Table Of ContentLukag Novak • Daniel D. Novotny
Prokop Sousedik • David Svoboda (Eds.)
CONTEMPORARY SCHOLASTICISM
EDITED BY
Edward Feser • Edmund Runggaldier Metaphysics:
ADVISORY BOARD Aristotelian, Scholastic,
Brain Davies, Fortham University, U.S.A. Analytic
Christian Kanzian, University of Innsbruck, Austria
Gyula Klima, Fordham University, U.S.A.
David S. Oderberg, University of Reading, U.K.
Eleonore Stump, Saint Louis University, U.S.A.
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CONTENTS
EXISTENCE
Edward Feser
Existential Inertia (cid:9) 143 I PREFACE
Gyula Klima
Aquinas vs. Buridan on Essence and Existence,
Just like any other philosophical discipline, metaphysics has a history and a
and the Commensurability of Paradigms (cid:9) 169(cid:9)
present. It flourished in the classical and mediaeval period, gradually declined in
the modern period and almost ceased to exist in the first half of the 20'h century.
MODALITIES Its present is characterised by a revival of some traditional speculative topics,
which has been taking place within analytical philosophy since the 1960s.
Edmund Runggaldier SJ
The fact that the current renewal of interest in metaphysics occurs in the
Potentiality in Scholasticism (potentiae)
context of analytical philosophy is somewhat surprising. Analytical philosophy
and the Contemporary Debate on "Powers" (cid:9) 185(cid:9)
has been deeply influenced by logical positivism with its strong anti-meta-
David Peroutka OCD physical orientation. Its proponents saw the task and future of philosophy in
Dispositional Necessity and Ontological Possibility (cid:9) 195(cid:9) the ontologically neutral analysis of scientific or natural language - not in
metaphysical speculations. Many were convinced that the progress of mankind,
Mark Faller
which they wished to assist, requires various obstacles to be cleared out of the
The Optimal and the Necessary in Leibniz' Mathematical Framing
way. Metaphysics was considered to be one such intellectual obstacle.
of the Compossible (cid:9) 209(cid:9)
How are we to understand, then, that the philosophical discipline, which the
older analytical philosophers stood so radically against, has reappeared within
PREDICATION the intellectual context of this very anti-metaphysical current? This question
does not seem to be satisfactorily answered yet, neither in socio-psychological
Uwe Meixner
terms nor in purely philosophical ones: answering it may require a time interval
The Interpretation(s) of Predication (cid:9) 229(cid:9)
which has not elapsed yet. One of the causes is most probably to be sought in the
Stanislav Sousedlk analytical philosophy itself. With time, its development came to cast doubt on
Towards a Thomistic Theory of Predication (cid:9) 247(cid:9) some of the anti-metaphysical points of departure. In this respect, for instance,
Wittgenstein's criticism of private languages, which problematised Cartesian
subjectivism, or Kripke's systematisation of modal logic, which facilitated a re-
Authors (cid:9) 257 turn to the previously rejected topic of modalities, ought to be mentioned.' The
General Index (cid:9) 263 renewed interest in these and similar topics advanced the revival of metaphysical
investigations.
Index of Persons (cid:9) 281
Of course, there are as yet many authors who reject metaphysics, as well
as some of its presuppositions, such as modal logic.' They consider analytical
metaphysics to be one of the many delusions of our time. Perhaps they think of
contemporary metaphysicians as of the prodigal son who has left his home and
LUDWIG WITTGENSTEIN, Philosophical Investigations, trans!. G. E. M. Anscombe (Oxford:
Basil Blackwell, 1963); SAUL KRIPKE, "Semantical Considerations on Modal Logic", Acta Philo-
sophica Fennica 16 (1963): 83-99.
In the 20th century modal concepts were subjected to criticism especially by WILLARD VAN
ORMAN QUINE, see his "Two Dogmas of Empiricism", in From a Logical Point of View (Cambridge,
MA: Harvard University Press, 1954); or his Word and Object (Cambridge, MA: MIT Press, 1960).
4 5
PREFACE PREFACE
wilfully violates the morality impressed on him by his parents. The prodigal son The section on metaphysical structure is closely connected to the previous one
should return home in order not to perish in a world full of delusion and hazard. in dealing with the most general ontological problems. In the first article, Michael
The editors of this publication are teachers of philosophy at Czech theological Loux contrasts two fundamentally distinct approaches to explaining the mould
faculties. In the controversy between contemporary analytical metaphysics of "familiar particulars": the "Aristotelian" or "constituent" strategy, and the
and its opponents they side with the renewal of speculative thinking. We are "Platonic" or "relational" strategy. Loux seeks first to clarify the dichotomy by
interested not only in the current debate but also in earlier discussions taking distinguishing it from the dispute over the nature of universals, and then proceeds
place within the tradition of Christian Aristotelism (the so-called First and Second to analyse the "constituent" approach and point out its various problems. In the
Scholasticism). Historical research has often led us to the remarkable observation following contribution Anne Siebels Peterson explores the Aristotelian notion of
that older scholastic discussions are in many respects similar to current debates. "prime matter" as the substratum of elemental transformation with no essence
This naturally induced in us the effort to enhance contemporary metaphysical of its own; she exposes certain conflicts between the theory of prime matter and
thinking by the treasures of the Aristotelian-scholastic past. Contemporary meta- other doctrines commonly ascribed to Aristotle. The concluding contribution of
physical speculation could thereby gain not only new stimuli and inspiration this section is by Ross Inman. It focuses on the notion of "essential dependence"
for solving challenging philosophical problems but also firm grounding in the and tries to show how scholastic analyses of this notion (especially those under-
intellectual history of the Western world. In this we are not entirely original taken by Duns Scotus) can help to remedy a certain void in contemporary ana-
but can follow up on the already existing tradition of Analytical Thomism. How- lytical discussions regarding the topic of truthmaking.
ever, unlike the proponents of Analytical Thomism we are inspired not only by The third section comprises three contributions related in some way or other
the legacy of Thomas Aquinas but also seek advice from the technically more to the problems of substance and accident. E. J. Lowe opens the section with the
elaborate Thomistic, Scotistic, and other traditions of Second Scholasticism, article "Essence and ontology", in which he tries to show how by combining a neo-
which have not been thoroughly researched yet. The endeavour of Renaissance Aristotelian account of essence with a neo-Aristotelian "four-category ontology"
and Baroque scholastic authors at technical refinement makes them intrinsically of individual substances, modes, substantial universals, and property universals,
related to the analytical tradition. a thoroughgoing metaphysical foundation for modal truths can be provided.
We are honoured that several outstanding proponents of contemporary ana- Lukag Novak continues in a similar vein by presenting an "Aristotelian" argument
lytical metaphysics as well as prominent specialists in the history of scholastic against the theory of the so-called "bare particulars", thus providing a defence of
philosophy have appreciated our idea of relating the traditional and the new an essentialist account of substances and accidents. Prokop Sousedik and David
metaphysics and accepted the invitation to the conference Metaphysics: Aristo- Svoboda, who jointly authored the concluding contribution of this section, pose
telian, Scholastic, Analytic (Prague, the Czech Republic, June 30 - July 3, 2010). This the question whether number is an accident. By way of an answer they develop a
publication is the fruit of this conference. It contains both historical and syste- neo-Aristotelian theory of number which attempts to steer a middle way between
matic contributions. We have grouped them according to their topic to form six "the Scylla of Aristotelian naturalism" and "the Charybdis of Platonic idealism".
sections titled Categories and Beyond, Metaphysical Structure, Substance and Accident, The fourth section is devoted to existence. In his article Edward Feser criticises,
Existence, Modalities, and Predication. from a broadly Aristotelian-Thomistic standpoint, the doctrine of existential
The first section, dealing with categories (and what is beyond), is devoted to inertia, contrasting it with the doctrine of divine conservation. In the other
the problem of ontological classification in general. It opens with the article by article of this section, Gyula Klima takes the comparison of two different accounts
Peter van Inwagen who explores the notion of ontological category such that it of the relation between essence and existence, namely those of Aquinas and
may be utilised in defining ontology. Inwagen proposes that "ontology proper" (as Buridan, as a point of departure for some more general thoughts concerning the
opposed to meta-ontology) is an attempt to set out a satisfactory list of ontological possibility of cross-paradigm argumentation.
categories. In the second article, Daniel D. Novotny broadens the scope of enquiry The subject of the penultimate section is the modality and its metaphysi-
by focusing on the problem of the ontological status of the so-called "beings of cal grounding. In the first contribution, Edmund Runggaldier reconstructs the
reason": entities or pseudo-entities beyond the confines of reality proper. In his scholastic theory of potentiality which draws an important distinction between
approach he fruitfully combines the contributions of scholastic and analytical subjective and objective potencies. He shows how these two kinds of potencies
thinkers, thus implicitly providing a positive answer to his concluding question allow for two complementary accounts of modalities, of which the first corre-
whether contemporary analytical metaphysics can draw some inspiration from sponds more to the "common sense" perception of modalities while the other
scholastic debates. approximates to modern possible-world semantics. In a further development of
6(cid:9) 7
PREFACE
the topic, David Peroutka combines the contemporary and Aristotelian analysis
of "powers" or "potencies" to explain the necessity of causal nexus and the
grounding of possibility in active and passive causal capabilities. The concluding
contribution by Mark Faller focuses on Leibniz's understanding of necessity and SECTION I
possibility. Working in quite a broad context, Faller tries to develop a unified
reading of Leibniz and praises him for his realist view of the nature of truth and
its corresponding reality.
The topic of the final section is predication in a metaphysical perspective. Uwe
CATEGORIES
Meixner provides an historical survey of various interpretations of predication
and its metaphysical basis. He defends the view that Frege, despite some deficits
in his conception, was the first to bring the philosophy of predication on the
right track, and proposes his own Frege-inspired theory. On the contrary, Sta- AND BEYOND
nislav Sousedik in the closing contribution defends a pre-Fregean notion of pre-
dication and presents a theory of his own, conceived as a modern recasting of the
Thom istic, metaphysically grounded identity theory of predication.
We would like to thank all the participants of the Prague conference for their
contributions, especially to the authors of the papers published in this book.
It was an honour and pleasure to work with them. Special thanks belongs to
our language editor and proofreader Svetla Jarogova, who has spared us many
errors and substantially contributed to the quality of the text. For any remaining
mistakes and shortcomings we take, of course, full responsibility. We are also
grateful to Rafael Huntelmann of Ontos Verlag for his interest in this volume
and his patience with our work on it. We are also obliged to express our gratitude
to His Grace, Right Reverend Michael Josef Pojezdnyr, O.Praem., the Abbot of the
Strahov Monastery, for generously providing the historical premises of the mo-
nastery for the conference. We are further indebted to the Dean of the Catholic
Theological Faculty of the Charles University Prague, Spectabilis ThDr. Prokop
Bra and to the Director of the Institute of Philosophy of the Academy of Sciences
of the Czech Republic, PhDr. Pavel Baran, CSc., for the sympathy with which they
accepted patronage of the conference. The conference was organised by the
Catholic Theological Faculty of the Charles University together with the Institute
of Philosophy of the Academy of Sciences of the Czech Republic.
The conference proceedings are being published with the financial support
of the Grant Agency of the Academy of Sciences of the Czech Republic, Grant
No. IAA908280801 "Metaphysics in contemporary analytical philosophy and its
relations to the metaphysics of modern Aristotelianism".
Stanislav Sousedik
David Svoboda, Prokop Sousedik
Daniel D. Novotny, Lukcig Novak
8
WHAT IS AN ONTOLOGICAL CATEGORY?
Peter van Inwagen
ABSITTnR RtAA heCC TTpa
In (cid:9)the author examines the concept of a natural class, and proposes a definition
of "ontological category" in terms of that concept. Say that a class is "large" if its membership
comprises a significant proportion of the things that there are. Say that a class is "high" if it is
a proper subclass of no natural class. Then a natural class is a primary ontological category if and
only if (a) there are large natural classes, and (b) it is a high class. (Secondary, tertiary, etc.,
ontological categories are defined by an extension of this definition.) The author defends the
definition, considers various ways in which it might be modified, and applies it to the problem
of constructing a taxonomy of ontologies.
As names of divisions of philosophy go, "ontology" is a rather new word. Al-
though it is older than that terminological parvenu "epistemology", it is much
newer than "metaphysics" or "ethics" or "logic" - and, of course, it is much newer
than "philosophy". But the word is as hard to define as any of her elder sisters.
within analytical philosophy,' one finds three understandings of the word "onto-
logy" - or, if you like, three conceptions of ontology.'
One of them, the use of the word by Bergmann and his school, is that ontology
is the study of the ontological structure of objects. I reject this conception of
ontology. I reject it as provincial, as the identification of a kingdom with one of
its provinces. (In my view - I defend this view in an unpublished companion piece
to this paper entitled "Relational vs. Constituent Ontologies" - that province is
uninhabited. But I do not reject the Bergmanian conception of ontology on that
ground alone: I contend that it is a provincial conception even if objects do have
ontological structures.)
There is, secondly, what I will call the "bare Quinean" conception of ontology.
Quine has famously called the question "What is there?" "the ontological
' For a discussion of the existential-phenomenological conception of ontology, see my
essay, "Being, Existence, and Ontological Commitment", in Metametaphysics: New Essays on the
Foundations of Ontology, ed. David J. Chalmers, David Manley, and Ryan Wasserman (Oxford:
Oxford University Press, 2009), 472-506.
This count - three conceptions of ontology - is problematical, owing to the fact that many
2
analytical philosophers who have made important contributions to ontology (on anyone's
conception of ontology) have not given an explicit statement of what they take ontology to
be. Perhaps I should say: Within analytical philosophy, one finds three potential or implicit or
tacit understandings of ontology (see note 3).
CATEGORIES AND BEYOND • 11
Peter van Inwagen Peter van Inwagen
WHAT IS AN ONTOLOGICAL CATEGORY? WHAT IS AN ONTOLOGICAL CATEGORY?
question", and one might incautiously infer from this label that he conceives of will indeed insist that it would be a mistake to try to provide such an account
ontology as the attempt to answer the ontological question. But neither Quine owing to the fact that those words are no more than expressions of the subjective
nor anyone else would regard just any answer to the ontological question as reactions of various philosophers to the degree of generality exhibited by various
the kind of answer a discipline called ontology might be expected to provide. existential theses.'
Quine himself has observed that one correct answer to the ontological question The third conception of ontology - it is the conception I favour - rests on the
is "Everything" - and we certainly do not need to turn to any science or discipline conviction that the notion of a "general" or "abstract" or "systematic" answer to
to satisfy ourselves that that answer is correct. Another sort of correct answer the ontological question can be given an objective sense. The third conception
might well be of the following form: a very long - no doubt infinite - conjunction rests on the conviction that there are ontological categories and that it is the
of existential quantifications on "low-level" predicates, a conjunction that would business of ontology to provide answers to the ontological question in terms of a
perhaps read in part "... and there are bananas and there are electron neutrinos specification of the ontological categories. I will attempt to give an account of the
and there are protein molecules and there are locomotives ... and there are colours concept on which this conception of ontology rests, the concept of an ontological
and there are political parties and there are nontrivial zeros of the Riemann zeta category.
function...". (Perhaps its final conjunct - if a sentence comprising infinitely many * * *
conjuncts can have a final conjunct - would be: "and there is nothing else".) If the
I begin with the idea of a natural class. One of the assumptions on which
only answers (other than answers that involve the "everything trick", answers
the third conception of ontology rests is that natural classes are real. By this
like "Everything" and "Locomotives and everything else") that can be given
I do not necessarily mean that there are objects called "natural classes", for an
to the ontological question are those provided by the investigative techniques
ontologian (why is there no such word?) may well deny that there are classes of
native to everyday life and the special sciences, then all answers to the ontological
any description." Indeed, anyone who did deny the existence of classes would ipso
question may well be of that sort. But if there is a philosophical discipline called
facto be engaged in ontology. What I mean by saying that there are natural classes
ontology, it will attempt to give an answer to the ontological question that is in
is a consequence of the thesis that there are natural - non-conventional - lines
some sense more general, more abstract, more systematic than a long conjunction
of division among things. This assumption was famously rejected by Hobbes,
of existential quantifications on low-level predicates. And the "bare Quinean"
and, following him, by Locke and the other empiricists. As Locke says (in the
will agree with this statement: on the bare Quinean conception of ontology, concluding passage of Chapter 3 of Book III of the Essay),
ontology is the discipline whose business it is to provide an abstract or general
or systematic answer to the ontological question - answers that are less abstract Recapitulation. - To conclude: This is that which in short I would say, viz., that all
the great business of genera and species, and their essences, amounts to no more
and more informative than "Everything" and less informative and more abstract
but this, that men making abstract ideas, and settling them in their minds, with
than "long list" answers.
names annexed to them, do thereby enable themselves to consider things, and
The bare Quinean will, however, be happy to regard the ideas expressed by discourse of them, as it were in bundles, for the easier and readier improvement
the words "general", "abstract", and "systematic" as entirely subjective. On the
bare Quinean conception of ontology, it is the business of the practitioners of
ontology to produce and defend answers to the ontological question that - as 3 I have not said that Quine or anyone else is a bare Quinean. I suspect, however, that
Quine would at the very least find bare Quineanism an attractive formulation of the nature
one might say - strike them and their peers as "general" and "abstract" and
of ontology (see note 2).
"systematic", answers that it seems appropriate to them to apply those terms to.
' The "classes" that figure in this essay are - or are if they really exist - much more
If, for example, I say that there are abstract objects or sets or temporal parts
like biological taxa than they are like sets. Like taxa, and unlike sets, they can change their
of persisting objects, the bare Quineans will almost certainly recognise this as membership with the passage of time and the membership of a class in one possible world
an assertion of the kind that characterises ontology. But if I say that there are may not even overlap its membership in another. Like taxa, and unlike sets, moreover, they
bananas or protein molecules or solutions to Einstein's field equations that are may have "borderline members" (if there is something that is neither determinately a cat
without physical interest, these assertions will almost certainly seen by the bare nor determinately a non-cat, that does not prevent "cat" from being a natural class). But
I am not seriously asserting that there really are things that have the properties I have
Quineans as having a place in ontology only as examples that illustrate some
ascribed to classes. I issue this promissory note: I could - the result would be rather awkward,
much more general existential thesis or as premises of some argument for some
I concede - eliminate the apparent reference to and quantification over classes in the sequel by
much more general existential thesis. And they will offer no account of what it
paraphrase. In my view, the only substantive philosophical issue raised by my talk of "natural
is for an existential thesis to be "much more general" than these theses. They classes" is whether there are real lines of division among things.
12 • CATEGORIES AND BEYOND CATEGORIES AND BEYOND • 13
Peter van Inwagen Peter van Inwagen
WHAT IS AN ONTOLOGICAL CATEGORY? WHAT IS AN ONTOLOGICAL CATEGORY?
and communication of their knowledge, which would advance but slowly, were their For any class, if its boundary marks a real division among things, then either that
words and thoughts confined only to particulars. class or its complement is a natural class - but not necessarily both.
I am not wholly convinced that what Locke says in this "recapitulation" is If you ask me, "In such a case, how do we determine which of two given
consistent with everything he says in the Essay (or even with everything he says complementary classes are natural classes?", I'm afraid I do not have any very
in Chapter 3 of Book III), but, whether it will do as an unqualified statement of informative answer. I could try this: The ones with "sufficient internal unity". It
Locke's views or not, it is a good statement of the point of view whose rejection does seem obvious to me that if the boundary between a class and its complement
is one of the assumptions on which the third conception of ontology rests. (From marks a real division among things, at least one of the two must exhibit sufficient
this point on, when I ascribe features to "ontology", I shall be speaking from the internal unity for it to be called a natural class. If this thesis is granted, the
point of view of the third conception - my own conception.) According to this existence of natural classes follows from the existence of real divisions among
anti-Lockean philosophy of classification, some classes of things - a minuscule things. Nevertheless, the concept of "natural class" cannot be defined solely in
proportion of them, if classes are anything like as numerous as sets - correspond terms the concept "real division." We must also appeal to the concept of "sufficient
to real divisions among things: in each case, the real division between the things internal unity" if we are to provide a full explanation of "natural class". (Or, at any
that are members of that set and those that are not.' To say that there are rate, we must appeal to some concept other than "real division") One might in fact
real divisions among things implies the existence of natural classes,' but this contend that, if we really have the concept "sufficient internal unity", we could
statement does not say enough to settle the question of what natural classes use it to define the concept "real division among things". (Suppose a class exhibits
there are - not even to settle it in the rather abstract and uninformative way "sufficient internal unity"; suppose its union with no unit class other than its unit
I want to settle it in this initial discussion of the natural classes. To show you what subclasses has this feature; then it is plausible to suppose that its boundary marks
I mean by this statement, I'm going to ask you to consider two questions about a real division among things.) Why, then, have I assigned such a fundamental
the relation between the concepts "real division among things" and the concept role to "real division" in my exposition of the concept "natural class"? Because,
"natural class". first, it seems to me that "real division" is a far easier idea to grasp than the idea
I shall introduce the first of these two questions by the following example. "exhibits sufficient internal unity". And because, secondly, in most interesting
Suppose that the line that marks the division between horses and non-horses cases in which the boundary between two complementary classes marks a real
is one of those real lines of division among things. Does it follow that "horse" division among things, it will be simply evident that - whatever internal unity
is a natural class? Before you answer, consider this question: Does it follow that may be - either one of them exhibits vastly more internal unity than the other or
"non-horse" is a natural class? That "non-horse" is a natural class certainly does they both exhibit an approximately equal (and very high) degree of internal unity.
not seem to be a thesis that should be true by definition. But the boundary of that Now the second question about the relation between "real division" and
class marks a real division among things. At any rate, it does if the boundary of "natural class". Consider the universal class, the class of all things.' Is it a natural
"horse" marks a real division among things, since the two classes have the same class? I propose to leave this an open question - to provide an account of "natural
boundary. We therefore do not want to say that a class is a natural class given class" that leaves it an open question.8 Does what I have said have any implications
only that its boundary marks a real division among things. for this question? The only relevant implication of what we have said is this: if the
I think that the following statement is a more plausible candidate for what we boundary of the universal class marks a real division among things, then either
want to say about the relation between "real division" and "natural class": the universal class or the empty class is a natural class. Well, what is the boundary
of the universal class? In one sense, it has no boundary - not if boundaries divide
5 Real divisions need not be sharp divisions. If one divides the world into things that
are determinately cats, things that are determinately not cats and things that are neither
determinately cats nor determinately non-cats, one may have thereby have marked a real ' Even those who are realists about classes will be well advised to treat the universal class
division among things. as a virtual class - that is to treat apparent reference to it as a mere - and dispensable - matter
6 Or, to speak more carefully (see note 4), it implies that those who have no objection to of speaking.
affirming the existence of classes should regard some of those classes as natural classes. And 8 Suppose that Meinong was wrong and that one name for the universal class is "being".
even nominalists who believe in real divisions among things may find it useful to speak as if Aristotle held that "being" was not a category. On the account of "ontological category" I shall
those divisions marked the boundaries of natural classes. (Such nominalists will presumably propose - and given that Meinong was wrong -, "being" will be a category if it is a natural
be able to eliminate, at least in principle, apparent reference to and apparent quantification class. I do not want to give an account of "natural class" that will imply either the truth or
over natural classes from their discourse.) the falsity of Aristotle's thesis.
14 • CATEGORIES AND BEYOND(cid:9) CATEGORIES AND BEYOND • 15
(cid:9)
Peter van Inwagen Peter van Inwagen
(cid:9)
WHAT IS AN ONTOLOGICAL CATEGORY? WHAT IS AN ONTOLOGICAL CATEGORY?
things from other things. But we might not insist that a boundary must divide proportion of the things that there are are bosons or fermions. We might, for
things. (Suppose the universe is finite in extent; adopt a relational theory of space. example, imagine that she supposes that, for any xs, the mereological sum of
Isn't it reasonable to say that in that case the universe has a boundary, a boundary the xs exists, and that among these sums are to be found atoms and molecules
that nothing is outside?) and cats and locomotives and galaxies and most of the tangible or visible things
The simplest way to leave it an open question whether the universal class is a that we unreflectively believe in. (And, of course, Alice believes that there are
natural class is to stipulate that it has no boundary (in which case our principle a vast number of convoluted gerrymanders most of which are not - considered
says nothing about whether it is a natural class). We say, that is, that a class has a individually - possible objects of human thought.) The class of cats, Alice con-
boundary if (and only if) both that class and its complement are non-empty. Those tends, is not a natural class: the vague and imperfect boundary we have drawn
who want to say that the universal class is a natural class - or that it is not - must around the cats is a mere product of convention and fails to reflect a real division
defend their thesis on some ground that does not involve the properties of its among things, unlike the boundary we have drawn around the bosons. And the
boundary (perhaps on the ground of its "internal unity" or lack thereof). It will same goes for the locomotives and the galaxies. (Of course most classes of sums
be observed that, in virtue of this stipulation, we have left it an open question are cognitively inaccessible to us, but, says Alice, if, per impossibile, we were to
whether the empty class is a natural class. I hereby stipulate that the empty draw boundaries around any of these classes, those boundaries would be merely
class is not a natural class - but for no profound reason; whether the empty class conventional - and with a vengeance.) And, of course, she maintains that the
is a natural class seems to be one of those "don't care" questions, one of those class of things that are neither bosons nor fermions is, as one might say, radically
questions that can properly be settled by stipulation, and stipulating that it is not deficient in internal unity and is not a natural class.
a natural class will simplify some of my definitions and the statements of some If Alice is right, ontology is, again, like astrology: a science that rests on a
of my theses. false assumption. For one of the assumptions on which ontology rests is this:
Are there any natural classes? Well, it seems plausible to suppose so. The class that membership in the natural classes is not restricted to any such minuscule
of electrons is a plausible candidate for the office "natural class" - as plausible proportion of the things that there are as Alice supposes it to be.
a candidate as there could be, in my view. (The boundary between electrons It is an assumption of ontology that there indeed are natural classes whose
and non-electrons is certainly a plausible candidate for the office "boundary membership comprises a really significant proportion of the things that there
that marks a real division among things", and it seems evident that the class of are. I am acutely aware that the idea of a class whose membership comprises
electrons exhibits vastly more internal unity than the class of non-electrons.) The a really significant proportion of the things that there are is an idea that it is
class of horses (members of the species Equus caballus) would be a rather more hard to give any precise sense to. But it does not seem to me to be an obviously
controversial but still reasonably plausible example. meaningless or entirely vacuous idea. Take our friend Alice. In her view there
Whether there are natural classes or not, it is one of the assumptions of are certainly a lot more things - even a lot more concrete things - than there
ontology that there are. (If there are no natural classes, ontology is like astrology: are things that are members of some natural class. If, for example, there are
a science that rests on a false assumption.) It is, moreover, one of the assumptions 10 exp 80 bosons and fermions, then there are 2 exp (10 exp 80) - 1 things
of ontology that, although some pairs of natural classes may have non-empty (abstractions aside): there are 10 exp 80 things that belong to some natural class
intersections otherwise than by one's being a subclass of the other, there are and ((2 exp (10 exp 80) - 1) - 10 exp 80 things that belong to no natural class, and
nested sequences of natural classes - sequences ordered by the subclass relation. the latter number is inconceivably larger than the former. (The ratio of the latter
The class of electrons, the class of leptons, and the class of fermions provide a to the former can be described this way. Think of the number that is expressed
plausible example of such a sequence. The class of horses, the class of mammals, by a "1" followed by eighty zeros. The ratio of the number of things that belong
and the class of chordates would (again) be a rather more controversial but still to no natural class to the number of things that belong to some natural class
reasonably plausible example. is a number that can be expressed by a "1" followed by - approximately - one-
One could, however, affirm the existence of natural classes and of nested third that many zeros.) Or if the number of bosons and fermions is denumerably
sequences of natural classes without involving oneself in ontology - or in any infinite, then the number of (concrete) things that belong to no natural class is
other part of philosophy. Suppose, for example, that Alice maintains that the indenumerably infinite.
largest natural classes are the class of bosons and the class of fermions and that There are various ways in which there might be natural classes whose mem-
every natural class is a subclass of one of these two non-overlapping classes. bership comprised "a really significant proportion of the things that there are".
And suppose that she also maintains that (in some sense) only a very small
16 • CATEGORIES AND BEYOND CATEGORIES AND BEYOND • 17
!
Peter van Inwagen Peter van Inwagen
WHAT IS AN ONTOLOGICAL CATEGORY? WHAT IS AN ONTOLOGICAL CATEGORY?
(Let us call such a class "large".) One of them is this: the universal class is a natural a-matter-of-convention classification. But remember that the highest links in the
class - for the membership of a class is certainly a "significant proportion" of itself. great chains of classification are primary ontological categories only if primary
Here is another way. It may be that, although the class of all things, the uni- ontological categories exist - just as the highest buildings are skyscrapers only if
versal class, is not a natural class, it is the union of a small number of natural skyscrapers exist. If our friend Alice is right about what natural classes there are,
classes. (A "small" number would be a number like 2 or 6 or 19. And what do the highest natural classes are not primary ontological categories. (If she is right,
I mean by "a number like"? You may well ask. But if you want a definition of "small the highest natural class, the class of elementary particles, is not an ontological
number", I offer the following. A number n is small in just this case: if a class is category, since there are no large natural classes.) Her world corresponds, in the
the union of n subclasses, the membership at least one of them must comprise a analogy, to a world in which the highest buildings are three stories high: highest
really significant proportion of the membership of that class.) buildings but no skyscrapers.
And here is a third. Say that a natural class is "high" if is not a proper subclass Having defined "primary ontological category", we may proceed to define
of any natural class. At least one high natural class is large - although some things "secondary ontological category", "tertiary ontological category", and so on, by
belong to no natural class. (Suppose, for example, that God exists and that a vast repeated applications of essentially the same device. We say that x is a natural
number of creatures exist and that everything is either God or a creature. Suppose subclass ofy if x is a subclass of y and x is a natural class. We say that x is a large
that God belongs to no natural class - and hence that the universal class is not a subclass ofy if x is a subclass ofy and x comprises a significant proportion of the
natural class - and that the class of creatures is a natural class.) members ofy. We say that x is a high subclass ofy if x is a natural proper subclass
Note that the assumption we are considering, that there are large natural of y and is a proper subclass of no natural proper subclass of y. Then, a natural
classes, leaves open the possibility that that there are high natural classes that are class x is a secondary ontological category if
not large. Our assumption is, for example, consistent with the following threefold
There is a primary ontological category y such that
thesis: everything is either a substance or (exclusive) an attribute; "substance"
-y has large natural proper subclasses
and "attribute" are both natural classes and every natural class is a subclass of
one or the other; there are finitely many substances and too many attributes to - x is a high subclass ofy.
be numbered even by a transfinite number. In this case, "substance" is a high
And so for tertiary ontological category, quaternary ontological category, ....
class, despite the fact that only an insignificant proportion of the things that And, finally, an ontological category (simpliciter)10 is a class that, for some /7, is
there are are substances. an n-ary ontological category."
We may now define "ontological category". Let us say, first, that a natural class
x is a primary ontological category just in the case that
'° In formulating this definition of "ontological category", I have assumed that every
- there are large natural classes sequence of natural classes ordered by the proper-subclass relation has a first member. (If
this were not so, there might be large natural classes but no high natural classes - and hence
- x is a high natural class.
no primary ontological categories and hence no ontological categories of any order. But it is
Consider for example the case presented in the previous paragraph. In this at least plausible to suppose that any large natural class is an ontological category, and even
more plausible to suppose that if there are large natural classes, some of them are ontological
case "substance" and "attribute" are high natural classes and are in fact the high
categories.) This is a consequence of the stronger statement that every such sequence is finite.
natural classes. And there are large natural classes - the class of attributes if no
I see no reason to question either of these theses.
other. "Substance" and "attribute are therefore primary ontological categories -
" Note that this definition allows ontological categories to overlap. Suppose that every-
and are the primary ontological categories.' thing is either an A or a B, that A and B are natural classes, and that neither is a proper subclass
The primary ontological categories are the highest links in the great chains of any natural class. Then A and B are primary ontological categories. But nothing we have
of classification - the great chains of non-arbitrary classification, of not-merely- said implies that A and B do not overlap. (Cf. n. 9). Suppose further that they do overlap and
that their intersection is a natural class that is not a proper subclass of any natural class.
Then their intersection is also a primary ontological category. Or suppose that A and B do not
Note that the definition does not rule out overlapping primary ontological categories. overlap, and that A can be partitioned into two subclasses C and D, each of which is a natural
9
Suppose, for example, that Phoebe maintains that "abstract" and "concrete" are the primary class and that B can be partitioned into two subclasses E and F, each of which is a natural class.
ontological categories. She may consistently go on to maintain that the proposition that Suppose that the union of C and E is a natural class that is a proper subclass of no natural class.
Socrates was a philosopher is abstract (in virtue of being a proposition) and concrete (in virtue Then the union of C and E is a primary ontological category that overlaps both the primary
of having a certain concrete object, Socrates, as an ontological constituent). categories A and B and the secondary categories C and E.
18 • CATEGORIES AND BEYOND(cid:9) CATEGORIES AND BEYOND • 19
