8/13/2019 Forgie W Frege s Objection to the Ontol Arg http://slidepdf.com/reader/full/forgie-w-frege-s-objection-to-the-ontol-arg 1/16 Frege's Objection to the Ontological Argument Author(s): J. William Forgie Source: Noûs, Vol. 6, No. 3 (Sep., 1972), pp. 251-265 Published by: Wiley Stable URL: http://www.jstor.org/stable/2214773 . Accessed: 18/01/2014 19:21 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . Wiley is collaborating with JSTOR to digitize, preserve and extend access to Noûs. http://www.jstor.org This content downloaded from 147.210.116.177 on Sat, 18 Jan 2014 19:21:23 PM All use subject to JSTOR Terms and Conditions
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8/13/2019 Forgie W Frege s Objection to the Ontol Arg
Frege's Objection to the Ontological ArgumentAuthor(s): J. William ForgieSource: Noûs, Vol. 6, No. 3 (Sep., 1972), pp. 251-265Published by: WileyStable URL: http://www.jstor.org/stable/2214773 .
Accessed: 18/01/2014 19:21
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp
.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
of scholarship. For more information about JSTOR, please contact [email protected].
.
Wiley is collaborating with JSTOR to digitize, preserve and extend access to Noûs.
http://www.jstor.org
This content downloaded from 147.210.116.177 on Sat, 18 Jan 2014 19:21:23 PMAll use subject to JSTOR Terms and Conditions
proposition 2 is a prime number we say that an object 2 - fallsundera first-levelconcept prime number whereas n the proposi-tion there is a prime number we say that a first-level conceptprime number - falls within a certain second-level concept. Thusfirst-level concepts can stand to second-level concepts in a similarrelation to that of objects to first-level concepts. ([7], pp. 569-572.See also [8], pp. 48-50).
In order to understand the import of this passage, we shall
have to have some grasp of Frege's terminology. As is well known,
Frege divides the world into objects and functions. ([8], p. 32;
[5], pp. 35-6). Conceptsare a
speciesof functions.
( .. . a
conceptis a function whose value is always a truth-value. [8], p. 30). There
are at least two types of concepts those of first-level (under
which objects fall) and those of second-level (within which first-
level concepts fall). ([8], p. 50). Corresponding to these ontological
distinctions are certain linguistic distinctions. Frege distinguishes
proper names and function-names. The former are names of
objects, the latter of functions. ([5], p. 81). Proper names are said
to be saturated , function-names unsaturated . ([5], pp. 34, 36).
Some function-names are names of concepts, and some of those are
names of first-level concepts, others of second-level concepts.
We shall be interested in the distinctions between those expres-
sions which Frege claims are names of objects, those which he
claims are names of first-level concepts, and those which allegedly
are names of second-level concepts. For the sake of brevity, let us
call these A-expressions, B1-expressions, and B2-expressions,
respectively. How can we tell whether a given expression is an A,
a B1, or a B2 expression?
A-expressions: Certain expressions (e.g., 'Nixon', '2', 'the present
King of France') can be used as the grammatical subject of a
sentence, but can never be used as the grammatical predicate of a
sentence. Frege regards such expressions as A-expressions. (See
[8], pp. 43, 47-48). Although many expressions which satisfy this
criterion (e.g., 'the least rapidly convergent series') will not actually
have a denotation, we are still to regard them as A-expressions.
([8], p. 58). Frege also regards any complete declarative sentence
(hereafter simply: 'sentence') as an A-expression. ([8], p. 63). Any
such sentence which has a truth-value denotes its truth-value; and
truth-values, the True and the False , are objects. ([8], pp.
63-4). Sentences which are neither true nor false do not have a
denotation, but are A-expressions nonetheless.6 Let us say that an
expression is an A-expression if either a) it is a sentence, or b) it can
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'God exists' can be translated into the Begriffschrift as 'TU ITa is
called God,' or '(aT a is identical with God.' Each of these
sentences is of the form 'my f(a),' in which 'f' represents a
BI-expression and 'aUT . . (a)' is a B2-expression. (See [8],
pp. 37-38. Frege's expression 'aUT f(a)' is equivalent to the
Principia Mathematica expressions' -. (x) -. (Fx)' and' (3x) (Fx)'.)This move is useless, for, again, whatever the predicative structure
of the Begriffschrift sentence, principle P shows that nothing
follows concerning the predicative structure of 'God exists.'
Although we no doubt gain many insights about sentences of
ordinary language by translating them into a formal symbolism, we
surely do not gain any insight into their predicative structures.
There is at least one passage in which Frege appears to concede
an exceptional character to singular existence sentences:
We must here keep well apart two wholly different cases that areeasily confused, because we speak of existence in both cases.In onecase the question is whether a proper name designates, names,something; in the other, whethera concept takesobjectsunder tself.If we use the words there s a. . . we have the lattercase.([8], p. 104).
These remarks suggest that Frege wants to make a distinction
between two kinds of existence sentences. In making assertions
with sentences of the form 'there is a b'we say of a concept that it
takes objects under itself, that is, we subsume a first-level concept
under the second-level concept, not being empty. But there is
another kind of case in which we speak of existence. Here, I
take it, Frege is thinking of singular existence sentences. In making
assertions with sentences of the form 'A exists' or 'the S exists' we
are not subsuming a first-level concept under a second-level
concept. Rather, we are saying of a proper name (in Frege's senseof 'proper name,' i.e., an A-expression - this includes both 'God'
and 'the Taj Mahal.') that it designates something, we are sub-
suming a proper name under the concept, having a designation. 1
If this is Frege's view about the predicative structure of singular
existence sentences, then three comments are in order. First, such
a view represents a departure from Frege's claim, in The Foundations
of Arithmetic, that affirmation of existence is a denial of the number
nought. A sentence of the form 'A exists' does not subsume a
first-level concept under the second-level concept, not being empty.Second, such a view also represents a departure from Frege's
syntactic-semantic principles (i.e., 1) the criteria for picking out
A, B1, and B2-expressions; together with 2) the rough procedural
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[7] , On the Foundations of Geometry, trans. M. E. Szabo, in E. D.
Klemke (ed.), Essays on Frege (Urbana, Chicago, and London, 1968).
[8] , Translations from the Philosophical Writings of Gottlob Frege, ed.,and trans., by P. T. Geach and M. Black (Oxford, 1960).[9] Kant, I., Der einzig m6glich Beweisgrund zu einer Demonstration des
Daseins Gottes, in E. Cassirer (ed.) Werke (Berlin, 1912), Vol. II: 76-79.[10] Plantinga, A., Kant's Objection to the Ontological Argument, Journal of
Philosophy, LXIII (1966): 537-546.[11] Shaffer, J., Existence, Predication, and the Ontological Argument, Mind,
LXXI (NS) (1962): 307-325.
[12] Wolterstorff, N., Referring and Existing, Philosophical Quarterly, XI (1961):
335-349.
NOTES
1 I am grateful to Nelson Pike and William Rowe for helpful criticisms of
earlier versions of this paper.2 I have here written in terms of what speakers do, not what sentences do.
Frege normally speaks of what sentences do. In this paper I will employ both
idioms interchangeably.3 For Frege, of course, one cannot identify a concept by means of the
expression 'the concept O'.One succeeds only in picking out or referring to what he
calls an object. See, for example, [8], pp. 46-47. For our purposes, however, this
difficulty can safely be ignored.
4 It is worth noting that Frege was not the first to argue in this way.His
argument, at least in broad outline, was put forth by Kant in [9]. This historical
parallel is not often noticed. There Kant claims that when we make an existence
assertion we are ascribing a property not to things, but thoughts, or concepts, or a
collection of properties. He concludes from this that existence is a property of
thoughts, or concepts, or a collection of properties - a second-level property.
5 It is obvious that if one holds that the concept of existence is not of first-level
he must also hold that when we make an existence assertion we are not subsuming
things (objects) under a first-level concept of existence. Frege evidently thinks his
claim about what we are doing in making any existence assertion is relevant in
showing that the concept of existence is of second-level, not of first-level. I take
him, then, to be making the following assumption: if an existence sentence sub-
sumes a first-level concept under a second-level concept, then it does not subsumean object under a first-level concept. For the purposes of this paper we need not
quarrel with this assumption.6 [8], pp. 62-63. Frege suggests that sentences of the form 'A is i,' or 'the S is
P.' will have no truth-value if 'A' or 'the S' have no denotation. It is for this reason,
he says, that the sentence 'Odysseus was set ashore at Ithaca while sound asleep'
may not have a truth-value.
7 [5], p. 81. More specifically, they are names of first-level functions of one
argument. For our purposes the distinction between names of first-level functions
of one and two arguments (ibid.) will not be important. In this paper all examples
of names of first-level functions will be names of first-level functions of one argu-
ment.8
For our purposes we will assume that all Bl-expressions have denotation.A name of a first-level function has a denotation if the A-expression which results
from its argument place being filled with an A-expression always has a denotation
if the A-expression in the argument place has a denotation. ([5], p. 84). Conse-
quently, a name of a first-level concept has a denotation if the sentence which results
from its argument place being filled with an A-expression always has a truth-value
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if the A-expression in the argument place has a denotation. Elsewhere, Fregesuggests that if a Bl-expression is to have a sense at all it must satisfy this condition.Otherwise, we should have to abandon the Law of Excluded Middle. See, forexample, [8], p. 159. That is, Frege seems to suggest that if a Bl-expression is to
have a sense it must have a denotation.9 We will assume that all B2-expressions have denotation. A name of a second-
level function has a denotation if the A-expression which results from its argumentplace being filled with a Bl-expression always has a denotation if the Bl-expressionin the argument place has a denotation ([5], p. 84). Consequently a name of asecond-level concept has a denotation if the sentence which results from its argu-ment place being filled with a Bl-expression always has a truth-value if the Bi-expression has a denotation. Since we are assuming that all B1-expressions havedenotation (see note 8), our assumption that all B2-expressions have denotation isthe assumption that, for any B2-expression, the sentence which results from itsargument place being filled with a Bl-expression always has a truth-value.
10Frege's general procedure here can be described as follows. First, we find
out what kind of expressions, whether A, Bi, or B2, make up a given sentence.This will tell us of what the various elements of the sentence are names. And thenwe can determine what is being subsumed under what. If the sentence contains anA and a Bi-expression, then that sentence subsumes an object (if there is one, i.e.,if the A-expression in fact has a denotation) under a first-level concept. If thesentence contains a Bi and a B2 expression, the sentence subsumes a first-levelconcept under a second-level concept.
11I am assuming that the distinction between the two kinds of existencesentences is to be drawn in terms of their predicative structures. It may be thatFrege wishes only to make the point that sentences of the form 'A exists' or 'the Sexists' express the same thought as corresponding sentences of the form 'the name
A (or the S ) has a designation.' For what are by now familiar reasons, such a
point will have no bearing on questions about the predicative structure of singularexistence sentences.
12 He might, of course, try to argue that there is no sense in which non-existententities can be said to have properties or fall under concepts. Recent work, however,has suggested that this line of response is not very promising. See, for example,Cartwright [1], Plantinga [10], Schaffer [11], and Wolterstorff [12]. Plantinga'spaper also contains a brief discussion (though differently motivated than the presentpaper) of Frege. See also Cocchiarella, [3] and [4], for a formulation and discussionof a logic of existence centering around a distinction between those attributes whichentail existence and those which do not. Although Cocchiarella agrees with thewriters just cited in holding that objects which do not exist may nevertheless haveattributes, the class of attributes which he claims do not entail existence appears to
be more restricted than it apparently is for these others - see [2].13Strictly speaking, all that has been argued is that Frege's view about the
predicative structure of affirmative existence sentences is compatible with holdingthat existence is a first-level property. For it was stipulated that, in this as well asin most of the preceding section, 'existence sentence' would mean simply 'affir-mative existence sentence'. It should be clear, however, that a similar line of argu-ment will show that Frege's view about negative existence sentences is also compat-ible with the claim that existence is a first-level property.