Modernizing (and Medievalizing) Analyticity

A project I've been hoping to do eventually is to re-work the concept-containment notion of analyticity. Something has always seemed to me intuitive about it, at least in the "Bachelors are unmarried" sorts of cases. (From the 19th century onward, for various reasons, the analytic truths seem to have become equated with the logical truths; this seems wrong to me.)

I'd also like to see whether the notion of analyticity comes up at all in medieval philosophy, and whether any of the tools of medieval philosophy could be of use for this project (or, what would be just as interesting, whether they would find the concept-containment notion of analyticity hopelessly confused).

There are several problems for the concept-containment approach, but a big one is this:

1. Forms of Analytic Judgments: Kant (sometimes) defined analyticity in terms of conceptual containment, roughly as: A judgment of the form 'A are B' is analytic iff the concept B is contained in the concept A.

The worry is that there are many judgments that do not seem to have this form, but where they seem to also be true in virtue of 'meaning' or 'concepts' (or something close). Some examples, taken from SEP:

(11) If Bob is married to Sue, then Sue is married to Bob.
(12) Anyone who's an ancestor of an ancestor of Bob is an ancestor of Bob.
(13) If x is bigger than y, and y is bigger than z, then x is bigger than z.
(14) If something is red, then it's colored.

Other examples, from Jerrold Katz:

(15) Mary walks with those with whom she herself walks.
(16) Mary walks with those with whom she herself strolls.
(17) Poor people have less money than rich people.
(18) Rich people have more money than poor people.

It's not totally clear how all of these examples can be analytic (assuming they all are) if we take analytic truth to mean that the predicate-concept is contained in the subject-concept.

I don't have a worked-out answer to this yet, but I suspect that some of the work in cognitive linguistics might be helpful. In fact, Katz' own work might be helpful here, though from what I understand Katz is a Platonist (rather than a "conceptualist") about meaning, and so it would have to be properly adapted.

In addition to these strategies, where medieval philosophy might be useful here is in seeing how we might, in fact, be able to reformulate all "basic" sentences and then parse them out so that they technically obey the constraint of "subject-copula-predicate" form.

As Terence Parsons points out, medieval scholastic Latin is unique in that it is a natural language and yet there is no distinction between a sentence's ordinary surface grammar and its logical form.

Now, if one had a close enough association between words and mental concepts, one might then be able to get a nice conceptualist-type semantics going. And it seems certain medieval thinkers did have precisely this sort of close association between mental concepts and meaning, viz., in the theory of "subordination" (I'm thinking of Buridan and Ockham right now).

This suggests that we could translate basic ordinary-language sentences into medieval subject-copula-predicate sentences, and the concept-containment idea could become more useful again.

I'm not sure it will be as simple as that or that this will solve everything, but I suspect it will make things easier.

There are some other issues for a conceptual containment theory of analyticity too:

2. Conceptual Containment: There are really at least two problems here: (a) a theory of concepts, and (b) a notion of containment. Can we give a plausible and clear theory of both? (And, what would be even better: Can we give a theory of both that is mathematizable and subject to rigor and computation once we are given a case?) And how neutral can we be here with respect to different theories of concepts and containment?

How can medieval philosophy help here? Medieval philosophy certainly contains much discussion of concepts, and that should certainly be useful.

As for the notion of containment, I can't help but think of Scotus' theory of "repugnance" and "non-repugnance" by which he assesses the modal status of basic propositions -- the kinds of propositions concept-containment seems to be after (see page 162, here). What's interesting is that Scotus seems to define repugnance as a relation holding between terms. That seems to make it a semantic relation rather than a conceptual relation for Scotus; moreover, the relation's holding is said to be grounded in "notae," which are in some sense objective features of the external world.

So this isn't exactly concept-containment analyticity; but still, in terms of its formal/logical properties, non-repugnance/repugnance behaves similarly to concept-containment/exclusion. (This seems to be an instance of a more "externalist," metaphysical picture of containment and exclusion relations; I get the sense that this sort of externalism is the norm in medieval philosophy, especially pre-Nominalism, though even after that as well.) Moreover, like repugnance-relations, concept-containment relations are supposed to ground the modal status of propositions, and moreover, they both seem to deal with the same sorts of propositions. So I can't help but think Scotus will be helpful here, even if he probably wouldn't have a view of analyticity like Kant's.

3. Rigor: How would a rigorous conceptual semantics go? Can we make it as formal, precise and mathematical as the non-conceptualist semantics have been? Some work has already been done on this sort of thing, but there's more to be said. Again, I wonder if the medieval logic might help us here, since Parsons and others have shown it to be entirely rigorous and fit for mathematical treatment. Medieval logic at its height was generally far more sophisticated than anything after it -- certainly more sophisticated than anything Kant did on logic -- and so I can only imagine it will make this project easier.

4. Externalism: Although the conceptual-containment approach seem plausible in certain cases, so does semantic externalism. Gillian Russell, a professor here at UNC, has done some brilliant work on updating analyticity to take these post-Kripkean insights into account. However, she tends toward the more externalist side of things, and I'd like to see whether we can salvage more of the connections between meaning, analyticity and concepts than she does, while still giving a reasonable account of the externalist insights (something I worry cognitive semantics a la Peter Gardenfors hasn't quite done -- see 4.1 here, for instance).

One thing I worry about in trying to find analyticity in medieval philosophy is that medieval philosophy seems to tend much more toward externalism about semantic content (though this is only a hunch I get -- I can't point to anything specific). But maybe I'm wrong and there is room for analyticity in medieval philosophy; and even if not, the project may still be worthwhile, since maybe we will find new reasons to either abandon or revise our conception of analyticity in interesting ways we've never thought of.

So I plan to do some research on medieval logic and semantics in the next few weeks, and maybe this will help my concept-containment project. Moreover, I think it is an interesting historical project in its own right to see whether something like analyticity can be found (or reformulated) in terms of medieval semantic categories.

The Critique of 'The Critique of Pure Reason' II: Preface to the Second Edition

In this post I'll note some areas of concern I have from an Aristotelian-Thomistic (henceforth just 'Aristotelian') point of view with Kant's B-edition preface. Again, as I said in my first post, this isn't really meant to be a summary of Kant's views, but more along the lines of a set of notes.

One thing which already indicates Kant has a different conception of reality than an Aristotelian realist view is his description of logic toward the beginning. Kant says that logic is "the science that exhaustively presents and strictly proves nothing but the formal rules of all thinking." But a realist will want to ask why logic is defined in terms of its applicability to our thoughts rather than to mind-independent propositions or even objects. After all, since Kant's time, many different logics have been developed, and we can think in terms of any of these if we want to. But this says nothing about which one more correctly describes reality. Of course, what Kant will want to argue is that what I am calling "reality" is actually a product of human cognitive capacities. So the difference to note here between the two views is not so much of whether logic is to be applied to reality, but rather, what reality refers to.

A second point of interest is Kant's discussion of mathematical knowledge at Bxii, where he takes as his example that of a Euclidean triangle. Kant uses this point to illustrate how he thinks it is that we acquire mathematical knowledge. What I would focus on though is his view that, more generally, Euclidean geometry is necessary. For Kant, a judgment is necessary if and only if it is a priori. The problem is that we now know that Euclidean geometry is not, in fact, necessary, since it doesn't even accurately describe the physical universe. So either euclidean geometry is not a priori or Kant was wrong to include necessity as part of something's being a priori. But it seems rather clear euclidean geometry was formulated a priori if anything was. So it must follow that not all a priori cognitions are necessary. But this is okay for the Aristotelian. The Aristotelian method of doing metaphysics or science has never been equivalent to discovering necessary truths which are wholly a priori; rather, it is empirical. We can delineate what is metaphysically possible and impossible through a priori reasoning and we see whether our theories correspond to empirical reality.

Kant's view of the a priori goes with his view of metaphysics. He defines metaphysics as "a wholly isolated speculative cognition of reason that elevates itself entirely above all instruction from experience." Not according to an Aristotelian view however. As Aquinas states in 'De Veritate', "Whatever is in the intellect was first in the senses." Of course, the reason Kant wants to make metaphysics a wholly a priori discipline is because he wants the certainty which he thinks the method of previous thinkers cannot provide. In his own words Kant thinks that "up to now [i.e. up until Kant] the procedure of metaphysics has been a mere groping, and what is the worst, a groping among mere concepts." But the Aristotelian wants to ask why it has only been a "mere groping among concepts"? For one, the metaphysician does not need to limit the scope of his inquiry to concepts, at least if we don't hold to the view that metaphysics must be a priori. As regards "mere groping," admittedly, we cannot be absolutely certain our metaphysical theories are true; but this is a far too strict condition upon knowledge which, were it not for Descartes, we would not think was necessary.

In the next post I will focus on the second half of the preface, examining Kant's solution to the problem of metaphysical knowledge as he sees it.

The Critique of 'The Critique of Pure Reason' I: Preface to the First Edition

As I study Kant's Critique of Pure Reason I am taking notes and trying to identify the points where someone sympathetic to a generally Aristotelian (particularly Thomist) view of metaphysics and knowledge would have reservations. So I will be essentially transferring my notes and other thoughts here as an ongoing commentary on Kant's great work. I will not be going line for line and explaining all his ideas. Rather, I will be picking out parts that I think are particularly pertinent to distinguishing him from, and criticizing him from the perspective of, a view which an Aristotelian is likely to take. I should note that, though I am coming from a decidedly realist picture and hence not particularly sympathetic with all aspects of Kant's thought, I certainly consider it a huge step up from Hume and a work of ingenious creativity. Kant definitely has my respect as one of the greatest thinkers to have lived, and I think he needs to be taken much more seriously than he is today.

With that said, let's look at the preface to the first edition of Kant's treatise. Though it does contain important information, since it is relatively short I will say more about the preface to the second edition. As a general remark, Kant seems to be primarily concerned here with the problem of metaphysical knowledge, whereas in the second edition preface he focuses in more on his own "Copernican revolution". Kant wants to know how it is possible for metaphysics to be justified. After all, in the very first paragraph Kant admits that metaphysics certainly deals in perennial problems which reason is always tempted to come back to.

One might wonder why we need any justification for thinking that we can have metaphysical beliefs. But Kant lays out a story as to what has happened to metaphysics up to the time of his writing:

"In the beginning, under the administration of the dogmatists, her rule was despotic. Yet because her legislation still retained traces of ancient barbarism, this rule gradually degenerated through internal wars into complete anarchy..."

Here the dogmatists represent the continental rationalists, especially people like Descartes, Leibniz, and Wolff. The anarchy was brought about by skeptical empiricists, Hume in particular. Kant considers the skeptical criticisms of rationalist philosophy to have been something of a deathblow, at least given rationalist assumptions about knowledge (such as a correspondence theory of truth or the doctrine of innate ideas). This is the background within which Kant hopes to provide a new, certain and complete theory which will solve the empiricist objections and provide a basis for metaphysics. Of course, right off the bat it is clear that no room between the rationalists and empiricists has been made for something like a more Aristotelian view of the matter, so it appears that Kant's argument will be a non-starter at least in terms of disproving the Aristotelian type of metaphysics and knowledge. This is a theme which will come up often, viz. that Kant, working within a certain philosophical movement, will fail to consider the Aristoteliean view which could solve the same problems he wants to without the seismic shift in our analyses of knowledge, objectivitiy, necessity, truth, etc.

In part II I'll examine the preface to the second edition of Kant's Critique and bring up some more specific points and objections.