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Two Types of Philosophical Analysis
Arkadiusz Gut Catholic University of
Lublin
I. Introductory Remarks
G. Frege in the introduction of his
"Grundlage der Aritmetik" formulates a general principle: "nach
der Bedeutung der Wörter im Zusammenhang,
nicht in iherer Vereinzelung gefragt
werden
mu" (G. Frege, Grundlage der Arithmetik,
Darmstadt 1961, p. XXII, p. 161. H.
Sluga,
Gottlob Frege, London 1980, p. 94.).
This
principle is often called a "context
principle". It is stated in there
that:
1) A term has a meaning when it belongs
to
a proposition (is one of its elements);
2)
Previous analysis of a proposition
is a condition
for analysis of the term. Such a view
presupposes
that proposition is something complex
and
heterogeneous i. e., its elements belong
to different semantic categories. The
principle
given above makes the following distinctions
possible: 1) Division of grammatical
elements
from logical elements, 2) Division
of subjective
(psychological) elements from
objective
elements. Quine in his Two Dogmas of
Empiricism
states that applying this principle
makes
an important reorientation in semantics—"the
reorientation whereby the primary vehicle
of meaning came to be seen no longer
in the
term but in the statement" (W.
V. O.
Quine, Two Dogmas of Empiricism, in: From a logical point of view, New York 1963, p. 39).
From the above
it is
easy to see that the meaning of a term
is
connected with its function in the
proposition,
for as we know the function depends
upon
it's location in the proposition. The
analysis
of terms at Twardowski's and his disciples’
theories is done "in abstracto."
It doesn't presuppose any existence
of proposition.
Hence different roles which terms play
in
a proposition (subject, predicate)
aren't
important for the analysis of the terms.
(K. Twardowski, Zur Lehre vom Inhalt und Gegenstand der Vorstellung, Wein (1994) p 1-15, T. Cze_owski, Logika,
Toru_ 1962, p. 11-12). To reveal the
proper
meaning of a term, it is necessary
to grasp
the term as lingual equivalent of presentation.
As judging presupposes the existence
of at
least one presentation so proposition
(judgement
in logical sense) presupposes the existence
of at least one name. And this makes
the
analysis of the name (term) possible
apart
from the proposition.
II. Name–Predicate
Twardowski defines the name in three
ways:
1) From an epistemological point of
view
- name is the equivalent of presentation;
2) From a semantic point of view -
every
name denotes an object. Any name always
has
its extension (denotation). (K. Twardowski,
Zur Lehre, p. 10-12, F. Brenatano,
Psychologie
v. emp. Standpunkt, t. II, Leipzig
1925, s127); 3) From an ontological
point
of view—an object belonging to the
denotation
of the name can be: a) ens habens actualen
existentiam, b) ens possibile, c) ens
rationis.
Such a determination of the name causes
that,
firstly, ordinary names, general names
and
fictious names are names in the same
way:
secondly, to be an object of the name
doesn't
mean to exist. Therefore Twardowski's
concept
of the name differs essentially from
the
concept of name, we can find in the
predicate
logic, whereas it is very close to
Le˙niewski's
language of "Ontology" (Küng G., Ontologie und logistische Analyse
der Sprache. Wien 1963.). What is the
most
important is that the same name can
occur
as a subject or a predicate in a statement;
the parts of the complex matter may
change
place arbitrarily. From the above it
follows
that there is no essential difference
between
the subject and the predicate of the
statement.
The same name can be a subject and
a predicate
( J. Jadacki, The Metaphisical Basis of K. Twardowski's Descriptive Semiotics, in RRR Lublin 1992, p. 57-70).
In the system of Frege and Russell
separate
characteristics of predicate and name
are
given. Predicate can be determined
in two
ways: a) in a semantic way as a general
name,
b) in a syntactic way as a propositional
form. The predicate which is determined
in
these ways is not a complete expression,
it doesn't designate an object i. e.
its
meaning is not derived directly from
their
denotation. Whereas the name is determined
as simple symbol, directly designating
an
individual, this individual is its
meaning:
if "a" is a name it must
name something.
Name is a term that can only occurs
as a
subject in a statement. We can easily
see
that category of predicate essentially
differs
from the category of name. (B. Russell, Introduction to Mathematical Philosophy, London 1919, s. 174, 179). Therefore as
given we have a distinction of that
which
presents a fact as such and of that
which
doesn't. Using Ajdukiewicz's terminology
we can univocally state that the predicate,
in Russell and Freges, understanding
is of
the [n, n] category.
III. Meaningful condition and truth
condition
In the second section we have stated
that,
according to Russell and Quine, the
subject
of the proposition refers to something
that
exists. It is stated that the sine
qua non
condition of predication is that the
subject
of proposition applies to an existing
object.
For example, whether the sentence is
true
or false depends on the success or
failure
of the predicate but the failure of
singular
term appears to deprive the predicate
of
the chance of either success or failure.
In this case, predication is made possible,
i. e. meaningful when there exists
an object
designated by the subject of the proposition,
and this means that a truth or falsity
characterization
of a predicate is possible. This is
the first
argument for connecting meaningfulness
conditions
with truth conditions Another argument
is
based on the thesis: a = a R (x (x
= a),
which by virtue of its meaning leads
to the
thesis (x (x, which says that "everything
exists." It is clearly seen that
the
thesis: (x (x = a) is such a thesis
which
guarantees the truth. This shows that
meaningful
conditions are essentially connected
with
truth conditions. In adding a term
to a language
it is presupposed that the term or
refers
to an existing object or is true of
something
existing.
In Twardowski's and his disciples view
meaningful
conditions are sharply distinguished
from
true conditions. The possibility of
analysis
of some statement's elements in abstracto,
i. e., out of the statement context,
shows
that condition laid on the elements
differ
from the conditions laid on the statement.
In Le˙niewski's "Ontology", by allowing all kinds of names, meaning
is distinguished from truth. Therefore
one
can define a meaningful proposition
in such
a way that the concept of designation
wouldn't
be used. Also a definition of synonymy
uses
the categories of meaning, not the
categories
of truth. So it is seen from the above
that
the conditions of meaningfulness differ
essentially
from the conditions of truth.
IV. Contradiction and Tautology: the
impossibility
of denying existence
We shall distinguish three kinds of
requirements
which account for the fact that tautology
appears in the assertion of existence
and
contradiction in the denial thereof.
These
requirements also give the basis for
the
thesis concerning what existence is
not.
1. Requirements as to the subject in
logical
propositions: (a) logical: proper names
must
fulfil the same existential condition
which
holds for individual terms in the predicate
calculus; (b) semantic: by definition
any
name in the logical sense necessarily
designates
an existing object. 2. Logical requirements:(A)
x = x R (y (y = x)(B) Pa R (x Px(C)
(x Px
R Pa3. The epistemological requirement:
an
object designated by a proper name
is given
directly. Russell understands "directly"
as tantamount to the impossibility
of denying
what is given. The above three ascertainment
constitute a reason why in this system
a
proposition of the form "a exists,"
where a is a name in the logical sense,
is
meaningless and a proposition of the
form
"a does not exist" is contradictory.
Demonstrating that the
proposition
"a exists" is tautological
and
the proposition "a does not exist"
is contradictory is sophisticated and
precise
way of expressing the view that existence
is not a predicate. For showing the
tautological
character of the former proposition,
consisting
in the fact that whatever was to distinguish
the term "exists" is already
contained
in the subject, serves in fact to show
that
existence adds nothing to the subject
of
that proposition (existence is not
sensorially
given). On the other hand the fact
that contradiction
arises whenever one attaches the phrase
"does
not exist" to the subject of a
singular
proposition shows that any use of a
name
in the logical sense either expresses
cognitive
contact with reality or presupposes
non-emptiness
of a domain. The merit of those ascertainments
consists in rejecting any possibility
of
considering existence as a predicate
independently
of any context this term may appear.
In Twardowski's
system the problem of tautology and
contradiction
of the propositions "a exists"
and "a does not exist" respectively
does not arise. For they accept the
following
ontological and logical arguments:
a) An
ontological aspect: expressions used
in a
judgement, in spite of the fact that
they
fulfil the function of designating
a certain
object, do not imply and do not justify
the
existence of that designated object.
The
function of designating, like the function
of presenting, is existentially neutral.
A judgement presupposes
the
meaningfulness of its expressions but
not
the existence of a designated object.
That
is, a judgement states the existence;
but
it does not presuppose the existence
as it
presupposes the conditions of its meaningfulness.
b) A logical aspect: Twardowski calls
into
question the classical law of subalternation
(SaP RSiP). As it is immediately seen,
truth
of this law depends also on an existential
assumption which states that for any
predicate
S there is such x that x is S [ (S)
((x)
Sx]. Negation of that assumption should
be
viewed in the context of a negative
interpretation
of the law of identity and this immediately
leads to rejection of the law x=x.
R (y (y
= x) traditionally grounding the principle
((x)((x) which results in the impossibility
of denying existence.
These conclusions, due
to the
negative formula for universal judgements
accepted by the Twardowski and his
disciples,
are considered to be incorrect. However,
rejection of the law of subalternation
indicates
also rejection of all existential assumptions
which were accepted in the classical
theory
of judgement. The assumption concerning
a
domain of objects of which something
is predicated
is meta-theoretical. In other words,
the
Twardowski rejects Quine's thesis
(x (x exists). It is a consequence
of the
above arguments that the function fulfilled
by a name is essentially different
from the
function fulfilled by the term "exist."
Another important result is that the
relation
of exclusion between the propositions
"a
exists" and "a does not exist"
is not guaranteed by the fact that
the proposition
"a exists" says something
about
a certain object in the proposition
"a
does not exist" does not. The
condition
of their mutual exclusion is based
on the
fact that the proposition (1) treats
something
as existing and (2) as non-existing.
V. Existential Proposition
We shall move now to propositions with
descriptions,
i. e., propositions where not a name
in the
logical sense but a description plays
the
role of a subject.
Descriptions are such language expressions
which do not possess independent meaning.
They are incomplete symbols. A definition
of a description is tantamount to a
definition
of a propositional form in which that
description
appears. Description is not a value
of name
variable. Identity of two descriptions
is
recognized not on logical but on empirical
grounds. Any description fulfils its
functions
regardless of whether a described object
exists or not. The above characteristic
indicates
an essential difference between descriptions
and proper names from a syntactic and
semantic
point of view. It shows that descriptions,
in contrast to proper names, are not
that
parts of propositions which correspond
to
appropriate parts of the reality. This
is
the reason why a description may be
a subject
of a sentence only in the grammatical
sense,
but not in the logical. In the latter
sense
it is either a predicate or a conjunction
of predicates.
Hence, in a logical analysis
the predicative function of description
should
be revealed. That is, one should create
a
situation in which the localisation
of a
given expression in a proposition would
conform
to functions fulfilled by that expression.
The most important things is, however,
that
giving descriptions an ontologico-syntactical
status different from that given to
names
should allow us to introduce the propositions
"a exists" and "a does
not
exist" to language. A logical
form of
propositions containing descriptions
is given
in the following formulas: (x (Fx (
Gx) for
indefinite descriptions and (x {Fx
( Gx (
(x [ ( Fy ( Gy) R ( y = x) ] } definite
ones.
Then, as Frege says, a proposition
"some
people are German" is as good
an existential
judgement as a proposition "some
people
exist" for a proposition "Leo
Sachse
exists" is tantamount to a proposition
(x (x=Leo Sachse), which states that
"there
is at least one things which is Leo
Sachse."
Quine on the other hand, following
the intention
hidden in the theory of description,
would
say, that each case of predication
including
names, let as say F(a) would be explained
as a shortening for quantification
((x) (Ax
( Bx). Such a proposition includes
neither
logical constants nor free variables
and
the formula "there exists at least
one"
or "there exists at most"
is followed
by a predication or a conjunction of
predications.
Propositions with a description as
their
subject have a different logical form
than
those with a logical name, although
the form
of a subject, taken in abstracto, does
not
need to reveal differences: a) it is
a general,
not an atomic, proposition; (b) it
is composed,
not simple. Such a proposition is an
existential
proposition and is not a contradiction
and
not a tautology. Thus, if propositions
with
descriptions are de facto propositions
containing
characterization, then it is a logical
consequence
that the existential proposition in
Russell's
view is a proposition with description.
That
is, one is allowed to talk about existence
if that object existence of which will
be
asserted is given through description.
Thus,
the question about existence, the question
which, as we saw, was a question of
whether
or not existence is a predicate, should
be
expressed as follows: is existence,
in the
sense of the existential quantifier,
a predicate
or is it not? The conceptual formula
first
elaborated by Frege and Russell and
later
developed by Quine leads initially
to a reformulation
of this question and then it dictates
a precise
answer.
According to Brentanists the principle
form
of judgement is "A exists"
or "AB
exists". In a judgement one affirms
or rejects something, and therefore
the judgement
quality is a condition of distinguishing
various categories of judgements. Twardowski
claims that the main reason for this
solution
is the fact that relations were usually
objects
of judgements and so in a natural way
one
looked for members or terms of that
relations.
The argument for a two-element structure
of judgement looks as follows: (1)
The motive
for passing a judgement is not an attempt
of unifying presentations into one
whole
but that of referring to a whole given
in
presentation and apprehended in a name.
(2) Two distinct presentations are
not necessary
for passing a judgement; one is sufficient
in order for judgement to appear. (3)
Twardowski
rejects the classical division of judgements
into general and singular. These two
latter
concepts acquire then a new meaning
and place
in proposition. The concept of "general"
is derivative with respect to negation
and
"singular" is derivative
with respect
to affirmation. (4) Matter of a judgement
(AB) is the same as that of (BA). (5)
For
Twardowski the difference between a
judgement
(a) "Socrates is bold" and
(b)
"a man is bold" is not a
difference
in existential commitment but lies
in the
fact that in the case of (a) the ground
of
that judgement is a complete presentation
and in the case of (b)—an incomplete
presentation.
This is the reason why the procedure
of reducing
(a) and (b) to an existential form
in both
cases is the same.
In a certain interpretation one could
say
that existence can be stated in propositions
consisting of a proposition-forming
functor
and its argument being an affirmative
or
a negative proposition. For existence
this
functor has a form "it is true
that"
and is joined to a proposition p or
not-p
as its argument. All propositions of
the
form "it is good that" and
"it
is true that" consist of modus
and dictum.
From a logical point of view modus
differs
from dictum for the former is a functor
and
the latter is its argument. From an
epistemological
point of view, on the other hand, that
what
is expressed in a dictum is presentable,
i. e. the content contained in a dictum
is
given in a presentation and the content
of
a modus is not; it is only stated in
a judgement.
Thus, between modus and
dictum
there appear the same categorical difference
as it does between presentation and
judgement.
Structurally, this difference consists
in
the fact, that a modus jointed with
a proposition
of the form (s/n) and (s/n, n), which
becomes
its argument, constitutes a category
which
is one level higher than the category
of
its arguments: s // s / n. This is
the reason
why propositions in which existences
is asserted
cannot be understood as functions of
a variable
x, that is of an argument "n"
but
should be interpreted as propositions
which
are specification of a function of
a variable
functor "f", i. e., "s".
VI. Existence
Our analyses in the previous sections
gave
us the context in which it is possible
to
introduce the term "to exist"
into
language without creating contradiction.
It is know that when something is said
to
"exist", it is always described
given. In the phrase: (x (x = Leo Sachse)
there is at least one thing that is
identical
with Leo Sachse. We maintained also
that
predicates, in contrast to proper names,
is characterised through an expression
"is
true of." A predicate does not
refer
to something but "is true of."
Saying that a predicate truly describes
a
certain object says something about
a predicate
itself (about a concept) and not about
an
object described by that predicate.
According
to Frege, in this aspect existence
has a
similarity to numbers (G. Frege, Die
Grundlage
der Arithmetik. Eine logish mathematische
Untersuchung uber Begriff der Zahl,
Darmastadt
1961, p. 64 ).
To say "something
exists" is to say that "Px
is true
or one argument satisfies a function
Px".
It is then evident that existence is
a predicate,
but a predicate which describes a predicate,
i. e. a propositional function (B.
Russell,
The Philosophy of Logical Atomism,
in Logic
and Knowledge, ed. Ch. Marsh, New York
1971, p. 232-234). If the fundamental
difference
between singular terms on the one hand
and
predicate on the other, existence must
be
a predicate. It cannot be a first-level
predicate
for this would create contradiction;
so it
must be a second-level predicate. Twardowski,
similarly to Frege and Russell, admits
that
existence is not a quality of things
and
that truth of a proposition is connected
to assertion of existence. However,
existence
does not appear as a meta-language
presupposition
and is not identical with non-emptiness
of
denotation or with fulfilment of a
certain
function. It is a specific functor,
which
appears when anything is something.
In Le˙niewski
we read: ex (a) = E
(b) - b is a: a exists if and only
if when
for a certain b, b is a ( Cz. Lejewski,
On
Le˙niewski's Ontology, in Ratio, I
( 1958)
n. 2, p. 150-176). That is, when something
is a. Thus, a functor of existence
does not
appear as a result of the existential
commitment
of a name which plays the role of a
subject.
This is so, for in the Lvov-Warsaw
School
"being an object', as it is evident
in Le˙niewski's system, is a distinct
thesis
[(a is b) then a is an object], logically
and epistemologically independent of
a functor
of existence. "To exist"
acquires
its meaning only from that it is connected
to. This verb describes nothing. Twardowski's
thesis that existence is not a predicate
is absolute, and any relativization
which
takes existence to be a second-level
predicate
is totally foreign to their approach.
Even
more, both in Brentano's and in Twardowski's
systems there is no possibility of
reformulating
a question of whether existence is
a predicate
into a question of whether it is not
the
case that existence is a second-level
predicate
and of connecting the category of existence
either with the existential quantifier
or
with the variable bound by a quantifier
or
at least with a propositional function
itself
Epilogue
Our analysis has shown that there are
many
differences between the two schools.
All
the sections show not only these differences
but also their particular foundations.
In
the light of this paper we can see
not only
that the thesis i. e. "existence
is
a second level predicate" is different
from the thesis: "existence is
not a
predicate at all" but also we
can see
what reasons for them are. It has been
shown
that applying logical tools to analysis
of
some philosophical problems presuppose
a
previous philosophical analysis of
these
tools. Because of that, the differences
shown
here have dealt not only with the analysed
object (i. e., existence) but they
also show
different analytical tools have been
used.
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