Appendix III
FREGE, RUSSELL, AND THE PUZZLES OF REFERENCE
Russell’s theory
of descriptions was conceived as a way to solve puzzles of reference. Frege’s
theory of sense suggests a different way to solve the same puzzles. These two
kinds of solution are usually considered to be irreconcilable alternatives.
Nonetheless, each of them has its own appeal. In this appendix I will propose
to build a bridge between Russell’s and Frege’s solutions by transforming each
of these views and maKing them fully reconcilable. I will proceed first by
subtracting from each of these views its metaphysical load, and then by showing
that if the appropriate changes are made they can be viewed as different ways
of saying the same thing.
Russell’s
solutions to puzzles of reference
I will first
present the puzzles and then Russell’s solutions to them by means of his theory
of descriptions.
(i) Reference to the non-existent.
Consider first a sentence whose grammatical subject does not refer to anything,
‘The present King of France is wise’. How can we attribute wisdom to someone
who does not exist? Russell’s
response is that this problem only arises if we understand the description ‘the
present King of France’ as a referential expression functioning as a proper
noun. But this is not the case. Calling the predicates ‘…present King of
France’ ‘F’ and ‘…is wise’ ‘W’, the theory of descriptions allows us to
symbolise ‘the present King of France is wise’ as: ‘(Ǝx) (Fx & (y) (Fy → y
= x) & Wx)’. Or, to use a more intuitive formulation in which we summarise
‘at least one and at most one’ as ‘exactly one’, we have the following false
sentence:
1.
There is exactly one x such that x is the
present King of France, and x is wise.
In any of these
formulations, one thing is clear: there is no wisdom predicated on a present
King of France. The definite description ‘the present King of France’ was
replaced by quantified predicates. Hence, we don’t need to assume the existence
of any present King of France.
(ii) Negative
Existential. The second puzzle, a variant of the first, concerns the
apparent impossibility of denying the existence of an object when the
expression that denies the existence is about the same object. To resolve the
problem, consider the following sentences:
1. The present King of France does not exist,
2. Sentence (1) is about
the present King of France.
Both sentences
seem to be true. But they are mutually inconsistent. If sentence (2) is true
and (1) is about the present King of France, then sentence (1) must be false
and vice versa.
Russell solves the riddle by suggesting that
(2) is a false sentence. In order to show this, he interprets the negation in
sentence (1) as possessing a narrow scope in relation to the definite
description. The form of sentence (1) is: ~(Ǝx) (Fx & (y)
(Fy → y = x)), or, in a more intuitive formulation:
2.
It is not the case that there is exactly one x such
that x is the present King of France.
This is a true
sentence, since it is the negation of a false conjunction. But it does not
commit us to the existence of the present King of France in order to deny that
he exists. We commit ourselves only when we deny the existence of anything that
has the property of being the present
King of France.
(iii) Identity
Sentences. The third puzzle is the Fregean paradox of identity. Consider
the sentence: (1) ‘The author of Waverley
was Scott’. This contains two referential expressions, both denoting the same
person. But if this is so, then sentence (1) should be tautological, saying the
same thing as (2) ‘Scott is Scott’. However, Husserl thinks that we know for
sure that (1) is a contingent and informative sentence. Why?
Russell’s solution is again to make the
definite description disappear. Calling Scott ‘s’, we can paraphrase the identity sentence as “(Ǝx) (Wx
& (y) (Wy → y = x) & (x = s))”.
Or, more intuitively:
3.
There is only one x
that is the author of Waverley, and
this x is Scott.
From these
formulations it is clear that (1) is an informative sentence, because what
seemed to be a tautological identity now appears as an informative statement.
(iv) Opacity.
A final riddle that the theory of descriptions is called upon to solve is that
of intersubstitutivity in sentences that express propositional attitudes,
which are relational states connecting a mental attitude to what we call
a proposition or thought. Consider, for example, the sentence (i) ‘George IV
believes that Scott is Scott’. This is true, since George IV was certainly able
to apply the principle of identity. But since the name ‘Scott’ and the
description ‘the author of Waverley’
refer to the same person, it seems that we can replace the first occurrence of
the word ‘Scott’ in sentence (i) with this description, obtaining the sentence
(ii) ‘George IV believes that the author of Waverley
is Scott’ so that (ii) preserves its truth. But this is not what happens: it
may well be that sentence (ii) is false, despite the truth of sentence (i). Why
is this so?
To respond to this objection, we can use the
theory of descriptions to replace the description that comes after ‘George IV
believes…’ as follows:
George IV
believes that there is only one x
that is the author of Waverley, and
that this x is Scott.
Certainly, this
is an informative belief that is clearly distinct from the tautological belief
that Scott is the same as Scott. This is why it can be false.
Fregean solutions to puzzles of reference
Frege has an
explicit solution for the last two puzzles of reference. As for the first two,
the solution can only be reconstructively suggested.
(i) Reference
to the non-existent. Frege suggested that in an ideal language a singular
term without reference could be seen as referring to an empty set. We can apply
this suggestion to ordinary language, suggesting that a sentence like
(1)
The present King of France is wise.
is false, since
the empty set isn’t wise. However, in addition to being artificial, this
suggestion leads to absurd conclusions, such as that the sentence ‘Pegasus is
the present King of France’ is true, since both ‘Pegasus’ and ‘the present King
of France’' refer to the same thing, namely, an empty set.
The alternative suggestion that I would like
to propose is that we can say things about non-existents simply because
singular terms without references still have senses. Consequently, through
these senses we can say something about them as possible existents. We are
still able to articulate the dependent sense of the predicate with the
independent sense of the singular term, producing a complete thought,
notwithstanding the fact that this thought is false, since the truth of a
thought demands not only that its predicate have its reference, but also its
singular term, which is lacking. This falsity (assumed by Husserl and denied by
Strawson) is not clear when we consider the statement ‘The present King of
France is wise’, which points to a property of the conceived thing. But the
falsity becomes clear when we consider other statements with a similar
structure, but with a richer and independent semantic content. Consider, for
example, the statements:
1.
Yesterday the present King of France cleaned my
mother’s pool.
2.
I saw the present King of France doing exercises on the
beach last week.
3.
The present King of France has forbidden tourists to
visit the Palace of Versailles.
4.
The present King of France isn’t wise, since there is
no present King of France.
The first three
statements are all in a clear way intuitively false. The reason why statement
(i) used by Strawson can be seen as lacking truth-value is only a pragmatic
one, namely, we normally regard a statement as false when the predicate does
not apply, while we normally assume that the singular term applies; so the statement
‘Bertrand Russell had a beard’ is obviously false; this is the standard case of
falsity in singular statements. However, we are not used to considering the
truth-value of statements when the singular term has no reference, since these
statements are very rare in our language. Indeed, it seems pointless to make
attributions to something we know does not exist! This is why statements (1),
(2) and (3) are clearly false; they lack of reference of a constitutive part of
them. The statement (4) is true, since it denies the truth of the statement
that the present King of France is wise and gives the reason for its falsity.
Well, it would not be true if the statement ‘The present King of France is
wise’ weren’t really false, and it is false by the same reason as the first
three statements.
Moreover, consider the statement ‘Santa
Claus has a white beard’. In a fictional context it is undoubtedly true. But if
understood as a statement about the real world, its truth-value does not seem
clear. The statement does not seem to be false, because it is about a known
property of Santa Claus, and we have difficulty seeing it outside its fictional
realm. But this kind of sentence shows itself to be definitely false when we
make a statement like ‘I trimmed Santa Claus’s white beard last Christmas’.
(ii) Negative Existential. It
is not so easy to give a Fregean explanation to the enigma of negative
existentials. However, consider the following statement:
(1) The present King of France does not
exist.
It is true that
‘the present King of France’ is a definite description and as such for Frege
does not refer to a concept. But suppose that in this case it refers to its own
sense, as in indirect discourse, which has the role of a concept. Since
existence is the property of a concept that at least one object falls under it,
then sentence (1) isn’t about the present King of France, but about the property
of the referred to sense-concept of being satisfied or applicable, which is
denied.
The same would apply to the denial of
existence regarding proper names. If proper names, as Frege would have
suggested, are abbreviations of bundles of defined descriptions, then a similar
strategy would be applicable to negative existential statements with empty
names, like ‘Pegasus does not exist’. What this sentence means is that the
sense-concepts expressed by some descriptions abbreviated by the name ‘Pegasus’
are not satisfied by any object.
(iii) Identity
Sentences. The riddle of identity between descriptions can be exemplified
by the most discussed sentence of analytic philosophy: ‘The morning star is the
evening star’. For Frege, this identity sentence is informative, because the
descriptions ‘the morning star’ and ‘the evening star’ express different senses
or modes of presentation of the same object, the first as the most brilliant
celestial body that appears to us in the east in the morning and the second as
the most brilliant celestial body that appears to us in the west in the
afternoon… It is informative to say that these two very different modes of
presentation are of the same object.
(iv) Opacity.
As for the enigma of opaque contexts, Frege suggests that in statements of
propositional attitudes the subordinate sentence does not have its usual
reference, but an indirect reference, which is its own sense. Thus, in saying
‘George IV believes that the author of Waverley
is Scott’, the reference of the subordinate sentence ‘The author of Waverley is Scott’ is neither its
truth-value (as Frege thought the reference of a sentence should be) nor the
corresponding fact, but simply the thought expressed by this sentence. As ‘The
author of Waverley is Scott’ expresses
a thought other than ‘Scott is Scott’, the statements ‘George IV believes that
the author of Waverley is Scott’ and
‘George IV believes that Scott is Scott’ are not interchangeable salve veritate.
I don’t wish to discuss here the objections
of detail that could be made to each of these solutions. I want to respond only
to the general objection made in Fregean-kind solutions of the riddles of
reference, according to which they induce us to accept some kind of Platonism
of senses and thoughts, unlike Russell’s ontologically more economical
solutions.
I do not believe that a commitment to
abstract entities is unavoidable in Fregean solutions. As we have seen in the
chapter on Frege, the best way to make sense of Fregean senses is to identify
them with psycho-semantic rules or their combinations in the determination of
the referential uses of expressions. In this understanding, the meaning of a
definite description is a rule of identification for the object it should refer
to.
Here too the objection can be made that we
are only replacing the word ‘sense’ with the word ‘rule’, and that this is a
merely verbal solution, because if senses are abstract entities, rules also
appear to be abstract entities. However, here too it is possible to answer, as
we have already done, that the rules in question do not exist outside of their
instantiations as cognitive-psychological events able to be demonstrated
publicly by means of behavioural manifestations, and that there is nothing else
beyond this. Such cognitions can be identified as precisely similar to
each other, not because they are instantiations of any abstract object (the
rule of identification in itself) but by qualitative identity between the
cognitive act of applying the rule of identification that we are taking into
account and the cognitive act of application (real or only in thought) of the
rule of identification that we are using as a model. This assumption prevents
our paraphrase of sense in terms of semantic rules from being unjustly severed by
Occam's razor.
Reviewing Fregean assumptions
Who
is right? Russell or Frege? Much ink has been spilled in the dispute over the
correct theory. As I noted at the outset, my hypothesis is that it is not a
matter of choice between two theories. If it were only a matter of choice, then
one or the other theory should already have been recognised as false. The fact
that we have achieved no consensus regarding the wrong theory leads us to the
suspicion that both theories have some truth. But then, why we do not see them
as two different ways of saying the same thing? The plausible answer is that
each of them has implausible metaphysical assumptions mixed with insightful
content, and that these implausible metaphysical assumptions make them appear
irreconcilable. Thinking in this way, my proposal is to reconstruct these
theories, eschewing their metaphysical assumptions and filling the gaps that
are left with more plausible assumptions. If our hypothesis is right, this will
allow us to show that they are only two different ways of saying the same
thing.
Let’s start with Frege. We have already seen
that we must eliminate the anachronistic ontological realism of the senses,
which should be replaced by psychological instantiations of semantic rules.
Repeating what has already been proposed in our reading of Ernst Tugendhat in
the introductory chapters, it is perfectly plausible to identify what Frege
called the senses in terms of semantic rules, so that
:
(i) The sense of a singular term
(mode of presentation of the object) is the same as the identification rule
(Identifizierungsregel) of
the singular term, whose application criteria are the identifying properties of
the object.
(ii) The sense of a general term (conceptual
content) is the same as its application rule (Verwendungsregel)
as a predicative expression, whose criteria of application would be the
singularised properties (tropes) associated with the object;
(iii) The sense of an assertive sentence (the
thought it expresses) is the same as its verification rule (Verifikationsregel),
whose criteria of application would be its truth-maker, which as we have seen
can be better identified (contrary to Frege) with the fact referred to by the
sentence (see chapter 3 of this book).
A second thing that must be done is to
replace some of Frege’s odd ideas concerning reference, like that of an
unsaturated concept as the reference of a predicate and truth-value as the
reference of a sentence, as we argue in chapter 3 of this book. It is more
plausible to see a concept in a natural way as the sense of a predicative
expression and the primary reference of a predicative expression not as a
truth-value, but simply as a fact (a secondary reference could be a universal
constructed out of tropes).
A further thing we do in chapter 3 was to
paraphrase the Fregean concept of existence. We saw that for Frege existence is
the property of a concept of being satisfied by at least one objec
t,
or, as we understand it, the property of a concept of applying effectively (and
not merely supposedly) to at least one object during some period of time (in
which the object can be said to be existent). To know that an object exists is
to know that its conceptual rule is effectively and continuously applicable
during the time in which the object can be said to exist.
Now, accepting the natural view of a concept
as the sense of a predicative expression, we get a further analysis of the
concept of existence. Existence is the property of a concept, that is, of the
sense of a conceptual expression, of being satisfied by its reference. More
precisely, since the sense of a conceptual expression is its rule of
application, existence must be the property of the rule of application of being
satisfied, that is, of being effectively applicable. Moreover, as we have seen,
this does not deprive existence of objectivity, because if the effective
applicability of a conceptual rule is a property of it, it is also the own
property of the object that we may conceive of having this rule effectively
applicable to it. This result can be admitted for each of the rules (senses)
already supposed by Tugendhat:
(i)
the existence of an object is the effective
applicability of the rule of identification of the singular term that names it,
(ii)
the existence of an s-property is the effective
applicability of the rule of application of its predicative expression, and
(iii)
the existence of
a fact is the effective applicability of the verification rule constitutive of
the thought of this corresponding fact as given in the world – its truth-maker.
Finally,
since the effective applicability of the verification rule of a
statement is the existence of a fact, and the verification rule is the Fregean
thought (proposition), then the existence of the fact is the effective applicability
of the f-thought expressed by the assertive sentence.
Now, what about the relation between
existence and truth? We have here the truth of a thought and the existence of
the fact depicted by the thought. If existence is the effective applicability
of a conceptual rule, then, since a thought is a complex conceptual rule, a
verification rule, the existence of what is thought, namely, the fact, is the
effective applicability of the thought. And the existing fact, the real fact,
the fact in itself, is a fact to which the verifiability rule of its thought is
applicable. This means that assigning existence to a fact is equivalent to
assigning truth to its Fregean thought. To say that the f-thought expressed by
the sentence ‘Socrates is bald’ is true is to say that this thought, namely,
the verification rule expressed by the sentence, is effectively applicable to
the fact, namely, that the criterial configurations that the rule requires to
warrant its application correspond to criterial settings that have in some way
been found, that it is a fact that Socrates is bald, that is, that this fact
exists. The existence of the fact is the truth of its thought.
Finally, I want to treat sentences without a
reference as being ultimately false and not as being devoid of
truth-value, as Frege suggested in some examples. After all, the reason why
Frege thought that sentences with unreferenced components are devoid of
truth-value lies in his insistence on the indefensible idea that the reference
of the sentence should be its truth-value. But as we are willing to admit that
the reference of a sentence is a fact, the absence of such a fact – due to the
lack of reference to the singular term – just leads us to the falsity of the
sentence, as we have shown in our discussion of the Fregean solution to the
question of the reference of non-existents. This greatly corrected view of
Frege’s insights is already pretty close to the position of Russell, who saw
sentences with empty set descriptions as false.
Reviewing Russellian Assumptions
Now it is time
to review the assumptions of Russell’s theory of descriptions. A first step is
to rule out the thesis according to which definite
descriptions and even our usual names (which for him are sets of descriptions)
are not referential expressions in the proper sense.
This Russellian thesis flies in the face of
our ordinary language intuitions. For what could better exemplify a referential
expression than a proper name or even a definite description? One could even
say that names and definite descriptions define singular terms, since they are
nominators, terms whose function is to refer to only one thing among all
others. They are what provide the templates for our understanding of
nomination: the singularisation of an object indicating which it is among all
objects of a certain domain. Russell’s intention in his logical atomism is to
use the theory of descriptions, paraphrasing definite descriptions and proper
names in terms of quantified predictive expressions and replacing them with
logical proper names. However, as we have seen in the second chapter of this
book, the doctrine of logical proper names espoused by Russell is hopeless, and
his form of semantic referentialism is implausible.
Once we reject the existence of logical
names, there is no reason to deny that definite descriptions are referential
expressions. Even when definite descriptions are analysed in the form of a
conjunction of quantified predicative expressions, as Russell does, they cannot
be referential expressions, for they are able to pick out one only object and
to distinguish it from all other objects of a given domain, and this is all
that is required for an expression to be referential. This reinforces our
abandonment of Russell’s metaphysics of logical proper names.
We must also reject a second assumption of
Russell’s, namely, his obscure suggestion that
definite descriptions do not have any meaning in themselves.
This sounds like an amalgam of two
Fregean ideas: the principle of context and the idea of the incompleteness of
predicates. If the meaning (sense) is the object, as the referential view of
meaning defended by Russell proposes, and if definite descriptions fail to
refer to the object, they cannot have meaning outside the context of something
else that can be offered only by the whole sentence. However, once we reject
the doctrine that meanings need to be referents, and we admit that reference is
usually given by means of semantic rules, it is clear that the requirement of
applying the predicate to a single object with such and such properties made by
Russellian analysis already constitutes a rule of identification, allowing us
to refer to something and as such constituting a complete sense. A definite
description should work as a fully meaningful term, and its meaning should be
given by the identification rule expressed by it.
Building a Frege-Russell theoretical bridge
Once in
possession of a different view of Frege’s and Russell’s analysis, one that
deprives them of their implausible speculative wrappers, the essential aspect
of my strategy is to use the rules of identification constitutive of the
senses, and the concept of existence as the effective applications of these
rules in order to build a conceptual bridge allowing us to travel from the
Fregean solutions of riddles of reference to the Russellian solutions and vice
versa. In this way I want to demonstrate that Frege’s and Russell’s answers to
puzzles of reference are intertranslateable. Here is how this can be done:
(i) Reference to non-existents. As
we have seen, the most reasonable answer to the Fregean problem of how to give
meanings to sentences referring to non-existent objects is that we can at least
understand how the incomplete sense of the predicative expression can be supplemented
by the complete sense of the singular term, thus constituting the complete
content of a thought. That’s what allows us to think that the present King of
France is wise without having to admit that he exists.
A better understanding emerges when we
translate Fregean senses in terms of psycho-semantic rules. In this case we
will say (returning to Tugendhat’s suggestion) that the true predicative rule
always applies to its usual reference by means of the application
of the identification rule. Coming back to an example considered at the start
of this book, at the sight of the Earth for the first time, the first
cosmonaut, Yuri Gagarin, said: ‘The Earth is blue’. But in order to express
this thought, he first needed to identify something in space, an object, the
planet Earth. And by means of this identification he could apply the predicate
‘…is blue’ to the s-property of the object that he had located. We see that the
rule for the application of the predicate ‘…is blue’ needs to be first, say, driven
by the application of the identification rule (which selects among others the
one called ‘Earth’) in order to find the object, only then being able to be
applied in the identification of the singularised property (trope) of the
object of being blue. The application of the predicate’s application rule
therefore needs to be made in combination with the object’s identification
rule, so that it can find out if the
object satisfies it or not. It should be noted that if the sentence were ‘The
Earth is red’, it would be false, because the object located by the
identification rule would not satisfy the application rule of the predicate
‘…is blue’.
Let’s consider now the case of empty
singular terms, the alleged reference to non-existents, as found in the
sentence ‘Vulcan is red’. As we know, ‘Vulcan’ is the name of a small planet
that astronomers once believed should exist between the Sun and Mercury in
order to explain variations in the perihelion of the latter. According to the
calculations of the astronomer Le Verrier, this new planet would have been
located approximately 21 million kilometres from the Sun… This is the Fregean
sense of this name: the mode of presentation of its reference. However, since,
as we now know, Vulcan does not exist, the reference of the name is empty and
its identification rule inapplicable. As a result, the application of the
application rule of the predicate ‘…is red’ is also impossible. As the
identification rule of the singular term doesn’t quite apply to any object, an
application of the predicative rule cannot be made either, remaining
non-satisfied by any property actually given, so that the predicate does not
apply, making the sentence false (pace Frege).
However, here we have a more appropriate
explanation for what happens. This explanation takes recourse to our capacity
for imagination. We are at least in some measure able to conceive what it would be like to apply
both rules in combination, although we are unable to apply them to the real
world. It is only to the extent that we are able to conceive the possibility of
applying both combined rules in the constitution of what Tugendhat called a
verification rule that we can understand the epistemic sense of the sentence,
its f-thought, even knowing that the proper name is empty and that this
f-thought has no effective application to any fact in the world.
This is why the sentence ‘The present King
of France is wise’ is already able to express a complete sense, a thought. We
are capable of conceiving the two rules used in combination in order to form
the verification rule, the sense of the sentence, the thought, which for lack
of an object and, therefore, for lack of a correlative fact, remains without
application, making the thought false.
To the question of how it is possible to
assign wisdom to something that does not exist, the answer is now clear: we are
capable, at least in some measure, of conceiving the application of
psycho-semantic rules in combination, and by doing this we give meaning to the
terms and to the sentence as a whole. We are able to make a fictive
predication, even if only to a limited degree, without assertive or
adjudicative force.
Now, in the light of this reconstruction, it
is easier to make the theory of sense agree with the theory of descriptions. We
can paraphrase the description ‘the present King of France’ in a Russellian way
as:
At least one x and at most one x is such that x is presently the
King of France.
And we can say that what is expressed here
is a different formulation of the Fregean sense, of the same identification
rule for the present King of France, which is seen as having two components:
(i)
the condition of uniqueness,
(ii)
the application rule of the predicative expression ‘…is
presently the King of France ’.
Together (i) and (ii) form a rule of identification, because they allow
us to distinguish at least one and at most one object through the criterial
properties derived from them, such as the presence of a hereditary head of
state (monarch) governing France today.
The non-existence of the present
King of France corresponds to the inapplicability of the identification rule
consisting of (i) and (ii) and, therefore, to the lack of reference. As for the
predicate ‘x is wise’, its application rule also does not apply, since
nothing exists that has the property of being the present King of France, to
which it can apply. But this predicate also expresses a rule of application and
therefore a Fregean sense. Pulling the threads together, with the sentence
‘There is only one x such that x is presently the King of France,
and x is bald’, we do nothing more than attempt to apply the same
verification rule expressed by the sentence ‘The present King of France is
bald’. Since we realise that the identification rule cannot find its bearer, we
realise that the application rule is also inapplicable, the same being the case
with their combination, namely, the verification rule. Analysing the case of
reference to non-existent things, we are already able to see how the ‘Fregean’
explanation can be exchanged for a ‘Russellian’ explanation and vice versa.
(ii) Negative Existentials. In
Chapter 3 we have, despite Frege’s view, identified the concept with the sense
of a predicative expression. To say that the present King of France does not
exist becomes the same as saying that the meaning of ‘the present King of
France’ does not determine a reference.
How would we express this by using
psycho-semantic rules in place of the sense? Well, we would say that the sense
or meaning or concept expressed by a singular term like ‘the present King of
France’ is given by the identification rule for this definite description. We
know this because we can at least to some extent conceive the applicability of
this definite description. But we cannot get an awareness of the effective
applicability of the conceptual rule, that is, we cannot say that the object
referred to by this definite description exists, since we know that this rule
cannot be applied.
Now we come to the corresponding
‘Russellian’ analysis. A description like ‘the present King of France’ is here
transformed into
‘At least one x and at most one x is such that x is
presently the King of France’.
Here again, this is the same as the
identification rule for a particular object, being composed of two sub-rules:
(i)
the condition of unity
(ii)
the rule of application of the
predicate ‘...is presently the King of France’.
Now, to say that the present King of France
does not exist is at least to say ‘It is not the case that there is at least
one x and at most one x such that x is presently the King
of France’, and this is to say that the identification rule composed of
conditions (i) and (ii) isn’t effectively applicable. What is the difference
between this rule and the Fregean sense of the description? The answer is that
it comes from diverse demonstrations of the same thing. The ‘Russellian’
analysis only decomposes the rule into two rules: a unity rule and a rule of application
for the predicate. Saying that the
present King of France exists is to say that the application rule of the
predicate ‘…is presently the King of France’ effectively applies, and that it
applies to a single object. Once more, the ‘Russellian’ and ‘Fregean’ analyses
of negative existentials converge towards becoming two different ways to say
the same thing.
(iii) Identity.
Consider now identity sentences like ‘the morning star is the evening star’.
How can this sentence be informative, if the two descriptions refer to the same
object? Frege’s reply is that despite the fact that these descriptions refer to
the same object, they express different modes of presentation of this object,
and that because of this they are informative. Paraphrasing the concept of
meaning in terms of a psycho-semantic rule, what Frege suggests is that the
sentence above is informative because it tells us that we identify the same
object through two different identification rules, which call for different
criterial settings.
In Russellian terms, calling the predicate
‘…morning star’ M and the predicate ‘…evening star’ E, the identity sentence
can be symbolised as:
(1) Ǝx
((Mx & Ex)
& (y) (My → y = x)) & (z) (Ez
→ z = x)).
In other words:
(2) There is exactly one x
that is the morning star, and the same x is the evening star.
In this case, what we are doing is (i)
making a conjunction of two different application rules of predicates, adding
to it (ii) that they both apply to the same object. Thus, the ‘Russellian’
analysis only assures us that the identification rule constituted by ‘Ǝx (Mx
& (y) (My → y = x))’ applies to the same object that the identification
rule constituted by ‘Ǝx (Tx & (z) (Ez → z = x))’ applies to, since by
transitivity y = z. But this is like saying that we
have two different identification rules, two modes of presentation, two
different Fregean modes of presentation of the same object. Again, the two
analyses turn out to be intertranslateable or interchangeable.
(iv) Opaque
Contexts. Finally, consider expressions of propositional attitudes such as:
(1) George IV
believes that Scott is Scott.
and
(2) George IV
believes that the author of Waverley
is Scott.
Why does the truth of (1) not guarantee the
truth of (2), if both subordinate sentences are identity sentences about the
same person?
For Frege, the answer is that in such cases
the subordinate sentence doesn’t have its usual reference, which for him is its
truth-value. Subordinate clauses refer, he thinks, to the thoughts expressed by
them, and the thoughts expressed by them in (1) and (2) are different. As a
consequence, the truth-value of the sentence that expresses a propositional
attitude ceases to be a partial function of the truth-value of the subordinate
sentence, making the intersubstitution
salve veritate impossible.
Since we reject Frege’s implausible idea
that the usual reference of a sentence should be its truth-value, we must first
reconstruct his solution. We can preserve his idea that in utterances of
propositional attitudes the reference of the subordinate sentence is its sense
as ‘aAp’, in which ‘a’ takes the place of the person who has
the attitude, ‘p’ replaces the thought referred by the subordinate
clause, and ‘A’ replaces the attitudinal verb, which can be one of belief,
knowledge, desire, etc. But in ‘aAp’, p expresses a proposition such that it no longer refers to some
fact in the world that p could
eventually match, making it true. In the statement of a propositional attitude,
what matters is a certain relationship between the contents of the main clause
(usually expressing a mood or mental act by a certain person) and the thought
expressed by the subordinate clause, so that the truth of a sentence of
propositional attitude depends only on the fact of this relationship being
really in the mind of person a independently of the truth or falsity of
the thought expressed by p. Indeed, according to this reasoning, Frege
is right: the subordinate clause has as its reference the content of the
thought expressed by it, of which we state that the person has the propositional
attitude. Thus, a statement of the form ‘aAp’ is true iff
the reference of aAp is a fact constituted by the existence of the person
a having his or her attitude A regarding
his or her thought p. This is why after all the thought expressed by the
subordinate clause cannot be overridden salve veritate: it is part of the fact
that is being referred to, and the entire fact is composed of A and p, that is, Ap.
Now, to paraphrase thoughts as verification
rules of sentences, we can say that the rules of verification of sentences (1)
and (2) are different, without thereby committing ourselves to the effective
applicability of these rules, to the actual existence of what satisfies them,
which is the fact that a has Ap. So, considering the singular
sense of the term as an identification rule, we can paraphrase (1) as:
(1') George IV
believes that the identifying rule (sense) that he has for Scott applies to the
same object as the identifying rule (sense) that he has for Scott,
and we
paraphrase (2) as
(2’) George
IV believes that the identifying rule (sense) that he has for Scott applies to
the same object as the identifying rule that he has for the author of Waverley.
As in (‘1) and
(2’), the contents of a thought represented by the identifying rules considered
by George IV are different and therefore the belief-contents are different,
and, as we have noted, since the truth-value of the propositional attitude
statements depends only of the fact that a
has the property Ap, and since these
properties are different in each case, we conclude that this truth-value
doesn’t need to be the same in each of them. The subordinate clauses cannot
replace one another salve veritate, because the
thoughts-references expressed by them are different.
Now consider a Russellian paraphrase: The
subordinate sentence of (1) can be stated as:
(1’’) George
IV believes that there is exactly one x which is Scott and that x
is Scott.
And the
subordinate sentence of (2) is analysed in order to obtain:
(2’’) George
IV believes that there is exactly one x that is the author of Waverley
and that x is Scott.
Now, as the
sentences ‘exactly one x that is Scott’ and ‘exactly one x that
is the author of Waverley’ express different predicates, ‘Scott is Scott’
cannot mean the same thing as ‘Scott is the author of Waverley’.
The point to be noted is that Russellian
analysis only better clarifies one aspect of our version of Fregean analysis.
After all, the Fregean analysis in (2’), for example, can also be presented as
(2’’’) George
IV believes that there is only one x such that the rule of
identification for Scott, as well as the rule of identification for the author
of Waverley, effectively applies to x.
But (‘2’) and
(‘2’’’) do not differ essentially. After all, to say as did Russell that George
IV believes that the rule of identification that he knows for the name ‘Scott’
and that the rule of application that he knows for the predicate ‘…is the
author of Waverley’ effectively apply to one and the same object, amounts to
the same (or nearly the same) thing as the Fregean suggestion that George IV
believes that the identification rule – the sense – he knows for the singular
term ‘Scott’ has the same referent as the rule of identification – the sense –
of the definite description ‘the author of Waverley’.
Thus we can clearly see: as well in the case of propositional attitudes the two
analyses are intertranslateable or interchangeable.
Conclusion
Summarising, we
can analyse the referential function of definite descriptions in at least three
ways: (i) in terms of abstract entities, as did Frege, when speaking of senses
or modes of presentation, (ii) in terms of semantic criterial rules, inspired
by Tugendhat’s approach that has its origins in Wittgenstein, and (iii) using
resources from predicative logic, as Russell did with his theory of
descriptions. These are, however, only different and complementary ways of
saying (approximately) the same thing.
The impression of strangeness of the
proposed approach comes from the acceptance of the metaphysical assumptions
that permeate what each of these philosophers wrote on the issue. Against
Russell’s belief, his paraphrases produced by the theory of descriptions are
nothing more than expressions of semantic rules. These make it possible to
formally express the referential function of the definite descriptions in their
attributive use, doing this with predicative expressions used in a domain that
grants them univocal application. Thus they appear as expressions of Fregean
senses or modes of presentation, which are nothing more than psycho-semantic
rules. Assuming that these rules only exist or apply either in imaginative
psychological experiments or in real cognitive instantiations, the
compatibility of the theory of descriptions so understood with our semantic-cognitivist
view is clear.
NOTES:
Ernst Tugendhat: Vorlesungen zur Einführung in die
sprachanalytische Philosophie, p. 262. See also Tugendhat and Ursula Wolf: Logisch Semantik Propaedeutik, chapter 13.
Each of these three cases can obviously be expressed
in a Russellian way in which referential terms are transformed into predicative
expressions. Thus, consider the existence of what is predicated in the sentence
‘Flying mammals exist’: symbolising ‘mammals’ as M and high-fliers as F, we
have ‘(Ǝ
x) (Mx & Fx)’. Consider now
the definite description in the sentence ‘The morning star exists’: symbolising
the predicate ‘…morning star’ as M we have ‘Ǝ
x (Mx & (y) (My → y = x))’. For the proper name in the sentence
‘Socrates exists’, abbreviating the descriptive content that the name can
contain with the predicate ‘socratises’ and symbolising this last predicate as
‘S’, we have (Ǝ
x) (Sx & (y) (Sy → y =
x)). Replacements like these can meet the objections of Kripke and others, but
they are easily answered if we have in mind my own version of the descriptivist
theory of proper names, summarised in appendix I of this book.
See also Ernst Tugendhat, Einführende Vorlesungen in die sprachanalytische Philosophie, p.
437.
Note that definite descriptions can refer to
different individuals in different possible worlds, unlike proper names. But as
we saw in appendix I, definite descriptions are accidental
or flaccid designators when they are semantically linked to proper names,
otherwise they become rigid. This demonstrates that there is nothing special
about the semantics of ordinary names, unlike modern referentials, as Kripke
believed.
‘I advocate that a denoting
phrase is essentially part of a
sentence, and does not, like most single words, have any significance on its
own account’. Bertrand Russell: ‘On
Denoting’, in Logic and Knowledge
(London: Routledge, 1994), p. 51.
We can speculate that if definite descriptions could
not be transformed into predicates, that would allow us to designate sets of
s-properties… that is, tropes. Russell did not have the notion of a
singularised property in space and time (trope).
I am assuming that George IV knows who Sir Walter Scott
is. In the case that he does not know this, the expression ‘that he knows’
should be omitted.
