Concepts, Facts, and Truth

Bryan Register


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)


I. Introduction

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.


II. Why Correspondence Theory?

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


'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)


'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)


'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)


'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)



F(i x)(Hx)


and from


(i x)(Fx)=(i x)(Gx)  and (i x)(Gx)=(i x)(Hx)


(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







and it is possible to infer from







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"


"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.


III. Why Picture Theory?

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.


IV. An Intrinsicist 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 supplementation, or unsaturated. Thus, e.g., we split up the sentence'Caesar conquered Gaul' into 'Caesar' and 'conquered Gaul'. The second part is unsaturated — it contains an empty place; only when this place is filled up with a proper name, or with an expression that replaces a proper name, does a complete sense [thought] appear. Here too I give the name 'function' to the referent of this unsaturated part. In this case the argument is Caesar. (Frege 1891, 139; I have replaced 'Bedeutung ' with 'referent')


Here, Caesar is the argument of the function referred to by the phrase 'conquered Gaul'. Since 'Caesar conquered Gaul' is true, and 'conquered Gaul' is a function, we may say that the referent of 'conquered Gaul' is a concept: "...a concept is a function whose value is always a truth-value." (ibid  139) What's key to functions, for Frege, is that they are 'unsaturated': "...a function by itself [without an argument] must be called incomplete, in need of supplementation, or unsaturated." (ibid  133) This is unlike what Frege calls objects: " object is anything that is not a function, so that an expression for it does not contain any empty place." (ibid  140) So Frege's picture is this. An assertion — an utterance which asserts a complete thought — makes reference with one part to an object, with another part to a concept, which is a truth-function. The object is the argument of this truth-function, which returns either truth or falsehood as truth-value. It's in virtue of their respective logical structures that the argument and the function — the object and the concept — are able to interact to generate a truth-value.

Likewise, it would seem, for Wittgenstein, whose spatial point is an argument. If this is the case, then properties which spatial points can exhibit should be truth-functions, that is, concepts. I do not say that Wittgenstein accepted this view, only that he might have done so, and could have done so without doing violence to the rest of his system. In general, the view suggested is that Wittgenstein was a realist, not a nominalist, in the Tractatus. (This view, by no means uncontroversial, is defended at greater length in Allaire 1963a). But Wittgenstein did not go into any detail about the nature of his arguments and functions (objects and concepts). Let us turn to Russell's writings of the same time for an account which may be of help in filling these gaps in Wittgenstein's account of facts.

It is obvious that arguments/objects and functions/concepts serve the same function in Frege's ontology that particulars and universals have traditionally served. Russell uses the traditional terms. For Russell, universals and particulars each serve two roles. Universals explain how different things can also be the same in some respect, and serve as the referents of predicates. Particulars explain how things which are identical with respect to properties can be distinct, and serve as the referents of names. Let us start with particulars.

For Russell, definite descriptions and ordinary names are not actually names at all, but complex propositional functions: "The names that we commonly use, like 'Socrates', are really abbreviations for descriptions..." (Russell 1918, 200) Nevertheless, he does accept a category of logically proper names which refer to particulars: "An atomic proposition is one which does mention actual particulars, not merely describe them but actually name them, and you can only name them by means of names.... The only words one does use as names in the logical sense are words like 'this' or 'that'." (ibid  200-1) These names serve as subject terms in sentences asserting the atomic facts, such as 'This is white'. The referent of 'this', a particular, is a sense-datum:


If you agree that 'This is white', meaning the 'this' that you see, you are using 'this' as a proper name.  But if you try to apprehend the proposition that I am expressing when I say 'This is white', you cannot do it. If you mean this piece of chalk as an actual physical object, then you are not using a proper name. It is only when you use 'this' quite strictly, to stand for an actual object of sense, that it is really a proper name. (ibid  201)


However, the particulars which Russell is introducing to play the role of referent of logically proper names are not the particulars which he had justified with the arguments of "On the Relations of Universals and Particulars". There, after having justified the introduction of universals to ground sameness, he introduces particulars to ground difference between qualitatively identical entities. Here is the argument. If two entities exhibited all and only the same universal characteristics and there were nothing to them but those characteristics, then they would not be numerically distinct. But it is surely possible for there to be a multiplicity of things which exhibit all and only the same characteristics. This is made possible by particulars. For each of the entities with all and only the same characteristics, there is a particular which possesses those characteristics. This particular is what individuates the entities. (Russell 1911, 112-3)

Let us now ask whether sense-data can individuate, or whether they themselves require individuation. Consider two identical patches of color, and ignore their spatial relations. These patches of color are sense-data, and they are identical with respect to characteristics: they possess the same shade of the same color, they are identical in shape, and so forth. Their numerical distinctness requires explanation, and we may introduce particulars to individuate them. But for just this reason, we may not employ sense-data themselves for the function of individuating other things. Particulars are not sense-data. (This is not to say that particulars are not given in perceptual experience, though the manner in which they are given is not quite clear. See Allaire 1963b for discussion.)

However, particulars were brought into the discussion of facts to serve as the referents of logically proper names. Can particulars which are not sense-data serve this role? They can (perhaps better than sense-data could have). This is because the particulars which were introduced to solve the individuation problem are the things which instantiate universals, or in which universals inhere. So, when I say "This is white", I have predicated whiteness over whatever sort of thing it is that the universal whiteness can inhere in, and this is, most naturally, a particular.

Russellian atomic facts, then, consist of a particular and a universal, and the inhering of that universal in that particular. There is no reason not to fill the gaps in Wittgenstein's account with these notions. Wittgensteinian facts, now, can consist of objects in relations, where some objects are particulars and some are universals. Objects may come in more than two flavors: there may be visual particulars and the universals which can inhere in them, and, distinctly, aural particulars and the universals which can inhere in them. But there is a distinction between two kinds of objects which gives us the outline of an ontology of facts.

With facts put in place between 2 and 2.063, Wittgenstein can move on to give the second part of a theory of truth, the discussion of truth-bearers and the correspondence relation. Wittgenstein says at 2.13-2.131 that "In a picture objects have the elements of the picture corresponding to them. In a picture the elements of the picture are the representatives of objects." Let us take Russell's atomic proposition "This is white." Applied to Russell's example, Wittgenstein's claim should tell us that 'This' refers to an object (a particular) and that 'white' refers to an object (a universal). What of 'is'? Perhaps 'is', along with the grammatical structure of the sentence, is discussed at 2.14: "What constitutes a picture is that its elements are related to one another in a determinate way." Logical operators and syntactic features of the sentence are there, perhaps, not to represent features of the world, but to relate the elements of the proposition to one another in a determinate way. 'Is' serves to indicate that the referent of 'this' and the referent of 'white' stand to one another on the exemplification relation: this exemplifies whiteness. This interpretation seems plausible because there is nothing other than this and whiteness to be referred to in the fact that this is white: just because this and whiteness will "fit into one another like the links of a chain" (2.03) there is no additional constituent of the fact that this is white, such as the exemplification relation, to be a referent of 'is'.

Wittgenstein's picture theory is concerned to show how it is that representations can represent. The basic idea is given at 2.15: "The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way." In a picture, elements are related to one another in some way. The picture depicts that the objects that its elements represent are identically related. That 'this' stands to 'white' as grammatical subject to predicate represents that this stands to whiteness as instantiating particular to instantiated universal.

At 2.221, Wittgenstein says that, "What a picture represents is its sense." Note that the relationship between a picture and its sense is the same one, representation, that the fact that 'the elements of a picture are related to one another in a determinate way' bears to 'that things are related to one another in the same way'. But at 2.14, Wittgenstein says that "What constitutes a picture is that its elements are related to one another in a determinate way." If we may substitute for a picture what constitutes a picture, then we may substitute for 'picture' 'that its elements are related to one another in a determinate way.'  Were we to make this substitution in 2.221, we would achieve a sentence identical to (the first sentence of) 2.15, except that the latter includes the phrase 'that things are related to one another in the same way' where the latter includes the word 'sense'. If pictures represent both of these things, it is reasonable to say that they are the same thing. We can then say that the sense of a picture is how it represents the world to be.

Now, at 2.131, Wittgenstein had said that, "In a picture the elements of the picture are the representatives of objects." If a picture represents its sense, and its elements represent objects, then it is not unreasonable to suggest that the sense of a picture is actually composed of the objects to which its elements correspond. We would accept the compositionality of sense: the idea that the sense of the whole of a picture is built up out of the senses of its parts. A certain ontological problem can thus be solved. When Wittgenstein says at 2.202 that, "A picture represents a possible situation [i.e., a fact] in logical space", we may reasonably wonder what is the ontological status of these possible facts. Are they in some realm of non-actualized possible facts? But if the sense of a picture is composed of the objects to which its elements correspond, and the sense of a picture — what it represents — is the same as the possible situation which it represents, then these possible facts are features of the objects which would compose them were they actual. Possible facts are possibilities of actual objects. If senses are meanings, then Wittgenstein can account for meanings without either saying that meanings are mental or that they reside in a Platonic realm (as Frege had suggested in Frege 1918, 337).

At 2.222-2.223, Wittgenstein completes his correspondence theory by saying that, "The agreement or disagreement of its sense with reality constitutes its truth or falsity. In order to tell whether a picture is true or false we must compare it with reality." If the sense or meaning of a picture — the possible fact it represents — is an actual fact, then the picture is true. The represented fact is an actual fact just in case it consists of all the objects represented, and these objects are related to one another just as their representative elements are related in the picture of the situation.


V. Bundles and Tropes

In the picture theory just developed, facts consist of bare particulars, universals, and the exemplification of the latter by the former. Entities are intrinsically distinct from one another, and intrinsically resemble one another, so facts are intrinsic constituents of the world. But Rand rejects both of the ontological commitments of the picture theory just discussed.

In that theory, universals were introduced to account for qualitative identity between entities, and bare particulars were introduced to account for numerical distinctness of entities. An alternative theory, one which Rand seems to have accepted, replaces universals with classes of what are called 'tropes', and entities with what are called 'bundles'. (Bundle theory is put forward in Stout 1921 and Stout 1923; trope theory in Williams 1953a and Williams 1953b.) Tropes can be characterized in (at least) two ways. First, were there universals, tropes would be the instances of them. For instance, pretend that whiteness were a universal. In that case, since the whiteness of p. 276 of Introduction to Objectivist Epistemology  is qualitatively identical to the whiteness of p. 277 of that book, the two whitenesses would be two instantiations of the same universal whiteness. Trope theory retains the individual instantiations of the property, but does away with the universal of which they are instantiations. There are simply the two color patches, and the fact that the two pages are both the same color must be explained with reference to something other than a universal which they both instantiate. The resemblance between the two color patches does the explanatory work. Second, tropes are respects in which entities can be similar or dissimilar to one another. For instance, take two entities which share color but have different shapes; say a red triangle and a red circle. The redness of the triangle is a respect in which it resembles the circle, while its triangularity is a respect in which it fails to resemble the circle. However, its having a having a shape and its having a color are both respects in which it does resemble the circle, since both the triangle and the circle have shape and color. Thus, the triangle's redness, its triangularity, and perhaps its being shaped and colored, are all tropes. Trope theory is thus a way of rejecting universals. Rand implicitly adopts trope theory when she rejects Aristotelian realism about universals (Rand 1990, 2)

Bundle theory, on the other hand, is a way of rejecting bare particulars. Bundle theory is the claim that entities consist exclusively of their properties; that an entity is just all of its properties bundled together. Rand appears to accept this when she says that, "No one attribute constitutes the whole entity, but all of them together are the entity — not 'possessed by' but 'are' the entity." (Rand 1990, 276) Also, Rand allows bare particulars to be rejected during this part of the discussions forming the appendices to her epistemological work:


Prof F: ...I have a memory or a misremembrance of someone saying that Objectivism does not accept the Aristotelian concept of "potentiality."

AR [Ayn Rand]: ...that wasn't me. Unless it was in some context of what Aristotle makes of it, as in regard to his form-matter dichotomy.

Prof E: Or if "potentiality" becomes the bare possibility of being something — as in his views on ultimate "prime matter." (ibid  286)


'Prime matter' is what philosophers in the Aristotelian tradition have called what I have been calling 'bare particulars'. Rand explicitly rejects the form-matter distinction, and fails to balk when Prof E claims that the notion of 'prime matter' is an instance of Aristotle making a mistake when he is working out his views on potentiality and change. We can take it that she does not accept the introduction of a theoretical entity which is distinct from the properties of an entity and in which those properties inhere. For Rand, "existence is identity" (Rand 1961, 125): something's existence and its identity — all of its properties — are the same. An entity is just all of its properties. This makes Rand's ontology a form of the bundle theory.

However, Rand does not deal with objections to the bundle or trope theories. I want here to deal with a few objections provided by Hochberg in various writings. I believe that Rand's anti-intrinsicism will allow her view to deal with these objections, while other versions of trope and bundle theory might find them more problematic.

The first objection to be dealt with is Hochberg's reiteration of Russell's well-known regress argument for universals. Trope theory is committed to rejecting the existence of any universals, including relational ones. This raises a problem when we attempt to explain how several tropes might be members of the same category. Let us say that a and b are members of the category F, and c and d members of the category G. Why might this be? Had we universals, we would say that a and b instantiate the same universal F-ness, and c and d instantiate the same universal G-ness. But we have no universals, so how can we justify our categorizations? Trope theorists, including Rand, appeal to the resemblances between a and b and between c and d.

Russell replies that, unless we are to make similarity  a universal, we have introduced two separate relations, similarity-of-a-to-b (s1), and similarity-of-c-to-d (s2). Now, why are s1 and s2 members of the same category, that is, why are they both similarities? Because there is a third similarity, similarity-of-s1-to-s2 (s3). But, since s3 is a similarity relation, as are s1 and s2, there are similarities between s3 and s1 (s4) and between s3 and s2 (s5). Naturally, s4 and s5 will be similar to one another, as well as to each of s1, s2, and s3, generating another group of similarity tropes, ad infinitum.  Hochberg claims that the regress is vicious because, "at any stage we have not specified sufficient conditions for the truth of the sentences involved." (Hochberg 1984, 196) Here is what Hochberg has in mind. When trope theorists claim that a is F, they must explain how a can be F by reference to a's similarity to other members of F. But this explanation is not complete until the similarity between a and other members of F (such as b) is fully explained, which requires us to introduce an infinite number of other similarity tropes. Since we must introduce an infinite number of explanatory entities to account for a's F-ness, we can never so account.

Before responding to the objection, I want to point out that it applies equally well to realists. Realism is the claim that qualitatively identical property-instances are numerically identical. This claim is either informative, or not. If it is not informative, then it should be abandoned in favor of the competitor theory, nominalistic trope theory. But if it is informative, then it must be informative to tell us that qualitatively identical property-instances are numerically identical. If this is the case, then there must be a relation, numerical identity, between various instances of the same property. But this relation must itself be a universal with multiple instantiations. Thus, its various instantiations bear instantiations of it to its other instantiations, resulting in a regress identical to the one the nominalist must have for similarity.

Beyond noting that this problem is as severe for the realist as it is for the nominalist, I think that Rand's version of nominalism is uniquely well-placed to solve this problem as it confronts nominalism because of two innovations with respect to the nature of similarity. For Russell and Hochberg, resemblance is a two-term relation between the two things which resemble one another. But for Rand, resemblance is a four(or more)-term relation between the two things which resemble one another, the subject which takes them to resemble one another, and the contrast object(s) which the resembling objects are both more dissimilar from than they are from one another. The realist's relation of similarity-between-a-and-b is replaced with the Objectivist's relation of similarity-between-a-and-b-to-S-in-contrast-to-C, where S is a subject with a conceptual faculty and C is a (or a set of) contrast object(s). The notion that a conscious subject's regarding things as similar is a prerequisite for their being similar, and that they are similar only in contrast to some third (fourth, etc.) thing(s) from which they are both more different, should allow us to solve the Russell problem.

First, the fact that similarity exists between two things only in contrast to other things makes it possible to grasp similarities without possessing the concept similarity. We can know that a and b resemble one another not because we have grasped the similarity relation which obtains between them, but because we perceptually experience them as more different from some contrast object than they are from one another. If this is the case, then we don't need to know that the similarity between a and b is a similarity trope in order to know that a is F. But this means that we don't need to know that that similarity trope is similar to other similarity tropes. So Hochberg is mistaken to claim that "at any stage we have not specified sufficient conditions for the truth of the sentences involved". We can specify sufficient conditions without pushing our grasp of a's similarity to b beyond the perceptual level.

Second, the fact that similarity exists between two things only in relation to a conscious subject which takes them to be similar eliminates all members of the regress that no subject has ever attended to. When Russell generates a regress of similarity tropes, he is actually creating the tropes by his unusual act of attention to the relations between similarities. The regress of similarity tropes is exactly as deep as we care to make it. Since we do not need to specify similarity relationships ad infinitum  in order to account for the truth of "a is F", there is no need to generate additional similarities beyond the ones between a and other things which are F, such as b. Being similar is not intrinsic to tropes, rather it obtains of tropes in relation to a conscious subject who compares and categorizes.

I think that there is good reason to accept Rand's version of the similarity relation rather than the realist's. To show this, I want to perform a thought experiment. First, imagine a possible world (R) which consists exclusively of red marbles in Newtonian interaction. Imagine, moreover, that these marbles are conscious of one another. Would any of these marbles have any reason to think of the other marbles as similar to one another? With all of the constituents of R qualitatively indistinct, there are no qualitatively distinct objects against which a marble could contrast its neighbors; there is no way that two objects could strike it as less different from one another than either of them are from something else. The notion that some of the other constituents of R are similar to one another would never occur to any marble. I think that this indicates that similarity should be construed as obtaining between two objects only in relation to other objects which are more different from each of them than they are from one another.

Second, imagine that R does include blue marbles, but that a given red marble never comes in contact with any of them. For that particular red marble, it is exactly as if R did not contain blue marbles, and so this marble would never experience other marbles as similar to one another. Similarity thus relies not only on the existence of contrast objects, but on contingent facts about which contrast objects a given conscious subject experiences. Since similarity exists not just in virtue of the existence of contrast objects, but in virtue of experience of them, similarity relies on the existence of a conscious subject.

There is a matter of interpretation which requires discussion. The phrase 'contrast object' does not appear, so far as I know, anywhere in Rand's work. Contrast object are discussed in Kelley 1984. The nearest Rand ever comes to talking about contrast objects appears to be here: "Man forms such concepts [of colors] by observing that the various shades of blue are similar, as against the shades of red, and thus differentiating the range of blue from the range of red, of yellow, etc." (Rand 1990, 14-15) It is on the evidence of this passage and Kelley's attribution that I say that Rand held that similarity obtains between two objects only in the context of contrast objects. It is because this implies, as I suggested in the previous paragraph, that similarity obtains between two objects only in the context of a knowing consciousness, and because of my interpretation of Rand's notion of objectivity, that I have attributed to Rand the idea that objects are only similar in relation to consciousness. The evidence for these attributions is thin and I might easily be mistaken in making them. If this is the case, though, I think Rand's work would be (even) more sterile for not containing the germ of these ideas.

Elsewhere, Hochberg runs a related argument, but one that does not turn on similarity but rather difference:


Since red1  and red2  (two tropes of red) are numerically different, there is an instance of difference — difference1. This instance is also numerically different, as well as qualitatively different, from both instances of red. So we have difference2  and difference3  and, likewise, infinitely many instances of difference. Thus, if the difference between any two things is a particular instance, we have infinitely many particular instances of difference generated by any two things. This is the kind of consequence that points to an absurdity in a philosophical position. (Hochberg 1988, 193)


As with the prior problem, this one turns out to be at least as bad for the realist as it is for the nominalist. Different instantiations of the same universal are different (instantiations) from one another, and this difference must be a universal. But its different instantiations must be different (instantiations) from one another, and so there are differences between differences ad infinitum.

The Randian approach to this problem should be similar to the last one. Let us consider entities first, then properties and relations. With respect to entities, difference is observer-relative. There is a numerical difference between pages 266 and 267 of Introduction to Objectivist Epistemology  if we are thinking in terms of pages, but if we think in terms of books, they will be indistinct from one another. Being numerically distinct is not intrinsic to entities, rather it obtains of entities in relation to a conscious subject who distinguishes. (A similar approach, I think, is taken in Radcliffe and Ray 2000. I don’t have confidence that I correctly understand Radcliffe’s and Ray’s views, though, so I don’t know how closely related their view is to my own.)

But likewise with respect to properties and relations. There is a numerical difference between two tropes (either properties or relations) only if we regard them as numerically distinct. (Likewise, I think, for numerical indistinctness.) The very fact that realism about universals exists indicates that it is possible to think of all the tropes of a certain property as numerically indistinct; as a single vast entity spread across space and time. While the view is certainly a bizarre one which is radically perverse from the point of view of human action, it is not an impossible one, and it may from some point of view even be a useful one. Being numerically distinct is not intrinsic to property and relational tropes, rather it obtains of tropes in relation to a conscious subject who distinguishes.

I have now claimed that tropes are similar to one another, and also numerically distinct from one another, only in relation to a knowing subject. One gets the feel that I have abolished the tropes themselves — surely, if their differences from one another relies on us, their very existence relies on us. However, this is not the case. I have made only two kinds of tropes dependent on consciousness: similarities and differences. All other tropes are intrinsic to the world and are radically independent of consciousness. Whether two tropes are two, and whether they are of the same category, depends on the distinguishing and categorizing acts of a conscious subject, but whether they exist and have various causal, logical, spatial, and temporal relations with one another is not at all dependent on us.

The most important of Hochberg's objections deal with regresses on similarity and difference, and I believe that a trope theory which, like Rand's, makes similarities and differences reliant on consciousness can solve these problems. I think that it's with respect to these regresses that Rand's theory has a uniqueness; Hochberg's other objections can be met by other trope theorists (see, for example, LaBossiere 1996). So I will leave them aside and just make a few clarificatory remarks about bundles and tropes.

The picture theory I developed in the last section involves facts which consisted of bare particulars, universals, and the latter inhering in the former (or, what is the same thing, the former instantiating the latter). Bare particulars had as their logical form that they would instantiate universals, and universals had as their logical form that they would inhere in bare particulars. Doing away with universals and bare particulars in favor of tropes and bundles changes this in some ways, but preserves the essential structure of the account.

Instead of bare particulars, the things which instantiate properties are bundles of properties. A bundle of tropes instantiates a trope just in case that trope is bundled together with the other tropes; instantiating is the same as being-bundled-with. A trope inheres in a bundle just in case that trope is bundled together with the other tropes; inhering is the same as being-bundled-with. The only difference between inherence and instantiation is that what is said to instantiate is a bundle of tropes, whereas what is said to inhere is a single trope. The two relations are identical, but one of them is from the bundle's and the other from the individual trope's point of view.

Instead of universals, the things which inhere in bundles are tropes. Tropes are organized into similarity-classes by conscious subjects. Thus the theory presently proposed has only one kind of ontological entity, tropes. However, tropes cannot exist independently of other tropes. As with Wittgenstein's objects, tropes always appear in states of affairs, that is, in connection with other tropes. Individual tropes, then, have two kinds of relations which are important for our purposes. They are members of similarity-classes of tropes, and they are bundled with other tropes to form complete entities. They could (and, in the absence of a conscious conceptualizing subject, do) exist without being members of similarity-classes, but they cannot exist without being bundled into entities. A given trope, then, might be both a member of a similarity-class and bundled into an entity. This pair of relationships will form the basis of facts.


VI. Facts and Truth

So the picture of facts which emerges is this. The fact that a is F obtains just in case the bundle which is the referent of 'a' includes as one of its constituent tropes is a member of the similarity-class which is the referent of 'F'. But let us spell this out a bit.

I want to start by remarking on Rand's and Peikoff's remarks on facts and truth, because what they say is often wrong. Rand says, with respect to facts:


The term "fact" can apply to a particular existent, to an aspect, to an attribute, or to an event.


Now, "fact" is merely a way of saying, "This is something which exists in reality" — as distinguished from imagination or misconception or error. So you could say, "That the American Revolution took place is a fact," or, "That George Washington existed is a fact." In the first case you refer to an enormously complex series of events over a period of years. In the second case you refer to just one individual. Both are facts.


"Fact"... can be [i.e., refer to] a particular narrow detail, or an entity, or an event, or a series of events. (Rand 1990, 241-2)


Rand is systematically misusing the term 'fact' in this discussion. The term 'fact' cannot be used to refer to any of a particular existent or entity, an aspect, an attribute, an event or series thereof, or a particular narrow detail. When Rand uses the term 'fact' she gets it right. She does not say that the American Revolution or George Washington are facts, but rather that the occurrence of the one and the existence of the other are facts. But, were particular entities such as Washington members of the extension of 'fact', then it would be sensical to say, "George Washington is a fact", when this sentence is clearly either elliptical or confused. Likewise for attributes; the whiteness of page 267 of Introduction to Objectivist Epistemology  is not a fact, though it is a fact that that page is white. In general, the members of the extension of the term 'fact' must be things which can be referred to (in English) only with the use of 'that'-clauses; only if it makes sense to say 'that p' can p be a fact. Only then we can refer to the fact that p.

Moreover, it is wrong to say that the concept fact  exists to allow us to distinguish between reality and error. It is a fact, albeit a fictional one, that Howard Roark was an architect. If 'fictional fact' makes sense, the word 'fact' can be used to refer not only to what really obtains, but also to what doesn't really obtain (what doesn't obtain in reality).

When Rand is asked whether "fact" (i.e., fact ) is an axiomatic concept, she says that it is not (ibid , 241). Rand says that, "An axiomatic concept is the identification of a primary fact of reality, which cannot be analyzed, i.e., reduced to other facts or broken into component parts." (ibid , 55) Let's consider just the axiomatic concept existence. Is existence  the identification of a primary fact, or indeed any kind of fact? What fact do I assert when I say, "Existence!"? None at all. So Rand is trivially right when she says that, " cannot analyze (or 'prove') existence as such, or consciousness as such. These are irreducible primaries." (ibid ) Facts, or perhaps assertions, are proved; things or single words are not. Thus it is irrelevant that existence is an irreducible primary; this is not a reason why it cannot be proved. Of course existence cannot be proved; it is not a fact but rather a thing. Likewise, Rand is wrong to say that


Since axiomatic concepts refer to reality and are not a matter of 'faith' or of man's arbitrary choice, there is a way to ascertain whether a given concept is axiomatic or not: one ascertains it by observing the fact that an axiomatic concept cannot be escaped, that it is implicit in all knowledge, that it has to be accepted and used even in the process of any attempt to deny it. (ibid , 59)


How would someone go about denying an axiomatic concept? It is impossible to do this, but not for the reason Rand mentions. Only assertions — those utterances by which we assert facts — can be negated. If I say, "The book is blue", you can negate this assertion by asserting in response, "No, the book is not blue". But 'Existence' is not an assertion, and so cannot be negated. (What might such a negation look like? "Existence No!"?) Axiomatic concepts cannot be negated, not because they are axiomatic, but because they are concepts.

(Despite Rand, we can give sense to the notion of axiomatic concepts. An axiomatic concept is one which cannot but have members (objects, or whatever). A negative existential claim about the referents of the word which is associated with an axiomatic concept is necessarily false. "Existence does not exist" or "Consciousness does not exist" are necessarily false for the reasons Rand cites.  [I imagine that this may be what Rand had in mind.] However, by this criterion, fact  is an axiomatic concept if we accept the correspondence theory of truth. "Facts do not exist" would be true just in case it corresponded to a fact, but if it so corresponded, then there would be a fact and so the sentence would be false. A sentence which is false if it is false, but also false if it is true, is necessarily false, and so its negation is necessarily true.)

With her talk of 'fact' referring to entities, and of 'Existence!' being the sort of thing one could (necessarily falsely) negate, Rand has denied the distinction between facts and things. In a world with only things, there would be no need to talk of facts; Strawson's critiques of the correspondence theory would be correct were we to confess at the outset that there were no facts above and beyond entities, attributes, and so forth.

Some of Leonard Peikoff's remarks on truth are similarly destructive. Peikoff says that claims for which there is no evidence are not true: "Claims based on emotion are widespread today... In the terminology of logic, such claims are "arbitrary," i.e., devoid of evidence..." (Peikoff 1991, 163), "An arbitrary statement is neither 'true' nor 'false.' " (ibid , 165, emphasis original) Consider now the following claim: "I own a cat named 'Bashful'". I make this claim, and then remain silent, providing no evidence. Does this mean that it is not the case that I own a cat named 'Bashful'? Surely not, as I do own such a cat, even if you don't know that I do. Whether there is evidence for the truth of an assertion is agent-relative: you can have evidence to which I have no access, and vice-versa . If truth rests on evidence, then truth is also agent-relative: what's true for you might not be true for me.

Peikoff argues that


The concept "truth" identifies a type of relationship between a proposition and the facts of reality. "Truth," in Ayn Rand's definition, is "the recognition of reality." In essence, this is the traditional correspondence theory of truth: there is a reality independent of man, and there are certain conceptual products, propositions, formulated by human consciousness. When one of these products corresponds to reality, when it constitutes a recognition of fact, then it is true....


A relationship between conceptual content and reality is a relationship between man's consciousness and reality. There can be no "correspondence" or "recognition" without the mind that corresponds or recognizes. (ibid )


It is not right to say that a mind corresponds, though it is right to say that a mind recognizes. Peikoff is running together two relationships between beliefs and facts. One of them is the evidentiary connection which is the concern of epistemology. A belief cannot count as a recognition of a fact unless it is appropriately justified, and that justification ought somehow to involve the fact which makes it true. However, there is another relation, that of meaning. This relation is studied by semantics and ontology. A belief is made true by the fact that is its meaning, but while this relationship rests on the mind's taking parts of the world as contents of concepts and beliefs, it does not rest on the mind's taking parts of the world as evidence for beliefs. There can be true beliefs for which the believer has no evidence.

Traditionally, a belief's truth has been taken as a prerequisite for its counting as knowledge. But Peikoff reverses the tradition, and requires that a belief count as knowledge for it to count as true. If a belief's truth consists in its correspondence to a fact, and a belief is true just in case it has been justified, it cannot correspond to a fact unless it has been justified. If a belief's truth consists in two factors — 1) correspondence to 2) a fact — and does not exist until the belief has been proved, then one of those two factors must be absent until the moment of justification. Let's consdider 2 first.

Assertions have as their meanings (and beliefs as their contents) facts. These facts are composed of bundles and similarity-classes of tropes. That a single trope is a member both of the bundle which is the referent of the subject of the assertion, and of the similarity-class which is the referent of the predicate of the assertion, is the fact which we assert by way of uttering the assertion. If an assertion is not true unless it is justified because there is no fact to which it can correspond unless it has been justified, then facts rest for their existence on our justifying our beliefs. But for Peikoff, facts ought to be radically independent of us. "Correspondence to reality" and "recognition of a fact" are treated by him as synonymous phrases, and reality is held to exist independently of minds. Thus facts must exist independently of minds, while making them reliant on whether justification makes them reliant on minds.

On the other hand, let's look at 1, the possibility that, though there are facts, our beliefs cannot correspond to them unless we have justified the beliefs. Consider an assertion for which no evidence has been presented, such as the assertion that I have a cat named 'Bashful'. How would we go about justifying this claim? Presumably, we would look around for the fact that I have a cat named 'Bashful': look at me and my abode for a cat, wait to see whether I call it 'Bashful', and so forth. But we can do this only because the unjustified claim already has as its meaning the fact that I have a cat named 'Bashful'. The claim thus has a relationship to the fact that would make it true — it means that fact — independently of whether that fact is known to obtain. Since a claim is true if it it corresponds to a fact that is its meaning — if that fact obtains — that a fact must be the meaning of a claim before that claim has been justified indicates that a true claim corresponds to the facts whether or not it has been justified. If this were not the case, we would not know what claims mean and thus could never look at the world to see whether a claim's meaing obtains. Knowledge would thus be impossible.

Claiming that truth relies on evidence thus leads us to deny either the existence of an independent world, or of knowledge of such a world. Since these claims are each self-evident, it cannot be the case that truth relies on evidence. (Peikoff's general conclusion that 'the arbitrary is neither true nor false' is, then, necessarily false.)

In "The Analytic-Synthetic Dichotomy", Peikoff says


Every truth about a given existent(s) reduces, in basic pattern, to: "X is: one or more of the things which it is." The predicate in such a case states some characteristic(s) of the subject; but since it is  a characteristic of the subject, the concept(s)  designating the subject in fact includes the predicate from the outset. (Peikoff 1967, 100)


Peikoff says this by way of rejecting the distinction between analytic and synthetic truths, and we will look at this distinction below. For the moment, though, let's concentrate on the basic pattern of truths: X is one or more of the things which it is. The predicate, Peikoff says, "states some characteristic(s) of the subject". What kinds of words perform this function? In general, verbs, adjectives, and prepositions do the main work. Rand says that


Concepts of motion  [i.e., concepts which are connected with verbs] are formed by specifying the distinctive nature of the motion and of the entities performing it, and/or of the medium in which it is performed... For instance, the concept "walking" denotes a certain kind of motion....


Prepositions  are concepts of relationships, predominantly of spatial or temporal relationships, among existents; they are formed by specifying the relationship and omitting the measurements of the existents and of the space or time involved — e.g., "on", "in"...


Adjectives  are concepts of attributes or characteristics. (Rand 1990, 16-17)


In general, then, concepts the words for which show up as predicates in the ordinary language are concepts of motions, relationships, and properties. The concepts words for which might show up as subjects in the ordinary language are, then, probably concepts of entities. This seems right, since the 'X' in Peikoff's "X is: one or more of the things which it is" looks very like a dummy name, that is, a word which refers to an entity.

In the appendices to Introduction to Objectivist Epistemology, the following exchange occurs:


Prof. A: If I ask you, then, what is the referent of "length," would you say "long objects"?

AR [Ayn Rand]: Not the objects, the attribute of length in all the objects which possess that attribute.

Prof. A: Isn't the referent something separated?

AR: It's mentally separated, but it is there in those objects. It doesn't have to be an entity to be a referent.

Prof. A: I don't understand then why the referent of the concept "red," say, isn't all the red concretes.

AR: How about the other attributes of all those red concretes? Is the referent of "red" the length and weight of all the red concretes?

Prof. A: No. (ibid  278)


Rand agrees with Prof. A's answer. We are to take it, then, that the referents of verbs, adjectives, and prepositions are motions, properties, and relationships respectively, but not the entities which perform the motions, exhibit the properties, and stand in the relationships. Concept-words, though, refer not to individual motions etc, but to whole categories of them. "Walking' refers to all the walkings that have ever, are now, or will ever be performed.

Recall that an entity is the bundle of all of its motions, properties, and the relationships in which it stands, and also that the general form of proposition is that "X is: one or more of the things which it is". If 'X' refers to a bundle of tropes, and the predicate refers to all of the members of a similarity-class of tropes, then the assertion will be true just in case there is a trope which is member of the bundle which is the referent of the name, and also a member of the similarity-class which is the referent of the predicate. Rand's ontology, then, gives rise to the present theory of facts and truth rather naturally once her own remarks on the nature of facts, and Peikoff's on truth, are set aside.

However, Rand is working on the surface grammar of sentences in the ordinary language. Earlier, I argued that the correspondence theory of truth can be preserved from the slingshot, and Fregean ontological expansions can be avoided, only if we accept Russell's theory of descriptions. Most of those interested in Rand's philosophy, though, do not accept Russell's theory. However, aside from the earlier arguments (which might not be rhetorically sufficient, though I think that they are cogent) which I've given for Russell's theory, here is a dialectical argument taking off from Peikoff's rejection of the analytic-synthetic distinction. If facts consist in tropes standing in relations to one another, then assertions ought to consist of predicates standing in relations to one another. Why is this? Peikoff argued that, because "the concept(s)  designating the subject in fact includes the predicate from the outset", all sentences are analytic and hence that there is no analytic-synthetic distinction. But in ordinary language, we often do not refer to entities with concept-words, but rather with names. If those assertions are to be analytic, then the names must disappear in favor of concept-words so that those concept-words can include the predicate from the outset as Peikoff says. But Russell's theory, when applied to names, just consists of replacing names with concept-words. So Peikoff must have tacitly accepted Russell's theory before he could make his claim; indeed, we must assume that Peikoff has accepted Russell's theory even to make sense of Peikoff's claim. So those who are inclined to accept Peikoff's doctrine about analyticity are committed to Russell's theory of descriptions.

I am not so inclined. Analyticity was never supposed to hold of sentences which referred to particulars, so Peikoff is clearly mistaken when he makes such sentences analytic (or even at issue). But this is beside the point; those who do  accept Peikoff's position are committed to Russell's theory for one reason, while I'm committed to it for others.

Moreover, Peikoff’s argument necessarily fails even if we accept Russell’s theory and hence accept that we refer to particulars (bundles) by way of words for concepts, that is, predicates. This is because, as Rand points out, these predicates refer to properties of things, not things. ‘Red’ refers to all of the rednesses, not all of the red things. Since a bundle is referred to by way of a group of predicates which together specify a bundle’s essential properties and determine that bundle uniquely, but that those predicates apply to a thing does not necessarily imply that the thing also possesses the properties applied to it by the predicate of the sentence, the predicates into which we analyze the subject term typically do not include the predicate of the sentence.

Here, though, is a final, somewhat vague, argument. What is the justification for having two linguistic types, names and predicates? Predicates refer to similarity-classes of tropes, but the referents of names are merely bundles of the same tropes which go in the similarity-classes. If an entity is always a bundle of tropes, then reference to it can always be secured by a descriptive phrase in which the descriptive predicates terms refer to the members of certain similarity-classes of tropes some of which are also bundled together to form the entity which to which we were trying to refer. Since names can be replaced by sets of predicates, but predicates cannot be replaced by names (without introducing universals), names are not necessary — we can ignore them at a certain level of abstraction from the ordinary language.

Hopefully, we are now clear on the structure of facts. Facts are always: that the bundle which includes tropes in these similarity-classes also includes a trope in that similarity-class. Those assertions and beliefs are true which represent facts which obtain.

There is a final consideration. Recall that universals and bare particulars have been rejected, and that the distinctness of entities and the similarities between their properties have been relativized. Entities are distinct in case we distinguish them; they are similar in case we treat them that way. However, our assertions always rely on our distinctions and categorizations. "The bundle which includes tropes in these similarity-classes" is a distinct bundle only if we distinguish it; "a trope in that similarity-class" is in that similarity-class only if we classify it as such. It seems that facts thus rely on us. Are we forced into some kind of idealism about facts?

I think we are. By adopting the picture theory but rejecting the intrinsicist entities which it relied on, I am forced into the situation of saying that facts, since they rely on the existence of numerical difference and qualitative similarity which in turn rely on our mental acts of distinction and categorization, rely on us. This is not, of course, to adopt idealism in general. Earlier, I argued that numerical difference and qualitative similarity rely on persons, but this does not imply that any other tropes rely on persons. The world would exist and be none the poorer for not having persons in it. It simply would not have similarities, distinct entities, or facts in it. The universe wouldn't notice the difference.

Things get even more radical when we note that the world can be categorized and divided differently by different persons. This implies that there might be different facts for different persons. The spectre of relativism looms. But if relativism involves the claim that what's true for me might be false for you, relativism does not threaten. If different persons divide and categorize differently, they will indeed be surrounded by different facts; facts are observer-relative. However, just because of the differences between their differentiations and categorizations, they cannot disagree with one another. There can be disagreement about facts only when there is agreement on underlying distinctions and categorizations. If I do not categorize a group of things together and form the concept table  to allow me to perform operations with respect to tables, there are no facts for me involving whether anything is a table. I can thus neither agree nor disagree with you about whether something is a table. It can never be the case that an assertion or belief is true for you but false for me, because if it is true for you it is either true for me it I can't have the relevant belief at all.

That our beliefs do not have to match a radically extra-mental world to be true does not imply that whatever we believe to be true, is true. I want to use Richard Rorty as a subjectivist foil here. Rorty defends a version of pragmatism in which


...there is nothing to be said about truth or rationality apart from descriptions of the familiar procedures of justification which a given socity — ours  — uses in one or another area of inquiry. The pragmatist... thinks that his views are better than the realists', but he does not think that his views correspond to the nature of things. He thinks that the very flexibility of the word "true" — the fact that it is merely a term of commendation — insures its univocity. The term "true," on his account, means the same in all cultures, just as equally flexible terms like "here," "there," "good," "bad," "you," and "me" means the same in all cultures. But the identity of meaning is, of course, compatible with diversity of reference, and with diversity of procedures for assigning the terms. So he feels free to use the word "true" as a general term of commendation in the same way as his realist opponent does — and in particular to use it to commend his own view. (Rorty 1991, 23)


Rorty's pragmatist view is closely related to my own, but there is a difference. For Rorty, someone's saying "this is true" is more or less the same as someone's saying "we all agree to this". I don't think that this could be right. Could we sustain the custom of claiming that things were true if we all knew that something's truth was just our agreement to it? It seems hard to simultaneously admit that saying that something is true is just commending it and also to say that something is true, for just the same reason that the mass public acceptance of emotivism would probably imply an end to moral utterances. Rorty-style pragmatism and emotivism seem to take away from certain terms ('true', 'good') just precisely the charm required for us to bother using them. But if that's the case, then we can hardly mean by them what Rorty and the emotivist claim we mean by them; I would never willingly engage in a self-defeating language-game.

But moreover, it seems that Rorty's view makes it difficult to say that a whole community is mistaken about something. If to say that something is true is just to say that it's agreed-upon by the relevant community ('ours '), then we can't say that some things that are agreed-upon are false. But surely, even if we thought that collective error never actually occurred, we would agree that it could occur. With respect to pragmatism, for instance, the sudden death or conversion to realism of all pragmatists would not make pragmatism false, nor does the fact that pragmatism is really not very popular suggest that it is false.

Hilary Putnam adopts the opposite position which I wish to skirt very closely but narrowly avoid. Putnam concludes his Reason, Truth, and History  with the following remarks:


We can only hope to produce a more rational conception  of rationality... if we operate from within  our tradition, but this is not at all to say that all is entirely reasonable and well with the conceptions we now have. We are not trapped in individual solipsistic hells, but invited to engage in a truly human dialogue; one which combines collectivity with individual responsibility.


Does this dialogue have an ideal terminus? Is there a true  conception of rationality...? Here philosophers divide, like everyone else. Richard Rorty... opt[s] strongly for the view that there is only the dialogue; no ideal end can be posited or should be needed. But how does the assertion that 'there is only the dialogue' differ from... self-refuting relativism...? The very fact that we speak of our different conceptions as different conceptions of rationality  posits a Grenzbegriff, a limit-concept of the ideal of truth. (Putnam 1981, 216)


For Putnam, the truth is not what we agree to now, but rather what ideal observers at the conclusion of all epistemic projects would agree to. Since Rorty seems to be wrong, we do need to go beyond the agreement of our own community to determine which facts obtain. But I do not think that we need go quite so far as Putnam does. In the present theory, whether there is a distinct entity or a category relies on human decision. But particular (even collective) decisions about which categories entities fit into might be mistaken. We should say, then, that an entity is a member of a category for me (and all those relevantly like me) — that is, that a fact obtains for me — just in case I would, at the terminal moment of all epistemic projects in which I could engage given my own distinctions and categorizations, decide that it was — that is, that it does. The point here is to retain the importance of human agency in determining what the facts will be, but not allow the possibility of human error to determine wrongly what the facts will be. To whatever degree our beliefs are false we have fallen short of an ideal determined by our own view of the world.


Austin, Texas, November 8, 2000




Edwin Allaire, Josh Dever, Chris Furlong, Cory Juhl, and David Sosa have read, discussed with me, and provided helpful comments on parts or the whole of this paper. My thinking on the slingshot and related issues was helped by participants in the discussion of the slingshot: Roger Bissell, Rafael Eilon, Chris Furlong, Kevin Knight, and Tom Radcliffe. Naturally, not all of these people agree with everything said in this paper. Indeed, some of them would be scandalized to find their name appearing at this conference!



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