Some Thoughts on an Aristotelian View of Propositional Logic

How would propositional logic fit with regard to the Aristotelian Organon? By the Aristotelian Organon, I mean the extended (medieval) Organon, which numbers the books of logic as nine:

1) Isagoge (Porphyry's)
2) Categories
3) Peri Hermeneias (De Interpretatione)
4) Prior Analytics
5) Posterior Analytics
6) Topics
7) Sophistical Refutations
8) Rhetoric
9) Poetics

We can set aside 1,7, 8, and 9 as not relevant to the question. Now, of the rest, we can roughly say that logic qua Categories discusses terms; logic qua De Interpretatione discusses the structure of non-complex propositions; logic qua Prior Analytics discusses the formal structure of deduction; logic qua Posterior Analytics discusses demonstrative argument; and logic qua Topics discusses dialectical argument. In a philosophy of logic structured according to the Organon, where would propositional logic fit?

There's a sense, of course, in which all formal structures fit into Prior Analytics, but that's not really a very interesting thing. But there is more to logical argument than formal structure alone on this view (there is beyond this the actual application of the structure to subject-matter), so that's not the whole answer. Demonstrative reasoning according to this view proceeds terministically: that is, it is in virtue of the terms of the premises that the deduction goes through. Propositional logic, however, is (by definition) non-terministic. So it can't be demonstrative, which means it would have to be dialectical. The application of propositional logic to actual subject-matter is a matter of dialectical reasoning rather than demonstrative reasoning. And this is exactly the Aristotelian view. So how does this sort of thing work?

Let's take as true a single complex proposition like (p -> q), i.e., q if p. One can reasonably ask why, given p, q follows; but this cannot be answered in purely propositional terms, since the answer to this question would require looking at the terms of the proposition. To say why (p -> q) is true requires looking at the terministic and operational structure of p and q. So what good is q if p in argument? An Aristotelian would reply in this way. Without complex propositions like these, one would have to argue directly for q. If, however, we can take (p -> q) as a principle agreed upon by all relevant persons, we can then argue for q indirectly by arguing for p. This radically increases the flexibility of our argumentative resources. So suppose we were arguing that Something is caused. If we can take it as agreed upon by all relevant persons that If something begins to exist, something is caused, we can then argue for our conclusion by arguing for the conclusion Something begins to exist. On some views (e.g., Aristotelian, or Shepherd's), If something begins to exist, something is caused is a necessary proposition, since something's beginning to exist is just its being caused (under a different description). But this is not necessary for the propositional logic itself; all we need for that to work is to be able to posit the complex proposition (p -> q). If that taken as agreed upon, our dialectical resources have been expanded.

This suggests something about what is going on in the so-called 'special topics'. Every special science is held to have (in addition to the general topics that govern all sciences) its own 'special topics' peculiar to it. Our little meditation on the dialectical work of complex propositions suggests that what these special topics usually (always?) do is provide inferential guidelines to expand our dialectical resources in that particular field. In other words, because they draw connections between different propositional truths, they allow us to substitute one thing for another. For instance, one might have in physics a special topic devoted to saying how one gets a proposition expressed in terms of energy from a proposition expressed in terms of matter. If one needs to know or prove something about energy, this sort of complex proposition allows one to tackle this problem by way of what one knows or can prove about matter. Such a complex proposition has increased one's resources for concluding things about energy. Now, it's possible that this complex proposition expresses a necessary truth; but this requires terministic analysis that the special sciences do not in their normal progress usually require, unless one wishes strictly to demonstrate something in an Aristotelian sense. All the special sciences require is that the complex propositions we choose not be arbitrary, but chosen due to their aptness for rendering true conclusions. This is all dialectical reasoning: we don't need to show the premises to be strictly necessary; all we need is for the premises to be agreed upon, for expert reasons, by the relevant experts.

[UPDATE: In a revision slip I originally stated that on an Aristotelian view or on Shepherd's view 'beginning to exist' is equivalent to 'being caused'. This, of course, is blatantly false; so I've fixed the error.]

Another Shepherd Summary

At Houyhnhnm Land I have put up a passage in which Lady Mary Shepherd summarizes her view of the psychological process involved in causal reasoning. I'm still not entirely satisfied with the style of the page; but when I get it to where I want it, I'll finalize it (e.g., double-check for browser compatibility, etc.) and use it as the basic format for all my additional pages. The idea is eventually to have a set of pages devoted to Lady Mary Shepherd's causal theory, with a number of key passages, commentaries, cross-referencing to passages in Locke and Hume, and so forth. I also want to start doing something similar with Malebranche, although that's a bit more complicated due to translation issues. (I've already translated the Preface to his Dialogues on Metaphysics and on Religion; this (French) Preface is unavailable in English, since Jolley and Scott oddly refused to translate it as being 'philosophically uninteresting'. I'll put it up as soon as I've gone over it, and in particular have reworked my translation of the Latin quotations, which are many and difficult to translate. It is this difficulty that I suspect is what 'philosophically uninteresting' really means!)

F&P

The April 2004 edition of Faith and Philosophy (journal of the Society of Christian Philosophers) arrived here yesterday. It looks interesting. There's an article about various positions cur Deus Homo, i.e., views about the purpose of the Incarnation. The biggest question in this, of course, is whether God would have become man had there been no sin. I've only looked briefly at it; it doesn't look like she really focuses on the only genuinely strong argument for the affirmative position (Scotus's argument from the predestination of Christ). There is also what looks like an interesting article contrasting Aquinas's and Aristotle's accounts of the virtue of magnanimity.

Boethii

There was a talk on Boethius of Dacia today; I couldn't go because I was meeting with students in a class for which I'm grading. But I've been very surprised at how many graduate students don't know that Boethius of Dacia is different from Ancius Manlius Severus Boethius. The latter is the Boethius, the one who wrote The Consolation of Philosophy. The former is a Latin Averroist, often associated with Siger of Brabant. Now, I can understand not being able to place Boethius of Dacia; but confusing them entirely just seems to me to be a bit odd. But perhaps that's just me?

For Reading

* At "Science and Politics", Coturnix has a series on biological time in Darwinian perspective, which looks at biological methodology. It's a bit long, so you might find it useful to print it out and read it at leisure away from the computer screen.

* A post on students at "Bitch Ph.D."

* The Maverick Philosopher gives a Kantian analysis of four kinds of pride.

* Hugo Schwyzer posts an Auden poem. I rather suspect that the upper room at midnight is one of those perpetual and inevitable iterations of human society, like taxes or death or the oldest profession.

UPDATE: Also, there's a good post on the nature of scientific explanation at "prosthesis".

Planck on the Metaphysical Foundations of Science

The essential point of the positivist theory is no other source of knowledge except the straight and short way of perception through the senses. Positivism always holds trictly to that. Now, the two sentences: (1) there is a real outer world which exists independently of our act of knowing and (2) the real outer world is not directly knowable form together the cardinal hinge on which the whole structure of physical science turns. And yet there is a certain degree of contradiction between those two sentences. This fact discloses the presence of the irrational, or mystic, element which adheres to physical science as to every other branch of human knowledge. The effect of this is that a science is never in a position completely and exhaustively to solve the problem it has to face. We must accept that as a hard and fast, irrefutable fact, and this fact cannot be removed by a theory which restricts the scope of science at its very start. Therefore, we see the task of science arising before us as an incessant struggle toward a goal which will never be reached, because by its very nature it is unreachable. It is of a metaphysical character, and, as such, is always again and again beyond our achievement.

This is from Max Planck's discussion of the issue in Positivism and External Reality (for some reason I didn't put any further information in my notes; I think it was quoted in Jaki's The Road of Science and the Ways to God - in the Planck chapter, of course). This conception of science pervades his writings on the subject, as can easily be seen by looking at the Scientific Autobiography and The Philosophy of Physics. Consider the following passage from Scientific Autobiography:

In any case, we may say in summary that according to what exact natural science teaches us, the entire realm of nature, in which we human beings on our tiny mote of a planet play only an infinitesimally small part, is ruled by definite laws which are independent of the existence of thinking human beings; but these laws, insofar as they can at all be comprehended by our senses, can be given a formulation which is adapted for purposeful activity. Thus, natural science exhibits a rational world order the inner essence of which is and remains unknowable to us, since only our sense data (which can never be completely excluded) supply evidence for it. Nevertheless, the truly prolific results of natural-scientific research justify the conclusion that continuing efforts will at least keep bringing us progressively nearer to the inattainable goal, and they strengthen our inner hope for a constant advancement of our insight into the ways of the omnipotent Reason which rules over Nature. (tr. by Frank Gaynor, Greenwood Press (1971) pp. 181-182)

Election Question for Non-U.S. Readers

On my New Mexico ballot for this past election, these were the things I had to vote for:

1) President/Vice President ticket
2) U. S. Representative
3) Justice of State Supreme Court (one to elect)
4) Justice of State Supreme Court (two, whether to retain)
5) Judge of the Court of Appeals
6) State Senator
7) State Representative
8) Public Regulation Commissioner
9) District Judge (two)
10) District Attorney
11) County Commissioner
12) County Clerk
13) County Treasurer
14) Director of Flood Control Authority
15) Bond questions (five)
16) Amendments to the State Constitution (three)

I'm just curious; for those who vote in elections other than those in the U.S., what sort of choices do you vote for when you go to the polls each election (and how many)? I realized recently that I probably just assume that people in other nations face similar sorts of choices, but never having voted in any other elections, I wouldn't actually know.