Arguments against a World Partition

While I'm on a roll, I figure I'll jot down what I have so far for my views on the relation between logic and reality. I'm trying to find some way of arguing for the position, or at least making it clearer; I'm attempting to balance listening to my intuitions with a desire to communicate clearly to others and be sufficiently critical of myself. So, here's the argument.

As stated earlier in my post on individuation and logic, logic requires individuals: things which are undivided in themselves (law of identity) and divided from everything else. I mentioned that this entails a partition of the world. I intend this in a mathematical sense: any application of logic would entail a partition P, which is a set of elements {a, b, . . ., z} such that for every x and y in P, the intersection of x and y is the null set, and the union of everything within P is the universe (everything, pretty much). The disjointment thesis I take to follow readily from the law of non-contradiction (there is an exact isomorphism between logic and set theory, from which I get the idea of a partition, where "and" -> "union", "or" -> "intersection", "not" -> complement, "false" -> "null set", and "true" -> "universal set").

The universality thesis I take to be a bit harder to prove. It's easy if you allow the law of the excluded middle, but as that is contentious I propose a different proof. Let's say that the union of all the elements in P does not contain everything. Then, there is something in the universe which is not in P (P', or ~P, or something of the sort). But then we can form the partition R from the union of P and ~P. ~P will be disjoint from everything in P, and so everything in R will be disjoint from everything else. Further, the union of P and ~P now does contain everything and by definition is the universal set. Therefore, R is the partition which we were looking for. I guess this ends up being an argument for the law of the excluded middle if one adopts the strict logical starting point.

So, my first argument is simply this: I don't see why I am forced to believe that this accurately describes the universe. Therefore, I am entitled to pursue a different research project. This I take to be the solidest, though of course least persuasive position.

The second argument is that it is possible that the universe does not hold up to such a partition. If this is possible, it is possible in some possible world. But if it is possible in some possible world, then (assuming our modal logic is at least reflexive) from that world it would be possible that the universe could be partitioned. If it is possible that the universe could be partitioned, then this would create a partitioning from the standpoint of that world. So the universe would be partitioned from the standpoint of that world, and it would not be true there that the universe would be non-partitioned. Therefore, if it is possible for the world to be non-partitioned, then it is non-partitioned. Ergo, etc. I think I'm playing fast and loose with the modal stuff here, and I need to work out details at some point, but that's at least the broad outline.

The third argument is the least developed. I'm not sure whether it confirms or denies my senior paper (which was on the inapplicability of Goedel's Theorem to reason; the key ambiguity being the definition of reason). More or less, here is how it would go: the elements in our partition would be isomorphic to some formal system which can express arithmetic. This is due to the fact that any decent partition actually deals with arithmetic and other mathematical facts. However, in this case Goedel's Theorem applies, and there exists some truth in the universe which has not been accounted for. But the partition was supposed to be universal. I think that I may be equivocating on "universal" throughout the various definitions, and this gets into the problem of the one and the many (is "universal" the most general thing underlying everything, or is it the collection of all the particulars?). Of course, I think this problem gives a pretty good impetus to the rejection of partitioning itself.

So, not really any fully developed ideas, but some which I have been batting around.

Suzuki on Logic

Currently reading:
Apologia Pro Vita Sua
   by John Henry Newman
Zen and Japanese Culture
   by D. T. Suzuki

I've been reading through Suzuki, and he's been making some points about logic which both intrigue and infuriate me. I'll try to cover why he is (at times) so anti-logic, the points at which I have my sympathies, and the points at which I think he is way off.

The first reason why Suzuki is against intellectualizing the world is nothing terribly particular to Zen. He claims that in conceptualizing things, we can lose track of the things themselves; what we really need is direct acquaintance with reality. I call this the practical anti-logic thesis: avoid logic if it is causing you to get caught up in the words instead of the reality. Ok, fine; but I find that to be pretty obvious advice. That's not to say that I don't get caught up in concept fixation at times, but I already recognize that as less than ideal. Any church I walk into will stress the need for a personal involvement instead of just a "head knowledge" of the faith.

So, there has to be more to Suzuki's position than this, though the above plays a pretty significant role (I may do a post sometime on his view of subjectivity). And this is were what I call the ontological anti-logic thesis steps in: the world just is not conducive to logical analysis. Note that, as I have been saying in previous posts, this does not entail that the law of non-contradiction is false. Suzuki doesn't care enough about abstracta to deal with that question. All that has to hold is that any application of logic distorts the world. The world is a totality, but not in a pantheistic way; full of particulars which each possess their source equally. I'm not quite sure what he's talking about either, but I don't see anything prima facie wrong with stating that reality is neither one nor many. Sure, such a reality would not fit into any nice categories of ours, but why should I assume that it would?

In connection with this, there seems to be two main places where logic breaks down throughout different philosophical schools, and upon which I think Suzuki and the Buddhist tradition draw. One is when dealing with human conceptual constructions. Of course, if we create the conceptual scheme, then there is no guarantee that it will prove consistent. Further, the scheme may end up being practical even if it fails logical tests; it may even be conducive to learning the truth about the way the world is (I should hope so; I doubt that my thoughts ever will be fully coherent, but I would like to think that I'll achieve something in my searches). So it may even make sense to hold to a contradiction, because although it is imperfect, it could be better than any other option we see. This is even more true if reality simply isn't conducive to logical analysis, in which case we need something (however imperfect) by which to communicate to others with our feeble attempts. The second area where logic seems to break down is with the will; but that is a different series.

So, given all of this, where do I have problems with Suzuki? With his emphasis on creative freedom instead of order. If conceptual schemata are all under a curse, it seems that there should be a place for form as well as formlessness (as in Mahayana Buddhism, form is formlessness, and vice versa). Zen monasteries are some of the most rigid out there. And my particular beef with Suzuki is the prioritizing of the creative artist's approach to an intuitive grasp of reality, while denigrating the analytic approach. As a former mathematician and a wannabe mediaevalist, I firmly disagree. Much of my life is about reaching and expressing my intuitive insights through logic. At times I fall apart into an illogical muddle, but this is hardly when I am at my best and when I have the clearest intuitions about reality. Rather, it is in the midst of Galois theory when I have a mystical vision of the beguiling, entrancing wholeness of all form, or in the subtleties of the Doctor Subtilis that I have my most encompassing vision of the reality of God as the ultimate final, efficient, and exemplar cause of all, the source of all harmony and diversity within unity. To posit such a sharp distinction between logical analysis and intuitive feeling is opposed to Suzuki's very project of removing dualities.

Scotus Congress

Currently reading:
Itinerarium Mentis in Deum
   by St. Bonaventure

I am now back from the Scotus Congress which was at St. Bonaventure's. It was a bit of a change in pace. At Trinity, I'm pretty much the resident scholastic. At the congress, though, I felt like an infant in the world of medieval studies. It was cool though to meet some other people with similar interests and to get some tips on how to proceed. The papers which I heard seemed to fall into three camps: the ones which were great, though I couldn't quite catch everything; the ones which were decent, but mostly rehash of stuff I know; and the ones which were pretty much a waste of time (either they weren't very good, or I couldn't follow them at all, or both).

I've regained some motivation, but the usual question of breadth vs. depth still plagues me. I want to learn everything, but I want to learn it all well. To really do medieval philosophy would require steeping in it for a good amount of time, it seems. So to do comparative work with, say, Madhyamaka and Yogacara Buddhism would be fascinating, but I couldn't really get all of the good stuff out of either then.

Also, if I were to go along a more purely medievalist route, would I want to do more with philosophy and theology, in which case I would continue with some training in modern philosophy in which case I could work with the thinkers as relevant to today, or would I continue in a more historical vein, understanding the context better and perhaps unearthing some less-studied (but nonetheless astute) thinker? Practical calculations also seem to play a role. I think I would prefer going with a straight-up medieval studies degree more (at least during the studies, I don't know about the subsequent career path), as I could dabble in other areas more easily (bored with philosophy? let's look at the historical context. Bored with history? What literature could be influenced by these thinkers?). However, it would be a fair bit easier to get a philosophy job (not that that would be a guarantee itself). In addition, there is the issue of where I could benefit the community the best. With my talents & interests and the current historical circumstances of American intellectual culture, would I better serve the community by bringing the thought of these guys into contemporary discussion (building conceptual bridges), or by working on critical editions, translations, and the like (building practical bridges)?

Principles of Sufficient Reason and Parsimony

I'm about to head off to the Scotus Congress in a few hours, so I thought that I'd jot down this thought before I go and absorb the subtle doctor for 4 days. It's probably something that has been noted before, but it has struck me as new, so you can smile and nod and play along for a couple minutes. There are two principles in philosophy which play a significant, though controversial, role. One is the principle of sufficient reason (PSR), which more or less states that there's got to be a reason for everything. On the other hand, there is the principle of parsimony (PoP) (also called "Ockham's Razor," "Scotus' Rule," and most likely other things) which says that we shouldn't postulate more entities than we need. Which therefore makes it the contrapositive of the former (and thus logically equivalent). Observe (where "E(x)" is "x exists" and "R(y)" is "there is a reason that y", ~ is not, and -> is implication):
PSR: E(x) -> R(E(x))
PoP: ~R(E(x)) -> ~E(x)
Granted, PoP is sometimes epistemological (don't postulate more entities than you have found a need for), but this seems to piggyback on the metaphysical claim (why should we choose the simpler explanation unless this gets closer to the reality of things?) So, on that note, if we expect the world to be strongly rational, then it also needs to be as simple as possible.

Now, maybe we think that PSR is too strong; maybe we want WPSR, the weak principle of sufficient reason, which can be stated as "if it is possible that there is a reason for x, then there is a reason for x." What would we get for an equivalent WPoP (where P is possible and N is necessary)?
WPSR: P(R(x)) -> R(x)
WPoP: ~R(x) -> ~P(R(x)); ~R(x) -> N(~R(x))
So, whatever cannot be explained, necessarily cannot be explained. I'm not sure that this is terribly profound; it seems like what it means for something to be explainable. But if WPoP is trivial, that means that WPSR is true.

The above seems to make R somewhat similar to the necessity operator (and WPSR smacks of a cross between an ontological and a cosmological argument), which I find intriguing, although I do note that ~R(x) isn't interchangeable for P(~x) (in fact, God is the main possibly-unexplainable entity, and I certainly don't want to say that God can't exist). So what are the relations between explainability (as an ontological feature, where things really do have some such relation between them) and necessity?

And now I'll let the reader make something coherent and profound out of the above, and attribute it to me (let me know about it). Ah, the rewards of obfuscation and pedanticness.