A Theory of Propositions

(Draft)

I. Introduction

“In what is the agreement of the thing [fact] and the statement [proposition] supposed to consist, given that they present themselves to us in such manifestly different ways?” (Heidegger 1967, p. 180)

In this chapter, I will offer a theory of the nature of correspondence. Included here is a theory of propositions and of the correspondence relation.

II. Propositions and Things Proposed

Recall from Chapter 1 that by ‘proposition’, I mean the primary bearers of truth and falsity. I would like to point out a connection between propositions and things that people propose. I take it that at least some things people propose are true; some are false. Therefore, I take it that at least some things people propose are propositions. I might even go so far as to say that propositions just are things that can be proposed. (I will not go that far, however: first, because I do not wish to be bothered by question of whether some propositions might be too complicated for anyone to possibly propose; second, because there is no need.)

I point out a connection between propositions and things proposed in order to draw a distinction between thinking of propositions as the things that are proposed, on the one hand, and thinking of propositions as proposed things, on the other. A thing is only called a ‘proposed thing’ if it has in fact been proposed. By contrast, the thing that has been proposed need not have been proposed. It could easily have never been proposed at all. To be clear, I am not suggesting that proposed things form a distinct ontological category from things that are proposed. On the contrary, I would say that proposed things are the things that are proposed; it’s just that we call a thing ‘a proposed thing’ only once it has actually been proposed. I draw this distinction so that no one will be tempted to think that propositions must be mind-dependent solely because she thinks propositions are proposed things. It should be an open question at the outset whether a thing that is proposed may exist independently of its being proposed.

Now someone may wish to reserve the term ‘proposition’ to refer only to those things that have actually been proposed (or to the kind, having been proposed). I have no problem with that usage of the term. I only wish to make it clear that I am using ‘proposition’ differently than that. I use it to refer to the sort of things that can be proposed—things that are true or false.[1]

II. Propositions are not Concrete

Some philosophers (Tarski 1944[2], Higginbotham 1991, Armstrong 1997[3], to name a few) believe that propositions are concrete things, such as sentences or brain states, or sums (or classes) of sentences or brains states. I will offer three reasons why I think this view is mistaken.

II.i. Reason One

Let Concrete name the thesis that every proposition is a concrete object located somewhere in space or space-time or is dependent upon an object or objects located in space or space-time.[4] The first step in the argument is to observe that Concrete is not a contingent thesis. That is, advocates of Concrete should (and most likely do) think that propositions must be concrete. (How, for example, could a sentence or brain state ever be abstract?) In other words, if Concrete is true at all, it should be necessarily true. Here is further support: given the modal axiom S5, if it is even possible for there to be necessarily existing abstract propositions, then there really are such things. Therefore, if Concrete is true at all, it better be necessarily true to rule out the possibility of necessarily existing abstract propositions.

The next thing to notice is that if Concrete is true, then it exists. (We may view this inference as an instance of ‘adjective-dropping’ in first-order logic: e.g. $x (xF & xG) → $x (xG), where F = ‘true’ and G = ‘identical to the proposition Concrete’.[5]) Notice also that the inference from being true to existing is probably not a contingent matter; it is plausibly a necessary truth. That is, it is plausible that it is necessary that if Concrete is true, then it exists. This is plausible given that it is plausible that there cannot be something that does not exist—and if there cannot be something that does not exist, then there cannot be a true proposition that does not exist. (A Meinongian may deny this step, but it is unlikely that a believer in concrete propositions would.[6]) What follows is that if Concrete is necessarily true, then Concrete necessarily exists.

The trouble is that there do not seem to be any necessarily existing concrete particulars with which to identify Concrete. Sentences on paper can be erased or destroyed by fire. Brain states can be damaged by oxygen deprivation. Mereological sums (or classes) of brains states or of sentences can dwindle away, though the process may take awhile. Perhaps science will reveal that there are fundamental spatial things—superstrings, say—that cannot cease to exist. But surely Concrete is not a superstring. So what could Concrete be?

Perhaps Concrete, along with every proposition, is part of a special class of particulars that are not reducible to anything investigated by empirical science. They are concrete alright, but they escape empirical detection: no one could say, “Look! That scratch is the impact of a proposition.” The trouble with this view, apart from sounding incredible, is that if it were true, then we would have had no way to come to believe that there are any propositions in the first place. If Concrete is floating in space—somewhere near the peaks of Mount Kilimanjaro, say—and is completely undetectable, how should we have ever come to grasp it? It seems that we would not have. Yet, clearly we have.

The reductio argument against Concrete, then, can be expressed as follows:

(1) Assume Concrete is true.

(2) If Concrete is true, then it is necessary that Concrete is true.

(3) Therefore, it is necessary that Concrete is true.

(4) Necessarily, whatever is true exists.

(5) Therefore, it is necessary that Concrete exists.

(6) No sentence or brain state (or sum of them) necessarily exists.

(7) Therefore, Concrete is not a sentence or a brain state (or sum of them).

(8) More generally, the types of concrete things whose existence might be conceived to be necessary are not themselves propositions (as no such thing exhibits any proposition-like properties).

(9) Therefore, Concrete is not concrete, which is a contradiction.

I take the reductio argument against Concrete to be fairly strong as far as philosophical arguments go. The three best ways out that I have been able to think of have serious costs, as I will argue next.

Objection 1: Concrete is necessarily true, but only if it exists.

Perhaps we can understand ‘necessary proposition’ as a proposition that is essentially true: it is true when and only when it exists. (A contingent proposition, by contrast, is true in some, but not all, situations in which it exists.) If we say this, we may then say that Concrete, though necessarily true, can fail to be true by failing to exist. Therefore, there is no need to affirm (2).

Unfortunately, this move has a cost. As Alvin Plantinga (2006) has noted, if necessary propositions are the same as essentially true ones, then there seems to be too many necessary propositions. Consider, for example, <there are brains>. That proposition does not seem necessary. Yet, if propositions are things that depend upon brain states (say), then clearly <there are brains> cannot exist unless it is true. In other words, <there are brains> would be essentially true, which means that it would be necessarily true. The result is the same if propositions depend instead upon sentences: <there are sentences> would be essentially true and so necessary. What we have here is the dubious consequence that the existence of brains or sentences (or whatever other spatial things propositions might depend on) is broadly logically necessary—no less necessary than the proposition than every square has four sides. Surely, that’s not correct.

Objection 2: It is not necessary that whatever is true exists.

Perhaps we can deny (4) by supposing that it is possible for Concrete to be true even if Concrete does not exist. However, if we say that, then we will have to give up serious actualism—the view that it is impossible for something to have a feature, or be predicable, unless it exists. Only then can we say that Concrete can be true even at times or in situations in which it does not exist. The problem is that no advocate of Concrete should be willing to give up serious actualism: no advocate of Concrete should be willing to say that there can be things, such as Concrete, that do not exist. A believer in Concrete who believed that would be committed to saying that during the times when Concrete does not exist, Concrete is still a concrete particular. In other words, she would be committed to saying that there can be concrete particulars that do not exist. No one should be willing to say that, it seems to me.

Objection 3: Concrete can be true at a world without being true in it.

Kit Fine (1985) introduces a distinction between ‘inner truth’ and ‘outer truth’. A proposition has inner truth relative to a world only if it exists in that world; it has outer truth relative to a world whether or not it exists in that world. An outer truth is supposed to be a truth that correctly describes a world without necessarily being in that world. It is true at that world, but not necessarily in it. (Thus, every proposition that is true in a world is true at that world, but not every proposition that is true at a world is true in it.) Using this distinction, perhaps we can say that Concrete is necessary in the sense that Concrete correctly describes every world, even though it is not in all of them. Concrete, like every necessary truth, is outwardly true relative to every world and every time, though Concrete only exists in a few worlds at a few times (see Iacona 2003).

I see two problems with this way out. One problem is that I know no plausible way to define ‘inner truth’ and ‘outer truth’. My best guess would be that ‘a proposition P is true relative to a world W’ means the same as ‘if W were actual, then P would be true’; and ‘P exists in a world W’ means the same as ‘if W were actual, then P would exist’. That would be my best guess if it did not imply that every outer truth just is an inner truth. But unfortunately, it does imply that every outer truth is an inner truth, if we assume that there cannot be things that do not exist (which was Objection 2).

To see why every outer truth is an inner truth given the above definitions, suppose P has outer truth relative to W. Then, if W were actual, P would be true. But if P were true, then P would exist, assuming that P cannot be anything, not even true, without existing. That means that if W were actual, then P would exist, which is what I would have guessed was meant by ‘P exists in W’. Thus, if P has outer truth relative to W, then it also has inner truth relative to W. This is so for any P. However, since it is clear that not every outer truth is supposed to be an inner truth, my best guess as to the meaning of these notions must be mistaken.

We may, therefore, try to work with a loose and vague understanding of the distinction between inner and outer truth. However, even the vaguest (or minimal) understanding leads to trouble—trouble that appears to have gone unnoticed in discussions of inner and outer truth. The trouble consists in there being fewer necessary truths than there seem to be. For example, if Spatial is necessary, then it seems that <Concrete is necessary> is also necessary. (This is an instance of S4.) But if we wish to make use of inner and outer truth, then we cannot say that < Concrete is necessary> is necessary without getting entangled in a contradiction. I’ll explain. Let Chaos be a distant future time after which brains and sentences (and anything else propositions might be) have long since been effaced from our universe. We can correctly describe Chaos as a time when there are no propositions, no truths, and no Concrete. Even on the vaguest (minimal) understanding of outer truth, it should be safe to say that a proposition that correctly describes a world or situation is outwardly true relative to that world or situation. Thus, it should be safe to say that <there are no truths> is outwardly true at Chaos given that it correctly describes Chaos. But recall our hypothesis: necessary truths have outer-truth at every world and time, including Chaos. It follows, then, that both <Concrete is necessary> and <there are no truths> are true (outwardly) at Chaos. A contradiction is now a step away. If <Concrete is necessary> is true at a situation, then so is <Concrete is true>. That means <Concrete is true> is true at Chaos, which in turn means that <there is a truth> is true at Chaos. Thus, both <there is a truth> and <there are no truths> are true at Chaos. That appears to be a contradiction. To avoid this contradiction, then, an advocate of the third objection is committed to saying that although Concrete is necessary, <Concrete is necessary> is not. But that is implausible.

II.ii. Reason Two

Consider, <some volcanoes erupted>. Intuitively, that proposition entails that there are volcanoes but does not entail that there are people. That is, if that proposition were true, then it is guaranteed that there are volcanoes, but it is not guaranteed that there are people. Yet, if there were no people, then there would be no sentences or brain states, or anything else that a concrete proposition might be identified with. In other words, if there were no people, then there would be no true propositions. Thus, <some volcanoes erupted> would not be a true proposition. Hence, if <some volcanoes erupted> were true, then there really would be people—the existence of people would be guaranteed. But that is not plausible; therefore, it is not plausible that <some volcanoes erupted> is a concrete thing.

How might someone reply? The best reply I have seen is to say that <some volcanoes erupted> does not entail that there are people because it describes situations or worlds in which people do not exist, despite the fact that the proposition itself would not exist were there no people. This reply makes use of the distinction between inner and outer truth: that is, <some volcanoes erupted> has outer truth but not inner truth relative to situations in which people do not exist.

I have already said why I do not think a distinction between inner and outer truth will help. I said that the distinction, if intelligible at all, has the counter-intuitive implication that a proposition P can be necessary even if is not. Here, I will express an additional concern. The concern has to do with what it might mean to say that a proposition describes, or is true relative to a situation or world. The relation of describing sounds like the relation of corresponding to. In this case, however, the object being described is not a fact; rather, it is a situation or world. I ask, “What is a situation or world?” And, “What is it to accurately describe a situation or a world?” If someone asked me those questions, I would answer thus:

A situation is an abstract state of affairs (or proposition). A world is a big (maximally big) state of affairs. A proposition accurately describes a situation by being entailed by it, that is, by being such that were the situation actual, the proposition in question would be true. Perhaps also, there is an important sense in which a situation mereologically includes any propositions that describe it.

Of course, that sort of answer is of-limits to the advocate of concrete propositions: first, because she will surely not include proposition-like abstract states of affairs in her ontology, and second, because she cannot allow there to be a situation (for example, one in which there are volcanoes but no people) that implies both the truth of a proposition and the non-existence of all propositions. But then, what answer can she give? What concrete things are situations or worlds, and how do propositions manage to describe such things?

David Lewis has an answer to the first question: worlds are causally isolated spatial-temporal universes, and situations (or “Lewis-propositions”) are sets of worlds. If an advocate of concrete propositions accepts the existence of Lewis worlds (though I suspect few do), she can say that concrete propositions describe concrete worlds or sets of concrete worlds.

Still, how do propositions manage to describe Lewis-worlds? We might attempt an answer in terms of intentional properties of sentences or brain states. However, it is difficult to see how intentional properties could grab on, so to speak, a particular world out of the sea of infinitely many similar worlds that neighbor it. We cannot say, for example, that an intentional property grabs onto a world by virtue of a certain causal connection between a world and a sentence (say), for worlds are causally isolated by definition. Someone might instead suggest that propositions describe worlds by virtue of corresponding to them (in the way that true propositions correspond facts), but then there is the equally difficult problem of seeing how concrete propositions should correspond to Lewis-worlds. I will offer an analysis of correspondence according to which propositions may, in principle, correspond to Lewis-worlds, but as we will see, my analysis entails that propositions are not concrete. It seems to me, then, that the prospects for finding an account of how concrete propositions might describe worlds or situations are grim. At any rate, advocates of concrete propositions who wish to employ the distinction between inner and outer truth have some explaining to do.

II.iii. Reason Three

Let P be a proposition whose existence is not necessary. Ask: if P were to have not existed, would it still have been possible for P to exist? It may seem so. Consider that P’s existence is possible right now (given that P actually exists right). How could that change? How could there be a situation (or world) in which it is not even possible for P to exist? It may seem that there could not be one. That is, it may seem that the possibility of P is itself necessary. (This is an instance of S5.) Suppose that is so. Now consider that if is possible, then exists (given serious actualism[7]). And if exists, then P exists, too. Therefore, by the contraposition, if P does not exist, then is not possible. But that contradicts the intuition expressed above: that is, if P were not to exist, it would have still been possible for P to exist. To avoid this contradiction, I suggest that we reject the starting assumption that there is a proposition whose existence is not necessary. Yet, if propositions exist necessarily, then they are most likely not concrete. Therefore, propositions are most likely not concrete.

This argument just given assumes that if something is possible, then it is necessarily possible. That is, being possible entails being necessarily possible. (Here is more technical way of putting the assumption: the accessibility relation between possibilities [propositions that are possible] is symmetric.) I suspect that many philosophers would (and do) find that plausible, but others may demur. This third reason against concrete propositions, then, should appeal to those who accept that being possible entails being necessarily possible.

III. Propositions as Arrangements

If propositions are not concrete, what kinds of things are they? Here is a hypothesis:

(10) Necessarily, for all x (if x is proposition, then x is an arrangement of properties that are individual essences),

where

(11) ‘x is an individual essence’ =_def ‘Possibly, there is a y (y exemplifies x, necessarily (if y exists, then y exemplifies x, and necessarily, for all z (if z exemplifies x, then z = y))’.[8]

According to this hypothesis, propositions are themselves arrangements of properties—specifically, of individual essences. It might also be that every arrangement of individual essences form a proposition (then we could analyze propositions as arrangements of individual essences), though the hypothesis under discussion here leaves that open.

To better understand the hypothesis, let us consider an example: <Tibbles is on the mat>. That proposition, according to the hypothesis, is an arrangement of individual essences. Which ones? These, perhaps: being Tibbles and being the mat. (I have not said anything precise about what being Tibbles or being the mat are. One might wonder, for example, if being Tibbles is the property of being the thing named by ‘Tibbles’, or if it is the property of being the one cat I got from my Grandma, or something else. Perhaps the answer depends upon what proposition ‘Tibbles is on the mat’ is supposed to express. Nothing I say here turns on how these details are specified.) Thus, <Tibbles is on the mat> is an arrangement of the properties, being Tibbles and being the mat.

The arrangement consists of being Tibbles standing in a certain relation R to being the mat. Which relation is R? Here is an answer: R is the relation that being Tibbles bears to being the mat, such that anyone who fully grasps R grasps the relation of sitting on. Or if you do not like that answer, here is another: R is the relation r, such that necessarily, if an x bears the sitting on relation to a y, then every haecceity of x bears r to every haecceity of y. On either answer, we might say that the relation of sitting on is a constituent of <Tibbles is on the mat> (for a definition of ‘constituent’, see Chapter 2, section VI).

One virtue of treating propositions as arrangements of individual essences is that it allows us to understand propositions in terms of the familiar category, Whole (thing with parts): a proposition is a whole that has individual essences as parts and that exists if and only if its parts are related in a certain specified way.

One interesting implication of treating propositions as arrangement of essences is that propositions themselves may be objects of correspondence for “high-order” propositions. For example, if <Tibbles is on the mat> is an arrangement consisting of being tibbles and being the mat, then there may be a proposition that corresponds to that arrangement. For example: <being tibbles bears R to being the mat>, where ‘R’ is the relation r, such that necessarily, if an x bears the sitting on relation to a y, then every haecceity of x bears r to every haecceity of y. This implication may help us appreciate why there are propositions in the first place. There are propositions because there are arrangements whose parts have individual essences, and propositions just are arrangement of those essences.

I’d like to now consider a couple worries that one might have concerning the hypothesis, (10). First, there are many types of propositions (negative, counterfactual, tensed, and so on), and we might wonder whether (10) can hold for every type of proposition under the sun. I will address this worry in Chapter 4 by showing how (10) may hold for the most challenging test-cases.

A second worry is that (10) makes use of individual essences. Some philosophers are skeptical that there are such properties (see Menzel 2008). They are skeptical in part because it is difficult to see how individual essences might be analyzed—either in terms of more familiar, qualitative properties, or in terms of their exemplifiers, and in part because their inclusion into one’s ontology adds unwanted metaphysical complexity. My purpose here is not to defend the existence of individual essences against objections (if a defense is possible, it would surely require a fully essay in itself). Instead, I will offer a brief reason to think that individual essences are no more (or less) problematic than singular propositions—propositions that ascribe a feature to a particular individual. Individual essences are no more (or less) problematic because they may be analyzed as a type of singular proposition. Here’s how:

(12) 'x is an individual essence' =_def 'there is a o (x is a singular proposition about o, and x is true if and only if o exists’.

I am assuming that we understand at an intuitive level what it means for a proposition to be about something. Suppose that is so, and suppose that we have no objection to the existence of singular propositions about things. Then I do not see why we would object to the existence of those singular propositions called ‘individual essences’—for example, propositions that report the existence of a particular thing. We can say that these propositions/individual essences are “exemplified” just by being true. (It may have been noticed that if individual essences are singular propositions, then there is no hope of analyzing propositions as arrangements individual essences without circularity. However, there is still the option of analyzing propositions that are not individual essences as arrangements of propositions that are individual essences.) I conclude here that although the existence of individual essences is a potential cost of our theory of propositions, it is only actually a cost if the existence of singular propositions is a cost, too.

IV. About Aboutness

If propositions are arrangements of individual essences, then we can explain what it is for a proposition to be about something: we can say that a proposition is about a thing by virtue of containing a part that would be exemplified by that thing if it existed. To be more precise, we can say the following:

(13) ‘x is about y’ =_def‘there is a p (p is a part of x, p is an individual essence, and necessarily, (if p is exemplified, then y exemplifies p)’.

(13) analyzes aboutness in terms of individual essences. This leads to circularity we analyze individual essences in terms of singular propositions about things. But we certainly do not have to analyze individual essences as singular propositions: recall (11). The reason I offered an analysis of individual essences as singular propositions was to show that including individual essences in our ontology is no more problematic than including singular propositions in our ontology: both are equally suited to be the building blocks for propositions. However, I will later offer a theory of the correspondence relation, and one way to test that theory is to see whether the theory entails that true propositions correspond to things they are about. If we hope to be precise in our tests, it will help to go beyond an intuitive grasp of ‘aboutness’. The purpose of this section, then, is to offer a reasonable account of aboutness so that we can later test more precisely whether true propositions correspond to things they are about. This account of aboutness is not essential to our metaphysical account of propositions and correspondence, however.

Think again about (13). Notice that (13) does not entail that when a proposition is about something, there is a thing that the proposition is about. When I say, for example, that a proposition is about Socrates, according to (13), what I am saying is that the proposition contains one of Socrates’ individual essences. To say that does not commit me to saying that Socrates exists. This is a favorable result because there is an intuitive sense in which propositions can be about things that do not exist: take for example, <Socrates died>.

It will also be useful to talk about propositions being indirectly about things. For example, consider <James believes <Socrates is wise>>. That proposition is primarily about a proposition, namely, <Socrates is wise>. But there is also a sense in which it is about Socrates. That sense might be spelled out recursively as follows:

(14) ‘x is indirectly about y’ =_def‘

basis clause: x is directly about y.

recursive clause: x is directly about a proposition that is indirectly about y’,

where ‘directly about’ just means what ‘about’ means in (13). To avoid confusion, I will now revise the definition of ‘x is about y’ as follows:

(15) ‘x is about y’ =_def‘x is directly about y, or x is indirectly about y’.

Or if you like:

(16) ‘x is about y’ =_def‘x is directly or indirectly about y or the parts of y’.

A virtue of this analysis of aboutness is that it seems to yield favorable results for propositions as well as for things that are not propositions. Consider first thoughts. Suppose that a thought is the grasping of a proposition. More precisely, suppose a thought is an arrangement consisting of a mind bearing the grasping relation (or some relation in the neighborhood) to a proposition. Take an example: I have the thought that Tibbles is on the mat. We may analyze this situation as an arrangement consisting of me bearing the grasping relation to <Tibbles is on the mat>.[9] Given this analysis, <Tibbles is on the mat> is part of my thought. (It is the content of my thought, as they say.) Since being Tibbles and being the mat are parts of <Tibbles is on the mat>, by transitivity, they are also parts of my thought. Since these parts are themselves individual essences of Tibbles and the mat, it follows from our account of aboutness that my thought that Tibbles is on the mat is about Tibbles and the mat. That’s the right result.

I believe we can get the right result for concepts, too. To do so, we might suppose that a concept is a grasping of (or a disposition to grasp) an individual essence. That is, suppose that a concept is an arrangement consisting of a mind bearing some mental relation to an individual essence. Then, every concept has an individual essence as a part and is thereby about whatever might exemplify that individual essence. For example, my concept of Tibbles is about Tibbles by virtue of containing a unique and essential description (an individual essence) of Tibbles as a part.

Of course, one may question whether my analysis of thoughts and concepts is correct. My point here is that the analyses are not unreasonable, and those who accept them have additional reason to accept our definition of ‘aboutness’.[10]

…

VI. The Nature of Falsehood

I have explained what it is to be true if CTT [the correspondence theory of truth] is correct, but I have said nothing about what it is to be false. It might be thought that if we can say what it is to be true, then saying what it is to be false will be easy—trivial even. Unfortunately, that is not so. The thought that it is easy to define falsehood in terms of truth might come from the thought that we can define falsehood like this:

(19) ‘x is false’ =_def‘x is not true’.

But (19) will not do: it implies that you and me are false given that we are not true; but surely we are not false. Suppose, then, we add the following “fix”:

(20) ‘x is false’ =_def‘x is a proposition, and x not true’.

This is better. But there are still a couple difficulties. First, I identified propositions as the bearers of truth and falsity. So if I define ‘false’ in terms of ‘proposition’, then that means I have identified propositions as things that are true or false propositions, which is clearly an unhelpful identification. A more serious difficulty is this: (20) does not define ‘false’ in terms of ‘true’; rather, it defines ‘false’ in terms of ‘not true’. We may ask, “What is the relationship between ‘true’ and ‘not true?” More generally: “What is the relationship between ‘is F’ and ‘is not F’?” Here is a tempting answer:

(21) ‘x is not F’ =_def‘not (x is F)’.

But that answer will only help if we know what a sentence of the form, ‘not (A is F)’ expresses. If propositions are themselves arrangements, then the most natural thing to say here is this: a sentence of the form, ‘not (A is F)’ expresses <<A is F> is false>, which is an arrangement consisting of the property being <A is F> standing in the relation of exemplification to the property being false. In other words, (21) should be translated as

(22) ‘x is not F’ =_def‘<x is F> is false’.

But then, (20) will be translated as:

(23) ‘x is false’ =_def‘x is a proposition, and <x is true> is false’.

And clearly that will not do: it is patently circular. What are we to do?

I suggest we do the following: we interpret ‘not (A is F)’ as ‘A lacks F’. Thus, (20) becomes:

(23) ‘x is false’ =_def‘x is a proposition, and x lacks true’, where ‘lacks’ expresses the relation of lacking.

According to (23), a proposition is false by bearing the lacking relation to the property being true. The relation of lacking is a relation a thing bears to something just in case it does not bear the having (exemplification) relation to that something. Put another way: for every property P and every thing T, either T exemplifies P or T lacks P. (This is not a definition of ‘lacks’ of course: ‘lacks’ is as much a primitive here as ‘has’ or ‘exemplifies’.) On this account ‘not’ gets analyzed in terms of ‘lacks’. If treating ‘lacks’ as a primitive is a cost, that cost is offset, I think, by the benefit of not having to treat ‘not’ as a primitive; everyone has to treat one or the other as a primitive.

That takes care of the difficulty of explaining the relationship between ‘true’ and ‘not true’. What about the difficulty of saying what propositions are without circularity? To handle that difficulty, I suggest that we identify propositions using the following definition:

(25) ‘x is a proposition’ =_def‘$y (x entails y)’.

The idea here is that propositions are things that entail things. In other words, the mark of a proposition is that it stands in the relation of entailment. As I explained above, an advocate of CTT may treat ‘entailment’ as a primitive: she may maintain that we grasp the relation of entailment by virtue of seeing (being aware of) propositions entailing other propositions.[11] (This is better than treating ‘proposition’ as a primitive because (i) ‘entailment’ is already treated as a primitive in the definition of ‘correspondence’ and (ii) it is not so clear that we grasp the general type, Proposition, just by grasping a particular proposition: do we grasp the type, Proposition, just by grasping <Tibbles is on the mat>?[12])

Therefore, an advocate of CTT may define ‘false’ in terms of ‘true’. It may not be trivial/easy to do it, but fortunately, it is not impossible.

Before closing this section, I’d like to point out an interesting implication of our account of falsehood. The account entails that every proposition is either true or false. That is, it entails bivalence. Some philosophers may regard this to be a virtue of the account, whereas others may regard it as a cost. I will not defend bi-valence against the charge of being a cost (that would be a dissertation in itself). I only wish to point out that bivalence may well fall out of CTT because

(26) If CTT is true, then truth is analyzable;

(28) If truth is analyzable, then so is falsehood;

(29) Falsehood can only be analyzed as a proposition that lacks truth, if it can be analyzed at all;

(30) Therefore, any proposition that lacks truth is false;

(31) If (30), then bivalence;

(32) Therefore, bivalence.

WORKS CITED

Armstrong, D. (1997). A World of States of Affairs Cambridge University Press.

____ (2004). Truth and Truthmakers Cambridge University Press.

Fine, K. (1985). “Plantinga on the Reduction of Possibilist Discourse,” in J. E. Tomberlin

and P. Van Inwagen, eds., Alvin Plantinga, Dordrecht: D. Reidel Publishing Company: 161-5, 170, 172-3.

Heidegger, M. (1967) Von Wessen der Wahrheit in Wegmarken. Fankfurt am Main.

Higginbotham, J. (1991). “Belief and Logical Form,” Mind and Language, vol. 6: 344-

369.

Iacona, A. (2003). “Are There Propositions?” Erkenntnis, vol. 58: 325-351.

Menzel, C. (2008). Problems with the Actualist Account. Stanford Encyclopedia of Philosophy.

Planting, A. (2006) “Why Propositions Cannot be Concrete,” in Essays in the

Metaphysics of Modality. Ed. Davidson, M. Oxford University Press: 229, 230; Cf. (1993) Warrant and Proper Function. Oxford University Press: 118, 119.

Plantinga, A. (1974). The Nature of Necessity. Oxford: Oxford University Press.

Tarski, A. (1944). Philosophy and Phenomenological Research vol. 4.

Van Inwagen, P. (1983). An Essay on Free Will. Oxford University Press.

[1] I suspect that propositions are the same thing as what philosophers sometimes call ‘abstract states of affairs’. Thus, I suspect that sentences propose states of affairs: for example, ‘John is tall’ is a proposal of the state of affairs of John’s being tall. That same state of affairs may be picked out from a different perspective: for example, ‘the proposal that ‘John is tall’ expresses’; or, ‘the proposition that John is tall’. If that’s right, then the property of obtaining will have the same analysis as the property of being true, namely, correspondence to reality.

[2] For Tarski, a “proposition”, understood as the primary bearer of truth, is a class of sentence tokens (1994, p. 14, footnote 5).

[3] Armstrong (1997, p. 131, 188) takes propositions to be classes of mental state tokens, where classes are spatially located. More recently (2004, p. 15-16), he favors the view that propositions are instantiated properties of beliefs or sentences. In either case, propositions are spatially situated.

[4] I’ll stipulate that sets of objects in causally isolated spatio-temporal worlds (a.k.a., Lewis propositions) don’t count as spatial particulars. Concrete is restricted to objects that fit into a single world.

[5] Such an inference is, strictly speaking, valid only for so-called intersective adjectives. An adjective is intersective if applying an adjective-noun complex that contains it, such as ‘a red car’, to an individual intuitively entails applying the adjective in that complex (‘red’) to that individual and applying the noun in that complex (‘car’) to that same individual. By this test, ‘true’, appears to be intersective since applying the adjective-noun complex, ‘a true proposition’, to a thing intuitively entails applying ‘true’ and applying ‘a proposition’ to that same thing. By contrast, ‘fake’ and ‘former’ are examples of non-intersective adjectives.

[6] For more on this point, see Objection 2 below.

[7] For a reply to the suggestion that serious actualism is false, see Objection 2 above.

[9] If we give that analysis, then we probably should say that ‘those thoughts are the same thought’ is equivalent to ‘those thoughts have the same propositional content’.

[10] This theory of aboutness also may provide a helpful framework for a theory of meaning and reference: for example, if words are stipulated to signal (call up, bring to mind) concepts, then we might say (i) a word refers to whatever the concept signaled by it is about (or to whatever the concept stipulated to be signaled by it is about); (ii) a word expresses the haecceity that is part of the concept signaled by it; (iii) two words mean the same thing if and only if they express the same thing; (iv) sentences are built from words, and they signal thoughts; (v) a sentence refers to an arrangement that the thought it signals is about; (vi) a sentences expresses a proposition that the thought it signals contains as a part; (vii) two sentences mean the same thing if they express the same proposition.

[11] Here is an alternative definition: ‘x is a proposition’ =_def‘$y (y is a level C category, x is a member of y, $z (z exemplifies y, and z is true).’, where ‘level C category’ is a term from Hoffman and Rosencrans used to express a type of fundamental category whose generality is superseded only by the categories, Abstract, Concrete, and Entity. Someone may prefer this definition, but I will not discuss it, given that I no know simple way to define ‘level C category’.

[12] If someone does treat ‘proposition’ as primitive, then she may define ‘entailment’ in terms of ‘proposition’ as follows: ‘x entails y’ =_def‘there is a r (for all p, there is a q (if p and q are propositions, then p stands in r to q), stands in r to p, and x stands in r to y).