Ted Sider
August, 2001
Note: abstracts are taken from the Philosopher's Index.
Universals
Some anthologies:
Articles and books:
An argument for realism (i.e., the ontological thesis that there
exist universals) has emerged in the writings of david armstrong, fred
dretske, and michael tooley. These authors have persuasively argued against
traditional reductive accounts of laws and nature. The failure of traditional
reductive accounts leads all three authors to opt for a non-traditional
reductive account of laws which requires the existence of universals. In
other words, these authors have opted for accounts of laws which (together
with the fact that there are laws) entail that realism is true. This argument
for realism which emerges from the work of armstrong, dretske, and tooley
is discussed and criticized. Conclusions from the discussion question the
tenability of all reductive accounts of laws.
The primary purpose of this paper is to argue that particulars in
the actual world are nothing but complexes of universals. I begin by briefly
presenting bertrand russell's version of this view and exposing its primary
difficulty. I then examine the key assumption which leads russell to difficulty
and show that it is mistaken. The rejection of this assumption forms the
basis of an alternative version of the view which is articulated and defended.
This paper examines the view that ordinary particulars are complexes
of universals. Russell's attempt to develop such a theory is articulated
and defended against some common misinterpretations and unfounded criticisms
in section one. The next two sections address an argument which is standardly
cited as the primary problem confronting the theory: (1) it is committed
to the necessary truth of the principle of the identity of indiscernibles;
(2) the principle is not necessarily true. It is argued in section two
that a proponent of the theory need not accept (1) and an argument against
(2) is presented in section three. The final section attempts to show that
russell's theory ultimately fails because of inadequacies in its treatment
of space and time. The paper closes with a suggestion for remedying this
difficulty.
One of the chief disputes among realists is over the question of
the relationship between universals and the concrete objects which exemplify
them. M j loux has invoked the framework of possible worlds to argue both
that there are universals which conform to the aristotelian account and
that there are universals which conform to the platonist account. The purpose
of this paper is to show that neither of these claims has been substantiated.
In this paper, the author traces and examines a line of reasoning
which, evidentally, led quine to accept platonism. Central to this reasoning
is the thesis that mathematics--at least the mathematics needed in science--is
'ontologically committed' to universals or abstract entities; and part
I of this paper is concerned primarily with this thesis. Thus the author
examines and criticizes in some detail various versions of quine's criterion
of ontological commitment. In part ii, the author sketches a line of reasoning
in support of platonism very similar to quine's but without resorting to
quine's criterion or even making use of the notion of ontological commitment.
The author concludes by briefly discussing some ways of avoiding the platonic
conclusion.
Different formal theories of predication are associated with nominalism,
conceptualism and realism as theories of universals. Two different formal
theories are associated with conceptualism, depending on whether concepts
are assumed to be formed only predicatively (under the constraint of the
vicious circle principle) or impredicatively as well. Two different formal
theories are also associated with realism, one Platonistic (logical realism),
the other Aristotelian (natural realism), with each validating different
versions of essentialism, but only natural realism also validating a logic
of natural kinds. All of the formal theories are described as second-order
logics, with only the logic of nominalism being based on a substitutional
interpretation of predicate quantifiers.
By extending the well-formedness conditions for the wffs of standard
second order logic so as to allow for the occurrence of nominalized predicates,
a number of different logics for nominalized predicates are described and
associated with different traditional philosophical theories of universals.
E.g., since for the platonist universals are individuals (in the logical
sense), the platonist takes a nominalized predicate to refer as a singular
term to the same universal designated by that predicate in predicate position,
i.e., when used predicatively. Universals are unsaturated entities for
a fregean, however, and not individuals; and so the fregean, who retains
the framework of standard second order logic takes a nominalized predicate
to refer to an object correlated with the universal designated by that
predicate. Abailardians resemble fregeans but differ in their interpretation
of subject position quantifiers insofar as nominalized predicates do not
refer at all as singular terms; and nominalists, who interpret predicate
quantifiers substitutionally, resemble abailardians but with an additional
restriction regarding quantification into predicate positions.
Aristotle's theory of universals is expounded by contrast with plato's.
Where plato had said that x is f iff x participates in the form of f, aristotle
has two analyses. If f is a substance predicate then x is f iff x is specifically
identical with an f. if f is an accidental predicate then x is f iff there
is a y in x which is specifically identical with an individual in the appropriate
category for f.
I examine an aristotelian solution to the problem of universals
proposed by m j cresswell ("what is aristotle's theory of universals?",
"the australasian journal of philosophy", volume 53, 1975, pages 238-247).
The solution is inadequate in too many respects to be a worthwhile alternative
to platonism: it cannot explain several prominent types of predicates (relational,
extensionless, negative, unique, essentially unique, for example). As for
the cases it can handle, the solution is circular in the way a coherence
theory of justification is--I compare the metaphysical and epistemological
enterprises on this score at the end.
In this paper I counter the chief arguments for trope theory in
Keith Campbell's book "Abstract Particulars". I argue that trope theory
faces a version of Russell's resemblance regress, and therefore that it
cannot dispense with universals. As a corollary, not all entities can be
analyzed in terms of tropes, and so trope theory lacks the explanatory
power Campbell credits it with. I further argue that trope theory needs
instantiation relations to tie tropes into complex bundles, and therefore
that trope theory is not more economical than the theory of universals.
I demonstrate that analyzing the resemblance of properties in terms
of partial identity has insuperable logical consequences. It follows that
the strategy of vindicating the realism of universals against particularistic
ontologies such as tropism by appeal to partial identity is incoherent.
The author develops a unified ontology of objecthood, essences and
causation. A principal tenet is that while the basic units of the physical
world are substances, particular properties are the analytic ultimates
of existence. Although properties must inhere in objects, individual things
are nothing more than compresences of properties at particular positions.
There exist no mysterious substrata. Principles explaining how properties
are held together in compresences are basically the same as those that
account for essences and for causal relations. There exist no objective
universals. Denkel defends a thoroughgoing particularism and offers purely
qualitative accounts of individuation, identity, essences and matter. Throughout,
the main alternative positions are surveyed and the relevant historical
background is traced.
Various calculi of individuals (atomistic and non-atomistic systems
of either unordered or sequential individuals) receive axiomatic, semantic,
and philosophical treatment with special reference to nelson goodman. Alternative
criteria regarding ontological implications are stated, proposed, and discussed.
Nominalistic models, which avoid universals as designata of predicates,
are used to define truth and validity for systems (often shown to be complete)
which seem appropriate to qualities, bundles of qualities, or concreta,
or formalize the notions of partial qualitative identity and of resemblance.
In "a theory of universals", david armstrong has proposed a theory
to account for the resemblance of universals--the fact that determinate
properties fall into natural groups or classes. According to armstrong,
this important fact is explained in terms of partial identity. Two universals
fall under a common genus if a single universal is a part of each. Although
the author is in agreement with major aspects of armstrong's theory of
universals, he thinks this explanation is mistaken. There are cases it
does not account for. He proposes a general theory of generic universals,
according to which such universals exist and bear a special relationship
to their determinate species. If a particular has a certain determinate
property, then it necessarily has each of the determinable properties under
which the former falls. The necessary connection between determinate and
determinables bears some resemblance to that between, e.g., color-properties
and spatial extensions.
In the "logica ingredientibus" abailard attacks the theory according
to which universals are collections of individuals. I argue that abailard's
principal objection to this 'collective realism', viz, that it conflates
universals with integral wholes, is actually quite strong, though it is
generally overlooked by recent commentators. For implicit in this objection
is the claim that the collective realist cannot provide a satisfactory
account of predication. The reason for this is that integral wholes are
not uniquely decomposable. In support of my thesis I first explicate the
medieval distinction between integral and subjective parts and then discuss
its application to collective realism.
It is argued that the relations of proportion introduced by Bigelow
and Pargetter should be excised from their theory of quantity. Retaining
the nation that quantities comprise numerical relations, I include a binary
composition operation and identify a quantity with the corresponding structure
of universals. I describe this further with seven (obvious) axioms.
This is a reply to david lewis's "against structural universals"
(same issue). The author examines the thesis which lewis relies on in his
article, and which the author calle's the either mereology or magic thesis.
He argues (1) that it does not follow from a conceptual analysis, (2) although
it has considerable prima facie appeal it is not robust enough to be used
to argue against structural universals, and (3) lewis himself is committed
to counterexamples to it.
In this paper I adapt bradley's argument of chapter two of "appearance
and reality", in order to establish a presumption against what I call hard
realism about universals. By that I mean the treatment of universals as
sufficiently like particulars to be called "things", without hesitation.
I leave open the possibility of overcoming this presumption.
The purpose of this article is to show the solution of nominalism
to the problem of universals, the indefensibility of its theory, and the
incompatibility of universals with individuals of basic particulars. The
solution is seen in the analysis of universals as a development of medieval
nominalists, and as a treatment of hobbes, or as a reassertion of quine
and goodman. Both the indefensibility and incompatibility are shown in
the critical evaluations of such critics as russell, wittgenstein, bochenski,
pears, strawson, and others. The final solution whether valid or invalid
is that universals, according to abelard are general concepts which exist
in singular things, while for ockham are concepts or general terms which
exist only in thought. Nevertheless, the theory of nominalism in its strict
sense is indefensible, since it considers only individuals, and therefore
fails to utilize the concept of identity. Finally, universals are incompatible
with individuals or basic particulars, because of their difference in consistency,
content and existence.
The paper is a response to Charles Lndesman's article in Philosophy
and Phenomenological Research and provides a "reductio ad absurdam" of
his argument for a realistic theory of universals.
Wittgenstein's concept of family resemblance, and its reformulation
by keith campbell, are critically considered. The theory is criticized
on a number of grounds but specifically on the ground that such a theory
can give no explanation of why general terms are limited in applicability.
The theory thus provides no solution to the traditional problem of universals.
Renford bambrough's theory is considered as distinct from wittgenstein's
and argued to be incoherent.
"The structure of appearance" is intended as a nominalist version
of the "aufbau", for carnap employs set-theory in his construction, whereas
goodman allows only mereology. But it is not clear that goodman's is the
more nominalistic enterprise, for his basis is of repeatable universals
(qualia), while carnap's is of unrepeatable particulars (elexes). The supposed
ontological preferability of goodman's enterprise rests on the principle
that two distinct entities cannot be made from the very same atoms; but
this principle, I argue, at least once the type-token distinction is taken
seriously, can be seen not to be acceptable.
Russell's late ontology sought to avoid "wholly colourless particulars"
(substrata, points of space, bare instants of time) by appealing to complexes
of compressent qualities in place of particulars that exemplify qualities.
Yet he insisted on i) calling qualities like "redness" "discontinuous,"
"repeatable" particulars, and ii) claiming that such qualities were not
universals, since they were not exemplified but were ultimate subjects
that exemplified universal relations and universal qualities. It is argued
that his choice of terminology is not only misleading, but is ironically
not consistent with the concept of universality implicit in his well-known
"proof" of the existence of universals, a proof he retained in his later
(1940-48) ontology. It is also argued that there are substantive grounds
for rejecting his classification that clarify the concept of a universal.
Russell's elimination of basic particulars, in "An Inquiry into
meaning and Truth" and "Human Knowledge: Its Scope and Limits", by purportedly
construing them as "bundles" or "complexes" of universal qualities has
been attacked over the years by A J Ayer, M Black, D M Armstrong, M Loux,
and others. These criticisms of Russell's ontological essay of "particularity"
have been based on misconstruals of his analysis. The present paper interprets
Russell's analysis, rebuts arguments of his critics, and sets out a different
criticism of "bundle" analyses of particulars of the Russellian kind.
The article attempts to throw light on question of whether a principle
of acquaintance is a guide in ontology. The author examines views of both
those who claim to be acquainted with such things as substrata or universals
and those who hold that they are acquainted only with phenomena (qualities).
He argues that the principle of acquaintance functions to differentiate
between qualities, but does not give assurance that one is acquainted with
universals. He concludes that adherence to the principle of acquaintance
forces one to abandon substrata.
The author contends that the radical differences between the arguments
that lead to the acceptance of particulars and those that lead to universals
reveal the former to be specious. To support his thesis, he defines and
examines three conflicting views on the problem of universals. He also
considers the ontological ties of exemplification and combination postulated
by these positions and discusses the nature of relational properties.
Nominalists have attempted to translate statements putatively about
universals--like 'red is a colour'--into statements about particulars alone.
In this note I reinforce and supplement extant realist arguments against
such attempts.
This article develops Thomas Reid's theory of individual qualities
and universals connecting his theory with recent work. Reid held that individualities,
now called tropes, were the basis for our general conceptions of universals
which, however, are not things that exist. His theory is related to prototype
theory in psychology and to nominalist ontology.
The author had complained against structural universals that (on
the otherwise most satisfactory conception) they violate a principle of
uniqueness of composition; Armstrong and Forrest replied that a friend
of universals would in any case reject that principle, because it is violated
also by structures composed of universals plus particular instances thereof.
To this the author says that the friend of universals might get by without
the structures; whether he can depend on what work he wants his theory
to do, in particular on whether he requires it to provide truthmaking entities
for all truths.
A structural universal is one such that, necessarily, any instance
of it consists of proper parts that instantiate certain simpler universals
in a certain pattern. Forrest has suggested that structural universals
could serve as ersatz possible worlds; armstrong has offered several reasons
why a theory of universals must accept them. The author distinguishes three
conceptions of what a structural universal is, and raises objections against
structural universals under all three conceptions. The author then considers
whether uninstantiated structural universals, which are required by forrest's
proposal, are more problematic than instantiated ones.
D M Armstrong puts forward his theory of universals as a solution
to the problem of one over many. But this problem, depending on how we
understand it, either admits of nominalistic solutions or else admits of
no solution of any kind. Nevertheless, Armstrong's theory meets other urgent
needs in systematic philosophy: its very sparing admission of genuine universals
offers us a means to make sense of several otherwise elusive distinctions.
The propositional functions of the first edition of "principia mathematica"
are different from the universals in "the problems of philosophy". Propositional
functions were to be logical constructions out of propositions which in
turn were to be logical constructions out of particulars and universals.
While the theory of types is primarily a classification of propositional
functions, russell also held that universals differ in type from particulars.
No well-formed term of pm stands for a universal; the closest one can come
is an expression for a propositional function.
The purpose of the article is to suggest that arguments for universals
from "ordinary discourse are probably invalid," but a case may be made
for an exposition from mathematical discourse. The author investigates
the former claim and alludes to the latter.
Two rival answers to the question "What is an object?" are examined,
one semantic and the other metaphysical. The latter is defended, this holding
that objects are entities possessing determinate identity conditions. Entities
may be "abstract" either in being nonspatiotemporal, or in being logically
incapable of enjoying a "separate" existence, or in being dependent upon
abstraction from concepts. "Universals" and "sets" are abstract objects
in the first two senses and their existence can be defended via explanatory
considerations.
The natural numbers are abstract entities, but universals rather
than particulars. They are not sets, but kinds whose instances are sets.
Thus 2 is the kind of two-membered sets. This view accords well with our
ordinary talk about numbers and avoids problems like Benacerraf's about
the identity of the numbers. Since kinds are not themselves sets, no circularity
ensues from saying that 2 can itself be a member of a set which is an instance
of 2.
It is argued that linguistic analysis does not deal with the problem
of universals in a satisfactory way. The contributions of ryle, wittgenstein
and pears are considered. It is held that the problem of universals is
a genuine metaphysical problem and does not admit of being disposed of
by conceptual analysis. Moreover, the failure of attempts by linguistic
analysts here must cast doubt on the soundness of their bold antimetaphysical
claims. It is concluded that the problem of universals is not primarily
one of naming, but rather of resemblances.
I argue that a full account of the logic of resemblance statements
requires the use of second-order predicates, giving the respect in which
the resemblance is to be noted. Thus, "x resembles y" gets expanded into,
"x resembles y with respect to some f." I then show that the full explication
of what is involved in the statement of this third, or context-conferring
term, must include values: the purposes for which the resemblance is to
be noted. Though not explicitly argued, the article was designed to illustrate
the utility of the assumption of the existence of universals.
The paper is a defense of negative and disjunctive properties against
the criticism of D M Armstrong in part II of "Universals and Scientific
Realism". Given a mereology of properties (properties which are parts of
properties) there must be negative and disjunctive properties. Moreover,
negations of properties can be causally efficacious, and disjunctions of
properties can be identical in different particular; they fulfill Armstrong's
own criteria for propertyhood; Hence they are properties in his sense.
I focus on the debate about the nature of qualities between nominalists
(qualities are abstract particulars) and realists (qualities are universals)
by examining abstract reference. Realists claim that sentences like (1)
"red resembles orange more than it does blue" and (2) "red is a color"
incorporate abstract singular terms, e.g., "red," that refer to universals.
Nominalists try to account for (1) and (2) by employing two basic strategies:
abstract singular terms refer to sets of abstract particulars or reductive
paraphrase. Both strategies are examined and rejected. Sentences like (1)
and (2) provide evidence for a realist assay of qualities.
After comparing extreme nominalism (qualities do not exist), nominalism
(qualities are abstract particulars called tropes), and realism (qualities
are universals), I focus on the nominalist views of Keith Campbell. His
understanding of a nominalist assay of qualities and quality-instances
is stated and subjected to criticism. The criticisms center on Campbell's
use of the distinction of reason to analyze a trope. I conclude that Campbell's
views are incoherent.
A formal theory of quantity "t $$subscript$$q " is presented which
is realist, platonist, and syntactically second-order (while logically
elementary), in contrast with the existing formal theories of quantity
developed within the theory of measurement, which are empiricist, nominalist,
and syntactically first-order (while logically non-elementary). "T $$subscript$$q
" is shown to be formally and empirically adequate as a theory of quantity,
and is argued to be scientifically superior to the existing first-order
theories of quantity in that it does not depend upon empirically unsupported
assumptions concerning existence of physical objects, e.g., that any two
actual objects have an actual sum. The theory "t $$subscript$$q " supports
and illustrates a form of "naturalistic platonism", for which claims concerning
the existence and properties of universals form part of natural science,
and the distinction between accidental generalizations and laws of nature
has a basis in the second-order structure of the world.
Armstrong's regress arguments depend on his claim that the analysans
of any analysis will contain a general term which must itself be subjected
to the analysis. This feature of analysis may be avoided by laying down
conditions of adequacy which any analysis should meet. The conditions actually
suggested in the paper make clear the structural reasons why platonic styles
of analysis might seem congenial.
This is a book about some of the basic concepts of metaphysics:
universals, particulars, causality and possibility. Its aim is to give
an account of the real constituents of the world. The author defends a
realistic view of universals, characterizing the notion of universal by
considering language and logic, possibility, hierarchiesof universals,
and causation. On the other hand, he argues that logic and languages are
not reliable guides to the nature of reality.All assertions and predications
about the natural world are ultimately founded on "basic universals", which
are the fundamental type of universal and central to causation. A distinction
is drawn between unified particulars (which have a natural principle of
unity)and arbitrary particulars (which lack such a principle); unified
particulars are the terms of causal relations and thus real constituents
of the world. Arbitrary particulars such as events, states of affairs,
and sets have no ontological significance.
immanent realism is a justly popular theory of universals which
is incomplete. It is not good enough to say that all universals are equally
real and all equally inhere in objects. Concepts come in hierarchies, for
example: "colored," "red" and "claret," where "claret" is a shade of red.
Only those at the very bottom of the hierarchy exist in objects, and are
rightly called properties. Only properties have causality as a criterion
of identity. Frege's functional account of concepts can be adapted to explain
how higher level concepts apply to objects. Between two concepts at different
levels there is a relationship called 'essential subordination', which
is different from all other relationships. That a person is said to possess
a concept of a property is to be explained in terms of a person possessing
certain mental capacity, which enables him to make certain judgments. Properties
are concepts which exist in objects.
The author discusses stout's contention that there is a natural
unity to the universe. Stout "holds that the unity of a class or kind,...
is just another one of these forms." stout's criticisms of the traditional
logical theory and nominalism are examined. The author concludes that "universals
must be found "in experience" in order that they may enable us to think
beyond the limits of the here-and-now."
David armstrong has claimed (in "universals and scientific realism")
that there is "a single, very powerful line of argument" for dispensing
with a large number of abstract entities. The central premise of armstrong's
argument is the "eleatic principle," that what does not possess causal
efficacy is not real. In this paper it is argued, firstly, that it is extremely
difficult to find an unobjectionable version of the principle, and, secondly,
that using the most acceptable version of the principle the argument does
not go through.
In his two recent books on ontology, "Universals: an Opinionated
Introduction", and "A World of States of Affairs", David Armstrong gives
a new argument against nominalism. That argument seems, on the face of
it, to be similar to another argument that he used much earlier against
Rylean behaviorism: the truthmaker argument, stemming from a certain plausible
premise, the truthmaker principle. This paper argues that Armstrong's new
argument is not logically analogous to the old, and that it is quite possible
to be a thoroughgoing or 'ostrich' nominalist while holding the truthmaker
principle. It also puts forward a general characterization of the principle,
as it might be held by such a nominalist.
The view that universals are meaning-like entities is defended.
Meaning and reference of abstract singulars is discussed in order to combat
objections to identifying meanings and universals, resulting in the definition
of a "revealing (rigid) (property) designator" (one such that knowing what
it means guarantees knowing what it refers to, though referent and meaning
remain distinct). Application of this definition clears up some vagueness
in Kripke's account of reference and helps explain how direct acquaintance
with instances of a universal produces knowledge of word meanings. Property
individuation via meanings (and "vice versa"), natural kind terms (which
are usually "not" revealing designators), and some non-existing universals
(to solve some paradoxes) are also discussed.
Armstrong deplores my alleged "ostrich nominalism," not perceiving
that I, like him, espouse a realism of universals. I limit my universals
to classes, but only because of the problem of individuating intensions
and not from nominalist pretensions. His lack of a clear standard of what
constitutes assumption of objects has the startling effect of reactivating
bradley's old worry of a regress of relations.
The problem of identity is discussed through an analysis of ostension
of spatio-temporally extended objects. The author begins by explicating
this system and then shows how it differs from the ostension of irreducible
universals, such as "square" and "triangle." the author concludes by explaining
that detachment from one's conceptual scheme is not possible, but the scheme
can be changed "plank by plank" to correspond with a pragmatic standard.
In this article I address the problem of universals by answering
questions about what facts a solution to the problem of universals should
explain and how the explanation should go. I argue that a solution to the
problem of universals explains the facts the problem of universals is about
by giving the truth makers (as opposed to the conceptual content and the
ontological commitments) of the sentences stating those facts. I argue
that the sentences stating the relevant facts are those like ""a" has the
property "F".
This anthology offers a comprehensive presentation of twenty-eight
analyses of the problem of universals. It opens with analyses proposed
by Plato and Aristotle and then provides selections from theviews of the
medieval scholars Abeland, Aquinas, Duns Scotus and Ockham. It them traces
the development of Western thought on this fundamental topic from the modern
through the contemporary period, and includes the work of Kant, Hegel,
Husserl, Heidegger, Russell, Quine, Strawson, Carnap and Allaire.
The author argues that although they are distinguishable from the
specific materials (sign designs) which embody them in historically given
languages, abstract entities are linguistic entities. In developing his
theory of universals and propositions, which makes use of "distributive
individuals" such as "man," he introduces notational devices, discusses
frege's ideas on concepts, considers exemplification, and comments on the
relations between abstract entities themselves.
The essay constructs an ontological theory designed to capture the
categories instantiated in those portions or levels of reality which are
captured in our common sense conceptual scheme. It takes as its starting
point an Aristotelian ontology of "substances" and "accidents", which are
treated via the instruments of mereology and topology. The theory recognizes
not only individual parts of substances and accidents, including the internal
and external boundaries of these, but also universal parts, such as the
"humanity" which is an essential part of both Tom and Dick, and also "individual
relations", such as Tom's promise to Dick, or their current handshake.
The claim is that ontological questions occur at three logically
distinct levels: (1) the existential statements implied by a first-order
theory; (2) the range of variables of a first-order language; and (3) the
extra-linguistic correlates of a semantic theory. Examples would be, respectively,
whether there is an even number which is not the sum of two primes, whether
the analysis of action-sentences must involve quantification over events,
and whether we must understand predicates as referring to universals. Close
analysis of quine's writings reveals three such notions, not clearly enough
distinguished.
The issue between nominalists and realists is unlikely ever to be
rationally resolved. Currently favoured tests, leaning on the notions of
reference and identity, do not yield a clear-cut way of resolving the issue.
There is no neutral vantage-point from which to determine whether the notion
of existence should be restricted to what is found in nature or should
be extended to include objects of thought exemplifiable but not locatable
in nature.
The author begins by noting that the problem of universals often
focuses upon the role which pronouns, common nouns, and adjectives play
in languages. The author's thesis is "that questions about the roles which
linguistic expressions play are often interpreted as questions about the
meaning of these words, and these, in turn, are thought to be questions
asking for the identification of differing sorts of objects in the universe
(e.g., particulars, universals)." the author tries to show why such interpretations
of ordinary questions are improper.
The following positions are distinguished: (a) that both predicables
and "property-names" refer to universals; (b) that predicables refer to
universals while "property-names" don't; (c) that "property-names" refer
to universals while predicables don't. Each position is discussed at length
and found wanting. Insofar as the three views are exhaustive of traditional
realism about universals, that too is found wanting; the legitimacy of
higher-order quantification, however, remains unassailed.
The author argues that the identification of the realist's entities
rests on a philosophical confusion. Specifically, he wants to argue that
any plausible account of what we mean by "abstract entities" does not provide
any account of what realists in the history of philosophy from plato through
peirce have meant by "universals." after exposing the confusion that leads
to the identification of abstract entities and universals the author gives
reasons for dismissing the issue of nominalism versus realism as itself
resting on confusion.
A fairly strong case can be constructed for claiming that aristotle
held a robust realism in which at least some universals are primary substances.
But a closer look at the texts shows that, although aristotle is a realist,
his realism is very tenuous in that each universal is just the many particulars
that fall under it and thus lacks numerical unity. This interpretation
relies on the notion that every particular in the natural world, including
particular forms, arises from an accidental predication and on applying
to these particulars the equivalence relation of "being the same in species
(genus) as."
This work shows how abailard elaborated and defended the view that
universals are words, avoided the pitfalls of an image theory of thinking,
and propounded a theory of "status" and "dicta" as objects of thought without
treating them as subjects of predication. His defense of these views is
shown to depend on certain fundamental departures from the aristotelian
term logic of his day, including a proposal for subjectless propositions,
the treatment of copula plus predicate noun as equivalent to a simple verb,
and a transformation of the 'is' of existence into the 'is' of predication.
This is an explanation of Russell's theory of universals for beginners.
It gives his reasons for introducing the theory, shows how he used it to
solve some philosophical problems, and criticizes his view of a separate
world of universals as unnecessary for his purposes. Russell's assertion
of universals of relations is emphasized.
In this paper I consider the merits of Realist theories of predication
vis- a-vis three varieties of nominalism, which Armstrong has dubbed predicate
nominalism resemblance nominalism, and ostrich nominalism. In Part I, I
argue that ostrich nominalism is the most satisfactory position of these
four, and that the realist view favored by Armstrong and many others is
prone to the same fundamental difficulty as the other two varieties of
nominalism. In Part II, I consider difficulties for the argument of Part
I.
Williams reviews the theory of tropes which he had presented in
"on the elements of being," "review of metaphysics" 7 (1953): 3-18 and
171-92. He places that theory in the context of his view that "absolutely
all there is is a four-dimensional plenum of qualia in relations," subject
to unrestricted mereology. He then asks how the existence of universals,
repeated identically from instance to instance, might be reconciled with
the trope theory. He retracts his earlier proposal that universals be equated
with (or supplanted by) sets of resembling tropes. He adopts instead the
"trope-kind theory" according to which universals simply "are" tropes,
spoken of and counted under a "relaxed" notion of identity. He classifies
the trope-kind theory as a form of immanent realism about universals.
In part I, N Wolterstorff distinguishes subjects from predicates
and general terms from singular. In part ii he argues that there are non-linguistic
predicable entities, defending the principle that "if something "is-f",
then there is such a thing as "f-ity"." states and actions as well as properties,
he says, are predicables. In part iii he maintains that such things as
symphonies and books are universals: not predicable universals but "substance"
universals. In part iv, wolterstorff denies that universals are either
paradigms, exemplars or perfect copies of themselves.
This article considers the task of translating linguistic expressions,
such as sentences of the form 'there are p's', to sentences of some other
form. The author is especially concerned with the view that such translations
enable us to avoid "ontological commitments." he takes an example from
morton white which allegedly provides a case of a translation which avoids
ontological commitments and argues that if the translation is adequate
then it is used to make the same assertion as the original and so makes
the same commitments. He concludes that those who take avoidance of ontological
commitment as the point of linguistic translations are obstructing our
view of the real point of such translations.
This work argues for nominalism in the philosophy of mathematics
and in metaphysics. Only by eliminating abstract objects via ontological
reduction, it urges, can we reconcile ontology and epistemology. After
developing an account of reduction for abstracta, it allays benacerrat's
fear of multiple reductions and quine's fear of a world of numbers. Finally
it presents a theory of ontological commitment, relating it to ontology
in general and devising an epistemological criterion for ontic decision.
Indispensability arguments for realism about mathematical entities
have come under serious attack in recent years. To my mind the most profound
attack has come from Penelope Maddy, who argues that scientific/mathematical
practice does not support the key premise of the indispensability argument,
that is, that we ought to have ontological commitment to those entities
that are indispensable to our best scientific theories. In this paper I
defend the Quine/Putnam indispensability argument against Maddy's objections.
In this paper quine's criterion of ontological commitment is examined
and rejected as incapable of distinguishing genuine from bogus ontological
commitments. Applying quine's strict test for ambiguity, "exists" is shown
to have two senses in application to properties, classes and numbers, a
formal sense and a material sense. In the material sense, to say that a
property exists is to say that it has instances; in the formal sense, to
say that a property exists is to say that it is possible to use a property-expression
meaningfully. The distinction is clarified by means of the notion of "semantic
ascent." such ascent is essential for explaining the meaning of formal
existence-statements. These are vacuous and do not genuinely commit one
to the existence of anything. Quine's purely formal test does not reveal
this and thus is responsible for setting spurious problems about "countenancing"
abstract entities.
A consistent interpretation of mathematical discourse is given in
which numerals do not denote, and in which no ontological commitment is
made to abstracta. The approach is formalistic, but unlike in historical
versions of formalism, the usual theorems of pure mathematics are counted
among the genuine truths rather than as mere marks. Applied mathematics
is also investigated, and classical theories of measurement are developed
into a semantics for sentences involving mathematical and non-mathematical
terms.
Fictional characters are referred to but not conceived as existing,
by speakers of everyday language. So the view that ordinary reference always
presupposes existence, from which the inference is drawn that everyday
language has a "bloated ontology," is mistaken. Thus it is not necessary
to turn to scientific reference for a criterion for ontological commitment.
Scientific references do generally denote existents, because science is
an extension of "some" of the techniques conceived as dealing with reality.
But there are other such techniques: everyday speakers employ a number
of criteria for distinguishing fictions from real things, among them spatio-temporal
location, perceivability, suffering and producing causal effects, and ability
to think. These criteria admit existents of different kinds: a country,
e.g., has a location and produces effects, though not perceivable and concrete.
Quine's approach to ontological commitment even in natural language
has been to employ objectual existential quantification. The ineliminability
of singular referring expressions from natural language presents the challenge
of presenting a type of substitutional interpretation of quantifiers, which
turns out to be a defensible one. Statements in which ineliminable singular
expressions occur can be interposed between quantified ones and reference
to the nonlinguistic world in this version of substitutional quantification.
Crispin Wright's case for arithmetical Platonism emerges in a refined
version from his recent and important work on truth ("Truth and Objectivity").
In this paper we pursue the question of the adequacy of that general minimalist
approach to ontology that supports Wright's arithmetical Platonism. We
suspect that minimalism yields a conception of being which is at once too
wide and too light to be acceptable. We articulate our suspicion by showing
that the minimalist criteria of ontological commitment that sustain Wright's
arithmetical Platonism will also secure an ontological commitment to fictional
objects.
Our concern in this paper is to defend the use of substitutional
quantification in set theory as a way of avoiding ontological commitment
to sets. Specifically, two objections to this procedure are addressed.
(1) charles parsons claims that substitutional quantification (at least
in set theory) is not ontologically neutral, but rather expresses a "bona
fide" sense of existence. We argue that he has failed to distinguish between
meta-linguistic commitment to expressions on the one hand and ontological
commitment to sets in the object language on the other. (2) t s weston
claims that a substantial interpretation of the quantifiers of zermelo-frankel
set theory (zf) is inconsistent with obvious theses of semantics. We argue
that he has artificially limited the ways in which the quantification of
zf can be rendered substitutional due to a misunderstanding of the finiteness
requirements for semantics. With the limitation removed, we give an example
of a substitutional interpretation of zf which is consistent if zf itself
is.
First-order arithmetic is interpreted via substitutional quantification
so that no ontological commitment to numbers is incurred, and all axioms
are logically true. An account of certain kinds of applicability of arithmetic
is suggested as the basis for understanding the atomic sentences of arithmetic.
Substitutional quantification is defended as an ontologically neutral
device for collecting sentences in referential languages. An attempt is
made to interpret the quantifiers of first-order arithmetic and davidsonian
action sentences substitutionally so as to avoid commitment to numbers
and events. The criterion of ontological commitment is then reformulated
in accordance with this method.
It has been argued (by, e.g., George Boolos and David Lewis) that
the interpretation of second-order variables as plural terms shows that
at least monadic second-order logic is free of ontological commitment to
classes. I refute this contention.
There is no inconsistency and a lot of common sense in taking the
so-called truth conditions' and associated theories of formal semantics'
to be false, though logically useful, presupposed conservative extensions
of a more economical system. Hence there is no need to regard such semantics'
as engendering an ontological commitment to sets, functions, or possible
worlds. A similar approach would allow the withdrawal of physical properties,
space, time and other non-material entities from our ontological commitments.
Discourse carries thin commitment to objects of a certain sort iff
it says or implies that there are such objects. It carries a thick commitment
to such objects iff an account of what determines truth values for its
sentences say or implies that there are such objects. This paper presents
two model theoretic semantics for mathematical discourse, one reflecting
thick commitment to mathematical objects, the other reflecting only a thin
commitment to them. According to the latter view, for example, the semantic
role of number-words is not designation but rather the encoding of cardinality-quantifiers.
I also present some reasons for preferring this view.
The author contends that these notions of "intrinsicality" and of
"standardness" are unintelligible. Accepting this theory is like thinking
that algebraists who speak of "the countable atomless boolean algebra"
are referring to a particular structure; instead the "standard" representor,
and thus the cardinal numbers, are fictions introduced to encode a fragment
of third-order logic into first-order clothing. The third-order nature
of arithmetic discourse is disguised partly by the success of this encoding,
and partly by an ambiguity between local and global notions of logical
form. The author elaborates on the distinctive nature of mathematical fictionality,
and sketches the formal logic underlying the encoding. The author also
sketches the way to handle two apparent difficulties: that of numbers applied
to higher-type entities, and the possibility that there are finitely many
actual objects.
I propose a way of formulating scientific laws and magnitude attributions
which eliminates ontological commitment to mathematical entities. I argue
that science only requires quantitative sentences as thus formulated, and
hence that we ought to deny the existence of sets and numbers. I argue
that my approach cannot plausibly be extended to the concrete "theoretical"
entities of science.
Peter Geach proposed a substitutional construal of quantification
over thirty years ago. It is not standardly substitutional since it is
not tied to those substitution instances currently available to us; rather,
it is pegged to possible substitution instances. We argue that i) quantification
over the real numbers can be construed substitutionally following Geach's
idea; ii) a price to be paid, if it is that, is intuitionism; iii) quantification,
thus conceived, does not in itself relieve us of ontological commitment
to real numbers.
In this paper, I defend a modified referential theory of ontological
commitment. I start by considering difficulties for quinean approaches
over the role of paraphrase in eliminating ontological commitment.
This paper presupposes and extends work done in "ontological commitment
to particulars" ("synthese", volume 28, 1974). A semantical criterion of
commitment to objects of a given kind is developed for the class of intensional
interpreted theories introduced in the earlier paper. Next the question
of the commitments of theories apparently treating pure abstract entities
(especially mathematical theories) is taken up and a criterion is offered.
Finally the criteria are modified so as to deal with theories apparently
treating both pure and non-pure entities.
An intensional notion of interpreted first-order theory is introduced
and semantical criteria for commitment of such theories to particular concrete
and (possibly) impure abstract entities are developed. Commitment "de dicto"
and "de re" are distinguished and numerous examples are discussed. The
work is extended to "kinds" of entities and to theories treating pure abstract
entities in a later paper in the same journal.
Quineans have taken the basic expression of ontological commitment
to be an assertion of the form 'there is something that is a phi'. Here
I take the existential quantifier to be introduced, not as an abbreviation
for an expression of English, but via Tarskian semantics. I argue, contrary
to the standard view, that Tarskian semantics, in fact, suggests a quite
different picture: one in which quantification is of a substitutional type
apparently first proposed by Geach. The ontological burden is borne by
constant symbols and truth is defined separately from reference.
In "Material Beings", Peter van Inwagen claims that although his
own metaphysical theory-- according to which there are no chairs, rocks,
or any other composite material objects except living organisms-- may appear
to conflict with the ontological commitments of ordinary language, this
appearance is illusory. The paper challenges this claim. It is argued that
van Inwagen must hold that ordinary discourse is systematically misleading
as to its ontological commitments, but that this radical thesis is not
supported by the analogies (including an analogy with Copernican astronomy)
to which he appeals in his attempt to reconcile his metaphysics with popular
usage.
The paper discusses the ontological commitment of elementary and
constructive theories in mathematics. In contrast to quine's position,
in dealing with finitary arithmetic it is necessary to consider alternative
conceptions of ontology from that based on classical quantificational logic.
An account of the existence of numbers is developed which might be taken
to claim the existence only of inscriptions, but it works only because
it uses a different conception of existence, involving modality. For this
reason it does not qualify as 'nominalist'. I argue that contrary to what
is suggested by some writers, stronger 'abstract' conceptions in constructive
mathematics require not a richer ontology (with intensional entities) but
additional predicates, e.g. truth predicates. It is explained how to interpret
predicative set theory in the same way.
In this paper several different (and non-equivalent) characterizations
of ontological commitment are extracted from the writings of w. v. quine,
and some of their characteristics noted. Then each is evaluated with respect
to its conformity to an intuitive notion of "what a theory says there is".
The paper examines theories of ontological commitment which construe
commitment to be an extensional relation between theories and objects.
It is argued that any such theory which assigns the same commitments to
logically equivalent theories, and which assigns at least as many commitments
to a theory as to its logical consequences, will assign exactly the same
commitments to all one-sentence theories whose sentences are of the form
'(ex)ax', regardless of what atomic predicate 'a' is.
Against views about ontological commitment urged by quine, I argue
that "no" second order theory is ontologically committed to anything beyond
what its "individual" variables range over.
This paper concerns the relationship between ideology and ontology.
The starting point is a series of recent programs whose strategy is to
reduce ontology in mathematics by invoking some ideology, typically a modal
operator. In each case, there are straightforward, often trivial, translations
from the set-theoretic language of the realist to the proposed language
with added ideology, and vice-versa. The contention is that, because of
these translations, neither system can claim a major epistemological advantage
over the other. The prima facie intractability of knowledge of abstract
objects indicates an intractability concerning knowledge of the "new" notions.
The prevailing criterion of ontological commitment, due to Quine, is that
the ontology of a theory is the range of its bound variables; but recall
that Quine insists on a fixed, and very austere ideology. It is proposed
here that, when this constraint is relaxed, the Quinean criterion is flawed,
and an alternative, in structuralist terms, is developed.
George Boolos's employment of plurals to give an ontologically innocent
interpretation of monadic higher-order quantification continues and extends
a minority tradition in thinking about quantification and ontological commitment.
An especially prominent member of that tradition is Stanislaw Lesniewski,
and shall first draw attention to this work and its relation to that of
Boolos. Secondly, I shall stand up briefly for plurals as logically respectable
expressions, while noting their limitations in offering ontologically deflationary
accounts of higher-order quantification. Thirdly, I shall focus on the
key idea of ontological commitment and investigate its connection with
the idea of truth-making. Fourthly, I shall consider how different interpretations
of quantification may sideline Boolos's work, but finally I shall largely
support his analysis of quantification involving nominal expressions, while
arguing, in the spirit of Arthur Prior, that non-nominal quantification
is noncommitting.
There is more than one way to kill a cat. What are ways? Very little
has been written about them in general, but they appear at crucial places
in many philosophical discussions. Clarity over the ontology of ways could
help in several areas of philosophy. After indicating where ways have been
mentioned. I discuss briefly the corresponding linguistic feature, adverbs
of manner, before outlining three theories: a Platonistic one making ways
a complex kind of function, a Davidsonian one in which ways are (mainly)
properties of events, and finally the theory I prefer, a particularist
one based on the concept of a higher-or-der trope. The latter is connected
with the theory of truth-makers and avoids ontological commitment to corresponding
general objects.
Suppose you hold the following opinions in the philosophy of logic.
First-order predicate logic is expressively inadequate to regiment concepts
of mathematic and natural language; logicism is plausible and attractive;
set theory as an adjunct to logic is unnatural and ontologically extravagant;
humanly useable languages are finite in lexicon and syntax; it is worth
striving for a Tarskian semantics for mathematics; there are no Platonic
abstract objects. Then you are probably already in cognitive distress.
One way to decease your unhappiness, short for embracing Platonism, is
to accept higher-order logic and look, as did Arthur Prior, for a plausible
way to neutralize the ontological commitment to abstract entities that
this acceptance appears to entail.
This article discusses Searle's criticism of Quine's "criterion
of ontological commitment" in "Speech Acts". I argue that Searle has misunderstood
Quine in several important respects, and that his arguments do not refute
Quine's real theses on "ontological commitment."
Apparently true sentences with fictional subjects, about possibilities
in the fully analysed sentences of possible world semantics, or even sentences
of mathematics cause theorists with robust intuitions ontological embarrassment.
They appear to commit us to the existence of fictional characters, possibilia
such as golden mountains, and numbers, respectively. It is tempting to
propose prefixing a phrase such as in such- and- such a story' or in such-
and- such a theory' to such sentences as a way both to eliminate the worrisome
ontological commitment and to retain versimilitude. I argue that because
this procedure changes so many vital implication relations the originals
had when combined with other sentences which we would not want to prefix,
the tactic is an utter failure.