Two Recent Trail Runs

13 K Copper Crawl Hill Climb, Miami, Arizona

Saturday morning April 17 found me toiling up the side of a mountain above the mining town of Miami, Arizona about 40 miles east of here on U. S. 60. The race is part of Miami's annual Boom Town Spree.  A great experience start to finish, from leaving the house at 5:35 AM to arriving safely home again six hours later.  A tough but interesting course mainly over dirt roads up, up, up into the foothills of the Pinal Mountains.  Out and back, with the turnaround point at Warnica Springs in the Tonto National Forest.  The race started from downtown near the corner of Live Oak and Adonis.  Great support, T-shirt, goodie bag, not to mention the  complimentary pancake breakfast and sports massage.

I enjoy the on-the-fly camaraderie of running events.  One has conversations, some of them unforgettable for a lifetime, with people many of whom one will  never see again.

Round Mountain Sunrise Challenge, Globe, Arizona, National Trails Day, 5 June 2010

I left the house at 4 AM, arrived at the trailhead in Globe around 5:15.  Gun went off at 6.  A very challenging 5 K (3.1 mile) rocky course through and over boulders and dry streambeds with plenty of elevation change.  Not even a worldclass trail runner could have negotiated the whole of this sucker at a run.  A delightful course nonetheless with scenic views and a friendly coterie of local diehards.  I took third place in the 60+ category.  (And yes, there were more than three in that category!)  But I had to pour it on at the end to keep from being overtaken by a crusty one-eyed 75 year old. 

What Colin Fletcher says of hiking is equally true of running, especially trail running: It is ". . . a delectable madness, very good for sanity, and I recommend it with passion." (The Complete Walker III, p. 3)

Black Backgrounds

Anyone whose website has a black background should be shot. Perhaps I should qualify my complaint: Anyone whose website is both content-rich and worth reading should be shot (figuratively speaking) if his background is black and/or there is anything in the reader's visual field that moves on its own. Content is king. Avoid clutter and newbie add-on crap. If you must advertise, do so unobtrusively.  Why drive readers away?

Word of the Day: ‘Ochlocracy’

From the Greek ochlokratia, from the Greek ochlos (mob) + -kratia (-cracy): government by the mob, mob rule. Example from an esteemed member of the MavPhil Commenter Corps: "I just tell my students and anyone else I know not to read the Wikipedia article [Philosophy] except for a laugh. It's one of those areas where the ochlocratic nature of Wikipedia really comes a cropper."

In case anyone is unclear, and I was, 'to come a cropper' means to fail badly, to get caught out, to fall.

Is There a Paradox of Conjunction?

There are supposed to be paradoxes of material and strict implication. If there are, why is there no paradox of conjunction? And if there is no paradox of conjunction, why are there paradoxes of material and strict implication? With apologies to the friends and family of Dennis Wilson, the ill-starred original drummer of the Beach Boys, let's take this as our example:

1. Wilson got drunk, fell overboard, and drowned.

Translating (1) into the Propositonal Calculus (PC), we get

2. Wilson got drunk & Wilson fell overboard & Wilson drowned. 

Now the meaning of the ampersand (or the dot or the inverted wedge in alternative notations) is exhausted by its truth table. This meaning can be summed up in two rules. A conjunction is true if and only if all of its conjuncts are true. A conjunction is false if and only if one or more of its conjuncts is false. That is all there is to it. The ampersand, after all, is a truth-functional connective which means that the truth-value of any compound proposition formed with its aid is a function (in the mathematical sense) of the TVs of its components and of nothing besides. You will recall from your college calculus classes that if f is a function and y = f(x), then for each x value there is a unique y value.

Now are the conjuncts of (2) related? Well, they are related in that they all have the same truth-value, namely True. But beyond this they are not related qua components of a truth-functional compound proposition. The 'conjuncts' — note the inverted commas! — of (1), however, are related beyond their having the same truth-value. For it is because Wilson got drunk that he fell overboard, and it is because he fell overboard that he drowned. So causal and temporal relations come into play in (1), relations that are not captured by (2).

Note also that the ampersand has the commutative property. But this is not so for the comma and the 'and' in (1). Tampering with the order of the clauses in (1) turns sense into nonsense:

3. Wilson drowned, fell overboard, and got drunk.

We should conclude that the ampersand abstracts from some of the properties of occurrences of the natural language 'and' and cognates. Despite this abstraction, (1) entails (2), which means that (2) does capture part of the meaning of (1), that part of the meaning relevant to the purposes of logic. But surely there is no 'paradox' here. Any two propositions can be conjoined, and the truth-value of the compound can be computed from the TVs of the components. It is the same with material implication: any two propositions can be connected with a horseshoe or an arrow and the TV of the result is uniquely determined by the TVs of the component propositions. Thus we get a curiosity such as

4. Snow is red –> Grass is green

which has the value True. This is paradoxical only if you insist on reading the arrow as if it captured all the meaning of the natural language 'if' or 'if…then___.' But there is no call for this insistence any more than there is call for reading the ampersand as if it captures the full meaning of 'and' and cognates in ordinary English.

What I am suggesting is that, just as there is no paradox of conjunction, there is no paradox of material implication either.

Israel and the Blockade

From Charles Krauthammer, Israel Refuses to Commit Suicide:

. . . the blockade is not just perfectly rational, it is perfectly legal. Gaza under Hamas is a self-declared enemy of Israel — a declaration backed up by more than 4,000 rockets fired at Israeli civilian territory. Yet having pledged itself to unceasing belligerency, Hamas claims victimhood when Israel imposes a blockade to prevent Hamas from arming itself with still more rockets.

[. . .]

The world is tired of these troublesome Jews, six million — that number again — hard by the Mediterranean, refusing every invitation to national suicide. For which they are relentlessly demonized, ghettoized and constrained from defending themselves, even as the more committed anti-Zionists — Iranian in particular — openly prepare a more final solution.

 

The Essence of Progressivism

From George F. Will, The Limits of the Welfare State:

Lack of "a limiting principle" is the essence of progressivism, according to William Voegeli, contributing editor of the Claremont Review of Books, in his new book "Never Enough: America's Limitless Welfare State." The Founders, he writes, believed that free government's purpose, and the threats to it, is found in nature. The threats are desires for untrammeled power, desires which, Madison said, are "sown in the nature of man." Government's limited purpose is to protect the exercise of natural rights that pre-exist government, rights that human reason can ascertain in unchanging principles of conduct and that are essential to the pursuit of happiness.

An excellent article.  Read it all.

Deflationism: Ramsey and Redundancy

I am using 'deflationism' as an umbrella term subsuming several different deflationary theories of truth, among them Ramsey's redundancy theory, Quine's disquotationalism, Horwich's minimalist theory, and others. Deflationary theories contrast with what might be called 'robust' or substantive' theories of truth. It is not easy to focus the issue that divides these two types of theory. One way to get a feel for the issue is by considering the traditional-sounding question, What is the nature of truth? This 'Platonic' question — compare What is the nature of knowledge? (Theaetetus); What is the nature of justice? (Republic) — presupposes that truth has a nature, a nature that can be analyzed or otherwise explicated in terms of correspondence, or coherence, or 'what conduces to human flourishing,' or what would be accepted at the Peircean limit of inquiry, or something else. 

The deflationist questions the presupposition. He suspects that truth has no nature. He suspects that there is no one property that all truths have, a property the having of which constitutes them as truths. His project is to try to account for our truth-talk in ways that do not commit us to truth's having a nature, or to truth's being a genuine property. Of course, we English speakers have and use the word 'true.'  But the mere fact that we have and use the predicate 'true' does not suffice to show that there is a property corresponding to the predicate. (Exercise for the reader: find predicates to which no properties correspond.)

So if we can analyze our various uses of 'true' in ways that do not commit us to a property of truth, then we will have succeeded in deflating the topic of truth and showing it to be metaphysically insubstantial or 'lightweight.' The most radical approach would be one that tries to dispense with the predicate 'true' by showing that everything we say with its help can be said without its help (and without the help of any obvious synonym such as 'correct.') The idea here is not merely that truth is not a genuine property, but that 'true' is not even a genuine predicate.

Consider two assertions. I first assert that snow is white, and then I assert that it is true that snow is white. The two assertions have the same content. They convey the same meaning to the audience. This suggests that the sentential operator  'It is true that ___' adds nothing to the content of what is asserted. And the same goes for the predicate '___ is true.' Whether we think of 'true' as an operator or as a predicate, it seems redundant, or logically superfluous. In "Facts and Propositions" (1927), Frank Ramsey sketches a redundancy or logical superfluity theory of truth. This may be the first such theory in the Anglosphere. (Is there an historian in the house?)

For Ramsey, "there really is no separate problem of truth but merely a linguistic muddle." Ramsey tells us that ". . . 'It is true that Caesar was murdered' means no more than that Caesar was murdered, and 'It is false that Caesar was murdered' means that Caesar was not murdered." (F. P. Ramsey, Philosophical Papers, Cambridge UP, 1990, ed. D. H. Mellor, p. 38) But what about a case in which a proposition is not explicitly given, but is merely described, as in 'He is always right'? In this example, 'right' has the sense of 'true.' 'He is always' right means that whatever he asserts is true. As a means of getting rid of 'true' in this sort of case, Ramsey suggests:

1. For all p, if he asserts p, then p is true.

But since "the propositional function p is true is the same as p, as e.g., its value 'Caesar was murdered is true' is the same as 'Caesar was murdered,'" Ramsey thinks he can move from (1) to

2. For all p, if he asserts p, then p.

If the move to (2) is kosher, then 'true' will have been eliminated. Unfortunately, (2) is unintelligible. To see this, try to apply Universal Instantiation to (2). If the variable 'p' ranges over sentences, we get

3. If he asserts 'Snow is white,' then 'Snow is white.'

This is nonsense, because "'Snow is white'" in both occurrences is a name, whence it follows that the consequent of the conditional is not a proposition, as it must be if the conditional is to be well-formed. If, on the other hand, the variable 'p' is taken to range over propositions, then we get the same result:

4. If he asserts the proposition that snow is white, then the proposition that snow is white

which is also nonsense. Unless I am missing something, it looks as if Ramsey's redundancy theory cannot succeed in eliminating 'true.' It looks as if 'true' is an indispensable predicate, and thus a genuine predicate. This does not, however, show that truth is a genuine property.   It merely shows that we cannot get rid of 'true.'

Geach on Assertion

The main point of Peter Geach's paper, "Assertion" (Logic Matters, Basil Blackwell, 1972, pp. 254-269) is what he calls the Frege point: A thought may have just the same content whether you assent to its truth or not; a proposition may occur in discourse now asserted, now unasserted; and yet be recognizably the same proposition. This seems unassailably correct. One will fail to get the Frege point, however, if one confuses statements and propositions. An unstated statement is a contradiction in terms, but an unasserted proposition is not. The need for unasserted propositions can be seen from the fact that many of our compound assertions (a compound assertion being one whose content is propositionally compound) have components that are unasserted.

To assert a conditional, for example, is not to assert its antecedent or its consequent. If I assert that if Tom is drunk, then he is unfit to drive, I do not thereby assert that he is drunk, nor do I assert that he is unfit to drive.  I assert a compound proposition the components of which I do not assert.  The same goes for disjunctive propositions. To assert a disjunction is not to assert its disjuncts. Neither propositional component of Either Tom is sober or he is unfit to drive is asserted by one who merely asserts the compound disjunctive proposition.

What bearing does this have on recent discussions?  I am not sure I understand William of Woking's position, but he seems to be denying something that Geach plausibly maintains, namely, that "there is no expression in ordinary language that regularly conveys assertoric force." (261)  Suppose I want to assert that Tom is drunk.  Then I would use the indicative sentence 'Tom is drunk.'  But there is nothing intrinsically assertoric about that sentence.  If there were, then prefixing 'if' to it would not remove its assertoric force as it does.    As I have already explained, an assertive utterance of 'If Tom is drunk, then he is unfit to drive'  does not amount to an assertive utterance of 'Tom is drunk.'  'If' cancels the assertoric force.  And yet the same proposition occurs in both assertions, the assertion that Tom is drunk and the assertion that if Tom is drunk, then he is unfit to drive.  I conclude that there is nothing intrinsically assertoric about indicative sentences.  If so, there is no semantic component of an indicative sentence that can be called the assertoric component.

'If' prefixed to an indicative sentence does not alter its content: it neither augments it nor diminishes it.  But it does subtract assertoric force.  Given that the meaning of an indicative sentence is its content, and the semantics has to do with meaning, then there is no semantic assertoric component of an indicative sentence or of the proposition it expresses.  Assertion and assertoric force do not belong in semantics; they belong in pragmatics.  Or so it seems to me.

Sentence, Linguistic Meaning, Proposition

I maintain that we must distinguish among declarative sentences, their linguistic meanings, and the propositions expressed by tokenings of declarative sentences by speakers in definite contexts. Furthermore, I maintain that propositions, not linguistic meanings, are the vehicles of the truth-values. Here are four declarative sentences in four different languages, English, German, Turkish, and Latin:  I love you; Ich liebe dich; Seni seviyorum; Te amo. 

Clearly, each of these sentences can be used to express many different thoughts or propositions. If Jack says 'I love you' to Jill, the proposition expressed is different from the proposition expressed if Bill says 'I love you' to Hill. Since one and the same sentence type can be used to express different propositions, it follows that sentence types are distinct from propositions.

We must also distinguish between a sentence type and its linguistic meaning, the meaning it has in virtue of the conventions of the language to which the sentence type belongs. The four sentences displayed above have the same meaning. Since one and the same meaning is possessed by these four different sentence types, it follows that linguistic meanings are distinct from sentence types. It follows from the two points just made that linguistic meanings are distinct from propositions. One proof of this is that one can have a complete understanding of the linguistic meaning of a sentence without knowing any proposition that the sentence has ever expressed. Let me explain.

Suppose a Spanish speaker learning English learns that 'Mary loves Carl' means the same as 'Mary ama a Carl.' The Spanish speaker then fully understands the linguistic meaning of 'Mary loves Carl' but without needing to know any proposition, any truth or falsehood, that the English sentence has ever expressed. (See Castaneda, Thinking and Doing, p. 35) Therefore, the linguistic meaning of a declarative sentence is distinct from the proposition expressed by the sentence on some occasion of the sentence's use. Some, blinded by the nominalist fear of reification, cannot admit this obvious distinction between linguistic meaning and proposition. One nominalist writes, "In summary, the meaning of a sentence is what it says, what it says is true or false, ergo the meaning of a sentence is a 'truth bearer'." The argument is this:

1. The meaning of a sentence is what it says.

2. What a sentence says is either true or false. Therefore,

3. The meaning of a sentence is either true or false.

The argument equivocates on 'what it says.' If premise (2) is true, then what a declarative sentence says is identical to the proposition it expresses. It is important to realize that I am not assuming any particular theory of propositions. Thus I am not assuming that they are Platonic entities. I am simply insisting that we need to distinguish between the linguistic meaning of a sentence (the meaning it has in virtue of the conventions of the language to which it belongs) and the proposition a sentence expresses when the sentence is uttered or otherwise tokened by a person in a definite situation. But in premise (1), the linguistic meaning of a sentence is identified with what it says. Thus 'what it says' is being used in two different ways, which fact destroys the validity of the argument. If a proponent of the argument says I am begging the question against him, I reply that he is failing to admit an obvious distinction. The distinction is not original with me. It ought to be visible to anyone. If an a priori commitment to nominalism blinds one to so obvious a distinction, then so much the worse for an a priori commitment to nominalism.