Barry Smith
THE ONTOLOGY OF REFERENCE:
STUDIES IN LOGIC AND PHENOMENOLOGY
Dissertation
University of Manchester
1976
SUMMARY
Ontology is sometimes conceived as having as its sole province the
totality of object-entities, by which is meant entities such as molecules, cells, organisms, organizations, numbers, shapes, and so forth. When we attempt to
extend ontology to the domain of meaning-entities (concepts, propositions, even
whole theories), we find that the criteria for individuating and re-identifying
objects cannot be carried over unproblematically to this area. We argue on this
basis that there is an ontological dichotomy between meaning-entities on the
one hand, and object-entities (individual objects, properties, relations,
states of affairs, events and processes) on the other, and that it is
illegitimate to impose standards appropriate to the latter in our
investigations of the former. One principal means by which such imposition is
effected is through the assumption that linguistic meanings are to be
individuated through the expressions
with which they are associated; the latter being conceived as belonging to the
category of object-entities. We argue, however, that meanings, unlike
expressions, are dependent on the contexts – both linguistic or extralinguistic – in which they are uttered and understood.
Our first application of
the meaning/object dichotomy as an instrument of philosophy is to the
interpretation of Frege’s ontology, and in particular Frege’s conception of a
‘realm of sense’ and a ‘realm of reference’. The most serious difficulty in
this ontology of ‘realms’ turns on those passages in the Frege corpus in which
it is suggested that we have to deal with two mutually exclusive categories,
something which conflicts with one crucial implication of Fregean semantics,
namely that every entity is a referent
(can be referred to by means of some suitably constructed categorematic
expression). However it is strictly speaking not referents with which senses or meaning
are contrasted ontologically, but objects.
This is because meanings themselves can serve as referents. Much of Frege’s
work in the field of logic seems to suggest that he conceived logic as a
discipline which was concerned exclusively with relations between senses (more
particularly between propositions or thoughts, the senses of complete
assertoric sentences). Nevertheless, we find a series of isolated arguments in
Frege’s writings according to which ‘logical laws are first laws in the realm
of reference and only mediately relate to sense’ (“Ausführungen
über Sinn und Bedeutung”,
1892-95, p. 134). The apparent contradiction can be resolved, we suggest, if
account is taken of the fact that the crucial ontological dichotomy lies not
between sense and referents but
between sense and objects, and if it
is recognized that those referents – principally truth-values and numbers –
which constitute the immediate subject-matter of logic in Frege’s eyes, ought
themselves more properly to be conceived as meaning-entities.
We take for granted the
conception of logic as the science that has as its subject-matter the
superstructural features of the realm of meanings, so that logic is concerned
exclusively with relations between meanings. We advance at the same time a
structuralist platonism as concerns the entities of
mathematics, viewing the latter interrelationships amongst abstract structures
in the realm of meanings. We then argue that the appeal of platonism
as a philosophy of mathematics rests in part on the fact that a platonism of meaning-entities is, for deep-seated reasons,
a less objectionable assumption than a platonism of
objects.
Mathematical rigour
(like logical rigour) is possible because mathematics
is exclusively a matter of relations between meanings. This thesis opens up the
possibility of a view of mathematical objects
as temporally determined entities, as entities whose ontological status depends
– like that of, for example, the objects presented in works of literature –
upon the existence of certain frameworks of conventions and upon the
construction of certain linguistic structures (called ‘formal theories’) the
understanding of which turns upon our regarding the propositions expressed as
propositions about objects of a
certain sort. Thus while objects are, from the point of view of mathematical rigour, strictly speaking superfluous, it is nevertheless a
matter of ‘practical necessity’ (Lorenzen) that the mathematician (the set
theorist, the number theorist) conceives himself as investigating a
pre-established totality of objects, which he ‘perceives’ in a way which
parallels both the ‘perception’ which the physicist has of the objects of his
discipline and the quasi-perception of fictional objects achieved through
readings of works of literature.
However
the status of mathematical objects as
temporally determined must not be misunderstood by analogy with that of
spatio-temporal objects, which have a simple structure of temporal properties.
For mathematical objects, like all intentional objects, have a peculiar double structure of external
properties and internal
characteristics. Consider, for example, the case of objects of fiction:
Here the properties with which we are concerned include, for example: the
property of having been created by Shakespeare, of having been psychoanalyzed
by Ernest Jones, of being non-existent, and of having such and such a stock of
internal characteristics. The latter then include, for example: being a prince
of Denmark, having suicidal impulses, having two arms and two legs, and so on.
But the latter are not properties,
since all objects which possess the property of being a prince of Denmark
thereby exist, and Hamlet – we may assume – did not exist. When we read
Shakespeare, for example as a literary critic, it is exclusively the stock of
internal characteristics with which we are concerned. And in just the same way,
when the set theorist is concerned with the sets projected by a particular set
theory it is exclusively the internal characteristics of these sets which fall
within the theory’s purview. What distinguishes sets, and mathematical and
abstract objects in general, from the purely intentional objects of fiction, is
that the latter have temporal determinations not only among their external
properties, but also among their internal characteristics (Hamlet, for example,
is represented as existing as prince of Denmark at a determinate time).
Mathematical objects, on the other hand, have no temporal characteristics.
Hence, again, the appeal of platonism as a philosophy
of mathematics.
The abstract objects of
mathematics and the non-existent objects of fiction form not merely a
peripheral extension of the universe of existent objects (the latter regarded
as somehow well-understood). Rather, following certain suggestions of Frege, we propose a view of objects – especially abstract
objects – as the results of certain types of demarcation – as for example the North Sea exists because of
certain intersubjectively accepted demarcations built
into naval charts. Such demarcations reflect demarcatory
acts, which exist because of complex cognitive and social structures (enabling
the creation of novels, maps, mathematical theories and the theories of natural
science). On this basis the universe of existent and
non-existent objects begins to take on the character of a massively complex
stratified structure, lower strata of microphysical particles combining
together to constitute progressively higher strata of animate and inanimate
material bodies, cities, nation states, civilizations, works of art, linguistic
structures, mathematical configurations, and so on.
The conception of this
stratified ontology rests upon a notion of object developed by inspiration
from, on the one hand the invention of existential quantification by Bolzano
and Frege, and on the other hand from the ontology presented by Ingarden in his
Der Streit um
die Existenz der Welt. Ingarden,
alone amongst all the major figures of the Austro-German tradition of Frege, Brentano, Meinong, Husserl
and Twardowski, succeeded in developing an alternative to the idealist paradigm
of creation of an object – according to which it is only autonomous objects,
including the real world itself, which can be ‘created’ – and thereby succeeded
also in pointing the way towards an adequate ontological theory of both
non-existent and existent objects and of both the lower and the higher strata
in the universe of objects as a whole.
But even Ingarden
was still too close to Husserl, Meinong and Brentano to derive as a consequence
of his new paradigm of creation – which has much in common with the
constructivist paradigm in the philosophy of mathematics advanced, for example
by Kronecker, Weyl and Lorenzen
– that the domain of objects as a whole is, while more inclusive than the
domain of existent objects, still subject to a quite parallel system of rigid
criteria for admission: not every thought about or belief in or assumption of
an object is thereby such as to have a referent (that is: to have some target
admissible as an object), just as not every thought about or belief in an
existent entity is valid, from an external point of view, as a thought about or
belief in that which it would claim to be directed towards. Hence perhaps the
most important task attempted in this work is the provision of such criteria,
that is the provision of necessary and
sufficient conditions for objecthood.
It is necessary, first of
all, to delineate the category of object-entities (that is of objects in
general, including not only individual objects but also properties, relations,
states of affairs) from the category of meaning-entities. We have already seen
that the status of the former as referents – whether for acts or for linguistic
expressions – cannot serve to distinguish them from meaning-entities. But it is
still possible to distinguish among referents those entities whose ‘proper’
position is in the referent or ‘target’ position for an act and those – in
particular meanings – who belong rather to the medium of articulation through which determinate reference is achieved. This implies a
distinction, recognized by Husserl as the distinction between ‘eigentliche und uneigentliche
oder bloss symbolische Vorstellung’
(between that which is properly intended and that which is improperly or merely
symbolically intended) and by Russell as the distinction between knowledge by
acquaintance and knowledge by description, between ‘fulfilled’ and ‘empty’ or generic reference.
We can now state in summary form
the first condition for objecthood: that entities are objects only if they are
entities for which we can achieve fulfilled
referential access.
The second condition
concerns the distinction between those entities – such as landmarks or public
functionaries – which are objects in their own right, but which yet do not
constitute an additional stratum of reality. This is because discourse about
landmarks and public functionaries, like discourse about, say, punctuality,
reciprocity, the platoon commander’s lack of a nap, the identity of the
murderer, is merely a stylistic variant of discourse concerning object-entities
of a more mundane sort. The criterion which determines whether we have to deal
with an additional stratum of entities in their own right, or with mere
linguistic simulacra of such entities is, as recognized by Dummett,
the existence of a field of predicates,
a special vocabulary within which proper names for the entities in question are
embedded. We possess such a vocabulary in the case of numbers (‘larger than’,
‘is prime’, ‘is composite’, ‘is perfect’, ‘is the square of’…), and also in the
case of colours (‘darker than’, ‘primary’,
‘secondary’, ‘monochrome’…), which implies that both numbers and colours constitute additional strata of self-subsistent
objects.
The third condition –
which embodies in its full force the recognition that objecthood is a purely
‘external’ matter for the attainment of which mere assumptions and beliefs are
always insufficient – serves to exclude those acts, such as the acts of
19th-century astronomers who were convinced of the existence of an intramercurial ‘plant Vulcan’, for which we have a suitably
rich field of predicates and apparent referential or ‘target’ access, yet for
which we have no object since a
simple ontological mistake has taken place. It is thus necessary to make a
distinction among acts between those which are ‘veridical’, in the sense that
they are protected from the possibility that, with future increases in
knowledge, it should be discovered that the purported object of the act was
merely the product of a private or institutional error or illusion, and
‘non-veridical’ acts, for which this is not the case. What is crucial is that
there are non-existent objects, acts
of reference to which are yet secure cases of veridicality: Hamlet, for
example, is such an object, since works of literature constitute ‘veridical
contexts’. Thus the third and final condition may be
formulated thus: entities, or purported entities, are objects only if they are embedded within a veridical context.
The theory of objects (Gegenstandslehre)
implied by these conditions is contrasted with the original theory of objects
put forward by Meinong, here subjected to a
thorough-going criticism. It is contrasted also with the ‘Fregean’
object-ontology, both as originally conceived by Frege, and as developed by
Christian Thiel, whose interpretation of Frege is
developed against the background of the constructivist theory of abstraction
defended by Paul Lorenzen. We also exploit this more
general ontological framework, with its dichotomy between meanings in general
and objects in general, in order to provide an interpretation of Husserl’s
philosophical works, both of his early, pre-phenomenological period and of the
period of the Ideen.
In particular we attempt to show that Husserl’s philosophy of logic and
mathematics is not only much closer than has been generally supposed to the
main (Frege-inspired) tradition, but also that it embodies certain crucial
insights which have been lost to that tradition, insights which derive from the
work of mathematicians and logicians such as Riemann, Schröder
and Cantor who were influenced by the advances made by mathematical analysis in
the 19th century, in contrast to thinkers such as Frege, Russell, Wittgenstein
and Quine, for whom arithmetic was sometimes all too important.
PART
ONE: THE THEORY OF MEANINGS (BEDEUTUNGSLEHRE)
Chapter
One Variations on the Theory of Sense and Reference
Chapter
Two Logic and Phenomenology: A Field of Problems
Chapter
Three The Philosophy of Number
Chapter
Four Essential Insight (at Arm’s Length)
Chapter
Five Meanings-in-General vs. Objects-in-General: An Ontological
Dichotomy
Chapter
Six Meanings as Noemata: Husserl’s Generalisation of Linguistic Meaning to the Field of All
Acts
PART
TWO: THE THEORY OF OBJECTS (GEGENSTANDSLEHRE)
Chapter
Seven Ontological Realism
Chapter Eight Stratification of the Universe of Objects
Chapter
Nine Realism vs Abstraction Theory
Chapter
Ten Towards a Generalised
Ontological Theory of Higher Strata I: Meinong’s
Attempt
Chapter
Eleven Towards a Generalised
Ontological Theory of the Objects of Higher Strata II: The Theory of
Intentional Objects
Chapter
Twelve Necessary and Sufficient Conditions for Objecthood
Notes and List of Abbreviations