The Fundamental Triple-Dichotomy

The fundamental triple-dichotomy is a set of three ways of dividing propositions into two exhaustive and exclusive categories. Exactly where each of these lines lies depends of course on exactly how each dichotomy is defined, and the fundamental character of the dichotomies makes precise definition difficult. Underlying these three dichotomies is, I claim, a single distinction important enough to deserve these three different pairs of concepts. The distinction is important because it connects with radical differences in method between a priori sciences such as mathematics and the empirical sciences. For this reason I urge an understanding of these concepts, and an attitude towards justification, which results in the coincidence of the three dichotomies.
The Dichotomies in Brief
Truth value determined by meaning alone.
Truth value depends not only on meaning but also upon some matter of fact.
Truth value the same in all possible worlds.
Truth value not the same in all possible worlds.
Justifiable or refutable without benefit of empirical observations.
Justification or refutation depends essentially upon empirical observations.

Justification of The Identities
I do not intend to attempt to prove these identifications, or to refute those who claim to have disproven them. Instead I intend to offer some rhetoric intended to persuade readers that:
  1. the terms analytic and necessary should be so defined that they clearly have the same meaning
  2. we should agree to accept only a priori justifications for necessary propositions and a posteriori justifications for contingent propositions.
What does it mean to say that meaning alone suffices to establish truth? What other possible determinants might there be? The simplest answer in the words of Quine is "extra-linguistic fact". i.e. all those facts that may vary from one possible world to another except the linguistic facts which determine the meaning of the statement under consideration. So, to say that a statement is analytic is to say that the proposition it expresses is true in every possible world, i.e. is necessary.
When we say that a proposition is necessary there is no intent to claim that the the truth of any sentence is independent of its meaning. A sentence expresses a necessary truth if, the meaning of the sentence (in context) determines its truth in any possible world (under the semantics in the context of use, ignoring the meaning it might have in these other possible worlds). Necessary truths are not independent of the meaning of the sentences in which they are expressed.
If you make explicit aspects of the model of language implicit in the definitions of analyticity and necessity these terms can be seen to have the same meaning. This can be made clearer and more precise by the use of a mathematical or formal model.
Necessary iff A Priori
It is a matter of choice for us as rational agents what kind justification we will require before we will accept some conjecture as established. My recommendation here is that we should accept an a priori justification only for a necessary truth (since an a priori justification, if sound, speaks with the same force for the truth of a conjecture in any one world as any other). An a posteriori justification, because it depends upon appeal to observations in one particular world, will not hold good in any world in which those observations might not yeild the same result. It should therefore be admitted as a justification only for a contingent conjecture.

It is important when evaluating the practical consequences of this recommendation to be aware that all facts about the meaning of natural languages are contingent, and that a justification of the truth of some statement (i.e. an assertion of a sentence in some context) will still be a priori even if some empirical enquiry proves necessary to establish the meaning of the statement. For example, if the meaning of the phrase "the number of planets" is deemed to be the number 9, then anyone who does not know that the number of planets is 9 does not know the meaning of the phrase "the number of planets". In this case the statement "the number of planets is 9" can be justified a priori since once its meaning is established it can be seen to be true without further empirical observations.

propositions I'm using this word here in a really sloppy way, since most of what I have to say doesn't depend on exactly what you mean by proposition. In the formal model however, though the term is still very loosely defined, it definitely serves as the name of things which are intended to be meanings of certain kinds of statements in context. If a proposition is the meaning of a statement, then it doesn't really make sense to talk about its meaning. So the term "analytic", as defined above, isn't applicable to propositions, though "necessary" and "a priori" are. You can see I've got myself into a terminological muddle, and I think I'm going to have to rework these pages so that the word proposition is used more tightly. In the page on the formal model there is an explanation of why the use of propositions in the model is OK, notwithstanding the widespread belief that propositions are a species of vapourware. I am endebted to my friend Roger Stokes for making me feel uncomfortable about my use of the word proposition here.

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