Tutorial Thirteen
Could be, would be, must be… Philosophical Logic and "Serious Metaphysics"

Because we’ll be studying how logic impacts meaning, truth, and logical truth (= what couldn't possibly be wrong) I’d like to call this chapter “Meaning and Necessity”. But that’s already been taken. (Carnap, 1947). I also thought about adding "or it all depends on how you define it...not!" as a subtitle. We'll try to see that meaning and necessity depends on far more than definitions we might give.

Some philosophers, extreme Rationalists, have thought that philosophy is the study of necessary truths that can somehow be known in an a priori way (without empirical evidence). True philosophy, on this view, might show that God exists as a necessary being. And the methods of philosophy would be unlike science: The evidence mustered for God's existence would be a matter of pure thought. No experiment or observation needed! So, knowledge of God would be a priori.

But there is a contrary tendency, going back at least to David Hume, to think that the only way a sentence can be necessary is for it to be knowable by logic alone. Any "metaphysics" attempting to show we can come to great conclusions from the philosophical armchair is just mysticism. So, Hume wrote, the only way to understand necessary truths will be in terms of the logical relating of ideas (e.g., if we relate the idea of a triangle with that of numbers of angles, we get to the necessary conclusion that all triangles have three sides...a mere matter of the meaning). A sentence, on this view, is necessary if it makes a statement about how we define words. And, so, the necessary sentence makes a statement that is a priori, knowable prior to any experience. Sentences about the world, on the other hand, express matters of fact and so are empirical and a posteriori. This view is in sharp contrast to the extreme rationalist described in the previous paragraph; so let's call the current paragraph's view "extreme empiricism".

OK, let's get started on necessity from the viewpoint of our logic work...

It might be thought that necessity just boils down to truth according to rules of logic, which is just deducibility in our formal system. Here's why...

Think about a sentence like

(*) If Sam is a female cellist, then she's female.

Duh...not much to this statement! But it surely couldn't be false. That is , (*) is logically true. And we can see why when we symbolize it:

(* symbolized)  (Fs&Cs)>Fs

OK:

... there needs to be more to necessity than this. For example, something like our

(**)     All triangles have three angles.

counts as true because of the logic of the grammatical structure "All ___ are ___" and the meaning of the word "triangle". But our system of deduction doesn't capture the meaning relation between "triangle" and "has a angle". In our logical system, we might represent "x is a triangle" with 'Tx' and "x has three angles" with 'Hx'. But there is no deductive relationship between 'T' and 'H'. So, our symbolization of "all triangles have three angles":

** symbolized:       (^x)(Tx>Hx)

is not a logical truth of our deduction system. But it is a necessary truth. So, Hypothesis 1 (above) fails to capture the notion of necessity.

Carnap

A better hypothesis?

...there may be a serious problem with Hypothesis 2. For a real language, like English, it may be hard to distinguish the meaning postulates from other facts. Some will be obvious. Our "all triangles have three angles" is clearly a matter of the definition of triangle. And "there are no triangles drawn on this page" is an empirical fact, but not a matter of meaning. However, there are lots of cases where the notion of meaning is far too unclear.

Everything green is extended. (Quine)

All water is made of H₂0. (Kripke, Putnam)

These would seem to be true...but they don't fit our meaning / fact distinction at all well. They seem empirical. And yet they also seem to be about meaning and to be necessary. For example, any possible molecule that wasn't H₂O would seem not to be water. So, the intuitions have it, there is no possible way for some possible substance to be water, real water, without being made of H₂0. So, water = H₂0 is necessary even if empirical.

Thus, necessity would seem to come to more than a priori deduction.