of fluid in the upper portion of the flask. Each portion of the liquid is clearly not a universal, so it is a particular, and it is not a trope, so it is an object.
Kistler’s critique of Lowe’s quasi-objects
is muddled by an uncritical acceptance of the Copenhagen interpretation of quantum mechanics, which I have refuted at length elsewhere. It is unfortunate that philosophers should show such deference to the philosophically incoherent thinking of physicists, thereby deforming metaphysics when instead metaphysics ought to impose itself as a corrective to the great quantum muddle,
as Karl Popper aptly termed the Copenhagen school of thought. Since even Richard Feynman admitted, No one understands quantum mechanics,
philosophers should know better than to accept the metaphysical interpretations of physicists uncritically.
Kistler and Lowe both assume that quantum mechanics has somehow firmly established
that two electrons in a helium atom cannot be taken to be individuals which could be described, as if they were bearing a tag.
Such an interpretation, as Kistler rightly notes, would imply that electrons become individual objects when they leave the atom and exist as individuals, where they can be perceived as such. However, this interpretation is by no means firmly established; it is but one interpretation of Fermi statistics. The behavior of fermions, such as electrons in an atom, is accurately described by a statistical model that differs from what we would expect using classical probabilistic theory by a factor of 1/N!. This is all that is firmly established.
It is a gratuitous interpretation that this means the electrons lack individuality. On the contrary, there are other aspects of quantum theory where the permutation symmetries of so-called identical particles
are explored with a transposition or particle-exchange operator. Although the wavefunction often does not change after particle transposition, the underlying permutation symmetry theory of identical particles explicitly assumes their individuality.
A pair of electrons can be in physically identical states with respect to the observables with which we are concerned, such as their distributions of positions and momenta. This is not the same as an ontologically absolute lack of individuality. In fact, if the electrons did lack such individuality, there would be no reason to expect an atom with two electrons to behave differently from an atom with one electron. If we are to regard the bound electrons as a homogeneous collective double-electron,
the fact remains that we can potentially split this double-electron, so that each part is an individual object, at least in potentia. Without a thisness
(or haeccity) to each electron, there is no means of distinction from the universal electron,
and no means of applying quantity or countability. We would have no way of knowing how many electrons are in an atom, since there would be no way of knowing if we are double-counting. In fact, we know exactly how many electrons are in an atom from their negative charges, which add extensively, proving that the electrons are distinct at least in charge space.
Moreover, the individuality of fermions is explicitly established by the Pauli exclusion principle, which prohibits two fermions from occupying the same physical state.
Particles that behave according to Bose statistics, or bosons, are capable of occupying the same energy state, and their wavefunction does not change under particle exchange, so bosons are more likely candidates for quasi-individuals than electrons or other fermions. Yet even bosons with their symmetric wavefunctions are subject to the same permutation theory as the antisymmetric systems of fermions, a theory that presumes the individuality of each particle. The proof of the physical relevance of this permutation theory can be seen when a symmetric (boson) state is crossed with an antisymmetric (fermion) state, creating a mixed state that follows permutation rules derived from the assumption that bosons are individually distinct.
In sum, quantum mechanics has done nothing to abolish the individuality of particles; on the contrary, at its deeper levels, it explicitly upholds their individuality. The mistaken belief that quantum statistics disproves individuality comes from a false identification between a particle and its (spatial or spin) wavefunction. The wavefunction only tells what state a particle is in with respect to some observable. If quantum probabilities sometimes are quantitatively analogous to a condition where particles are not individually distinct, this only proves that the individuality of particles has no bearing on the physics in question, a fact that does not abolish the individuality of particles as such.
Using his erroneous interpretation of quantum mechanics, Kistler halfheartedly tries to rehabilitate Lowe’s notion of objecthood by using a weaker condition, such as the requirement that a particle have individuality only sometimes. This would again create the problem that objecthood depends on contingencies. Alternatively, we might say that an object only needs to have the potential for individual identity. However, Kistler finds an objection with entangled quantum states, contending that we cannot say that an electron in an entangled state is potentially an object, because there is no definite it
(the electron) that can be identified in the entangled state. This is another misreading of quantum mechanics, similar to what was discussed above. Our inability to observe the electron as a distinct individual in no way abolishes its distinctness from its partner in an entangled pair. Their individuality is evidenced, for example, by the fact that their charges add to -2, and on a deeper level, the fact that their wavefunction would change by a factor of -1 under particle exchange. More importantly, the identity of a particle as an individual object should not depend on its physical effects or its ability to exist in an empirically distinct state. It suffices to show that their properties can be extensively added or that their underlying permutation theory presumes distinctness. More simply, it would suffice to show that they are not universals and not tropes.
Kistler’s one legitimate criticism of Lowe’s definition of objects is that it disqualifies pieces of continuous, homogeneous matter as objects. Lowe’s requirement that only a maximal collected part of stuff
can be an object reduces objecthood to physical contingency, since no piece of stuff is necessarily maximal, as it is always possible to add another piece. Thus all pieces of stuff are effectively disqualified from objecthood, contrary to clear intuition.
These problems might have been avoided if Lowe had retained in view the simple dichotomies between universal and particular, substance and accident, without attempting to impose additional conditions in order to achieve harmony with poorly understood physical theories. If ontology has any merit, it should not depend on this or that theory of physics, since physics only describes some aspects of reality, while ontology must be all-encompassing. It has become an unfortunate habit among philosophers to disregard intelligible concepts as meaningless if they do not neatly correspond to a construct of empirical science. This form of criticism, used for example against causality by Hume and Russell, misunderstands the concept of meaning, and ascribes to physical science a potency and scope that most scientists would be unwilling to claim. Such critiques generally misuse physical science as a basis for rejecting concepts that philosophers in fact object to on ideological grounds.
Kistler next turns to Lowe’s treatment of universal substances, or kinds,
which have always been a contentious area of ontology, even among classical realists. He disputes that kinds or species meet the requirements defined by Lowe:
A kind, or species, being a universal object or substance:
- is a genuine property bearer
- has determinate identity conditions and is countable[!]
- has ontological independence
The first two requirements (minus the misguided countability requirement) are the same as those for an individual object, and may be regarded as the definition of substance
in general, whether universal or particular. The third condition differs from that for individual substances in that there is no requirement of unity or countability, but only of the ontological independence that distinguishes substance from accident. We note the loose similarity to the Aristotelian definition of substance, which is simply that which is not in a subject
in the formal sense discussed earlier. Lowe’s inclusion of a countability requirement in condition (2) is a serious mistake, since it erases any distinction between universal and individual objects, a weakness Kistler will exploit much later.
According to Kistler, kinds do not bear properties in a more genuine sense than (first-order) properties.
First, he suggests that being numerous or rare are clear cases of properties of kinds,
so Lowe is wrong to reject these. This criticism is misguided, since a universal is abstracted from any individual instantiation, so that being numerous is a property of a set of individuals, not the universal. Kistler makes the common modern mistake of equating a universal with a set of individuals instantiating that universal. When we speak of being numerous or rare, we are speaking in the order of particulars. A kind or species must be defined by a universal property. Elephant
(in the universal sense) does not change whether there are many or few individual elephants.
A more substantive argument by Kistler is that Lowe’s examples of properties of kinds seem to be properties of the members
(note Kistler’s set-theoretic terminology, rather than the more appropriate individuals
) of each kind. Addressing the example of salt’s water-solubility, Kistler argues that the property of being water-soluble is only properly attributable to particular samples of salt, not the kind,
as only the former can dissolve in water. In effect, he is asserting that since only individuals have the potential to actually manifest instantiated properties, that only they can bear properties. Kinds may be characterized by universal properties, but this is different from bearing them. Using our classical terminology, we would say that exemplifying a universal accident (property) is different from being differentiated (characterized) by a universal accident. Kistler is basically arguing that bearing
properties entails exemplification, which is impossible for universal substances. This is not necessarily so, for we may say that a universal substance bears properties in the sense that the definition of the property is contained in the definition of the substance, so that the universal species contains
all that is essential to the universal property. The species man,
defined as rational animal,
contains in its essence all that belongs to the property rational.
While it is certainly not the case that the universal man
exemplifies rationality, or anything else for that matter, it is begging the question regarding the existence of universal substances to deny that they can bear
properties in a more abstract sense, containing the essence of properties in their own essence. If it is conceded that properties may exist as universals, it hardly seems necessary that only an individual is sufficiently palpable to bear them.
Kistler’s presumption against the existence of universal substance is shown by his strange account of being gold
as a property. He says:
If being constituted by atoms with the atomic number 79 characterizes being gold, this is because the former property is a constitutive part of the latter, complex property.
This conception of properties is more linguistic than ontological, as it evades the necessity of universal substances by describing them in adjectival rather than sortal terms. Instead of the property having atomic number 79
being a differentia of the species gold,
it is to be regarded as a constitutive part
of being gold,
which is considered a complex property.
Treating being gold
as a property is a serious category mistake, since being gold
does not depend on being in a subject, as properties do.
It is not enough to phrase something as being X
to make X a property. The whole point of category theory is to define categories or classes of being. Being
itself transcends all categories, which may be said to describe different ways or senses of being. We could apply the phrase being X
equally well to a universal or particular, substance or accident. It would clearly be a mistake to regard being this particular piece of gold
as a universal property, since individuality is contained in the definition or statement of essence. Similarly, to regard being gold
as a property presumes what Kistler pretends to prove, that gold
is an accident. Embedding an entity X in the phrase being X
cannot change its category, since the meaning of being
is specified by the category of X
If gold
(the element, not the color) really were nothing more than a complex property, it would necessarily exist in a subject
Y such that Y is gold.
Since Kistler rejects universal substances, the only possible subject for gold
would be individual pieces of gold. Yet gold
is conceivable independently of its individual instances, and the relationship between individuated gold
and gold
is fundamentally different from the relationship between individuated gold
and a property such as heavy,
since heavy
cannot be instantiated without the presence of a subject in which instantiated heaviness inheres, while gold
can be directly instantiated without recourse to some other subject. The relationship between "gold" and individual gold
therefore can be nothing other than simple instantiation, assuming we accept that individual gold
is an object, while heavy,
being a property, cannot be instantiated as individual heavy
except as manifested in an individuated subject. A universal accident is still an accident, while the dependence
of universal substances on objects is not that of an accident-subject relationship, but a relationship of simple instantiation.
If Kistler’s argument reducing gold
to a complex property were valid, it could apply just as well to individuated gold,
making it a trope, since the instantiation of a property is a trope, not an object. The abolition of objects has plausibility only to those trope theorists who would use our flawed understanding of physics at the microscopic level to overturn what has already been established with certainty at the macroscopic level: the existence of objects. No arcane quantum uncertainties can abolish or even lessen the palpable reality of macroscopic objects, so any ontology that tries to solve quantum paradoxes by abolishing objects is a failed theory, since an ontology must account for all facts, not just a preferred subset. In his zeal to deny universal substances, Kistler has introduced an unfortunate argument that would also abolish objects.
Kistler raises another linguistic conundrum when he suggests that relationships among the four classes of being ought to be regarded as relations
in the accidental sense. The term relation,
in the most general sense, is something that is predicable of two or more things. These things need not be ontological entities, but could be any formal or conceptual construct whatsoever. In ontology, relation
also has a more specific meaning, as a type of accident that has two or more subjects, where the subjects are necessarily ontological entities. Relation
in this accidental sense is predicated of entities within the four classes, but the relationships
Lowe among the classes are predicated of the classes themselves considered as concepts, not of the entities they contain. Kistler’s argument relies on purely linguistic confusion. Relationships among the ontological classes are not relations
in the accidental sense, as the classes are not ontological entities, notwithstanding the grammatical fact that we must speak of classes as though they were substantives (nouns).
Treating the ontological classes as though they were entities leads to absurdity.
Consider the class of properties, supposing it were a genus (universal substance) of all universal properties. What are the individual instances of this genus? That would be the properties—but those are universals! Further, the relations between entities in the classes would not hold for the classes themselves, treated as entities. The genus of tropes
does not instantiate the genus of properties,
nor is the set of tropes an element or subset of the set of properties, if we were to follow Kistler’s misuse of set theoretic concepts. None of the four classes, considered as entities, are predicable of each other, so there can be no true ontological relations among them.
Absurdities abound when we neglect to recognize that substance,
accident,
universal
and particular
apply only to entities. Making meta-entities out of the four ontological classes does not work, because being an entity in one of the four classes is immediately predicable of primitive being,
allowing no intermediate ontological level between the entities of the four classes and being itself. Thus, if we were to reify the class of individual substances, considering it as the set of every object in (potential) existence, this unfathomably diverse set would be collectively predicable only of being
in the most generic sense.
Notwithstanding the impossibility of making entities out of the four classes, there may still be relations
of sorts between entities belonging to the different ontological classes. Here we use relation
not as a type of accident, but in the broader sense of ontological predication. In this sense, instantiation,
exemplification,
or differentiation
might be considered relations.
Yet we should not confuse these kinds of relations with relation
in the narrower sense, which refers to the comparison of accidents between two substances. It would be a weak sophism to use the broader meaning of relation
that includes instantiation
to prove that universal substances are really accidents, implicitly applying the more restrictive meaning of relation. The relation between subject and accident entails a special kind of predicability, in which the existence of the latter is predicated of the existence of the former in the intimate manner discussed in >Part I. It would be a clumsy leap of logic to apply the subject-accident relation to any two entities that share any predicability relationship whatsoever.
Another approach to the critique of universal substances is to invoke the apparent failure of essentialist concepts of species and genus in biology, which are taken by Kistler to be paradigmatic kinds.
There is certainly a degree of arbitrariness in the definition of species, but this does not necessarily mean that they are without reality and purely nominal. Neither is it germane that species do not have the intrinsic unity that would make them intrinsically, or absolutely, countable,
since it is not necessary for a universal to be countable, notwithstanding Lowe’s misguided definition. They do not need unity, but only definite identity to be regarded as substances. Kistler exploits Lowe’s apparent conflation of substance with objecthood, which is a narrower concept applying only to particulars. His critique on this point effectively amounts to a complaint that universal substances are not individual substances.
Kistler maintains there are only two approaches to defining species: either one relies on the natural sciences studying those kinds or one relies on psychology (or linguistics) to find out about our naive classifications.
This is a needlessly impoverished view of metaphysics, reducing it to a mere handmaiden of the physical sciences, but Kistler draws ammunition from the fact that Lowe has wedded his concept of universal substances to the terms of physical laws. Since Lowe’s kinds are the bearers of laws, the metaphysical concept of kind had better fit scientific kinds.
While this demand sounds reasonable enough, it ignores the fact that scientists themselves do not agree on the ontological status of the kinds
that are objects of their laws, absurd as that may be. Thus, the mere absence of a coherent scientific
(empirical) notion of kinds is not an argument against the ability of kinds to bear
physical laws (or more properly, the properties defined in such laws).
Kistler cites M.A. Khalidi as showing that taxonomic hierarchies in biology are not unique, a point we fully acknowledged in our previous discussion. This proves that biological species do not have any inherent or absolute criterion of identity giving them intrinsic unity.
Of course, we have noted that universals do not require such unity, which is characteristic of particulars. Kistler’s exploitation of Lowe’s definition conflating universal and particular substances leads to the conclusion that Lowe’s kinds are nothing more than sets of objects. A kind is simply defined by dividing the set of objects according to a criterion chosen according to our practical interests.
The kinds are countable by virtue of that criterion, or rather, because Kistler has redefined kinds as sets of individuated objects.
When we dispense with the requirement that universal substances must be countable (Lowe’s mistake, which Kistler has exploited at length), there is no obstacle to regarding kinds as having determinate identity conditions, defined universally as an X that has Y.
It is true that we can classify objects differently, so that there are different hierarchies of genera, but this does not abolish the reality of an X that has Y,
since both X and Y can be real. The problem of universals is not so simply resolved that universal substances can be dismissed a priori. Furthermore, we have no way of being certain that metaphysics might not find its own basis for preferring one hierarchy over another, on non-empirical grounds, based on the orders of being or causality that are only poorly understood by empirical science. Phylogeny gives us one reason to prefer certain biological hierarchies over others, but it is not a comprehensive basis for biological hierarchy. It is needlessly nihilistic to disregard all hierarchies as purely nominal, when hierarchies such as phylogenetic taxonomy certainly can correspond to physical reality. A hierarchy need not be comprehensive to be real, and it is not purely arbitrary to say that the backbone is a more fundamental characteristic than having four toes.
Kistler’s final critique is that kinds lack ontological independence, since kinds come into being with the first individual instantiating them.
This is a debatable proposition, as we might regard the kind dodo
as still existent, even though the last dodo has died. Kistler insists on equating kinds with sets of objects, or alternatively, as properties. In the latter case, the dependence on instantiation clearly does not hold, as a property may exist even if not instantiated. Kistler’s claim that a kind lacks ontological independence on account of its supposed dependence on instantiations, if it were valid, would apply equally well to universal properties, making them dependent on tropes. His critique amounts to nothing more than a denial of universals by making individuality a criterion for being. This is begging the question, and the problem of universals is not to be solved so trivially. Classical realists may freely admit that a kind is a secondary
substance, with primary existence belonging to the individual substance, yet this does not mean kinds are completely dependent on individuations.
For one thing, it is conceivable that an individual need only potentially exist in order for the kind to actually exist. Regardless of whether potential or actual existence of an individual is necessary for the existence of the kind, when we say an individual,
we are not specifying a particular individual, but any individual of the species would suffice. Thus the kind is not dependent on a determinate individual. Of course, an indeterminate individual is no individual at all, so the kind is not ontologically independent on any individual.
Kistler correctly complains that Lowe’s allowance of transubstantiation (not to be confused with the Catholic doctrine), where an object can change its species, abolishes the dependency of objects on species, so Lowe is wrong to say:
It is true of any particular oak tree that it could not have failed to be an oak tree.
This is true of the particular oak tree qua oak tree, but not qua particular object (i.e., that piece of materia prima).
The lack of ontological dependence of objects on kinds is an argument against Platonism, but not all forms of classical realism. The supposed dependency of a kind on the existence of at least one instance does not make kinds dependent on any determinate set of individuals, so Kistler is rash to conclude that kinds ought to be regarded as properties. As noted above, even if the existence of a kind required an individual to actually exist, we would not necessarily have an ontological dependence of kinds on individuals.
Kistler says the possibility of transmutation implies that a particular oak tree could exist, even if the kind oak tree does not exist, say because all oak trees have been transmuted into maple trees.
Yet if such a transmutation did occur, the particular oak tree would no longer exist as an oak tree, but as materia prima in the form of a maple tree. Kistler’s claim that a particular oak tree
could exist without the kind oak tree
is erroneous, though it is true that a particular object (i.e., the materia prima of which the former oak tree was constituted) may have an ontological independence of universal substances.
Kistler’s critique of Lowe, coming from the perspective of a property-object ontology, does not undermine the four-category ontology as such, but only successfully criticizes some of Lowe’s subsidiary claims. Lowe is wrong to make countability a criterion for universal substance, but Kistler is equally mistaken in applying set theoretic concepts to fundamental ontology, making kinds mere sets of individuals. Kistler’s attempt to reduce kinds to properties confuses linguistics with ontology, as does his treatment of the four classes as entities with relational accidents. Overly reliant on particular theories of physical science and mathematics, Kistler constructs far too narrow a basis for metaphysics, which ought to encompass all of reality. As his property-object ontology already contains both universal-particular and substance-accident distinctions, he has no a priori basis for discarding any of the four categories. Instead, he relies on set theory, poorly understood quantum mechanics, and the lack of essentialism in biology to show that universal substances are in actuality unnecessary, if not impossible. This criticism misunderstands the concept of the universal, confusing it with a set
or class
in mathematics or computer science, and demands of species-genus taxonomies a level of realism that few of their proponents would assert.
Ryan Wasserman of Western Washington University has offered a critical review (in Philosophy Reviews 2006.04.11) of Lowe’s 2006 book, The Four-Category Ontology: A Metaphysical Foundation for Natural Science, focusing on two of Lowe’s claims, namely that his four-category ontology provides the best account of (a) laws of nature and (b) the dispositional-categorical distinction.
Wasserman’s critique undermines Lowe’s contention that all four categories are necessary to account for scientific reality, though it does not disprove the four-category ontology.
First, it is necessary to distinguish Lowe’s account of natural laws from that of other realists such as the Australian philosopher David Armstrong, who believes in universal properties but not kinds. For Armstrong, laws are relations between universal properties having the form, All Fs are Gs,
where the properties F-ness and G-ness are linked by necessity, a stronger requirement than merely saying, All Fs happen to be Gs.
Lowe, by contrast, represents physical laws in the form K is F
or Ks are F,
where K is a kind and F is a property. In Lowe’s conception, it suffices that the simple predication K is F
be true for it to be a physical law; there is no need to invoke Armstrong’s additional condition of necessity.
While Lowe’s account, by not requiring the condition of necessity, would have some advantage of parsimony, we must recognize that not all physical laws are of the form K is F.
In fact, it is more common in physics to see equations relating properties, and arguably (though this is outside our present scope) all physico-mathematical laws can be expressed as relations between properties. In any event, we should note that the views of Armstrong and Lowe are not mutually exclusive, and it is possible, indeed likely, that both accounts are needed to fully describe physical law. If both types of laws are needed to describe reality, this would favor the four-category ontology, which encompasses both properties and kinds.
Lowe does not consider the condition of necessity to be essential to physical law, so he allows laws to have exceptions. We noted that this omission of Armstrong’s necessity condition may give Lowe’s account an advantage of parsimony, but this advantage is negated by Lowe’s need to invoke a distinction between necessary and probabilistic laws. Similarly, the apparent parsimony of having a simple predicate relation define laws between properties and kinds without a necessitation
relation is undermined by the need to invoke a characterization
(differentiation) relationship between kinds and properties. I have always found parsimony to be a dubious reason for preferring one theory over another, but here there is no clear advantage for either system in any case. The necessity of the four-category ontology must be established on other grounds, such as by showing that Armstrong’s account is not a complete description of physical law. Lowe might have used kinds as an alternative to the obscure necessitation relation,
but he defeats this purpose by allowing exceptions to his laws.
In his review of Lowe’s book, Wasserman claims that both Lowe and Armstrong are vulnerable to the so-called inference problem,
a supposed paradox stating that facts about universals do not support inferences about particulars. For Armstrong, the problem is:
(F-ness necessitates G-ness) ?⇒ (a is F → a is G)
First, we may see that this inference does in fact hold when F and G are of the form being X,
as in the example:
Example 1
Suppose:
Being a Red Soxnecessitatesbeing a baseball player.Then:
David Ortiz is a Red Sox→David Ortiz is a baseball player.
This also works for properties not of the form being X,
as seen below.
Example 2
There is no difficulty proceeding from (1) to (2), but (2) does not imply (1). In other words, we can proceed from universals to particulars, but not vice versa. Wasserman and others seem to have a problem with this because syntactically there is no distinction between inferring (1) from (2) or (2) from (1), so both ought to be equally invalid. This pseudo-paradox results from applying symbolic logic without fully taking into account the type of being the symbols signify. We can see the supposed inference problem
more clearly in Wasserman’s critique of an example by Lowe, stated formally here:
- Premise 1: This material (A) is sodium chloride (B).
- Premise 2: Sodium chloride (B') is water-soluble (C').
- Conclusion: This material (A) is water-soluble (C).
Since B' and C' are universals, B' ≠ B and C' ≠ C, so the inference does not hold as it is written. However, this declaration of invalidity is premature, as it ignores the fact that B and B', C and C' share a very intimate bond, such that one is an instance of the latter, so what is predicated of B' is predicated of B. How do facts about universals tell us anything about particulars? Quite simply: a particular
is a particular universal! The inference problem dissipates when the concept of particular
is fully grasped. When we say This material (A) is sodium chloride (B),
we are declaring a link between a particular object (A) and the universal sodium chloride
(B'). We are not saying that this material (A) is the universal sodium chloride
(B'), but that it is a particular instance of sodium chloride (B). To be an instance of sodium chloride means that the essence of sodium chloride (B') is manifested in a particular object (A). If sodium chloride (B') is water-soluble (C') essentially and not just accidentally (as it must be since a universal is nothing but its essence), then it is necessary for the essence of water-solubility (C') to be manifested or instantiated in the object A. The universal water-soluble
(C') is identical to instantiated water-soluble
(C), except that the latter is limited to a certain substance (A). This condition of particularization does not abolish or distort the essence of water-solubility (C'), but on the contrary is the means by which that essence is manifested in an object. In other words, instantiation is a bridge between universal essences and instantiated entities, rather than a change in essence. Thus B' ≠ B and C' ≠ C only in the sense of logical identity, not in the order of essence.
An inference problem
exists only in that it is impossible to explain with formal logic how instantiation works, but this is unsurprising, since we are dealing with a radically primitive relationship, more primitive than first-order logic. The key to resolving the paradox is to understand that the universal and the particular, though not identical, share the exact same essence. To deny this would be to deny the concept of particularization altogether. Whatever may be said of the metaphysical status of universals, particularization is an intelligible, coherent a priori concept, so it is not to be denied on logical grounds.
Wasserman, like Kistler, is on sounder ground when he critiques Lowe’s treatment of the distinction between dispositional (hypothetical/potential) and categorical (actual/occurrent) properties. Lowe strangely claims that these are merely different ways of attributing the same property. Wasserman understandably finds Lowe’s distinction of these types according to two routes
on the ontological square to be elusive
in its details. He examines Lowe’s example of the rubber eraser where he claims:
Dispositional: This piece of rubber is disposed to stretch, or is stretchy, because the eraser (1) is of the kind
rubber,which (2) is characterized by the property ofstretchiness.Both (1) and (2) hold even when the rubber is not actually stretching.Occurrent: If the eraser is actually stretching, it (3) is characterized by an instance of stretchiness, which (4) instantiates the property
stretchiness.(3) and (4) are both true only when the rubber is actually stretching.
As I expounded earlier, we should always be able to follow both routes of the ontological square equivalently, so Lowe has obviously displayed some sleight of hand here. The error, which Wasserman points out, is that in the two examples we are not talking about the same property. The first (dispositional) case deals with the property of being stretchable,
while the second (occurrent) case deals with the property of being stretched.
Lowe’s account of each property is sound, but his equation of the properties treated in the two examples is not, so his association of dispositional and occurrent properties with routes
on the ontological square is unfounded. To prove the point, we can trace the opposite routes in each example.
Dispositional: This rubber eraser is stretchable because it (3) is characterized by an instance of
stretchable,which (4) instantiates the universalstretchable.Occurrent: This rubber eraser is being stretched because it (1) instantiates the kind
stretched rubberwhich (2) is characterized by the universal propertystretched.
There ought to be no more objection to defining a kind stretched rubber
than there is to the kind hydrogen atom in excited energy state.
We can characterize kinds according to dispositional or occurrent properties equally well, so the distinction between these types of properties must be established on some other ground. It is erroneous to restrict universals to bearing dispositional properties on the ground that universals cannot actually manifest properties, for this confuses actuality with particularity or concreteness. Universals may exist as secondary
substances regardless of whether we are dealing with dispositional or occurrent properties.
There might be some cases where Lowe’s scheme can apply, if we admit for example that being stretchy
and being stretched
are different aspects of the same property, or that they are complementary properties, related by the proposition: X is disposed to being stretched if and only if the kind of X stretches.
Still, there are undoubtedly properties where such a construction cannot be made, and Wasserman provides counterexamples in each direction of implication.
Claim: X is disposed to F ↔ Y (the species of X) Fs
Counterexample 1:
Lions (Y) hunt (Fs), but a domesticated lion (X) is not disposed to hunt (~F).Counterexample 2:
A car (X) made of salt is disposed to dissolve in water (F), but cars (Y) don’t dissolve in water (~Fs).
These counterexamples abolish any strong connection between the disposition of individual objects and the properties that characterize universal species. In both cases we are dealing with non-essential, or accidental, attributes. The first counterexample exploits Lowe’s tolerance of merely contingent relationships between kinds and properties, while the second is a simple example of an object possessing a trope that is not essential to its kind. Wasserman concludes: On Lowe’s account, all objects of the same kind must have the same dispositions. But that seems patently false, at least if we consider forms or kinds like car, lion or person.
As we have said previously, the only thing that objects of a kind have in common are the differentiae constitutivae.
Even if Lowe’s dual-route account were correct, this would only account for the dispositional-categorical distinction in objects. Yet kinds also have this distinction. Using Wasserman’s example of the universal benzene:
Dispositional: Benzene is flammable.
Occurrent: Benzene is made of carbon and hydrogen.
We remark in passing that chemistry is a good paradigm for universal substances, as we can empirically distinguish this benzene molecule from that one (without strange quantum statistics), yet the properties of each molecule are those of the universal benzene.
In the second statement, we are not asserting that the universal benzene
is performing some determinate act, but rather that being benzene
entails being made of carbon and hydrogen.
Here the term categorical
seems more appropriate than occurrent,
as universals do not have determinate temporal states. A universal is incapable of determinate action, since such determination would particularize it. We could not say, for example, (Universal) man walked to the store,
since the store is a determinate location. The same limitation holds for dispositional properties. If the universal benzene
cannot ignite in a determinate act, neither can it be said to have the potential or disposition to ignite in such a determinate act. Both dispositional and occurrent (or categorical) properties of universal kinds must be considered only generically for individuals of that kind. More pertinently, the admission of both dispositional and categorical properties among kinds is not reconcilable with Lowe’s dual-route account, which channels only dispositional properties through kinds. Instead, we find there is one common direct route between properties and kinds, namely characterization, which applies to both dispositional and categorical properties.
Wasserman also criticizes Lowe’s postulation of modes or tropes. While it may seem impossible to deny the existence of tropes, which are the stuff of perception, property-object theorists ascribe the thisness
(haeccity) of tropes to objects, leaving only universalized properties. This conceptual manipulation will not withstand scrutiny, as we will show in due course. Nonetheless, Wasserman raises important questions about the nature of tropes and the inconsistency of Lowe’s treatment of these with what he has asserted elsewhere.
One sees a rose (object) by seeing its color (trope). If the perceived color were a universal, then by looking at a particular red rose, one would thereby see the red in all other flowers of that hue, a conclusion Lowe finds absurd. This would indeed be bizarre if we knew that perceiving a property suffices to perceive its object, since seeing the rose would then allow one to see all other red objects, or at least a certain aspect of them. Wasserman resolves the difficulty by proposing that various objects act as windows into the same universal, so we truly do see the universal red
in all red objects. This account, we shall see, does not contradict the existence of tropes, properly conceived.
As noted in Part I, the relationship between property and trope is closer to identity than that between species and individual. An individual (Socrates
) certainly has the essence of its species (man
), but it can also have other accidental qualities. Socrates is more than an instantiation of manhood,
for he may have curly hair, a snub nose, expertise in philosophy, and other attributes that are not essential to manhood.
A trope, by contrast, has no accidental qualities beyond the essence of the property it instantiates. It is an instantiation of the property and nothing more. This blurs the distinction contained in the question: Do we perceive the universal property or the trope?
Whether we perceive the property or the trope may be a question mal poseé. Rather, we perceive the object, in a manner modified by its tropes, which are nothing other than instances of properties.
The notion of perceptibility is incompatible with universality. We can not perceive a universal as such, since universals are independent of the contingencies of its instantiations. The redness of object A
is perceptible only when object A is perceptible, and the redness of object B
is perceptible only when object B is perceptible. One may be perceptible in one region of space, while the other is perceptible only in another region, showing a meaningful distinction between the two instantiations. This locality of perceptibility may be extended to other effects of instantiated accidents. That which is hot may only heat what is in its vicinity, for example. These local, determinate effects are incompatible with universality. When the intellect apprehends the universal redness,
this concept is divorced from any determinate instantiation. This independence from particulars may be seen from the fact that our apprehension of universal redness
would in no way diminish if object A or B were destroyed. This would seem to suffice to show that properties are not identical to their instantiations or tropes.
When a universal property is exemplified in an object, it is necessarily instantiated, as its effects are confined by the locality and other determinate contingencies of the object. Still, as the redness of this red
is no different from that of universal redness,
we truly do see the essence of the universal, but we see it instantiated. In other words, the trope is not to be conceived as something distinct in essence from its universal, nor does it have any accidental differences. Thus we can truly say that we perceive the property instantiated.
Admitting that the property must be instantiated in an object, a property-object ontologist might object that the instantiation of a property does not need the intermediary of a trope, but the property is directly instantiated in the object. This contention does not contradict the existence of tropes, for trope
simply denotes the state of a property being manifested or instantiated in an object. We do not hold that a trope is stuff
other than the property it instantiates. Lowe’s term modes
is highly appropriate for tropes, as a mode is the way an object exists. Since a mode or trope is a characterization of a particular object, it must itself be particular. Thus it is not superfluous to assert the existence of tropes.
Those who acknowledge that properties and objects exist have implicitly accepted both the distinctions of substance-accident and universal-particular, so the other two classes of the ontological square, kinds and tropes, must be admitted at least as logical concepts. Property-object ontologists such as Wasserman and Kistler would deny that tropes have any reality beyond mere formal existence, attributing their thisness
to objects and their essence to properties, leaving no apparent need for tropes. Yet we have seen that the locality of a trope’s effects or perceptibility is evidence of a real distinction from universal properties.
Lowe exposes himself to valid criticism when he posits tropes as answers to the dubious truthmaker principle,
which asserts that every proposition has a truthmaker
whose existence is sufficient for the proposition to be true. He maintains that modes or tropes are needed as truthmakers for statements of the form P is Q,
where P is an object and Q is a universal property. P and Q will not suffice as truthmakers, for the existence of this apple
and the universal red
do not make the proposition, This apple is red,
true. Lowe suggests that the trope this apple’s redness
is a truthmaker.
Armstrong instead holds that a truthmaker is a state of affairs, such as this apple’s being red.
Despite the semantic dissimilarity between states of affairs and tropes, they fulfill similar roles. A trope is the intersection of a universal property’s essence with the determinate conditions of its object; it may be considered the state of the property being instantiated in the object. A state of affairs such as this apple’s being red
similarly reifies the intersection of the property’s essence and the object’s thisness.
The state of affairs this apple’s being red
differs from the trope this redness
only in that the state explicitly declares the object apple,
while the trope this redness
only refers to the apple by implication, since its thisness
corresponds to the determinate conditions of the apple. States of affairs merge object and trope into a single entity, while speaking in terms of tropes or modes emphasizes a distinction from the objects in which they inhere.
Wasserman finds that tropes are less promising than states of affairs as truthmakers. He observes that there are many contingent truths without corresponding modes or tropes. Among these are negative existentials such as There are no unicorns,
and statements about universals such as Benzene is flammable.
The first type of statement cannot be made true by the presence of any mode or trope (except perhaps, by the collective presence of tropes preventing all objects from being unicorns), while a state of affairs is a broad enough concept to include negative existential situations. Since Lowe allows for contingent laws, the statement, Benzene (universal substance) is flammable (universal accident),
can be regarded either as a necessary or contingent law. If it is a necessary law, Wasserman argues, then the universal substance and universal accident suffice as truthmakers. If it is contingent, then the universal substance and universal accident do not suffice as truthmakers, and as no particular could make this statement true, Lowe is left without truthmakers!
Accepting the validity of Wasserman’s critique, this is not a strong problem for Lowe’s defense of tropes, since he only needs to show that tropes are necessary for some truths. Nonetheless, the problems raised by application of the truthmaker principle to negative existentials and contingent universal laws present real difficulties. The problem lies with the truthmaker principle’s demand that there ought to be an ontologically simple (or group of ontologically simple) truthmaker(s) for a composite (subject-predicate) statement. This requirement is by no means self-evident, and indeed is counterintuitive for complex statements. The only plausible candidates for all-purpose truthmaking are states of affairs,
but we will see that these are not ontologically simple at all.
Consider the state of affairs depicted in the above diagram specifying the sizes and relative positions of circles 1 and 2. In order for the state of circles 1 and 2 being in this spatial situation
to exist, we need circles 1 and 2 to exist, for each of them to have a particular size, and for them to have a particular relative position. It is trivial that a state of affairs
can be defined to encompass all these realities, but we could clearly break this state down into simpler entities, such as the state of circle 1 existing,
the state of circle 2 having a certain size,
etcetera. Once we have reduced the complex state of affairs to its simplest constituent states, we might as well dispense with the construction the state of…,
and just say this circle,
this size,
etc. The state of affairs is nothing more than a synthesis of objects, properties and relations, and it is illogical to make these entities dependent on a state of affairs that can only be defined in terms of them. It is true that some states of affairs, such as negative existentials, may be defined without reference to the existence of a particular object or property. Yet such a state of affairs is indeterminate, for the state of unicorns not existing
does nothing to specify what does exist, if anything. If ontology is the science of being, states of affairs cannot be considered ontologically fundamental, since they either (a) depend on the being of objects, properties and relations or (b) do nothing to specify what exists. As for simpler states of affairs, such as this apple’s being red,
these are effectively nothing more than tropes considered as united to their object.
States of affairs make better truthmakers than the traditional ontological classes because they simply restate the proposition as a gerund, so there is always a state of affairs for every proposition. As such, they are no more primitive than the proposition they objectify. If the proposition is complex, the state of affairs will be complex. The simplest states of affairs, which are unions of objects and tropes, may be considered primitive in the empirical sense that you cannot separate the apple from its redness, so there is only the red apple.
Yet the apple could be green, and other things can be red, so red apple
is not ontologically simple.
We have seen that classical ontology remains highly relevant to understanding modern discussions, as the various realist ontologies of today amount to a dispute over which of the four categories have a claim to reality or ontological priority. The four-category ontology is the only ontology that spans all the possibilities of realism, so it is the most suitable tool for a priori analysis. None of the criticisms of this ontology refute the possibility of the four categories, but rather deny the necessity of some of them on empirical grounds. This a posteriori finding is in some cases clouded by a muddled understanding of quantum mechanics, as in the case of Kistler, but at any rate has no bearing on what is a priori possible.
Modern discussions of ontology tend to focus narrowly on what is empirically demonstrable, a constriction of scope that would make most of metaphysics impossible. Even Lowe tries to justify his ontology in terms of its utility for explaining empirically derived laws of nature, forcing himself to deform classical ontology to this end, as in his tortured account of dispositional and occurrent states. This novelty, along with his odd requirement that species ought to be countable like individuals, exposes Lowe to several potent criticisms that do not bear directly on classical four-category ontology as such. The compulsion to test everything under empiricism is a serious mistake made by many philosophers, which is informed more by our culture of scientism than by rational necessity. Not only does this practice reduce philosophy to an ancillary discipline of physics, eliminating most of its classical metaphysical scope, but philosophers tend to understand physics poorly, so they contribute little even in this limited domain. If philosophers insist on being the untalented pupils of physicists instead of their teachers in metaphysical matters, we will remain with the banality of attempting to explain everything in terms of set theory, mathematical logic, or mathematical physics.
Modern realist positions, as they tend to narrow the scope of metaphysics, may all be contained within a classical four-category ontology. Only Armstrong’s factualism, which grounds reality in states of affairs, appears to lie outside this scope. Yet we have seen that many states of affairs are not ontologically simple, and in fact are predicated on the existence of a corresponding object, property, relation, or trope. States of affairs nonetheless are broader in scope than the ontological square since they encompass negative existentials, but this is only because they are not ontological entities, but merely reifications of propositions. Classical ontology, then, suffices to account for all conceivable ontological entities.
In sum, classical ontology is the ontology of modern realists, whether they admit to it or not, since all the various realist ontologies are encompassed in its scope, and its categories are challenged only on a posteriori grounds. We have explored these objections and in doing so discovered important limitations to the explanatory power of a classical ontology, as well as the value of not introducing novel definitions of categories beyond what is required by the distinctions of universal and particular, substance and accident. As we return to our discussion of classical ontology in Part III, we should remain mindful of these lessons.
Before proceeding with a discussion of the classical ten categories of substance and accidents (not to be confused with the more fundamental four categories,
which are really ontological classes), we should examine one last high-level distinction that is made in modern ontology, that between abstract and concrete objects. It arose from Gottlob Frege’s (1848-1925) recognition that mathematical objects are real entities, combined with the modern rejection of Platonic Ideas, universal substances, and incorporeal substances. Having divested themselves of the ontological classes that might account for mathematical objects, modern realists have had to resort to the ill-defined distinction of abstract versus concrete. As more than a few modern commentators have noted, this vague distinction actually encompasses several different concepts. The modern distinction between abstract and concrete is a conflation of disparate classical concepts, such as form (Idea) and matter, substance and accident, corporeal and incorporeal, universal and particular.
Abstraction is a broad concept that can encompass such disparate conceptualizations as considering a substance apart from its accidents, an ideation independently of spatiotemporal existence, or a universal apart from any of its instantiations. In other words, an entity is considered abstractly when some condition of its being is indeterminate. Abstraction may be seen most generally as a mental operation whereby we consider an entity independently of some condition of being. These conditions could be accidents, including spatiotemporal accidents, or substantial individuations. In the latter case, the abstract entities must be universals, not particulars.
In modern philosophical terminology, abstract
and concrete
entities are considered subclasses of particular objects, hence they are always particulars. This is an astonishing claim, considering how the notion of abstraction is easily broad enough to encompass universals. The abstract-concrete distinction is not an apt ontological distinction, since it distinguishes things with respect to a mental operation that can treat disparate ontological distinctions. We can choose to abstract substance from its accidents, spatio-temporal or otherwise, or a universal from its individuations, for example, so the operation of abstraction does not uniquely specify the ontological status of the thing abstracted.
Of special concern is the question whether mathematical abstract entities might all be reduced to particular objects, since the admission of the reality of mathematics is what motivates the abstract-concrete dichotomy among otherwise hardened empiricists. The classification of mathematical entities as particular objects seems to defy intuition, for mathematical objects are paradigmatic Platonic Ideas, abstracted from all spatio-temporal accidents and from individuation. When we say the equilateral triangle,
we are abstracting from any determinate spatiotemporal matrix. The equilateral triangle
exists only in an arbitrary space, not a definite space. It is a universal, abstracted from real space, though it can be instantiated in real space.
There is no thisness
(haeccity) to geometrical entities such as the equilateral triangle,
considered purely in the abstract. It is true that we can specify the coordinates of a triangle or other geometrical object in some abstract space, but this specification of size and location does not necessarily individuate the triangle, since the space itself is an arbitrary abstraction, containing no determinate objects as reference points to make the space a principle of individuation. The coordinate system of a mathematical space is purely relative, and we can shift from one system to another arbitrarily. For this reason, there is no single, determinate circle that is the unit circle centered at the origin.
Since the origin and unit of measure are arbitrarily determined, any abstract circle could be regarded as the unit circle centered at the origin
by a coordinate transformation, so mathematical space fails to render objects determinate. In other words, abstract circles lack thisness,
since the use of an abstract coordinate space does not allow us to distinguish this circle
from that circle.
Even if we have multiple iterations of a geometrical entity considered in the same abstract space, such as three concentric circles or four adjacent equilateral triangles, this need not imply individuation. Individuation requires thisness
in addition to enumerability. The fact that even reiterated mathematical objects lack thisness
is shown by the fact that the formal geometrical situation is identical if we swap equilateral triangles in the diagram below, or make the innermost and outermost circles exchange sizes.
Not only is there no formal distinction, but there is no material distinction either, as we are not dealing with determinate, palpable entities. It would be meaningless to ask which
triangle is in the middle, as if these were determinate, material triangles, when we are in fact dealing with abstract entities. There is similarly no ontological distinction engendered by the virtual swapping of any other geometrical iterations. There is no individuation, so each object is its own kind.
The immateriality of abstract objects is what renders individuation impossible, which is unsurprising to those already familiar with the Aristotelian (or Thomistic) principle that (signate) matter is the principle of individuation. This classical understanding led to the conclusion among medieval theologians that each incorporeal substance, such as an angel, was its own unique species. We have seen that there can be multiple iterations of an abstract object, but all of these have a material indeterminacy that renders individuation impossible. Although we may treat each iteration grammatically as though it were an individual, the iterations lack the thisness
that is essential to individuality.
We can only regard iterations of a mathematical object as individuals when we confuse representations of the object with the abstract object itself. When we draw reiterated geometrical objects on a chalkboard or a sheet of paper, we create material, individuated objects. These material symbols or models are not themselves mathematical objects, so we cannot use the former in substitution of the latter as though there were no loss of information. This conflation of symbolic models with ontological reality, as Lowe has noted, is a common mistake among modern philosophers who apply mathematical syntax to philosophical argument. In mathematics and physics, it is common to apply formalisms (either considered as symbols or abstract concepts) without worrying about philosophical interpretations, but in philosophy it does not suffice to apply formalism without understanding.
Another way to see that mathematical objects are not particulars is to appeal directly to Aristotle’s is (not) said of
distinction between universals and particulars. A particular cannot be said of
any real entity. For example, we cannot say, X is a Socrates,
where Socrates is an individual, though we can say, X is a man,
since man
has a universal sense. The essence or definition of man may be predicated of many different conceivable individuals, but the determinate individuality of Socrates belongs to none but Socrates, nor can this individuality be part of a universal essence. We can say, X is an equilateral triangle,
which means equilateral triangle
has a universal sense. If we admit that equilateral triangle
in this proposition is an abstract object, it follows that (mathematical) abstract objects cannot be a subclass of particulars.
Mathematical abstractions need not be universal substances only, for they can also be universal accidents, as is apparently the case with number. In the statement, These are three apples,
these
refers to individual substances and apple
is a universal substance, so the three
that qualifies apple
must be a universal accident. Three
cannot be a particular object, for an individual cannot qualify a universal. One cannot say This is a Socrates man,
as if Socrates were a qualifier of man
or a kind of man, rather than a determinate individual. The fact that we can coherently say, These are three apples,
eliminates the possibility of three
being a particular object. In other contexts, three
could be a particular accident or trope, but not when it is qualifying a universal.
In summary, the modern distinction between abstract and concrete poses no serious obstacle to our forthcoming analysis of classical ontology with its ten categories of substance and accidents. This modern distinction is poorly defined and encompasses several disparate classical distinctions, making its ontological necessity dubious in the extreme. Mathematical objects can be treated more simply and effectively with a classical ontology, once we admit the possibility of universals and incorporeal substances. Modern philosophy too often limits its scope to that of empiricism, and its clumsy handling of mathematical objects shows how these pose an uncomfortable incongruity between the Platonic reality they represent and the radically empiricist ethos of our academic culture.
© 2008 Daniel J. Castellano. All rights reserved. http://www.arcaneknowledge.org
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