Bill Vallicella – Page 800 – Maverick Philosopher

Further Modal Concepts: Consistency, Inconsistency, Contradictoriness, and Entailment

I argued earlier that the validity of argument forms is a modal concept. But the same goes for consistency, inconsistency, contradictoriness, and entailment. Here are some definitions. 'Poss' abbreviates 'It is broadly-logically possible that ___.' 'Nec' abbreviates 'It is broadly-logically necessary that ___.' '~' and '&' are the familiar truth-functional connectives. 'BL' abbreviates 'broadly logically.'

D1. A pair of propositions p, q is BL-consistent =_df Poss(p & q).

Clearly, any two true propositions are consistent. (By 'consistent' I mean consistent with each other. If I mean self-consistent, I'll say that.) But there is more to consistency that this. It is a modal notion. Consistency cannot be defined in terms of what is actually the case. One must also consider what could have been the case. As long as p, q are contingent, they are consistent regardless of their truth-values. If both are true, they are consistent. If both are false, they are consistent. If one is true and the other false, or vice versa, they are consistent.

D2. A pair of propositions, p, q, are BL-inconsistent =_df ~Poss(p & q).

D3. A pair of propositions p, q are BL-contradictory =_df ~Poss(p & q) & ~Poss (~p & ~q).

Note the difference between inconsistency and the stronger notion of contradictoriness. If two propositions are inconsistent, then they logically cannot both be true. If two propositions are contradictory, then they are inconsistent but also such that their negations logically cannot be true.

Example. All men are rich and No men are rich are inconsistent in that they cannot both be true. But they are not contradictory since their negations (Some men are not rich, Some men are rich) are both true. All men are rich and Some men are not rich are contradictory. Some men are rich, Some men are not rich are neither inconsistent nor contradictory.

D4. P entails q =_df~Poss(p & ~q).

Entailment, also called strict implication, is the necessitation of material implication. If '–>' stands for the material conditional, then the right hand side of (D4) can be put as follows: Nec (p –> q).

(Alethic) modal logic's task is to provide criteria for the evaluation of arguments whose validity or lack thereof depends crucially on such words as 'possibly' and 'necessarily.' But if I am right, many indispensable concepts of nonmodal logic (e.g., standard first-order predicate logic with identity) are modal concepts.

The Difference Between Possibility and Contingency

Over lunch yesterday, Peter Lupu questioned my assertion that possibility and contingency are not the same. What chutzpah! So let me now try to prove to him that they are indeed not the same, though they are of course related. To put the point as simply and directly as I can, possibility and contingency are not the same because every necessary proposition is possible, but no necessary proposition is contingent. Perhaps this requires a bit of explanation.

We first divide all propositions into two mutually exclusive and jointly exhaustive groups, the noncontingent and the contingent. The first group subdivides into two mutually exclusive and jointly exhaustive subgroups, the necessary and the impossible. A proposition is necessary (impossible) just in case it is true in every (no) possible world. A proposition is possible just in case it is true in some possible worlds. It follows that if proposition p is necessary, then p is possible, but not conversely.

Since we know that there are necessary propositions, and since we know that every necessary proposition is a possible proposition, we know that there are necessary propositions which are possible. But we also know that no necessary proposition is contingent. It follows that we know that there are possible propositions that are not contingent. It follows that the extension of 'possible proposition' is different from the extension of 'contingent proposition.' This suffices to show that possibility and contingency are not the same. Here are some definitions. I have included definitions not fomulated in the imagery of possible worlds for those who are 'spooked' by his imagery.

A proposition p is possible =_df there is a possible world in which p is true.

A proposition p is possible =_df it is not necessary that p be false.

A proposition p is contingent =_df there is a possible world in which p is true and there is a possible world in which p is false.

A proposition p is contingent =_df p is both possibly true and possibly false.

Example. No color is a sound is possible but not contingent. There is a possible world in which it is true, but no possible world in which it is false. Tom's favorite shirt is red is contingent. There is a possible world in which it is true and a possible world in which it is false.

UPDATE (21 February): David Brightly provides a very useful map of the modal terrain in the Comments.

Are There Non-Intentional Mental States?

The thesis of this post is that there are non-intentional mental states. To establish this thesis all I need is one good example. So consider the felt pain that ensues when I plunge my hand into extremely hot water. This felt pain or phenomenal pain is a conscious mental state. But it does not exhibit intentionality. If this is right, then there are mental states that are non-intentional. Of course, it all depends on what exactly is meant by 'intentionality.' Here is how I understand it.

Continue reading “Are There Non-Intentional Mental States?”

The Cartesian Dream Argument and an Austinian Contrast Argument

J. L. Austin, in a footnote to p. 49 of Sense and Sensibilia (Oxford, 1962), writes of ". . . the absurdity of Descartes' toying with the notion that the whole of our experience might be a dream." In the main text, there is a sort of argument for this alleged absurdity. The argument may be set forth as follows:

Continue reading “The Cartesian Dream Argument and an Austinian Contrast Argument”

Contrast Arguments

One of the weapons in the arsenal of Ordinary Language and other philosophers is the contrast argument. Such arguments are used to show the meaninglessness of certain terms, typically, the terms we metaphysicians like to bandy about. One type of contrast argument has the form:

1. If a term T is meaningful, then there are items to which T does not apply.
2. There are no items to which T does not apply.
Ergo
3. T is not meaningful.

Continue reading “Contrast Arguments”

This Running Life: Sheehan Remembered

You cannot convey to the nonrunner the romance of the road any more than you can bring a spiritual slug to savor the exquisite joys of philosophy and chess. But if you are a runner you should be able to appreciate the following passage from On Running, pp. 166-167. George Sheehan (1918-1993) has been dead for some time now and it pains me that he is pretty much forgotten. He was one of the pioneers along with Jim Fixx and Kenneth Cooper. The young runners I query haven't heard of him, and an old guy I talked to the other day at the starting line hadn't either. Sic transit gloria mundi. Here's the passage:

One of the beautiful things about running is that age has no penalties. The runner lives in an eternal present. The passage of time does not alter his daily self-discovery, his struggles and his sufferings, his pains and his pleasures. The decline of his ability does not interfere with the constant interchange between him, his solitude, and the world and everyone around him. And neither of these happenings prevents him from challenging himself to the ultimate limit, putting himself in jeopardy, courting crisis, risking catastrophe.

Because he refuses to look back, the runner remains ageless. That is his secret, that and the fact that his pursuit of running is in obedience to, in Ellen Glasgow's phrase, "a permanent and self-renewing inner compulsion."

In my 50s, I am aware of all this. Like all runners, I live in the present. I am not interested in the way we were. The past is already incorporated in me. There is no use returning to it. I live for the day. Running gives me self-expression, a way of finding out who I am and who I will be. It makes me intimate with pain. I know the feeling of too little oxygen, of too much lactic acid. I have, always within reach, the opportunity to test my absolute barriers, to search out the borders set up by straining muscles and a failing brain.

Phantom Runners

I took up running almost 35 years ago in the summer of 1974 in that romantic hub of running, Boston on the Charles, the Athens of America, where Hopkinton is Marathon and the road to Athens traverses Heartbreak Hill. It was a great time and place to be alive, young, studying philosophy, and running down the road. ‘Boston Billy’ Rodgers was in his prime; I lived a couple of blocks from the Boston Marathon course, and my training runs took me around the Chestnut Hill reservoir and past Rodger’s running center at Cleveland Circle. I actually ran abreast of Rodgers once on Commonwealth Avenue. He was headed for the Boston College track, racing flats in his hands, to run intervals. (I’ll leave it to the reader to figure out how I could possibly have been abreast of a marathoner who won Boston one year running at a blistering 4:54 min/mile pace. No, he didn't overtake me, and of course I didn't overtake him.)

Continue reading “Phantom Runners”

Ruminations After a Road Race; Philippians 4:13

The following was written 19 February 2006. This year I did better, achieving a personal best for this course, completing it in 2:23. That's nothing to crow about, but without us rank-and-file pavement pounders, the real runners would not shine in all their glory.

………………

This morning I had occasion once again to verify the proposition that the strenuous life is best by test, but also the proposition that I am not much of a runner: it took me 2:26 to jog through the 13.1 mile Lost Dutchman half-marathon course. But we do the best we can with what we've got, and given my age, modest training base, and paucity of fast-twitch fibers, I am more than satisfied. I have never regretted any road race, hike, backpacking trip, or indeed any Jamesian 'strenuosity' whether physical, mental, moral, or spiritual. We are simply not made for sloth but for exertion, with Hegel's Anstrengung des Begriffs as important as any. Whatever the reason, experience teaches that we are most happy when active, or better, when actuating our powers, including our powers of contemplative repose.

Continue reading “Ruminations After a Road Race; Philippians 4:13“

Retortion and Non-Contradiction in Aristotle, Metaphysics, Gamma 3, 4

Retortion is the philosophical procedure whereby one seeks to establish a thesis by uncovering a performative inconsistency in anyone who attempts to deny it. It is something like that benign form of ad hominem in which person A points out to person B that some proposition p that B maintains is inconsistent with some other proposition q that B maintains. "How can you maintain that p when your acceptance of p is logically ruled out by your acceptance of q? You are contradicting yourself!" This objection is to the man, or rather, to the man's doxastic system; it has no tendency to show that p is false. It shows merely that not all of B's beliefs can be true. But if the homo in question is Everyman, or every mind, then the objection gains in interest. Suppose there is a proposition that it is impossible for anyone (any rational agent) to deny; the question arises whether the undeniability or ineluctability of this proposition is a reason to consider it to be true. Does undeniability establish objective truth? Consider

Continue reading “Retortion and Non-Contradiction in Aristotle, Metaphysics, Gamma 3, 4“

Leon Trotsky, Gabe Kaplan, and Today’s Road Race

I was in Tempe, Arizona a while back for a book fix. At the coffee bar in the Border's Bookstore, the thirty-something counterman remarked that I look like Gabe Kaplan, an observation seconded by some bystanders. Having no idea who Gabe Kaplan is, I commented that some people think I look like Leon Trotsky — which comment elicited a puzzled expression. Turned out the 'tender had never heard of Trotsky. So I asked, "Ever hear of Vladimir Lenin?" That too drew a blank. It wasn't until I worked my way back to Karl Marx that a glimmer of recognition emerged. I tried the experiment on his twenty-something female co-worker. Same result.

Trotsky, Schmotsky. Lenin, Lennon.

Borders is just around the corner from Arizona State University. Draw your own conclusion.

During today's Lost Dutchman Half-Marathon, a woman who looked to be a bit older than me pulled alongside and remarked that I resemble her Salt River kayak instructor. I mentioned that some think I resemble Leon Trotsky. She said she didn' know who he was. Turning to her companion, she asked if she knew who Trotsky was. She didn't either. Calling to mind the earlier Tempe experience, I didn't bother to explain. I ran on with George Santayana's "Those who cannot remember the past are condemned to repeat it" in my head. (I cannot vouch for the accuracy of that quotation. I have a number of Santayana's works in my library, but not the The Life of Reason.)

Maverick Philosopher Makes The Times Online 100 Best Blogs List

A tip of the hat to Dave Lull for pointing me to A guide to the 100 best blogs – part I. Maverick Philosopher makes the cut. See page 5. Excerpt:

Two good philosophy blogs make the point that this is a subject made for bloggery. Philosophy is arguing, and arguing is what bloggers and their readers do best — or at least a lot, in an obsessive-compulsive sort of way. Both are highly recommended if you fancy stepping out into an intellectual blizzard with, occasionally, real snow.

I will resist the temptation to comment except to thank Bryan Appleyard for his article and also the MP Commenter Corps. Without them this site would be much less interesting. I have a half-marathon to run today, but later I hope to respond to at least some of the recent comments.

Wittgenstein, On Certainty #348: ‘I am Here’

Ludwig Wittgenstein writes:

. . . the words 'I am here' have a meaning only in certain contexts, and not when I say them to someone who is sitting in front of me and sees me clearly, — and not because they are superfluous, but because their meaning is not determined by the situation, yet stands in need of such determination.

Part of what LW is saying in this entry is that the meaning of an expression is determined by its use in a given context. In a slogan: meaning is use.

Continue reading “Wittgenstein, On Certainty #348: ‘I am Here’”