Table Of ContentTHE LOGIC OF INTENTIONAL OBJECTS
SYNTHESE LIBRARY
STUDIES IN EPISTEMOLOGY,
LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE
Managing Editor:
JAAKKO HINTIKKA, Boston University
Editors:
DlRK VAN DALEN, University of Utrecht, The Netherlands
DONALD DAVIDSON, University ofCalifornia, Berkeley
THEO A.F. KUIPERS, University ofGroningen, The Netherlands
PATRICK SUPPES, Stanford University, California
JAN WOLENSKI, Jagiellonian University, Krakow, Poland
VOLUME269
J acek Pasniczek
Maria Curie-Sklodowska University,
Lublin, Poland
THELOGICOF
INTENTIONAL OBJECTS
A Meinongian Version of
Classical Logic
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-4968-1 ISBN 978-94-015-8996-3 (eBook)
DOI 10.1007/978-94-015-8996-3
Printed on acid-free paper
All Rights Reserved
© 1998 Springer Science+Business Media Dordrecht
Originally published by K1uwer Academic Publishers in 1998
No part of the material protected by this copyright notice may be reproduced or
utilized in any fonn or by any means, electronic or mechanical,
inc1uding photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS vii
INTRODUCTION 1
CHAPTER I. INTRODUCING SUBJECT -PREDICA TE FORMAL
LANGUAGE: CAN NAMES AND QUANTIFIERS SHARE THE
SAME CA TEGORY? 7
1.1 Why logic differentiates between quantifiers and names? 8
1.2 The language with derivative predicates 10
1.3 The language with entangled predicates 12
1.4 Variables in Classical Logic. Areinterpretation of grammar for
quantifiers 15
1.5 Deductive properties of individual constants 18
1.6 The uniform semantic interpretation of names and quantifiers 20
1. 7 The generalised quantifier perspective 25
1.8 Subject-predicate formulas and subject-predicate languages 27
CHAPTER H. M-LOGIC 30
2.1 Syntax of M-Iogic 31
2.1.1 M-language 31
2.1.2 M-system 32
2.1.3 Selected Theses and Syntactic Properties of M-system 33
2.2 Semantics of M-Iogic 45
2.2.1 Models and Satisfaction. Soundness Theorem 45
2.2.2 M-logic and Classical logic. Completeness Theorem 47
2.3 M-Iogic with defmition schemata for new terms 52
CHAPTER III. ONTOLOGICAL INTERPRETATION OF M-LOGIC 58
3.1 Meinongian ontology 59
vi TABLE OF CONTENTS
3.2 M-ontology as a Meinongian ontology 63
3.3 Existence and identity in M-ontology 66
3.4 Properties in M-ontology 70
3.5 Reduction of M-properties to M-objects 73
3.6 Ontological commitment of M-Iogic 77
CHAPTER IV. EXTENDING M-LOGIC 82
4.1 Free M-Iogic 83
4.2 Modal M-Iogic 88
4.3 Non-standard possible worlds and the logic of generalised
operators 97
CHAPTER V. REFERENCE AND INTENTIONALITY 106
5.1 Theory of reference in M-Iogic 106
5.2 Classical theories of intentionality and M-Iogic 112
5.3 The dual ontological structure of intentional objects 120
5.4 Paradoxes in formal theories of objects of thought 125
5.5 Intentional objects vs. intentional states of affairs. Aspectual
and horizontal objects 128
CHAPTER VI. TWO-SORTED AND INTENSIONAL M-LOGIC 139
6.1 Weak two-sorted M-Iogics 139
6.2 Higher-order two-sorted M-Iogic 144
6.3 Circular, self-referential, and many-Ievel M-objects 151
6.4 Intensional M-Iogic 155
APPENDIX. M-LOGIC AS A LOGIC OF FICTIONAL ENTITIES 163
A.I Fictional objects as M-objects 164
A.2 M-Iogic: fictional objects vs. fictional worlds 172
NOTES 179
REFERENCES 200
INDEX OF SYMBOLS 206
INDEX 207
ACKNOWLEDGMENTS
I wish to express my gratitude to all those who read the manuscript at
various stages of its composition and revision and whose comments and
criticisms made an essential contribution to the improvement cf this book.
Special thanks are due to Barry Smith, and Wojciech Zelaniec. Also, amongst
those whose comments and suggestions proved invaluable in the preparation
of this volume are Bill Rapaport, Dale Jacquette, and Terence Parsons. I am
grateful to members of the Philosophy Department for stimulating discussions
and friendly atmosphere during my one-year stay at the University of
Buffalo, where I carried out most of my research. My work on this book has
been made possible by agrant from the Polish Research Council (No. 1 PlOl
010 06).
Parts of the book are drawn from the previously published material of
mine. Section 4.3 is based on 'Non-Standard Possible Worlds, Generalised
Quantifiers, and Modal Logic', in: Jan Wolenski (ed.), Philosophical Logic
in Poland, Kluwer Academic Publishers, pp. 187-199. Section 5.2 inc1udes
parts of 'Relational vs. Directional Conception of Intentionality', in: A.
Zeidler-Janiszewska (ed.), Epistemology and History, Rodopi, pp.373-383.
I thank publishers for their kind permission to use this material.
INTRODUCTION
The notion of intentional object, or object of consciousness, remains
notoriously ambiguous despite extensive contemporary studies devoted to the
topic of intentionality. On the one hand, the intentional object can be
conceived of as areal object to which an act of consciousness is directed.
When I see a black cat it is just this cat that is the intentional object of my
act of seeing. On the other hand, however, intentional objects can be mere
objects of thought, dream, imagination, desire, etc. When I am thinking about
(dreaming, imagining, ... ) the monster of Loch Ness, a golden mountain,
Sherlock Holmes, the seven dwarfs, these objects of my thought do not exist
in the usual sense of the word.
What are intentional objects then if there are any? Are they a kind of
immanent objects, merely psychic or mental objects, as some claim?
Philosophers, both traditional phenomenologists and contemporary analytists,
tend to agree that (1) every act of consciousness has an intentional object,
and (2) that it is so independently of whether or not the intended object
exists, and (3) that in both cases it has the same ontological status (this does
not mean that they are blurring the difference between existence and non
existence). In other words, to use a more sophisticated terminology, the
existence of an object is indifferent to intentional content of consciousness,
to how the object appears to consciousness. Although, according to the
traditional school of intentionality (Brentano, Twardowski, Meinong, Husserl,
Ingarden), the intentional relation holds between acts of consciousness and
intentional objects, it is methodologically admissible to focus our attention
on the second relata only and study intentional objects from the purely
ontological perspective (thus neglecting acts and intentional relations).l
Perhaps the best example of this kind of ontology is Meinong's theory of
objects (other examples being: Husserl's theory of noemata and Ingarden's
theory of purely intentional objects).
It is not the primary goal of this mono graph to clarify and define the
notion of intentional objects, although we will be concemed with problems
of intentionality. We use "intentional object" since, despite its ambiguity and
vagueness, it is a very broad ontological term. The modifier "intentional"
does not narrow down the meaning of "object". It simply points to the
epistemological context, relating objects to a conscious subjecL Thus objects
simpliciter become possible objects of consciousness. In particular, when we
2 INTRODUCTION
adopt such an understanding of intentional objects, our considerations of non
existent objects are no longer mysterious. Recently there have appeared
several theories of objects, inspired mainly by Meinong's ontology. We have
in mind theories that have been created by Terence Parsons, Richard Routley,
Hector Neri-Castaiieda, William J. Rapaport, Edward Zalta, Dale Jacquette,
and also by ourselves2• Although those theories have a lot in common, so
that, generally speaking, one can say that they pertain to the same subject
matter, they differ in their terminology. Thus we read about 'non-existent
objects', 'guises', 'Meinongian objects', 'abstract objects', and 'non-entities'. It
seems that, apart from details of these theories, they all refer about inten
tional objects.
But anyway, what are intentional objects and how to study them from the
logical point of view? Although the question is extremely general and
difficult, we need at least a provisional answer in order to know how to start.
So we set forth here a "working hypothesis": to be an intentional object is to
be a subject of predication. What distinguishes objects simpliciter (pure,
noumenal, per se, in thernselves) from intentional objects is that the latter are
aspectual, they are such and such, they are objects sub specie determinations.
An intentional object, whether it is perceived, imagined, or mentally
construed, appears to consciousness in some way and thus it is in asense
opposed to some determinations, properties that it is supposed to have. The
subject-predicate form is characteristic of intentional objects whether this
form is further categorised as nominal (this as a black cat) or as propositional
(this is a black cat). We will focus here on the subject-predicate propositional
form since, on the one hand, it is more convenient for logical investigations
and, on the other, both particular forms can be regarded as formally
equivalent.
This very rough idea of intentional objects will be made specific in the
form of a linguistic criterion for distinguishing these objects, which will help
us to construct a logic of these objects. The criterion in question rnay be
phrased in the following way: everything that can be referred to by a subject
of subject-predicate sentence is an intentional object and every subject stands
for an intentional object. We assume here that subjects of sentences are
categorematic express ions and the relation of reference is conceived very
broadly. When speaking about subject-predicate sentences we basically mean
naturallanguage. We can anticipate some objections that may be raised even
at this stage against that criterion. The first one is that since the criterion is
INTRODUCTION 3
linguistic it naturally exeludes all possible objects of consciousness which are
not expressible in a language Ce.g. intentional objects of perception). The
second one is that languages differ with respect to what expressions may
occupy the subject positions Ce.g. there is a considerable difference between
English and Polish). Also one can notice that according to this criterion,
some dubious cases, such as quantifier objects Ce.g. every dog, some dog)
will fall through the net. To respond briefly the first argument we may say
that what matters for predication and for identity of intentional objects, can
be expressed in a sufficiently rich language. Trivially, what is not expressible
linguistically, lies beyond the scope of logic. Surely languages differ with
regard to the category of noun phrases but these differences will not affect
our logic - our discussions will be confined to those (logical) characteristics
of languages which are shared by all of them Ce.g. we will neglect some
English noun phrases which are absent in Polish). We are perfectly aware of
the controversial nature of considering quantifier objects as intentional
objects. Apart from some philosophical motivations, it will be evident that
such an ontological decision is theoretically quite natural.
It is worth emphasising that our linguistic description of intentional objects
as referents of subjects of sentences is implicit in elassical conceptions of
intentionality like those of Brentano, Meinong, Twardowski, Husserl, and
Ingarden, although none of these philosophers explicitly stated such a
criterion. Certainly, Russell's early views on denoting are very elose to our
way of characterising intentional objects. He maintained that every grammati
cally correct subject Cdenoting phrase) stands for an object and, in particular,
he regarded quantifier objects, like every dog or some dog, as denoting
expressions.3 Consequently, his liberal ontology closely resembles Meinong's
ontology of objects.
But why do we adopt this linguistic criterion? Would it not be enoughjust
to enumerate the categories of possible - existent or non-existent - entities
Ce.g. individuals, properties, relations, propositions, etc.)? We have certainly
not answered exhaustively the arguments against the linguistic approach to
intentional objects, and some other objections may be put forward. Neverthe
less, we insist on this approach since it focuses the ontological discussion of
intentional objects on problems of predication. As we will see, predication
has a highly complicated structure in the case of intentional objects and, in
particular, splits into two different modes. Anyway, the logic of intentional
objects is to be a subject-predicate logic and if one is not satisfied with our
