A certain philosophical issue has been occupying my thoughts lately, and that is the concept of "analyticity." I came across the word in a Notre Dame Philosophical Review book review I was reading, and looked up articles about it in the Stanford Encyclopedia of Philosophy, a wonderfully useful online resource. The article "The Analytic/Synthetic Distinction" was particularly informative about the contours of the issue and the history of thought about it. It's a subject as intractable as it is tantalizing (accordingly so, that is to say), and has led me through many pages of thought-scribbling to work out my own thoughts on it. As much rumination as I've done on this so far the last week or two, my thoughts on it are still at a somewhat embryonic stage with not all loose ends tied up and all, but I think I've come to some important conclusions on my own.

Consider the following statements (these are all lifted directly from the SEP article):

1. Some doctors that specialize on eyes are unmarried.
2. Some ophthalmologists are unmarried.
3. Many bachelors are ophthalmologists.
4. People who run damage their bodies.
5. If Homes killed Sikes, then Watson must be dead.
6. All doctors that specialize on eyes are doctors.
7. All ophthalmologists are doctors.
8. All bachelors are unmarried.
9. People who run move their bodies.
10. If Holmes killed Sikes, then Sikes is dead.

In successive times, philosophers have gone on to amend or emend Kant's treatment of the analytic/synthetic distinction in order to make an externally sensible account of epistemology, how we know things, particularly how we can know "a priori" truths, like those of logic and mathematics, as such. Philosophers have had high hopes for a robust characterization of the analytic, that it might provide an independent basis for the truth of assertions in logic, mathematics, science, or indeed anything else.

The enormously influential Harvard philosopher W.V. Quine, around the mid-20th-century, treated upon the subject of the analytic in a way that is still considered the last major word on it, and that has caused some philosophers to despair of making sense of the analytic/synthetic distinction at all, and with that, presumably would go any stock we would place in would-be "a priori" knowledge, as such. Quine considers all assertions to be not confirmable or infirmable in and of themselves, but only corporately and interdependently in a kind of "web of belief", where all statements are ultimately revisable in light of sense experience. This idea has a kind of plausibility, elegant self-consistency, and attractive parsimony, especially when assertions of scientific theory are considered (in fact, Quine got the idea from his examination of early-20th-century philosopher of science Pierre Duhem's observations of the interdependence of scientific theories: that no single fact tends to confirm or disprove a theory, but the corpus of knowledge is treated as a whole; Quine extrapolated this idea to treat of all would-be analytic assertions). The idea has come to be known as "confirmation holism." I think it's clear, though, that for all its self-consistency, Quine's "web of belief" says nothing at all about analyticity except to tacitly legislate it out of existence by fiat. This, in spite of the obvious fact that statements like "red is a color" and "there exists no number so large that 1 cannot be added to it" are certainly not "revisable in light of experience", even in principle: this notion is akin to one I had already hit upon in my "generalities" treatment—genuine analytic statements are used in such a way that no possibility is left for a proviso that there may exist any case in which such statements do not hold.

An important conclusion I've come to about analyticity is that it comes in discrete flavors (tentatively four). Failure to recognize this, and ill-fated attempts at treating of all analyticities as though there must be only one kind, leads the author of the "Analytic/Synthetic Distinction" article through some obvious dead-end observations such as that "there is no explicit contradiction in the thought of a married bachelor, in the way that there is in the thought of a bachelor who is not a bachelor" (that's because the word "bachelor" is not just an aggregation of letters— it has a meaning—duh!) as well as some very plain absurdities, such as "What in the concept of marriage ensures that it's a symmetric relation?" (Exactly—you just answered your own question!!) Here are the four kinds of analyticity I've drawn out from examples I've come across so far:

1. Logical truths: statements reducible to formalisms based on the axioms of logic. Statement (6) given above is one trivial example. A subset of these are analytic truths that can be changed into logical truths through substitution-by-definition, which is itself a kind of nested double-application of logical predication. Taking the definition of ophthalmologists as "doctors who specialize on eyes", and substituting it into the statement just given, we obtain statement (7). We can also arrive at statement (8) through a similar substitution-by-definition.
2. Conceptual entailments: largely if-then statements, such as statements (9) and (10) above, in which the consequent is a sine qua non of the very concept invoked.
3. Instantiation-predications: like Kant's "containment" notion, but stated in reverse, these are "a is b" statements in which a is an instance of b, or put another way, a is "contained" in b. For example, "red is a color", or "murder is immoral". These have to do with generalities, of the a priori type I described, again, in my "Generalities" treatment.
4. Mathematical statements of equivalence or inequality, quantitative in nature: arithmetic, algebraic, or otherwise. Statements of equivalence would be a subset of this general quantitative category I place here in their own category outside of inequalities, which can be considered instantiation-predications, since "greater than" or "less than" are generalities in which any number of possible quantitative instances may apply. Also, equalities have the unique property of commutativity, whereas statements of inequality require full obversion—conversion of terms and inversion of sign—to remain true. Just to clean up, mathematical propositions of the form "There exists _____ such that ______" are also instantiation-predications: a relational concept is being ascribed the general property of existence (Note: this may be considered an important pathway to treatment of existence as a "property"; as not embodied by concepts with no instances).

As you can see, deeply related to analyticity in a way that I'm not even sure yet how to characterize, as identical, or whatever, since I've been so busy working out particular details within it, is the idea of the a priori itself. The tendency in modern philosophy is to be deeply skeptical upon the very mention of a priori knowledge, because of its "track record": among the things that present themselves as would-be "a priori knowledge" are logical fallacies and schizophrenic delusions. The tacit argument seems to be that if there exist false "a priori knowledge", then anything "a priori" must by that token be immediately suspect. I'm convinced that this "throwing out of the baby with the bathwater" is inherently fallacious: stated in the modus tollens, what if everyone agreed about all would-be "a priori knowledge": would that prove it was all true? I think it is simply a matter of experience that genuine a priori knowledge—knowledge that is simply "true by knowing", or, known to be true prior to stating it in language—does exist, as such. The fact that there exists putative "a priori" knowledge that can be shown to be untrue or doubtful should not present a problem: the fact that it can be disproven a posteriori does not cast aspersions on the possibility of truly knowing a priori, for the thing to notice is that for genuine a priori knowledge, the way of knowing is the knowing (this was another "eureka" moment!), and therefore false would-be "a prioris", being false, are not "known by knowing", and therefore the possibility of "knowing by knowing" is still intact. As abstruse a notion as this certainly begs more explication, but suffice it to say for now that I think it is the only sensible way of conceiving of a priori knowledge, if it is to be honestly proposed to exist on its own terms. The strange fact remains that there exist, even alongside one another, genuine a priori insights, and falsely-believed, apparent instances of such. This is the idea that I think any philosopher who wants to treat seriously of the a priori needs to come to grips with.

At the root of the veiled but deep-rooted hostility many modern philosophers feel toward the idea of the a priori is, I take it, in the "naturalistic turn" that philosophy has taken over the past 3 decades or so. For the philosophical naturalist can give no account of why, for example, mathematical truths should exist both a priori, and a posteriori, observable in nature (the theist, on the other hand, has a ready answer: God gave us the ability to make true insights into universal truths). Quine, in his scientism, sits firmly in this camp, and would be expected to militate against the possibility of the a priori, which in fact is what his philosophy amounts to. What the anti-a priori philosopher is up against is common experience; for example, that we do in fact know, a priori, that "there exists no number so large but that 1 can be added to it." It simply remains for someone to throw a counterweight into the arena by firmly proclaiming that the anti-analytic Emperor has no clothes, and that genuine a priori insights do exist even though falsely apparent ones exist as well (again, the Christian theist, viewing human nature as originally good but corrupted and flawed, should have no problem with this). Perhaps I should take that on as a personal objective. As quickly and copiously as my thoughts on the subject seem to be flowing so far, I don't have much trouble imagining coming up with a book's worth of material on it. Subsequent work will certainly require some close reading of primary sources, certainly Quine, and others besides. I just wish I had time to do all the reading I'd like. The books-to-read just seem to pile up...

Whoa—that's entirely too much to expect anyone to read at one sitting, if at all. Oh, well, sorry about that.

Currently listening to: Explosions in the Sky – The Earth Is Not a Cold, Dead Place