Forum:
Enlightenment’s First Online Conference, January 2001 (published November,
2000)
"So you are saying
that human agreement decides what is true and what is false?"—It is what
human beings say that is true and false; and they agree in
the language they use. This is not agreement in opinions
but in form of life. - Ludwig Wittgenstein (1958, para. 241)
When Rand writes things like, "Truth
is the recognition of reality. (This is known as the correspondence theory of
truth.)", and "Truth is the identification of a fact of
reality", she seems to be claiming that truths are true in virtue of the fact
that they stand in some sort of relation — recognition, correspondence, or
identification — to something known as a 'fact'. Yet one can peruse her works
without ever learning what a fact might be, or how our beliefs or assertions
correspond to them. Here as so often elsewhere Rand has more commitment than
content.
The goal of this paper is to propose an Objectivist account of facts and truth.
In general, I will be guided by a heuristic suggested by Rand in the
"Concluding Historical Postscript" to the appendices of her Introduction to Objectivist Epistemology .
Rand is, I take it, explaining that she formed her theory of concepts by
engagement with the Aristotelian theory; specifically, by rejecting the
intrinsicist components of Aristotelianism but without surrendering the epistemic
norms which those intrinsicist components had supported. I want to discuss this
heuristic for a moment.
I see this heuristic, Rand's rejection of intrinsicist and subjectivist
approaches to various philosophical problems, as central to Rand's philosophy.
But, as Sciabarra points out, "Rand does not literally construct
a synthesis out of the debris of false alternatives. Rather, she aims to
transcend the limitations that, she believes,
traditional dichotomies embody." (Sciabarra 1995, 17) Here, the relevant
dichotomy stems from a radical divide supposed to lie between the subject and
object of knowledge. Much of the philosophical tradition, especially since
Descartes, has viewed the subject and object of knowledge as externally
related, so that one could be understood without reference to the other (except
insofar as the one doing the understanding is herself a knowing subject). But
Rand would not accept that such a divide exists. In perception, she is a direct
realist, claiming that the contents of perceptual states are themselves
external objects, but perceived by way of the senses in accordance with their
own functioning; with respect to concepts, she again argues that the contents
(objects, referents, or whatever) of concepts are things in the world, but
treated by the mind as similar in some respect. Ironically, claiming that the
relation between subject and object is an internal one is nowadays referred to
as 'externalism': the thesis that mental states are to be type-distinguished
and type-identified by reference to their external contents.
The radical divide between subject and object gives rise to the false dichotomy
between the two theses Rand calls intrinsicism and subjectivism. Intrinsicism
proposes that the subject passively reflects the intrinsic features of the
world, and thus that the world as known by us shows no signs of our activities
as knowers. The subject, then, is internal to or an epiphenomena of the world,
but the world — including all of its features, from beauty to similarities to
value-ladenness — is external or absolutely prior to the subject. Subjectivism
proposes that the object passively reflects the knowing activities of the
subject, and thus that the world as known by us shows little other than our
activities as knowers (or the knowing activities of a transcendent knower). The
world, then, is internal to or an epiphenomenon of the subject, but the subject
is external to or absolutely prior to the world. A third, Objectivist,
alternative will try to transcend the false duality of subject and object,
understanding the subject and object as they relate, internally, to one another
through the processes of cognition and action.
This paper undertakes to discuss a wide variety of topics by way of getting
clear on facts. Naturally, some of this discussion will be fairly superficial
and little of it will be fully satisfactory. But I hope that the general line
to be proposed, and the basic rationale for adopting it, will be clear and at
least somewhat compelling. The basic idea is that facts are structured entities
with which our beliefs and assertions share logical structure. Thus the theory
is similar to Wittgenstein's picture theory, proposed in the Tractatus Logico-Philosophicus.
I aim to begin by discussing some challenges to the correspondence theory.
Frege attacks the correspondence theory and proposes his own theory of truth,
and deflationism is a popular and highly intuitive account of truth. A powerful
and clever argument known as the slingshot has been used to critique
correspondence theories. This all requires some discussion, and the slingshot
raises a number of crucial issues about the structure of beliefs and assertions
which must be dealt with.
I will then move on to consider the challenge presented to all theories similar
to the picture theory which develops from the classic debate between Austin and
Strawson. Correspondence theories of Austin's type are, I think, decisively
inferior to those of Wittgenstein's type.
I will then construct a picture theory, building from Wittgenstein and from
Russell and Frege. The point of doing this will be to have an intrinsicist
theory as a foil; this is where I will be working according to the heuristic
mentioned before. This intrinsicist theory will involve a number of ontological
commitments which are, I think, mistaken. In the next section I will criticize
the theory I've constructed and present the preferred ontology, in which universals
are replaced with sets of similar 'tropes' (property-instances) and bare
particulars are replaced with 'bundles' of tropes. Here the preferred ontology
appears to be Rand's.
In the final section — after discussing some of Rand's and Peikoff's remarks on
truth — I will show how the ontology of bundles and tropes works with the
earlier discussion of the structure of our beliefs and assertions within the
general idea of a picture theory to generate a theory of facts and
correspondence.
In this section, I will discuss Frege's
comments on truth, the minimalist alternative to substantive theories of truth,
and the argument known as the slingshot.
Frege's view of truth seems to have two major components. First, truth is not a
property of sentences, beliefs, or thoughts. Second, the referent of a sentence
is its truth-value. The two claims are linked in the following way. A sentence
of the form "'p' is true" appears to have subject-predicate form,
with 'is true' as the predicate. If this were the case, then being true would
have to be a property. However, since Frege will argue that it is not, he must
give an alternative analysis of sentences of this form. The alternative
analysis appears to be that the hidden structure of sentences of this form is,
"'p' refers to the True", or perhaps that the hidden structure is an
identity claim: "the referent of 'p' is identical to the referent of
'True'". Frege's arguments for each of these two claims seem uncompelling.
Let us look first at the proposal that truth is not a property.
Frege's main argument for this view involves a regress on any substantive
theory of truth as a property. He appears to give the argument here:
...could we not maintain
that there is truth when there is correspondence in a certain respect? But
which respect? For in that case what ought we to do so as to decide whether
something is true? We should have to inquire whether it is true
that an idea and a reality, say, correspond in the specified respect.
And then we should be confronted by a question of the same kind, and the game
could begin again. So the attempted explanation of truth as correspondence
breaks down. And any other attempt to define truth also breaks down. For in a
definition certain characteristics would have to be specified. And in
application to any particular case the question would always arise whether it
were true that the characteristics were present. So we
should be going round in a circle. (Frege 1918, 327)
As I see it, three different arguments,
of varying plausbility, can be read from this passage. The least plausible
argument (and probably not one Frege had in mind) suggests that defining truth
would lead to a circle; this argument can be read from the last three
sentences. It would go like this. We ask whether 'p' is true. But we have
defined 'true' somehow: truth is the property (of a belief or assertion) of
corresponding to the fact held to obtain (by that belief or assertion) — for
short, 'correspondence'. So we can know that 'p' is true only if we know that
'p' corresponds. But we know that 'p' corresponds only if we know that 'p' is
true. So we are in a circle.
This argument fails. Consider a different case. We ask of a certain organism
(called 'O') whether it is a person. But we have defined 'person' somehow; let
us say as the rational animal. So we can find out whether O is a person only by
finding out whether it is a rational animal. But we will know whether O is a
rational animal only if we know whether it is a person. So we are in a circle.
Does this mean that being a person is not a property? Surely not. How does this
argument go wrong? It goes wrong in assuming that replacing 'true' with
'corresponds to the facts', and then replacing 'corresponds...' with 'true',
involves a circle which is in any way significant. Assuming an extensional
context and that 'corresponds' is a good definition of 'true', the replacements
are not replacements at all in terms of meaning; rather, they are mere
rewordings. Replacing 'is true' with 'corresponds' and vice-versa is circular only in the sense that changing "'p' is
true" to "it is true that p" and vice-versa is
circular; the sentences have exactly the same meaning.
The second argument also involves a regress on an analysis of 'true'. This one is
suggested by an alternative reading of the same three sentences as the last,
and goes like this. Assume the same definition of 'truth'. We ask whether 'p'
is true. But to know that 'p' is true, we would have to know whether 'p'
corresponds. But to know this, we would have to know whether "'p'
corresponds" is true. But to know this, we would have to know whether
"'p' corresponds" is true" corresponds, and in turn would have
to know whether "'p' corresponds" is true" corresponds" is
true. So we are involved in a regress in which the even-numbered steps involve
'true' and the odd-numbered steps involve 'corresponds'.
However, let us assume that 'corresponds' is a good definition of 'true' and
that this argument uses only extensional contexts. In that case, 'corresponds'
and 'true' can be intersubstituted throughout the argument without making any
change. We will still have the same regress. The switching, at each step of the
regress, from 'true' to 'corresponds' gives us the appearance that it is
defining 'true' which yields the problem. But this is not the case. Rather, the
problem is that 'true', or its definition, can apparently be applied to
sentences in which 'true', or its definition, appear as predicates. This, and
not the fact that we have defined 'true', is what yields the regress. In fact,
if defining 'true' stopped the regress, we would know that we had
misdefined it. A good definition of 'true' ought to behave the same way as
'true', so if 'true' can generate a regress, then so ought its definition be
able to generate a regress.
To generate the third and strongest argument, suggested in the first five
sentences of the passage above, substitute a token of 'true' for every token of
'corresponds' in the regress of the second argument. This regress involves only
the claim that truth is a property, and does not rely on any claim about that
property's being definable. The regress looks like this. To know whether p, we
must know whether 'p' is true. But to know whether 'p' is true, we must first
know whether "'p' is true" is true. And so forth.
One might be tempted to respond to this regress similarly to the way I
responded to the first circularity claim, like this: the regress is not a
regress, because each step is identical to the one before. The claim that 'p'
is true is identical in meaning to the claim that p. However, to respond like
this is to adopt deflationism about truth. I will discuss deflationism below
and suggest some reasons why it ought not be adopted. (Frege, however, appears
to adopt a form of deflationism at Frege 1892, 158.)
Frege's regress is essentially epistemic in the following sense. It claims
that, were truth a property, we could never know whether p, because knowing
this would require that we know whether 'p' is true, and so forth. Frege thus
assumes that, if at time t, you
do not know that 'p' is true, you cannot at time t +1 know that p. Frege provides no argument for this
conditional, but moreover it does not seem to be correct. We can easily
conceive of someone knowing, for instance, that it is raining, without even
possessing the concept of truth. Children who are not linguistically reflective
might not think about the verity of their belief when they adopt it. There
could be a language in which no metalinguistic claims, such as claims about the
truth of sentences in that language, could be made; monolinguistic speakers of
that language would never believe that as assertion was true, they would simply
believe the assertion.
The regress requires the following logical equivalence: necessarily, p iff 'p'
is true. We can now define 'q' as the claim that 'p' is true and generate:
necessarily, p iff q. But we can also generate: necessarily, q iff 'q' is true.
It's this set of logical equivalences which generate the regress. But in general,
it is not necessary to know a given sentence to know other sentences which are
logically equivalent to that sentence. Were this the case, we could never learn
any logic or mathematics, because in order to know any basic mathematical or
logical claim [e.g., 2+2=4, "x(x=x)],
we would have to know Fermat's Last Theorem, which is logically equivalent to
all other truths of logic or mathematics.
Since anyone who understands the use of 'true' grasps the set of logical
equivalences which generate the regress, it's the case that anyone who knows
both the meaning of 'true' and that p is in a position to know that 'p' is
true, and that it's true that 'p' is true, and so forth. But the infinite
implications of p need not be known by us for us to know that p, nor need they be the same claim as the claim that
p. The fact that those who know the meaning of 'true' are put, by their
knowledge that p, in a position to know an infinite number of other things like
that 'p' is true, does not imply that all of these things are the same.
Before turning to minimalism, let me briefly look at Frege's other major
doctrine concerning truth: that a belief or assertion's truth-value is its
referent, just as a person is the referent of that person's name.
Frege's argument attempts to identity an assertion's referent with its
truth-value by a pair of premises, but this pair can be interpreted in two
ways. Here is the first interpretation.
First, we are concerned with the referent of a part of a sentence only when we
are concerned with the referent of the sentence as a whole (where we have a
concern with something just in case we wonder whether the something exists and,
if so, what it is). Second, we are concerned with the referent of a part of the
sentence only when we are concerned with the truth-value of the sentence. Since
having a concern with a part of a sentence is a sign both of concern with the
referent of the sentence and with the truth-value of the sentence, the referent
of the sentence must be its truth-value.
Let us assume that the two premises are correct. Nothing follows but that we
are concerned with the referent of a sentence only when we are concerned with
its truth-value. This is not an argument for identifying referent and
truth-value.
However, of the two premises, one is not justified and the other is false.
First, let us consider the premise that we have a concern with the referent of
a part of a sentence only when we are concerned with the referent of the whole.
Frege introduces this claim here:
Is it possible that a
sentence as a whole has only a sense, but no referent? At any rate, we might
expect that such sentences occur, just as there are parts of sentences having
sense but no referent. And sentences which contain proper names without
referent will be of this kind. The sentence 'Odysseus was set ashore at Ithaca
while sound asleep' obviously has a sense. But since it is doubtful whether the name 'Odysseus', occurring
therein, has a referent, it is also doubtful whether the whole sentence
does.... The fact that we concern ourselves at all about the referent of a part
of the sentence indicates that we generally recognize and expect a referent for
the sentence itself. (Frege 1892, 156-7; I replace 'Bedeutung ' with 'referent' throughout)
Note the opening question of this
passage: Frege is wondering whether or not sentences have referents. He then
claims that we have a concern with whether or not a proper name appearing in a
sentence has a referent only if we are concerned with whether or not the
sentence has a referent. But how does he know this? We don't yet know whether
sentences have referents; how are we to discover that they don't have referents
if their parts don't? What Frege says may be true, but it is in principle
impossible for Frege to argue for the claim at this point.
Frege accepts the idea that the sense of the parts of a sentence compose the
sense of the whole of the sentence. By composing the sense of the whole, the sense
of the parts determine the sense of the whole. While Frege will deny that the
referents of the parts of a sentence will compose the referent of the whole of
the sentence, he may think that the referents of the parts of a sentence will
still in some way determine the referent of the whole. If this assumption is in
the background, then Frege's point becomes that we have a concern with the
referent of the part of a sentence only when we are concerned with what that
referent (partly) determines: the referent of the whole. But this assumption,
however plausible it may be, requires defense which Frege does not give.
The second claim, that we are concerned with the referent of a part of a
sentence only when we are concerned with the truth-value of the whole, seems to
appear here:
...why do we want every
proper name to have not only a sense, but also a referent? Why is the thought
not enough for us? Because, and to the extent that, we are concerned with its
truth-value. (ibid, 157; I
replace 'Bedeutung ' with 'referent'
throughout)
This claim is false. There are sentences
which are known to be untrue, but which contain proper names about which we may
wonder whether they have referents. I am quite confident, for instance, that no
one has ever received any commandments from God. So I am quite confident that
it is not the case that Moses ever received any commandments from God. This
confidence is quite consistent with wondering whether or not Moses existed. In
general, wondering whether a proper name has a referent is consistent with
already believing that a sentence in which that name appears is not true.
Why might Frege have introduced this premise? The assumption which may have
rendered the first premise plausible was that the referents of the parts of a
sentence determine the referent of the sentence. This premise requires defense.
However, it is surely the case that the referents of the parts of a sentence
determine the truth-value of that sentence. Whether a sentence is true or false
depends on how things stand with the referents of its parts. Frege may have
assumed, then, that we cannot be concerned with the referent of a part without
being concerned with what that referent (partly) determines: the truth-value of
the whole. But, as my Moses example shows, this is not true.
We could, however, interpret Frege's argument differently. The second
interpretation preserves the first, unjustified, premise, but replaces the
second, false, premise with a different premise which Frege may introduce here:
In hearing an epic
poem... we are interested only in the sense of the sentences.... The question
of truth would cause us to lose aesthetic delight for an attitude of scientific
investigation.... It is the striving for truth that drives us always to advance
from the sense to the referent. (ibid,
157; I replace 'Bedeutung ' with
'referent' throughout)
What exactly this means turns on what the
last sentence refers to. Does it refer to the referent of a part of a sentence?
In that case, Frege does not make the following argument. However, it may refer
to the referent of the whole of a sentence. In that case, Frege's second
argument has as its second premise that we are concerned with the referent of
the whole only when we are concerned with the truth-value of the whole. The whole
argument, then, is this: we are concerned with the referent of a part only when
we are concerned with the referent of the whole, and we are concerned with the
referent of the whole only when we are concerned with the truth-value of the
whole. Thus, the referent of the whole is the truth-value of the whole. This
argument seems to be even weaker than the previous one. Here is a suggestion as
to what Frege may be trying to do.
He is trying to show the identity between two things: sentence-referent and sentence's
truth-value. How do we justify the introduction of identity claims, such as the
claim that the Morning Star is the Evening Star? One way might be to show the
same thing — e.g., Venus — under both of its aspects and get us to agree that
the two aspects are aspects of the same thing. Thus what Frege is trying to do
is get us to look at what sentences refer to under both of its aspects:
sentence-referent, and truth-value. We will then see that being the referent of
a sentence and being Truth (or Falsity) are the same. This would be analogous
to showing that being the Morning Star is the same as being the Evening Star.
However, Frege is working under a handicap: he hasn't shown that sentences have
referents. This would be like trying to show that the Morning Star is the
Evening Star under the circumstance that no one had ever seen the Morning Star.
Frege's claim that we have a concern with the referent of a part only when we
have a concern with the referent of the whole is an attempt to show us the sentence-referent.
Having given us a sign of the sentence's referent — it's the other thing we
have a concern with when we have a concern with the referent of a part, or
perhaps it's the thing, our concern with which makes us have a concern with the
referent of a part — he can then try to show that whatever having a
concern with the referent of a part is a sign of, it is also the truth-value of
the sentence. However, since the first premise is still unjustified, this
argument cannot succeed. Having a concern with the referent of a part is not a
sign of having any other concerns, as the example of Moses suggests.
Whatever intuitive appeal Frege's position may have can, I think, be captured
by a correspondence theory of truth. Let us define the referent of a true
assertion as that fact the obtaining of which makes the assertion true. Let us
further suggest that facts are composed of the referents of words in sentences
(justifying this suggestion is the burden of later parts of this paper). So the
fact which makes an assertion true — the referent of that sentence — is
composed of the referents of the part of the assertion. But the truth-value of
an assertion is determined by whether the assertion has a referent, and hence
how things are with the referents of the parts of the assertion. So the
referents of the parts constitute, and so determine, the referent of the whole,
and also determine the truth-value of the whole, though the referent and
truth-value of the whole are not identical.
Now let us turn to deflationism about truth, which was the other possible
response to Frege's regress argument that truth is not a property. Various
versions of deflationism about truth have been held by Frege (Frege 1918),
Strawson (Strawson 1949, 1950b, 1965) and Horwich (Horwich, 1998) among a great
many others. Contemporary versions of deflationism typically take off from
Tarski's (Tarski 1944) theory of truth for formal languages, and claim that
after we have given all of the T-sentences — that is, all sentences of the form
"'P' is true if and only if P" — we have said all that there is to
say about truth. Deflationism's positive content consists in its explanation of
what we use the phrase 'is true' to do. Strawson has suggested that
"...any sentence beginning 'It is true that...' does not change its
assertive meaning when the phrase 'It is true that' is omitted. More generally,
to say that an assertion is true is not to make any further assertion at all;
it is to make the same assertion." (Strawson 1949) If this is correct,
then why would we have these phrases? Notice that the sentence which is said to
be true in "'P' is true" is given within single quotation marks. This
means that the grammatical subject of this sentence is a name: ''P'' names 'P'.
There are occasions on which we may wish to make a great many assertions at
once, and not want to spend a great deal of time with it. In that case, we can
whip out a name for all of the assertions we wish to make, and use this name as
the grammatical subject of a sentence similar to "'P' is true", such
as "Everything Frege ever said is true". By uttering this sentence,
one can assert everything Frege ever asserted at once. The predicate 'is true'
makes this possible, but this is its only important role (aside from letting us
be emphatic and so forth).
However, deflationism is not without its critics (see, for instance, Gupta
1993). I want to make two criticisms of deflationism, not so much to decisively
refute the theory as to show why other projects (such as a correspondence
theory) are worth pursuing when there is such a simple and intuitively
plausible alternative available in deflationism.
Let us consider our sentence which illustrated the point, according to
deflationism, of the truth-predicate: "Everything Frege ever said is
true". If we use this sentence to make each and every assertion which
Frege ever made, then the sentence ought to have exactly the same meaning,
compressed, as P & Q & so
forth, where Frege said 'P' and 'Q' and so forth. But this is not the case. A
conjunction does not, in general, have the same meaning as a universally
quantified sentence which, after universal instantiation, is made true by just
those constants which appeared in the conjunct. "x(Fx) does not have the same
meaning as Fa & Fb & so
forth. This is because the universally quantified sentence implies a negative
existential claim, while the conjunction does not. If "x(Fx), then ¬$x(¬Fx). But Fa & Fb & so forth does not imply
this. Two sentences which are unlike in logical implication can hardly be said
to be alike in meaning.
A second, related point, is this. We have certain beliefs about truths in
general, such that they will result from a rational course of inquiry and that
believing them is more likely to lead to success in action than believing
falsehoods. Presumably, we come to these universal convictions by a form of
induction. We can vary the rationality of our courses of inquiry and see that
the truth-value of the results of inquiry also varies; we can vary the
truth-value of our beliefs and see that the success of our actions also varies.
We can perform this sort of inductive inference, though, only if there is a
property, truth, which we observe to co-vary with rationality and success. But
deflationism denies the existence of such a property, or at least denies that
it is a property in the substantive sense necessary for an inductive argument
to turn on it. So if deflationism is true, we could never justify these
beliefs. Perhaps the beliefs are unjustified, but it seems more likely that
deflationism is not true.
Let me now turn to the slingshot. The slingshot is an argument which has been
used (e.g. in Davidson 1967) to attack correspondence theories of truth. An
important service rendered by Neale (in Neale 1995; see also Neale and Dever
1997) in his complete discussion of the slingshot is the clarification of
exactly how the slingshot works and how to avoid its implications. Here, I will
discuss the basic nature and implications of the slingshot, leaving out most
details; this discussion is sketchy at best but should serve.
The slingshot works because it applies two inference rules, which are valid in
extensional contexts, within the context of a certain sentential operator to
show that all sentences are made true by the same fact.
The first inference rule is that, given a sentence Fa we may substitute
the sentence a = (i x)(x=a & Fx),
and contrariwise, given a = (i x)(x=a & Fx)
we may substitute Fa . (‘i’ is ‘the’) This is
known as iota-conversion. (Neale 1995, 788-9) For example, we are able to infer
from 'Caesar is bald' that 'Caesar is the thing who is Caesar and bald', and
vice-versa.
The second is that, given a sentence G(i x)(Fx) and that (i x)(Fx)=(i
x)(Hx), where 'F', 'G', and
'H' are ordinary predicates, we may infer G(i x)(Hx). This is known as
iota-substitution. (Neale 1995, 784-7) Here is an example. The table at which
I'm sitting is white, and the table at which I'm sitting is the table on which
is my computer. So the table on which is my computer is white. I take it that
both of these inference rules are intuitively obvious.
To run the slingshot in a way that makes a difference to theories of facts, we
need to introduce the notion of a sentential connective. (Neale 1995, 780-783)
Neale defines a sentential connective as "any expression that combines
with one or more sentences to form a sentence..." (ibid, 781). For instance, if we have the
sentences "The bridge collapsed" and "The steel was weak",
we may use the sentential connective "...because..." to form the new
sentence "The bridge collapsed because the steel was weak". Given the
sentence "a=a", we may use the sentential connective
"necessarily..." to form the new sentence "Necessarily,
a=a". Given the sentence "Kant is hard to read", we may use the
sentential connective "unfortunately,..." to form the new sentence
"Unfortunately, Kant is hard to read".
Let us define the truth-maker-connective (hereafter, TM-connective) "'Fa'
is made true by the fact that ( )". The sentence with which the
TM-connective combines replaces the parentheses and the space between them. The
TM-connective might, then, combine with the sentence Fa to generate the
true sentence "'Fa' is made true by the
fact that Fa", or it might combine with the sentence Gb
(where Fa and Gb are intuitively very different claims, such
as "Grass is green" and "Snow is white") to form the false
sentence "'Fa' is made true by the fact
that Gb ". If we could somehow infer the latter sentence from
the former, we would have brought about a disaster for the correspondence theory
of truth. We would have shown that a true sentence is made true not just by the
fact that we expected would make it true — the fact that it represents — but by
every fact. If "grass is green" is made true by snow's being white,
then every fact makes true every sentence. Alternately, if we think that there
is only one fact which can make a given sentence true, then, since every fact
makes true every sentence, there is only one fact.
The slingshot is the means by which we can, in fact, infer the latter sentence
from the former. We assume that two sentences are materially equivalent — that
they have the same truth-value — but that they do not intuitively state the
same fact. The sentences are Fa and Gb ,
and we show that they do not intuitively state the same fact by assuming that ¬(a=b) , that $x(Fx & ¬Gx)
, and that $x(¬Fx
& Gx) ; thus the sentences
are about different things and assert different properties of the things. The
sentences might be "Aristotle is funny" and "Bertrand is
grouchy". We further assume that 'Fa'
is made true by the fact that Fa . From these four assumptions, Fa, Gb,
¬(a=b), and 'Fa' is made true by the fact that Fa, we
can show that 'Fa' is made true by the fact
that Gb. The structure of the argument can be seen at Neale 1995,
789-90, and for reasons of space I'll just leave it at the reference.
However, all is not lost. What the slingshot shows is that the TM-connective
allows for the substitution of materially equivalent sentences if, but only if,
it allows for iota-conv and iota-sub from one TM-connected sentence to another.
Iota-conv is necessary to infer from
‘Fa' is made true by the fact that Fa
to
'Fa' is made true by the fact that a=(i x)(x=a & Fx)
and from
'Fa' is made true by the fact that b=(i x)(x=b & Gb)
to
'Fa' is made true by the fact that Gb
.
Iota-sub is necessary to infer from
'Fa' is made true by the fact that a=(i x)(x=a & Fx)
to
'Fa' is made true by the fact that a=(i x)(x=a & ¬(a=b)).
All of these inferences and others of the
same form are necessary to make the slingshot work. What this means is that, if
it is possible to infer according to iota-sub and iota-conv from one
TM-connected sentence to another, then it is possible to infer from a
TM-connected sentence which says that 'Fa' is true because of the fact that Fa
to another TM-connected sentence which says that 'Fa' is true because of the
fact that Gb. There are exactly three possible solutions to the slingshot which
can preserve the correspondence theory of truth: deny iota-sub, deny iota-conv,
deny both. I suspect that both should be denied, on independent grounds.
However, here I'll only consider iota-sub, which I think should definitely be
rejected. (For a critical discussion of iota-conv, see Searle 1995, 225-6)
Let us consider iota-sub. Should we be able to infer from
'Fa' is made true by the fact that a=(i x)(x=a & Fx)
to
'Fa' is made true by the fact that a=(i x)(x=a & ¬(a=b)?
I don't think so. In general, this sort
of substitution in extensional contexts is necessary for each of the following
inferences: from
F(i
x)(Gx)
(i
x)(Gx)=(i
x)(Hx)
to
F(i x)(Hx)
and from
(i
x)(Fx)=(i
x)(Gx) and (i x)(Gx)=(i
x)(Hx)
to
(i
x)(Fx)=(i
x)(Hx) .
Surely both of these substitutions are
valid: co-referring terms are intersubstitutable salva veritate. However, this kind of substitution is valid
only in extensional contexts, and sentences within the TM-connective seem to be
in an intensional context. So within this context, the inference is no longer a
valid one.
Consider, however, the same situation with respect to names, rather than
definite descriptions. It is possible to infer from
Fa
a=b
to
Fb
and it is possible to infer from
a=b
b=c
to
a=c
and these are arguably even
intersubstitutable within the context of the TM-connective: many have thought
that a=b is indeed made true by the same fact that
makes true a=c (if both of these sentences are true).
However, there are sentential connectives (those defining intensional contexts)
for which this is not the case. Consider the G-connective: "George
wondered whether..." George is not much of an astronomer, but he is a
curious sort; a bit of an idealist, he would like to think that all is one.
'Hesperus' and 'Phosphorus' are names
of the planet Venus, but George knows them as names of a bright light which
appears in the evening, and an apparently distinct bright light which appears
in the morning. We are apparently able to infer from "George wondered whether
Hesperus is Phosphorus" to "George wondered whether Hesperus is
Hesperus" because we can substitute the one name for the other. But this
does not seem right.
When faced with this problem, Frege (Frege 1892, 151-3, 160-161) introduced
senses — which are semantic values of referring words distinct from and
determining their referents — and suggested that when words appear within
intensional contexts they take their ordinary sense as their reference. (In
Frege's original theory, senses were Platonic entities; in contemporary
versions, senses are mental entities. I will be discussing contemporary
versions.) For example, the word 'Hesperus' has a referent, the planet Venus,
and a sense. The sense is whatever it is that we grasp when we understand the
meaning of the word 'Hesperus'. It is because we express the sense of
'Hesperus' when we utter it that we refer to its referent. If we think
'Hesperus is hot', then the content of our thought is the sense of the word
'Hesperus', the sense of the word 'hot', and so forth. When we are discussing
someone's thoughts, then, we are referring to senses. When we say that someone
thinks (wonders, imagines, and so forth) something and use a sentence to
specify the something, the sentence takes its ordinary sense as its referent.
Thus, we could not substitute 'Hesperus' for 'Phosphorus' within the
G-connective, because though 'Hesperus' and 'Phosphorus' are ordinarily
co-referential, within the G-connective, they are not.
There is an easier and less ontologically expansive solution to this problem
(whether the ontological expansion occurs in a Platonic realm or in our minds).
Instead of introducing senses to explain why co-referential names cannot be
substituted within intensional contexts, we could adopt the solution which
Frege had adopted in the Begriffsschrift (Frege 1879, 64) and think of names as
definite descriptions. Frege is considering the nature of identity claims,
specifically a=a and a=b.
These ought to be different claims in some sense, but they seem to be the same
because they each make reference, twice, to the same thing and assert that the
thing is self-identical. But Frege asks what we are actually saying when we
claim that a=b. Are we asserting
a's self-identity? Or are we asserting a meta-linguistic claim about the names
'a' and 'b ', to the
effect that they are co-referential? He suggests that the latter is the case.
If this is right, we can read the two claims as, respectively, "the thing
called 'a' is the thing called 'a '" and "the thing called 'a' is the thing called 'b '".
These are clearly different, which is as it should be.
There is a problem with this meta-linguistic solution. Consider the Hesperus-Phosphorus
case again. Imagine that a Chinese astronomer, who has never heard the language
in which 'Hesperus' and 'Phosphorus' are words, discovers that Venus, the
bright light which appears early in the morning, is Venus, the bright light
that appears early in the evening. It seems that the Chinese astronomer has
discovered the same thing that speakers of the language in which 'Hesperus' and
'Phosphorus' are words assert when they claim that Hesperus is Phosphorus. But
the claim that the latter speakers assert is that "the thing called
'Hesperus' is the thing called 'Phosphorus'". The Chinese astronomer
probably didn't discover that. So the meta-linguistic solution fails. I think,
though, that it gives the correct form for the solution. I'll return to the
point later. For now, let's pretend that the meta-linguistic solution
succeeded.
Recall that we are apparently able to infer from "George wondered whether
Hesperus is Phosphorus" to "George wondered whether Hesperus is
Hesperus" because 'Hesperus' and 'Phosphorus' are co-referential. But if
we treat 'Hesperus' and 'Phosphorus' as definite descriptions in this context,
then the inference will fail. We cannot infer from "George wondered
whether the thing called 'Hesperus' is the thing called 'Phosphorus'" to
"George wondered whether the thing called 'Hesperus' is the thing called
'Hesperus'".
However, it's not at all clear that progress has been made. Traditionally, it
has been assumed that definite descriptions are very much like names in that
they are used to refer to that which they describe. If this is the case, then,
even after we analyze names so that they turn into definite descriptions, we
will still be left with linguistic entities which can be manipulated just like
names can. The great achievement of Russell in his seminal paper "On
Denoting" was to solve this problem by treating definite descriptions not
as referring phrases but as incomplete symbols.
Russell puts forward his theory of descriptions to solve three puzzles, only
one of which will concern us here. Russell discusses the case which I have used
the G-connective to discuss: "...George IV wished to know whether Scott
was the author of Waverly ; and
in fact Scott was the author of Waverly. Hence we may substitute Scott for the author of 'Waverly', and thereby prove
that George IV wished to know whether Scott was Scott. Yet an interest in the
law of identity can hardly be attributed to the first gentleman of
Europe." (Russell 1905, 47-8) In essence, Russell is using the
G-connective with respect to 'Scott is the author of Waverly'. We should not be able to perform iota-sub within
the context of the G-connective because we will end up with George wondering
whether Scott is Scott, but if 'the author of Waverly
' is a referring term co-referent with 'Scott', then we are so able.
Russell's solution is to suggest that, contrary to appearances, definite
descriptions are not referring phrases. Rather, these are phrases which are
incomplete symbols and are only meaningful in the context of a complete
sentence in which they play a part. The correct analysis, Russell says, of
'Scott is the author of Waverly '
is not the identity 'Scott = the author of Waverly
', but rather the quantified $x["y(Wy « y=x)
& s=x] (where 'W' is 'wrote Waverly ' and 's' is 'Scott'): there is a
thing such that whatever wrote Waverly is that thing, and that thing is Scott.
Now, there is a new problem. The letter 's' in the symbolization and the name
'Scott' in the informal version of this analysis of 'Scott is the author of Waverly ' are names, but we analyzed
names, á la the early Frege, into definite descriptions. How shall we eliminate
this name from the analyzed sentence? First, we replace the name with a
definite description of Scott. Then, we analyze the description with a
predicate or set of predicates which uniquely determine what we had thought was
the referent of the name to be replaced. Thus, in place of the name 'Scott',
let us have the predicate 'Scottizes' (according to a suggestion in Quine 1948,
7-8). Thus 'Scott is the author of Waverly'
has, as its actual logical structure, $x["y(Wy « y=x) & Sx]:
there is a thing such that whatever wrote Waverly is that thing, and that thing Scottizes.
('Scottizes' is just a placeholder for a real set of predicates which uniquely determine
Scott. Also, a truly complete analysis would eliminate the name Waverly , but this need not concern us
here.) (Of course, the theory of descriptions is not uncontroversial. Critical
discussions appear in Strawson 1950 and Searle 1969; defenses appear in Quine
1948, Russell 1957, and Mates 1973; obviously this list is far from
exhaustive.)
This analysis of names and definite descriptions allows us to deny iota-sub in
the context of the TM-connective. This is because it is incorrect to infer from
"The sentence
'There is a thing such that whatever wrote Waverly is that thing, and that thing Scottizes' is
made true by the fact that there is a thing such that whatever wrote Waverly
is that thing, and that thing Scottizes"
to
"The sentence
'There is a thing that Scottizes which Scottizes' is made true by the fact that
there is a thing such that whatever wrote Waverly is that thing, and that thing
Scottizes".
Now let us return to the nagging issue from our discussion of Frege: the
problem that the meta-linguistic account of names cannot succeed. However,
unless we are to have senses as semantic baggage, then we must give an analysis
like Frege's in structure. That is, we must analyze names into definite
descriptions somehow, even if not according to the meta-linguistic route. I
think that the best move to make here is to follow the suggestions of Kripke
from Naming and Necessity . This
may be surprising, given that I have rejected that names refer at all, but I
think that it can be made to work.
Kripke thinks of names as rigid designators:
Let's use some terms quasi-technically.
Let's call something a rigid designator if in every possible world it designates the
same object, a nonrigid or accidental designator if that is not the case. Of
course we don't require that the objects exist in all possible worlds.
Certainly Nixon might not have existed if his parents had not gotten married,
in the normal course of things. When we think of a property as essential to any
object we usually mean that it is true of that object in any case where it
would have existed. (Kripke 1972, 48)
...whereas Fregean theories of reference
make names nonrigid or accidental designators. Fregean theories do this by
placing a sense between the name and its referent. A name's sense, in
contemporary Fregean theories (such as that in Searle 1958) is made up of a
cluster of descriptions subjectively associated with the name which, together,
uniquely determine the referent of the name. This leads to certain problems
which Kripke discusses. Perhaps the worst such problem is this. Let us imagine
that the name 'Aristotle' has, as its sense, a cluster of descriptions
including 'writer of the Metaphysics
'. Now, whatever it is that we refer to with the name 'Aristotle', it must be
something uniquely described by the cluster of descriptions associated with
that name. In this case, we cannot say 'Aristotle might not have written the Metaphysics ', because whatever we refer
to with 'Aristotle' must have written that book. Otherwise, we wouldn't have
referred to him. This implies that it would have been impossible — in the sense
of inconceivable — for Aristotle to have failed to write the Metaphysics . But even the hardest
determinist would agree that it makes sense to think of Aristotle having failed
to write that book. The problem is that, given Fregeanism, the name 'Aristotle'
refers nonrigidly to whatever the descriptions one subjectively associates with
the name describe.
Thus, Kripke proposes, rather than believe that a name refers by way of a
cluster of descriptions which determine the appropriate reference, let us
believe that names refer directly to their referent, without any go-between.
While something like a cluster of descriptions is, no doubt, associated by us
with the names we use, this cluster is not the meaning of the name. Being
associated with this description is not a semantic property of the name, though
it may be an important property when we come around to explaining how we use
the name.
Now, the cluster of descriptions view seems very amenable to my own approach,
since I prefer that fully analyzed sentences contain no referring terms, only
predicates, variables, and operators. Given the cluster view, we can replace a
name with the cluster of descriptions associated with it; the descriptions
become predicates in the fully analyzed sentence. Thus, 'Aristotle was Greek'
becomes $x["y(Ay « x=y)
& Gx] (where 'A' is the
cluster of descriptions associated with Aristotle, and 'G' is 'Greek'.)
Kripke's view, by eliminating the cluster of descriptions, appears to make it
very difficult to give this kind of translation. 'Aristotle', it appears, is
ineradicably a name on Kripke's view. But Kripke continues to remark:
Suppose the reference of
a name is given by a description or a cluster of descriptions. If the name means the same as that description or cluster of descriptions, it will not be a
rigid designator. It will not necessarily designate the same object in all
possible worlds, since other objects might have had the given properties in
other possible worlds, unless (of course) we happened to use essential
properties in our description. (Kripke 1972, 57)
Notice the last phrase. If we could only
select out Aristotle's essential properties, and build our cluster of
descriptions out of them, then we could have both direct reference and fully
analyzed sentences without any referring items. This is because the directly
referring name would disappear into a cluster of descriptions which were
guaranteed to pick out the appropriate item; guaranteed because the desription
would list Aristotle's essential properties and we count something as Aristotle
because (but only because) it has Aristotle's essential properties.
We can see that what's wrong with the original cluster view is its
subjectivism. A name does not refer to whatever happens to match some
descriptions we associate with the name; rather, it refers to whatever has the
essential properties of the thing to which we intend to refer. So an
essentialist cluster view doesn't have the same problems as the Fregean cluster
view, but it also eliminates referring items from fully analyzed sentences.
How does this solve the original Hesperus-Phosphorus puzzle case? What we
discover is that the thing which has Venus's essential properties is itself.
The information carried by 'Hesperus is Phosphorus' that is not carried by
'Hesperus is Hesperus' is subjective information, dealing with different ways
that we might take the planet Venus. This explains why the names 'Hesperus' and
'Phosphorus' are not intersubstitutable in
intensional contexts : many intensional contexts occur when we are
discussing a human subject, and so subjective information would be expected to
have an effect on what we can say in such contexts.
In his debate with Austin, Strawson
(Strawson 1950b, 1965) makes some telling remarks against Austin's
correspondence theory of truth. These are interesting from our point of view
because they tell against Austin's theory, rather than the picture theory.
Since the picture theory involves us in some rather heavy metaphysics and deals
with a lot of issues that might well be avoided by having a correspondence
theory of the Austin type rather than the Wittgenstein type, we should justify
giving a picture theory as against a theory of the Austin type. Strawson's
critiques, it seems, do justify this.
Austin sought to wind his way between the picture theory, with its 'linguistic Doppelgänger ' (Austin 1950, 123) and the
deflationary theory, with its several problems. To do this, he postulates two
sets of conventions governing the correspondence of sentences to facts. First
are the descriptive conventions. These govern how the world must be for a given
sentence to be true. Second are the demonstrative conventions. These govern
which part of the world a sentence is correlated with. If a sentence is
correlated to a part of the world by the demonstrative conventions to which it
is also correlated by the descriptive conventions, then it is true.
An example may help. The sentence "The cat is on the couch", as
uttered by me now, is correlated by demonstrative convention to my cat Apollo's
being on the couch right behind me. But the sentence is also correlated by
descriptive convention to any situation in which the cat to which we refer with
'The cat' is on the couch to which we refer with 'the couch'. Since Apollo's
being on the couch is a the-cat's-being-on-the-couch type of situation, the
sentence is true.
Austin, then, hopes to avoid saying anything about the internal structure of
facts because he thinks that they lack any such structure. Sentences do not
represent the world because they share form with it, such that both sentence
and fact have a logical structure. Rather, sentences represent the world
because they are doubly correlated with states of affairs by conventions.
Strawson rejects Austin's distinction between the two sets of conventions. He
argues (Strawson 1965, 239) that
If the division of types
of convention is really a dichotomous division, we shall at any rate be able to
give a residual characterization of demonstrative conventions as all those
conventions relevant to the truth or falsity of statements which are not
descriptive conventions. But now we must ask how well Austin's positive
characterization of demonstrative conventions fits this residue of
non-descriptive conventions. The positive characterization... is this: demonstrative
conventions correlate particular utterances of sentences with particular
historical situations... to be found in the world. But this characterization is
surely too ample for any residue of conventions that remains when descriptive
conventions have been subtracted; for it embraces descriptive conventions too.
It would be most unplausible to maintain that none of the latter has any part
to play in correlating sentences as uttered with particular historical items to
be found in the world... (Strawson 1965, 239)
Strawson's point is that the conventions
which govern which type of situation a sentence must be correlated
with are exactly the same as those conventions which determine which particular situation a sentence will be correlated with. So there is no
correlation but the descriptive one. In general, Strawson's point is that the
referring part of the sentence determines what thing in the world is under
discussion, and the predicative part of the sentence then determines what that
thing must be like for the sentence to be true. But there is no general set of
correlations between the sentence and the world. This is surely correct, and
militates decisively against Austin's theory.
However, it seems that Austin's theory suffers from a further, perhaps more
severe defect. Among the things which we sometimes say to be true are not only
sentences but thoughts or beliefs. What sort of conventions govern the
correlations between thoughts and situations? Some thoughts must be had before
any convention is adopted, because otherwise there could not be thoughts about
conventions. So the relation between truth-bearer and truth-maker cannot be a
wholly conventional one.
Another of Strawson's points is that facts and true sentences match both ways.
We introduce facts into discourse just to have something to make our sentences
true. The conviction that there are facts is, in this regard, quite unlike the
conviction that there are referents of names. We do not introduce referents of
names in order to have something to which to refer; rather, we introduce
referring in order to refer to referents of names. Since we designed facts to
be the sort of thing which make our sentences true, it comes as no surprise
that they do this. Strawson makes the point like this: "Of course,
statements and facts fit. They were made for each other. If you prise the
statements off the world you prise the facts off it too; but the world would be
none the poorer." (Strawson 1950b, 197) The point is that facts, by their
very nature, match in structure the sentences they were designed to make true.
Since Strawson thinks that it is absurd to populate the world with 'linguistic Doppelgänger ', but since facts are
necessarily linguistic Doppelgänger
, it is absurd to believe in facts. But there is no explanation offered for why
it is absurd to believe in linguistic Doppelgänger
.
From our point of view, what's important about this claim of Strawson's is
that, if it is correct, then facts, if they exist at all, are linguistic Doppelgänger . But this is just exactly
what they should be if a picture theory is correct.
Austin does not appear to respond to this point, but Searle does in introducing
his own Austin-like theory of truth. In general, Austin's theory suffered from
a failure to explain what facts are and from a failure to get sentences to
represent the world such that they could correspond to it — the demonstrative
conventions were his attempt to do this. Searle's theory is just as vague. But
he does argue against the view that facts are necessarily structured to match
the sentences which state them:
The word
"fact" in English has come to mean that in virtue of which true
statements are true. This is why Strawson is right to think that in order to
specify a fact, in order to answer the question "which fact?" we have
to state a true statement. When it comes to specifying their essence, facts can
only be stated and not named.
But it does not follow
that facts are somehow essentially linguistic, that they have the notion of
statement somehow built into them. On the contrary, on the account I have given
they are precisely not linguistic because the whole point of having the notion
of "fact" is to have a notion for that which stands outside the
statement but makes it true, or in virtue of which it is true, if it is true.
(Searle 1995, 211)
In one sense, the disagreement between
Searle and Strawson comes down to a question of social construction. Strawson
thinks that the facts are socially constructed; they are there only insofar as
we treat them as being there for the purposes of making our statements true.
Searle, on the other hand, thinks that the facts are basic to the world, and
only the notion of fact is constructed, and only because all
concepts are constructed.
Why should we adopt one view rather than another? There is no reason to think,
with Wittgenstein (2.161), that all representations must match in terms of
structure that which they represent. Perceptual experience does not match the
structure of its objects. (Kelley 1986) But there is good reason to accept that
many representations can represent their objects only because they share
structure with what they represent. Maps can only represent geography because,
like the geography they represent, they are spread out in space. An audio
recording is a representation of that of which it is a recording only because
it is spread out across time. On which side of this divide are truth-bearers,
whatever they may be?
Despite the fact that some representations do not share form with what they
represent, all representations can represent what they represent only in virtue
of some feature(s) that they possess. Visual experience represents the world
because of its causal connections with the world and the regularity of the
correlation between felt experience and perceived features. Maps represent
geography only because they look something like what the mapped area would look
like from very high above. And so forth. What are the features of truth-bearers
in virtue of which they can represent? Whatever these features are, they must
be possessed both by thoughts and sentences, and so cannot involve spatiality,
being perceivable, or even conventions.
I shall not attempt to say how, in general, concepts are representations of the
world. But they do represent sets of objects or properties. Whatever it is
about truth-bearers that makes it possible for them to represent facts cannot
be possessed by individual concepts, which cannot represent facts. The
differences are twofold. On the one hand, truth-bearers are constituted by
multiple representations of sets of things in the world. On the other hand,
these representations are structured in the truth-bearer. They are not simply
agglomerated. (Wittgenstein 3.141) It's something about this multiplicity and
structure which allows truth-bearers to represent facts. But if it's
specifically this multiplicity and structure which allows truth-bearers to
represent facts, then what is it about facts that allows them to be represented
by structured things with multiple internal representations of sets of objects?
The most natural answer is: because they consist of the things represented by
the representatives within the truth-bearer, and because those represented
things stand in some relation which is represented by the structure of the
truth-bearer.
And this seems correct. "The cat is on the couch" is true in virtue
of how things go with the cat, the couch, and being on. Were we to remove one
of these things from the world, we would have made the sentence no longer true.
But the order of the representatives in the sentence is equally important. Were
the cat and the couch related such that one of them were on the other, but in
the wrong order, the sentence would again be false. Facts can make sentences true only because they consist of the
referents of the words in the sentence, and because those referents are
structured just as the sentence says they are . Without this common
structure, facts could not make sentences true and sentences could not
represent facts. Strawson and Searle owe us an explanation of why this is
absurd; they don't give us one. In light of the failure of Austin's theory to
explain how sentences represent the world, and Searle's failure to even try to
do this in a way inconsistent with the picture theory but consistent with any
correspondence theory, we should feel free to continue to pursue a picture
theory.
The goal of this section will be, first,
to present Wittgenstein's picture theory as he gives it in Tractatus
2-2.225, and then to fill in the gaps which concern me with features
drawn from Russell's closely related logical atomism and from Frege's ontology,
which was influential on Wittgenstein. We shall assume that both beliefs and
assertions are pictures, and so what Wittgenstein says about pictures will
apply to both beliefs and assertions.
For Wittgenstein, facts are arrangements of objects. He says a little about the
objects, and about their arrangements. First, let us consider objects. At
2.011, Wittgenstein says that "It is essential to things that they should
be possible constituents in states of affairs", at 2.014 that
"Objects contain the possibility of all situations". Here, 'states of
affairs' and 'situations' are facts. Objects go together to make up facts, and
it is their possible combinations that make facts possible. Objects, though
they are not necessarily components of any given fact (2.021: "Objects
make up the substance of the world....", 2.024: "Substance is what
subsists independently of what is the case.", 2: "What is the case
[is] a fact..."), are necessarily components of some fact: "Things
are independent in so far as they can occur in all possible situations,
but this form of independence is a form of connection with states of affairs, a
form of dependence. (It is impossible for words to appear in two different
roles: by themselves, and in propositions.)" (2.0122). What Wittgenstein
means here is that a thing is independent of a particular state of affairs just
insofar as it can be imagined to have been a component of a different state of
affairs, and insofar as it might actually at a different time be a component of
a different state of affairs from the one of which it is presently a component.
It can never appear outside a state of affairs, just as a word can never
(meaningfully) appear outside a sentence.
Beyond constituting states of affairs, objects have an additional feature that
makes this possible, form: "Form is the possibility of structure"
(2.033), where "The determinate way in which the objects are connected in
a state of affairs is the structure of the state of affairs." (2.032). A
fact, then, has structure, which is the arrangement of the objects which
compose it. These objects have form, which is the possibility of the facts
which they can constitute. The general nature of facts, then, is to be constituted
by a structured group of objects which have being a member of this structured
group as possibilities.
An example may help. While one cannot be sure, Wittgenstein hints that the
possession of a particular color by a particular speck in the visual field
might be a fact. This is because, at 2.0131, when he is talking about objects
in general and giving examples, Wittgenstein says that:
A spatial object
[because of its spatial form] must be situated in infinite space. (A spatial
point is an argument-place.)
A speck in the visual
field, though it need not be red, must have some color: it is, so to speak,
surrounded by color-space. Notes must have some pitch, objects of the sense of touch some
degree of hardness, and so on.
Since Wittgenstein is talking about the
form of objects, we can assume that the speck in the visual field, the note,
and the object of the sense of touch are all objects and that having color,
pitch, and hardness are possibilities inherent in those objects. But not only
must specks in the visual field have some color, but colors themselves appear
to be objects. This is because Wittgenstein seems to indirectly attribute them
form at 6.3751: "For example, the simultaneous presence of two colors at
the same place in the visual field is impossible, in fact logically impossible,
since it is ruled out by the logical structure of color." Since we have
determined that specks in the visual field are objects, that Wittgenstein is
discussing their possible combination with something other than themselves —
color — is already evidence that Wittgenstein regards color as an object. How
else could color combine with those objects which are specks in the visual
field? But when Wittgenstein says that color has logical structure, and that
this is what makes it impossible for colors to appear in certain states of
affairs, he seems to be suggesting that color has form. This is because form is
the possibility of something's appearing in a state of affairs. But objects are
the things which have form. Moreover, it is 'logical structure' which
Wittgenstein is attributing to color, and logical structure is made possible by
form. It seems that Wittgenstein is indirectly or unclearly saying that colors
have form. Thus they must be objects.
In this case, an example fact might be that the speck in the visual field at
which I am looking at blue. The speck has form, which allows it to combine with
colors and requires it always to be so combined; the color has form, which
allows it to combine with specks in the visual field (and, perhaps, requires it
always to be so combined).
What does Wittgenstein mean when he says that a spatial point is 'an
argument-place'? Here, one can guess that he is alluding to the work of Frege.
Frege writes that:
Statements in general... can be imagined to be split up into two parts; one complete in itself, and the other in need of supplemen