Notes and Links

* Liar, Liar, Pants on Fire. Alan Rhoda at "Alanyzer" has a nice post on Liar Paradoxes. He takes the route I prefer not to take (holding that sentences like "This sentence is false" express no proposition), because it seems to me to be either false or arbitrary, and, what is more, to concede more than is required -- namely, that the inference in the paradox we're supposed to make from the proposition's falsehood is a legitimate one, which I think it clearly is not. But it's a nice post worth reading. For my discussion of a similar approach, see my post on the Propositional Depth Response to the Liar Paradox.

* The Wonder of His Work Displays the Firmament. Rebecca has a post on natural revelation at "Rebecca Writes."

* Scars of Honor. There's an interesting post at "Disputations" on Aquinas's following Bede in discussing why the Risen Christ bore scars.

* So Say We All. If you need your Battlestar Galactica fix, you can start by watching the webisodes of The Resistance, which presents some of the events after the occupation. Of course, what I want to see is Laura Roslin; but Cally, Tyrol, and Tigh will do for the moment.

* Which Reminds Me....

You scored as President Laura Roslin. You may be ill but you have a job to do. Fate has put you in a powerful position by accident, but it turns out you are damn good at it. You are no warrior, but in the political arena you are without peer. President Laura Roslin 81% Commander William Adama 69% CPO Galen Tyrol 63% Capt. Lee Adama (Apollo) 56% Number 6 50% Tom Zarek 44% Col. Saul Tigh 38% Lt. Sharon Valerii (Boomer) 38% Lt. Kara Thrace (Starbuck) 31% Dr Gaius Baltar 25% What New Battlestar Galactica character are you? created with QuizFarm.com

* My internet access has been a bit more sporadic of late than usual; so that's the explanation if I seem to be posting a bit less than my normal amount. But there are several things in the pipeline.

Sortal-Relative Identity

While I have my doubts about the claim that all identity is sortal-relative (i.e., that things are never merely identical to each other but always only are the same something-or-other), it always astounds me how bad some of the arguments against relative-identity theorists are. One very popular argument that strikes me as bad is the following (with variations).

Suppose you have two individuals, a and b; and these two individuals are each of a certain kind, K. On this supposition, a is a K, b is a K, and a is not the same K as b. If a is a K, it's certain that a can't be a different K from a. That means that a and b are distinguishable (discernible, to use the common term in this type of situation). If a and b are discernible, however, they cannot be the very same K*, because they cannot be the very same anything. So if a and b are each K's and K*'s, they can only be the same K when they are the same K* (whatever K* may be). Thus identity is not sortal-relative.

There are a number of obvious problems with this type of argument. But the most obvious is that the relative-identity theorist needn't -- and, one would imagine, wouldn't -- accept the claim that if if a and b are of a different sort that a and b can't be the same sort (when the 'sort' is different). If I say, "The blue of this chair is the same color as the blue of that wall," it's not an adequate argument against taking this as a sortal-relative identity that the two are obviously different colors because one is a chair-color and the other is a wall-color. The relative-identity theorist will just say, and probably rightly, that you have stopped giving serious arguments and are now just being silly. But that's precisely what we have here. Let "The blue of the chair" be a, and "The blue of the wall" be b. Now, "The blue of the chair" is obviously not absolutely identical to "The blue of the wall"; obviously, as the silly objector said, one is the color of the chair and the other is the color of the wall. So they differ. But they are the same color, ex hypothesi. Now, we know that "The blue of the chair" can't differ from "The blue of the chair". That means there's a way in which "The blue of the chair" and "The blue of the wall" can be distinguished -- one can differ from "The blue of the chair" and the other can't. But, says the objector, this means that they can't be the same anything as each other. And, of course, if this is taken broadly, the objector is obviously wrong: as we've already said, they are the same color. But if it's taken in a more narrow sense, the objector is just begging the question: the only way it follows from the premises is if the only sort of identity is not sortal-relative.

A common counter-response to this is to note that we make arguments of the following form all the time:

a is P
a is the same K as b
∴ b is P.

And this is true. If the relative-identity theorist is right, however, inferences of this form are not (as written here) valid; sometimes the inference will give you the right conclusion, and sometimes not. When it does, it will have to be because it is enthymematic. And, it would seem, we have no account of just when these inferences work and when they don't. But I don't see that there's any great mystery here. Obviously, the inferences will work as enthymemes when the account for why a is P and the account for why b is P have something relevant in common. The most obvious such case would be when a is P because it is K, the very same K that b is. In such a case, b would obviously be P, because it would be P for the very same reason a is, by the very nature of the thing.

So this line of thought seems to me to be a dead-end in this dispute. There are other, more interesting arguments, of course. And it's possible that I'm just missing something obvious. But the argument just doesn't seem workable.

Jottings on Jenkins on the Philosophy of Flirting

Carrie Jenkins, "The Philosophy of Flirting" (via OPP):

What matters, I suggest, for distinguishing flirtations from these other actions, is the fact that in any genuine flirtation there should be an element of playfulness. Flirtation is, of its essence, playful, and intentionally so.

I think this is quite clearly false. Of course, people can flirt playfully, and probably enjoy themselves more when they do, but it doesn't take much to find people who don't. Some people who flirt are simply drunk; and there are all sorts of reasons not to consider drunk people playful. It takes a certain finesse to be playful, a bit of wit, and for most people alcohol is not conducive to either. For some people flirting seems to be more painful than playful; shy people, for instance, are only occasionally playful when they flirt. Jenkins notes this latter point; but apparently thinks that 'playfulness' need not be enjoyable. This might be so, although I think it doubtful, but it's not enough to get around the problem of painfully shy flirtation. Talking about playfulness also overlooks how desperate some flirting is; and desperation and playfulness don't seem to mix well.

Moreover, playfulness doesn't make much sense of most of the things people do and say when they flirt. It's difficult to see what's playful in saying, "Hi; I like that shirt; it brings out the color of your eyes," and that's sometimes all it amounts to. Saying something like this playfully would probably be counterproductive; it would make it sound less serious and straightforward than it was intended to sound.

Most people seem to spend most of their flirtation hoping that the other person will pick up tiny little signals rather than (as Jenkins makes it sound) setting out with great resolution and confidence "to raise the issue of romance/sex to salience" (as Jenkins puts it). Most people are not very good at it, and aren't trying to get much out of it; they're just trying to catch the other person's attention, or have a little fun, or express how gee-golly-gosh the other person is.

It's also probably not true that flirtation, as such, has such a direct relationship with romance and/or sex as Jenkins thinks. For one thing, not all flirtation is for the purposes of romance or sex, or even for making it salient, whatever precisely that might mean. Genuinely playful flirtation, in fact, is often very ambiguous in this way -- some people flirt just for the fun of it, and not because they have any sort of romance or sex in mind. They might even be annoyed if the possibility were raised, because it would break the fun of a harmless flirtation that no one thinks is going anywhere.

Actual Being

I said in a previous post that I didn't think that Thomas Aquinas's esse overlapped very well with our 'existence' (unless we are deliberately using the latter in an unusual way, which does sometimes happen). There are lots of reasons for thinking this, actually; but you'll just have to trust me on the quantity. For this post I thought I'd just flesh out one of those reasons. It starts out with an analogy St. Thomas makes in the De Ente et Essentia:

Just as if someone through one quality could perform the operations of all the qualities, he would have every quality in that one quality, so God has every perfection in His very esse.

I find this an interesting analogy. 'Existence' as it is often used indicates what we might call a mere fact: existence is the bare fact that something exists. It is clear that this is not anywhere in the vicinity of what Thomas intends. He really does have an emphasis on the actual of 'actual being'. If something actually is, it is because it is 'in act', actual; and because it is actual, it is active. Esse is not quite an action -- what we generally think of as actions, of course, all presuppose actual being. But it is certainly not the bare fact that something exists -- it is that about the actual thing that makes it to exist, which makes it actual, and actions are possible because they presuppose a more fundamental act, namely, the act of being.

So we have an analogy here between activated qualities (like powers) and divine esse. It is only an analogy, of course, but the point is that the analogy can be made. This is why Thomas has no problem saying that God's esse or being is abundantly perfect. Just as a high-level quality can have the perfections or excellences of lesser qualities in a higher way (because it can, as he says, effect the operations of those qualities, and lacks many of the limitations of those lesser qualities), so can God's esse have the perfections or excellences of being that lesser esse's have, but in a more excellent way. Aquinas's esse or being is something for which it makes sense to talk about 'fullness of being' or 'richness of existence' (if you must translate it as existence). And this is all the more important when Thomas talks about God's simple being. This simplicity is not a mere-ness (as it were); to say that God has simple esse is not to say that God merely exists. Quite the contrary. Think of the analogy again. A more excellent power, when activated, can do more and be more than lesser powers, but it can do so in a more unified way -- what you can do with two more limited powers, you can do with one less limited power. That's crude, of course, but it gives the idea: the greater the excellence of the power, the more it can do, and the more it can do as one power. Analogously, the more excellent the being (esse), the more perfect it can be on its own. Unlike creaturely being, which requires all sorts of supplementation in order to be fully excellent, divine being needs no such supplementation; it's rich, abundant, overflowing with excellences, and can do more than creaturely being can.

The analogy is rough (Thomas doesn't intend it to be more than rough), and there is a lot more that can be said about this, whether for or against or in order to develop it further. But it makes clear a reason why there is more to the Aquinate notion of esse or actual being than we usually find in our usage of the rather spare and weak term, 'existence'.

Sommers-Englebretsen Term Logic, Part VII

In previous posts in this series I've been attempting to provide a rough characterization of basic SETL. In Part I, I noted the basics of SETL, in a rough way. In Part II and Part III, I discussed briefly some special cases and how SETL handles them. In Part IV, I discussed some basics of argument using SETL. Part V looked at some simple arguments for which SETL gives us a better sense of what's going on than ordinary predicate logic does. (There will be a post at the end of the series giving references and supplementary readings.) Part VI discussed how one might go about extending SETL to cover modality. In this post, I'd like to look at another interesting extension of SETL, which might be called precise or numerical quantification. In this post I'll largely be following the work of Wallace Murphree.

Infinitely Many Valid Syllogisms

When we use ordinary quantification (all/no/some/some...not), we have only a small number of valid syllogisms. But these basic quantifiers are not the only possible quantifiers. This is where precise quantification comes in. Consider the following argument:

At least all but 5 M's are P
At least all but 4 S's are M
∴ At least all but 9 S's are P

This is a valid variation of a standard Barbara syllogism; Barbara alone has infinitely many valid 'precised' counterparts. Moreover, we can make use of maximal and minimal existential suppositions. For instance, if we suppose the minimum-presupposition that there are at least eleven S's, the above premises also yield the conclusion that at least 2 S's are P. If we make the maximum-presupposition that there are at most nine M's, the following is valid:

At least 7 M's are P
At least 5 S's are M
∴ At least 3 S's are P

So the natural question is: how does this all work in the context of SETL?

Ordinary Quantification and Precise Quantification

Ordinary quantification can be seen as particular cases of numerical quantification. In fact, modern interpretations of . "Some S is P" is equivalent to "At least one S is P" while "Some S is not P" is equivalent to "At least one S is not P." It turns out that you can render universal propositions fairly easy, as well. "No S is P" is equivalent to "At most zero S's are P." "All S is P" is rendered in the slightly more complicated form, " At least all but zero S's are P". Or to put it in other terms: ordinary universal quantification assumes no exceptions. Precise quantification allows for exceptions to the universal quantifiers. The basic pattern for A-type propositions is "All but x S's are P"; when x = 0, we have a standard A proposition. The basic patter for E-type propositions is "At most x S's are P"; when x = 0, we have a standard E proposition. The two are related, of course. "All but x S's are P" is equivalent to "At most x S's are nonP," and "At most x S's are P" is equivalent to "At least all but x S's are nonP."

With this in mind we can build a numerical term logic that uses precise quantification. The correspondences are as follows:

All but x Ss are P = -xS+P
At most x Ss are P = -xS-P
At least x Ss are P = +xS+P
At least x Ss are not P = +xS-P

It's easy to see that this is just ordinary SETL with x's, and that if x=0, the first two are equivalent to ordinary SETL's -S+P and -S-P, while if x=1, the second two are equivalent to ordinary SETL's +S+P and +S-P.

One tricky feature of this new numerical part of the sentence is that denial of the whole sentence requires a change of numerical quantifier. The denial of -0S+P is +1S-P; and we find that it's a general truth that the denial of a universal sentence with x in its quantification results in a particular sentence with x+1 in its quantification, and the denial of a particular sentence with x in its quantification results in a universal sentance with x-1 in its quantification.

Syllogisms with Precise Quantification

Syllogisms in this extended SETL are very similar to syllogisms in ordinary SETL. An ordinary Barbara syllogism would be:

-0M+P
-0S+M
∴-0S+P

Nothing very surprising here. We can use higher numbers, though. For instance:

-11M+P
-333S+P
∴ -344S+P

Syllogisms with particular premises are only slightly more tricky:

-11M+P
+30S+M
∴ +19S+P

We can establish as a general rule the following principle: to achieve the strongest conclusion the premises can bear, the numerical value of the quantifier in the conclusion is equal to the sum of the numerical value of the quantifiers in the premises.

Now, one of the problems raised by these syllogisms is the failure of the backbone of any syllogistic, DDO, because it puts us in situations where we aren't saying P of all M. Murphree proposes a generalization of DDO, in which we understand it to mean, "Whatever is said of all but x Ms is said of all but x of whatever is M." However, there are still complications, because cases where DDO would give us negative numbers in our quantification are awkward, since we usually prefer to avoid negative quantification. Murphree therefore also suggests an additional principle, a dictum de aliquid (DDA): "Whatever is said of some Ms is said of all but the rest of the Ms."

And we can add in our above reasoning about maximum- and minimum-presuppositions. So here's an example of what you can get. Take the following syllogism:

At least eleven members are philosophy majors.
At least fifteen members are sophomores.
There are at most 20 members.

What's the conclusion? We can convert to Murphree-expanded SETL:

(1) +11M+P
(2) +15M+S
(3) -20M-M

From the first and third we get:

(4) -9M+P

From this and the second we get:

(5) +6S+P

At least six sophomores are philosophers. (4) follows from (1) and (3) by DDA; (5) follows from (2) and (4) by DDO. We could use DDO to get an analogue of (4); it would be the claim that at least negative nine philosophy majors are not members. This is certainly a validly derived conclusion, and might be useful in some circumstances; but with maximum-presuppositions DDA will often get us a handier result.

Relations with Numerical SETL

One of the interesting things about this extension of SETL is that you can dis-ambiguate some natural language claims very easily. Consider the following sentence:

Three teachers gave four students two books.

This might mean that each of three teachers gave each of four students two books each:

+3T₁ + ((G₁₂₃ +2B₂)+4S₃)

Then there were 24 books given. Or it might mean that three teachers together gave two books total to four students as a group:

+1[3T]₁ + ((G₁₂₃ +2B₂)+1[4S]₃)

Then there were only two books given. It might also mean that three teachers together gave two books total to each of the four students:

+1[3T]₁ + ((G₁₂₃ +2B₂)+4S₃)

That gives us a total of eight books given. It could also mean that each of three teachers gave two books to four students as a group:

+3T₁ + ((G₁₂₃ +2B₂)+1[4S]₃)

That's a total of six books given. So, whether it's 24, 2, 8, or 6 books given, this extension of SETL can clarify. This is not at all surprising, because it offers a finer degree of discrimination in quantification. Inferences with relationals, of course, work just as one would suspect.

So that's the Murphree extension of SETL. In my next post on this subject I'll sum up and give links and references for further reading.

The Golden Mouth

Since it's the Feast of John Chrysostom, it seems fitting to post something. This is from his Homilies on Titus:

Knowing therefore that it is better to want glory, than to possess it, let us not seek for honors, but evade them when they are offered, let us cast them from us, let us extinguish that rulers of the church, and to those under their rule. For a soul desirous of honor, and of being glorified, shall not see the kingdom of heaven. This is not my own saying. I speak not my own words, but those of the Spirit of God. He shall not see it, though he practice virtue. For he saith, "They have their reward." (Matt. vi. 5.) He then, who has no reward to receive, how shall he see the kingdom of heaven? I forbid thee not to desire glory, but I would wish it to be the true glory, that which proceeds from God. "Whose praise," it is said, "is not of men, but of God." (Rom. ii. 29.) Let us be pious in secret, not cumbered with parade, and show, and hypocrisy. Let us cast away the sheep's clothing, and rather let us become sheep. Noting is more worthless than the glory of men. Should thou see a company of little children, mere sucklings, wouldest thou desire glory from them? Be thus affected towards all men with respect to glory.

It is for this reason called vainglory. Dost thou see the masks worn by stage-players? how beautiful and splendid they are, fashioned to the extreme height of elegance. Canst thou show me any such real countenance? By no means. What then? didst thou ever fall in love with them? No. Wherefore? Because they are empty, imitating beauty, but not being really beautiful. Thus human glory is empty, and an imitation of glory: it is not true glory. That beauty only which is natural, which is within, is lasting: that which is put on externally often conceals deformity, conceals it from men until the evening. But when the theater breaks-up, and the masks are taken off, each appears what he really is.

Let us therefore pursue truth, and not be as if we were on the stage and acting a part. For of what advantage is it, tell me, to be gazed at by a multitude? It is vainglory, and nothing else. For return to thy house, and solitude, and immediately all is gone. Thou hast gone to the market-place, thou hast turned upon thee the eyes of all present. What hast thou gained? Nothing. It vanished, and passed away like dissolving smoke. Do we then love things thus unsubstantial? How unreasonable is this! what madness! To one thing only let us look, to the never seek the praise of men; but if it falls to us, we shall despise, deride, and reject it. We shall be affected as those who desire gold, but receive clay. Let not any one praise thee, for it profits nothing; and if he blame thee, it harms thee not. But with God praise and blame are attended with real gain and loss, whilst all is vain that proceeds from men. And herein we are made like unto God, that He needs not glory from men. "I receive not" said Christ, "honor from men." (John v. 41.) Is this then a light thing, tell me? When thou art unwilling to despise glory, say, "By despising it, I shall resemble God," and immediately thou wilt despise it. But it is impossible that the slave of glory should not be a slave to all, more servile than slaves in reality. For we do not impose upon our slaves such tasks, as glory exacts from her captives. Base and shameful are the things she makes them say, and do, and suffer, and when she sees them obedient, she is the more urgent in her commands.

You can read up on Chrysostom's life at The Way of the Fathers.

Literary Taste and Age

I sometimes wonder if certain literary works are best read at certain stages of life. People who seem to read Romeo and Juliet later in life have a more cynical view of the actions of the two young lovers than those who read it in (say) high school. That's just something I've found to be occasionally the case; it could be that this is just a misleading sample. But there's perhaps an argument here, although it's slippery. I'm not talking, of course, of the difficulty of the work, but simply of its suitability to a stage of life.

Hume suggests something similar to this in his essay on the Standard of Taste:

A young man, whose passions are warm, will be more sensibly touched with amorous and tender images, than a man more advanced in years, who takes pleasure in wise, philosophical reflections concerning the conduct of life and moderation of the passions. At twenty, Ovid may be the favourite author; Horace at forty; and perhaps Tacitus at fifty. Vainly would we, in such cases, endeavour to enter into the sentiments of others, and divest ourselves of those propensities, which are natural to us. We choose our favourite author as we do our friend, from a conformity of humour and disposition. Mirth or passion, sentiment or reflection; whichever of these most predominates in our temper, it gives us a peculiar sympathy with the writer who resembles us.

This is not quite the same; Hume is talking about taste, while I am talking about what Hume would call good taste (i.e., things we should have a taste for). Hume is, however, noting that taste can vary with age. Since variations of taste constrain good taste -- which involves our considered judgment on the basis of wide experience and practiced discernment -- if there is sufficient regularity of variation with age across the population, and if (as is plausible) no age can be given a completely privileged position (because the variation simply involves "a conformity of humour and disposition"), then we would have an interesting argument for the claim that good taste should (to an extent) be relativized to stage of life. To use Hume's example (which is not, I think, to be taken as Hume's own view of how the authors relate to different stages of life, but simply as an example), not only may a man of twenty have more of a taste for Ovid than a man of thirty, but a taste for Ovid might be more indicative of good taste in a man of twenty than it would be in a man of thirty.

We do sometimes seem to make judgments of this sort. You might not think comic books are ever in themselves indicative of bad taste; but you might think that a taste for comic books is a better indication of good literary taste in a teenager than in a senior. You might think that a taste for both Dickens and Austen is good literary taste, simpliciter, but that preferring Austen to Dickens at seventy is better literary taste than preferring Austen to Dickens at twenty (or some such). This is perhaps better seen in other cases of good and bad taste. We might think anarchism a sign of bad political taste in any age, for instance; but hold that it shows worse taste in an eighty-year-old than in an eighteen-year-old.

On the other hand, there is a good reason why Hume takes variation across age to be a sign of the limitations of a standard of taste -- i.e., to be a case showing that our account of good taste can only be made so precise. If the difference between two cases of good taste is merely temperamental, the variation between the two doesn't itself seem to be a matter of good taste, and so doesn't seem to admit of any standard. If one person prefers Dickens over Austen because he has a more vivid imagination, and another person prefers Austen over Dickens for some other purely temperamental reason, there's a sense in which they are incommensurable. They can both be examples of good literary taste; but they can't be relativized because there's not really anything to relativize it to. It's just a quirk that good taste in one leads to a preference for Dickens and good taste in another leads to a preference for Austen, not a sign of anything profound or important about good literary taste itself, and we can't really say that it is better taste for the one to prefer Dickens over Austen, and better taste for the other to prefer Austen over Dickens -- precisely the point of good literary taste is that it transcends the merely quirky. The analogy in political taste seems to become irrelevant here; at least, one of the reasons why we might think anarchism less a matter of bad taste in a teenager than in a senior is that we might think the quirks of being a teenager make bad political taste more forgivable than the quirks of being a senior.

What you'd need to do is find a way to look at the situation so that people of good taste of all ages could in principle agree (allowing for quirky divergences) that it is better literary taste to have a taste for X at a certain age than at another age. This seems a tall order. On the other hand, it's perhaps not impossible. After all, good taste is about measured and rational appreciation, and it could be that people of certain ages can better appreciate certain literary works. But to return to the other hand, it could also be that age is incidental to the whole matter. And that does seem to be more likely. It's an interesting question.

Edward Confessor and the Ring

A legend of King St. Edward the Confessor, taken from Percy Dearmer's The Little Lives of the Saints:

One day, another legend says, the old king was attending the dedication of a church in honour of St. John, when a poor man came up to him, and begged an alms "for the love of St. John." St. Edward put his hand to his purse, but neither silver nor gold could he find. He sent for his almoner, but he was lost in the crowd; and still the poor man stood before him and begged. Edward was in great distress, till he remembered that he wore a large and very precious ring. This he drew from his finger; and for the love of St. John he gave it to the beggar, who thanked him gently, and disappeared.

And now you shall hear what happened to the ring. That night, far away in Palestine, two English pilgrims lost their way in the wilderness. The sun had set behind the bare mountains, and the two men were all alone in the desolate place, knowing not which way to turn, nor where to find shelter from robbers and wild beasts. As they were wondering what to do, a band of youths in bright raiment appeared before them; and in their midst was an old man, white and hoary, and wonderful to look upon.

"Dear friends," he said to the pilgrims, "Whence come you? Of what creed and birth are you? Of what kingdom and king? What seek you here?"

"We are Christians, and from England. We have come to expiate our sins, seeking the holy places where Jesus lived and died. Our king is named Edward; and we have lost our way."

"Come after me, and I will conduct you to a good hostelry for the love of King Edward." So he led them to a city, where they found an inn with the table laid for supper; and, after they had eaten, they went to rest.

Next morning the old man came to them, and said: "I am John the Evangelist. For the love of Edward I will not fail you, and you shall arrive safe and sound in England. Then go to Edward, and say you have brought a ring which he gave to me at the dedication of my church, when I besought him in poor array. And tell him that in six months he shall come to me in Paradise."

The pilgrims came back to England without misadventure, and gave the ring back to Edward with St. John's message.

When the king heard that he was soon to die, he gave away all his money to those who were in need, and passed his time in devotion.