I suppose I ought to begin to tell this story about truth I've been talking about. I can only hope that it will end up somewhere with positive results. I do not want to be merely a negative party pooper or something like that.
In the first entry of this thing I indicated that the story begins with my study of modal logic. So this is where we shall begin. I do not want to give too much detail about the actual systems of modal logic I studied because that would be tedious and probably pointless. However, I do need to explain some of the more philosophical aspects about a particular type of modality--the
alethic modalities of
possibility and
necessity. In particular I will speak about necessity, for this is the heart of the matter.
So we say "necessarily,
p" when it is the case that '
p' must be true. Philosophers like Alvin Plantinga are ready with the example of mathematical statements such as "seven is prime" wich are just such "propositions," they say, that are not capable of being false "in any possible world." Hence we say that "necessarily, seven is prime" is true. Another case is "all bachelors are unmarried men." They say that it is the case that "necessarily, all bachelors are unmarried men" because the "proposition expressed" by "all bachelors are unmarried men"
must be true, or its denial "some bachelors are not unmarried men" is "self-contradictory"--whatever that means.
If you ask why "all bachelors are unmarried men" must be true, Plantinga will respond by saying that it is due to the meanings of the terms "bachelor" and "unmarried man." The set of bachelors is contained in the set of unmarried men, and to say otherwise implies a special meaning of one of those terms (See Plantinga's
Nature of Necessity for all of this.)
If you say that the contingency of the meanings of the words "bachelor," "unmarried," and "man" make the proposition contingent (because these words mean what they do by mere human convention) Plantinga will reply that you are confusing the
sentence with the
proposition. The state of affairs that S expresses
p is contingent has nothing to do with the contingency or necessity of
p. It is true that it is not necessary that S expresses
p, but this does not mean that
p is not necessary.
This brings us to the heart of my criticism of the notion of "necessity" as Plantinga discusses it. The notion of necessity relies on an entity called the proposition. Strictly speaking, sentences are never necessary because their meanings are contingent (by convention), but the propositions they express exist in some ethereal realm separate from space and time, and
they are the bearers of being necessary or contingent.
In order to make sense of a proposition being true necessarily, Plantinga revives the Leibnizian notion of possible worlds. He makes the notion respectable to 20th century philosophy by defining in precise terms what a "possible" world is. He begins with the notion of a
state of affairs. For example, "being in love", "being white", "being an American in the year 2004 in the town of Hillsboro, Kansas" to name a few. Roughly, a state of affairs is of the form "being P" where P is some property.
We require a couple more notions prior to defining a possible world:
inclusion and
preclusion. A state of affairs S
1 includes a state of affairs S
2 iff (if and only if) it is the case that if S
1 obtains, then S
2 obtains as well. A state of affairs S
1 precludes a state of affairs S
2 iff it is the case that if S
1 obtains then S
2 does not obtain. For example, "being an American in the year 2004 in the town of Hillsboro, Kansas" includes "being in Hillsboro, Kansas" but precludes "being in Budapest, Hungary."
Now we are ready for the grand definition. A possible world
w is a state of affairs such that for
every state of affairs S, exactly one of the following holds: (1)
w includes S or (2)
w precludes S. In short, a possible world is a
maximal state of affairs.
Now we must say that
p is necessary iff it is the case that
p is true in every possible world. (Note:
p is true in a world
w iff
w includes the state of affairs that is logically equivalent to
p.)
This is all very elegant of course, but it does no help for the overall validity of the notion of necessity because it once again posits an entity: the state of affairs, which is not much different--metaphysically--than the proposition.
So far I have only explained some of the background of our subject, and I haven't even really began to touch the heart of the matters about truth in general. At the present my criticism is that propositions are entities which are purely metaphysical at best. They are mathematical creations, and I think that their explanatory power is severely limited in the face of the "real" world. They work very nicely for a mathematical description of the world but they do very little to help in addressing real issues of philosophy--e.g. the meaning of human existence. The story shall continue.
