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ACTA PHILOSOPHICA FENNICA
VYol. 63
CONCEPTS AND OBJECTS
PAVEL MATERNA
HELSINKI 1998
Copyright © 1998 The Philosophical Society of Finland
ISBN 951-9264—-34-5
ISSN 0355-1792
TUMMAVUOREN KIRJAPAINO OY, VANTAA 1998
Preface
The title of the present study may remind us of the title used by Quine, viz.
Word and Object. The similarity, albeit unintended, is not absolutely
contingent. Quine’s book could be construed as one of the works mamfesting
a shift from semantics to pragmatics, from a priori to experience, from
abstraction to mere generalization. The present study tries to show that this
shift, if intended as replacing semantics by pragmatics etc., 1s unjustified,
and that the respective theories are, in the best case, a kind of misunder-
standing. Thus the slogan don't ask for meaning, ask for use 1s here
confronted with ask for meaning before asking for use.
Acknowledgments
First of all my gratitude belongs to the Finnish Academy of Sciences, and to
all the outstanding Finnish logicians who supported my intention to write a
book on a theory of concepts. My meetings with Finnish logicians and
philosophers in Helsinki, Tampere and Turku impressed me very much, and
it is impossible to name here all those rationally thinking, friendly Finnish
aca demicians who took part in discussions with me. All the same — omitting
many outstanding names — let me mention Prof. Veikko Rantala, who
introduced me to the young scientist Jart Palomaki, which initialized fruitful
discussions about the theory of concepts and concept theory, and Prof.
Gabriel Sandu whose comments on my conception have been most valuable.
Also, I cannot but remember gratefully my meeting with the late Prof.
Raili Kauppi.
My thanks belong to Marie Duzi, who actively cooperated in creating
many ideas involved in the present book, and helped to complete it as
regards the technical matters.
[ have to appreciate the patience of my family, in particular of my wife
Helena; a logician who works out a new conception 1s mostly not always the
most pleasant partner.
The atmosphere in the Department of Logic in the Institute of Phtlosophy
of Academy of Sciences of Czech Republic helped me to realize my
intention, due to many discussions with the members of the department
(especially Petr Kolaf, Vladimir Svoboda, Jaroslav Peregrin, and Timothy
Childers, who made linguistic corrections and formulated some interesting
comments).
4 Preface
Last but not least, this study would never come into being if my late
friend Prof. Pavel Tichy had not worked out his inspiring theory of trans-
parent intensional logic.
The working out of the present study has been partially supported by the
Grant of the Grant Agency of the Czech Republic No. 401/97/0157.
Prague, April 1998. Pavel Materna
Contents
o Introduction . . . . L . e e e e e e e e e
Notesto Chapter O . . . . . . ... .. . . it
. Church’s scheme . . . . . . . . e e .
Notesto Chapter I . . .. .. . ... .. .. . .. :
. Firstorderobjects . .. ... .. . ... e e
2.1 Intensions, extensions I. . . . ... .. ... .. ...
2.2 Simple types . . . ... .
2.3 Possible worlds . . . . . ... . . . e e
2.4 Intensions, extenstons II. . .. ... ... ... ... . .. ... . .. .. ..
2.5 Concluding remarks . . ... ... ... ... . ... . .
Notesto Chapter 2 . . . . . . . .. . e e
. COnStTUCHIONS . . . . .t e e e e e e e e e e e s e e e e e e e
3.1 BasiCiDMItIONS . . . . . . v i e e e e e e e e e
3.2 Vanables . .. ... .. . . .. e e
3.3 Tovializatlon . . . . . . . . e e e e e e
3.4 CompositioOn . . . . . . .t it e e e e e e e e e
3.5 Closure . ... e e e e e
3.6 Concluding remarks and examples . ... ..................
Notesto Chapter 3 . . . . . . . ... . . . i e
. The Ramified hierarchy . . . ... ... . ... ... .. . .. ... ...,
Notes to Chapter 4 . . . .. . . .. . . . e :
cComeept . ..e e e e e .
5.1 Basic intuitions. Historical comments . ... ................
5.1.1 Concepts are non-mental entities . . .. ... ............
5.1.2 Concepts are extra-linguistic entities . . . .. ... .........
5.1.3 Concepts identify objects . . .. . ... ... ... ... .....
5.1.4 Historical examples ... ...... ... ... . ...
5.1.4.1 Traditional doctrine . . . .. ... ..............
5142 Bolzano .. ... .. ... ... ... e :
5143 Frege—Church . .. ... .. .. ... ... ........
5.14.4 Bealer ... ... ... ... . . ... . :
5.1.45 Kauppi . .. ... ... . . .. .., :
5.1.4.6 Summing up: A set-theoretical approach? ..... .. .
5.2 ConCePt® . . e e
5.2.1 Conceptsand concepts™ . . . .. ... .. ... . ... . .. .....
5.2.2 Extensionof aconcept* . . ... ... ... ... . ... ... .. :
5.2.3 Intension of aconcept* .. ... ... ... ... .. . ... .. ...
5.3 Quast-identity . . .. . ...e e
6 Contents
54 CONCEPS . . . . o it i e
5.5 Using and mentioning CONCEPLS . . . . .« . ¢ vttt vt it
Notesto Chapter 5 . . .. .. . ... . i e
6. Conceptual systems . . ... ... .. . . .. e,
6.1 Simple concepts and ‘primitive concepts’ . ... ... ... ... ... ..
6.2 Some properties and relations of conceptual systems . ...... .. .,
Notesto Chapter 6 . . . . . . .. ... .. .. ... i,
7. Languages and conceptual systems . . . ... ... ... ...
7.1 Meaning vs. pragmatic meaning . . . . . . . . . . . ...,
7.2 Expressions and Concepts . . . . .. .. ... ...
7.2.1 Homonymy, Ambiguity . ... ... ... .. .. ... . .......
7.2.2 Synonymy, Equivalence, Coincidence . .. .. .. .........
7.2.3 Vagueness: ashortremark . ... ...... ... .. ... .. ..
7.3 Simple concepts and simple expressions . . . . ... ... .........
7.4 ‘Sublanguages’ . . . . ... ...e
Notesto Chapter 7 . . . . . . . ... ... . e
8. Definitions . .. .. . . .. . ., :
8.1 Tradition .. ... ... . . . . . . . . .
8.2 Definability of objects in a conceptual system . ............. :
8.3 Explicit definitions in a ‘sublanguage’ .. ................. :
8.4 EXpPressive POWEI . . . .. . . . it .
8.5 ‘Implicit defimitions” . . . ... ... ... ... ...
8.6 Explication . . . ... ... ... ... ... . ... .. :
Notesto Chapter 8 . . . . . . .. .. . . e :
9. Concluding remarks ... ... ... ... . e, :
9.1 Conceptsand objects . . . ... ... ... . ... ... .. ... :
9.2 Concepts and meanings . . . . . . . . .. oo ottt i i :
9.2.1 Intentionality: the genéralcase . .................. :
9.2.2 ‘Zalta’s case’: Existential and existential generalization,
Substitution, ‘Strong extensionality’ .. ...............
Notes to Chapter 9 . . . . . . . ... . . . e e
Bibliography . . ... ... . .. . . e .
List of Deflnitions . . . . . . . . . . . e e e e e e e e e e e e e
Index of NaINeS . . . . . . o o e e e e e e e e e e
0. Introduction
Once upon a time Pavel Tichy opened a dialogue with me by asking: “Do
we define expressions, concepts, or objects?” At that time, a bud of my
present theory of concepts was already in my head; I construed definitions as
linguistic means for associating concepts with some (“new”) stmple expres-
sions. Therefore I answered: “Well, for me, definitions concern expressions,
so that we define expressions.” Tichy laughed. “Imagine™, he said, “that you
should define the expression ‘prime number’. What would you say?” “0O.K.
Prime numbers are natural numbers divisible exactly by two numbers.”
“Surely not; if what you define is an expression your defimtion would be:
‘the expression whose first letter is p, the second letter r, etc.” I explained
my motivation: an essential feature of (explicit) definitions consists in
assigning the definiendum with a meaning (1.e., with a concept). Tichy did
not assent. He said: “Imagine a function having as its domain the set of
natural numbers, and returning 1,2 or 3 depending on whether the given
argument 1S divisible by at most two numbers, or by more than two and less
than six numbers, or by more than six numbers, respectively. Have I defined
this function?” I admitted that he had. Tichy: “But I have not introduced any
new term for denoting this function: there is no definiendum here.”
This dialogue was characteristic of Tichy’s aversion to the dominate
trends connected with the so called ‘linguistic turn’.! He even invented a new
term: using an etymological paraphrase of psychologism (as an old and
already defeated enemy of logic) he spoke about glossologism (as a rather
new-fangled danger). His philosophy of logic and language was extremely
hostile to Quinean behaviorist pseudo-semantics and late Wittgensteinian
linguistic games.?
I share Tichy’s views, which result in his transparent intensional logic
(TIL), and I already have made some attempts at applying his conception.?
The present study belongs to such attempts; its starting intuitions can be
for mula ted as follows:
(D The (contingent, conventional) connection of an expression with an
object (‘aboutness’) 1s realized due to the fact that expressions (of a
language) encode (Godel: “fix™)* abstract entities which may be called
(their) meanings or concepts (of the respective objects).> Whereas
these objects are ‘flat’ in that they are structureless (at least in the
sense that they do not mirror the structure of the respective expres-
sion), the meanings (concepts) are structured and their structure is
mirrored by the respective expression. Moreover, two distinct lan-
8 Introduction
guages (on approximately the same level of development) do not differ
by encoding distinct meanings (concepts) but by the rules that connect
expressions with these meanings. Thus meanings (concepts) are a kind
of ‘paths’ (abstract ‘procedures’) which contain particular ‘intellectual
steps’® leading (in the best case) to the identification of the respective
object. Further, concepts can identify other concepts; the latter play
the role of ‘quasi-objects’. Finally, objects (and quasi-objects) which
are identified by concepts are always identified a priori: objects
identified by empirical concepts are intensions; they are never the
contingent values of these intensions in the actual world. A paradig-
matic example is: the concept PLANET (encoded, e.g., by the English
expression ‘planet’) identifies a property of individuals; it does not
identify the set {Mercury, Venus,...}.
(This position could perhaps be called ‘neo-Fregean’, as in Forbes (1987,
pp. 5—6).)
Many points in this ‘confession’ could be criticized from the very
beginning, of course. The main objections would come from Quinean
behaviorists’ and ‘late Wittgensteinians’s; the don 't ask for meaning, ask for
use-slogan would reject any assumption that there would be some abstract
entity like meaning. Indeed, no nominalist can accept such an assumption.
(On the other hand, if an explication of ‘concept’ (‘meaning’) were success-
ful, Quine’s weli-known argument about circularity” connected with attempts
to define the triple analyticity-synonymy-meaning would break down.!'V)
There are two ways of defending the above intuitions. One of them 1s
‘direct’: arguments supporting these intuitions could be formulated and alltes
in the history of philosophy enlisted. This way is not very effective: where
the dissent concerns such basic intuitions as I have introduced in (I) direct
arguments are usually not helpful (even if they point to some essential
problems connected with the rejection of these intuitions). A far more fruitful
way consists 1n applying the following strategy: We start with our intuitions
and show that they help us to solve many fundamental semantic problems!!
and that they do not In principal block the solution of other semantic
problems.
Indeed, choosing this strategy we do not intend not to use arguments. So
on the one hand we do not pretend that we have proved, e.g., realism (an
unattainable goal, of course), but on the other hand we will try to give
arguments supporting, e.g., realism.
The central theme of the present study is the problem of explicating the
notion of concept. Yet no historical survey of all or even of most of the
theories of concept can be expected:'? this is an original conception (based
on TIL), so that offering a neutral (= non-critical) outline of theories of
concept 1s not our intention.
