Proposition
A proposition is ordered
whole whose parts are only individual
essences (Or if you don’t like individual essences, my back-up theory is
that propositions not expressible by a sentence of the form, S exists, are ordered wholes whose parts
are propositions expressible by a sentence of the form, S exists.). Alternatively, a proposition is a thing that stands in
the relation of entailment to other things. I treat ‘entailment’ as a primitive term graspable by way of direct awareness of
the entailment relation when one is aware of one proposition entailing another:
e.g. the proposition that Jim is taller than Sue entails the proposition that
Sue is not taller than Jim. For more on this account of propositions, see an
except from my dissertation chapter on propositions here.
What about abstract states of affairs? What is their
relationship to propositions? I suspect that they just are propositions. The apparent difference lies in the
differences between our linguistic and/or conceptual manner of approaching
propositions versus states of affairs. Someone might think that the
linguistic/conceptual data motivates drawing distinction between propositions
and states of affairs. But I suspect that this data can be explained away by
viewing a proposition as a state of affairs that’s proposed (through language or in one’s mind’s eye). I might be
wrong about this.
Some people think that propositions are concrete things, substances or
arrangements of substances, like scribbles on a sheet of paper or physical
brain states. I’ll offer three reasons why I’ve become convinced that this is
mistaken.
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.[1]
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. there is an x
(xF & xG) → there is an x (xG), where F =
‘true’ and G = ‘identical to the proposition Concrete’.[2]) 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.[3])
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.
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
<P is necessary> 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.
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 <P
exists> is possible, then <P exists> exists (given serious actualism[4]).
And if <P exists> exists, then P exists, too. Therefore, by the contraposition,
if P does not exist, then <P
exists> 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.
Much
more work needs to be done on propositions. Existence and identity conditions
for propositions have yet to be worked out. I think we can learn a lot from the
attempts to provide existence and identity conditions of sets.
Some of the same paradoxes applied to sets show up for propositions, too.
Consider, for example, the proposition P that every proposition that isn’t
about itself is an interesting one. Ask: is P about itself? Apparently it is
only if it isn’t! I’ve worked out a solution
to this paradox in Chapter 4 of my dissertation.
In
Chapter 4, I also discuss the metaphysics of various
types of propositions, including these: disjunctive, conjunctive, tensed,
modal, negative, universal generalization, and counterfactual.
References
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.
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.
Van Inwagen, P. (1983). An Essay on Free Will. Oxford
University Press.
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.
Tarski, A. (1944). Philosophy
and Phenomenological Research vol. 4.
[1] 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.
[2]
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.
[3] For more on this point, see Objection 2 below.
[4] For a reply to the suggestion that serious actualism is false, see Objection 2 above.