Saturday, May 09, 2020

The Parable of the Knaves and the Brahmin

A pious Brahmin, it is written, made a vow that on a certain day he would sacrifice a sheep, and on the appointed morning he went forth to buy one. There lived in his neighbourhood three rogues who knew of his vow, and laid a scheme for profiting by it. The first met him and said, “Oh Brahmin, wilt thou buy a sheep? I have one fit for sacrifice.”

“It is for that very purpose,” said the holy man, “that I came forth this day.” Then the impostor opened a bag, and brought out of it an unclean beast, an ugly dog, lame and blind. Thereon the Brahmin cried out, “Wretch, who touchest things impure, and utterest things untrue, callest thou that cur a sheep?” “Truly,” answered the other, “it is a sheep of the finest fleece, and of the sweetest flesh. Oh Brahmin, it will be an offering most acceptable to the gods.”

“Friend,” said the Brahmin, “either thou or I must be blind.”

Just then one of the accomplice’s came up. “Praised be the gods,” said this second rogue, “that I have been saved the trouble of going to the market for a sheep! This is such a sheep as I wanted. For how much wilt thou sell it?” When the Brahmin heard this, his mind waved to and fro, like one swinging in the air at a holy festival. “Sir,” said he to the new comer, “take heed what thou dost; this is no sheep, but an unclean cur.”

“Oh Brahmin,” said the new comer, “thou art drunk or mad!”

At this time the third confederate drew near. “Let us ask this man,” said the Brahmin, “what the creature is, and I will stand by what he shall say.” To this the others agreed; and the Brahmin called out, “Oh stranger, what dost thou call this beast?”

“Surely, oh Brahmin,” said the knave, “it is a fine sheep.” Then the Brahmin said, “Surely the gods have taken away my senses;” and he asked pardon of him who carried the dog, and bought it for a measure of rice and a pot of ghee, and offered it up to the gods, who, being wroth at this unclean sacrifice, smote him with a sore disease in all his joints.

Thomas Babington Macauley, "Mr. Robert Montgomery (I)" (Edinburgh Review, April 1830), Critical, Historical, and Miscellaneous Essays, Volume 2. Macauley attributes the story to Pilpay, i.e., the Panchatantra. In the version translated later by Ryder, the story works in reverse: the priest has a nice clean animal and the rogues con him out of it by convincing him that it is unclean; but there are many different versions of the work.

Friday, May 08, 2020

Of Discourses About Fascism

I do not have a high opinion of Jason Stanley's work -- any of it at all, I'm afraid; one tries to be openminded but this sort of thing happens nonetheless -- and much of his recent work on fascism seems to me largely to be repackaged and warmed over work by other people, mangled into strained shapes by analogies in his head rather than serious analysis. (It all reminds me a bit, actually, of Peter Singer's book, The President of Good and Evil, which was not so much a book as a grift, reassuring partisans of a particular type that, yes, they are the insightful and intelligent ones, and see more deeply than their opponents, and in the process both fleecing them and putting himself in a convenient spotlight for his career. The book is, unsurprisingly, of very poor quality; if you've never read Singer's reflections on passages in the speeches of George W. Bush, you have done better at avoiding pages and pages of bad analysis and meandering argument than I have.) But I did find this New Yorker profile on his classes interesting, although in part because it captures very clearly a common desire among the intellectually inclined: to see the current events of any given moment in terms of an identifiable pattern of past action that gives them deep insight into the course of history. The same desire, I think, is why academics have a very bad track record on political questions; the desire creates the temptation to think that they already know what is going on. But the patterns of history, while they do exist, do not fall so neatly or easily into our laps. In reality, there is no more sense to seeing fascism in every bit of bullying, corruption, and abuse of power one sees in a political opponent than to seeing Marxism in the same; fascism is a kind of programmatic policy, namely one of unifying all forces in the control of the state, not a specimen-collection of political wrongdoings and corrupt rhetorical appeals. The mistake seems to be quite common across the board, though, as the "it's-not-big-enough" critics show; 'fascism' is not a name for a size of badness. Gentile was not a Fascist because he did horribly bad things; he was a Fascist because he thought politics should extend through the whole realm of human thought. And one sees a similar problem when people speak as if not regarding every abuse of power as fascism would be somehow not to regard it as an abuse.

We should be skeptical of this label-slapping, for one of the perennial reasons why we should consider whether to be skeptical: it tempts us to think we understand more than we do. We recently had a situation in which a bunch of well-placed academics were discovered by the broader public to be fomenting against homeschooling; they thought it unacceptable that parents could educate their children without thorough regulation by the state and one in particular even stated that families only exist because they are legally recognized by the state. Now, it is entirely reasonable to think of this as advocating a step toward totalitarianism; it is exactly the sort of view of education that fascists historically have had. Would we learn anything from calling it fascism? All we would actually be doing is shortcircuiting understanding, substituting a pre-determined classification for an actual causal analysis. Of course, one does this for polemical purposes, or to express disapproval; that's fine, I suppose, but it's not an actual understanding of the situation.

Or take another example, from the Singer book I mentioned above. Singer, responding to Bushian comments about giving taxpayers back their money, puts forward the theory, common among a certain set of academics, that it's not their money; that since all pay depends on government distribution, taxation is not taking from people what they already own. Setting aside the fact that this theory is inconsistent with how almost every tax system in the world is actually set up, this is also quite clearly inconsistent with every serious account of labor's right to pay; it posits that the state has a non-obvious totality of authority in economic transactions, and it is exactly the kind of view of taxation that is consistent with a fascist view of the state. Have we actually understood the underlying situation giving rise to this view if we call it fascist? Do we really know how it will unfold? We do not. That can't be done by a classification.

Fascism, again, is not a collection of bad things; it is a policy of unified states governing 'totalitarianly'. One opposes actual fascism by supporting the rational pluralism of societies, that is, the actively and practically implemented view that human beings are members not merely of one society but of many distinct societies -- family, church, profession, civil society, humanity -- each of which has claims on them that must be respected, and none of which has the right to treat itself as the sole society; that these societies are not mere instruments of the state but that membership in these multiple societies constitutes the power and freedom of the person; that a society appropriate to a human being is one negotiating peace with these other societies, so that no one society has supremacy over everything. Human good is too vast a thing for any one society wholly to capture. The great political evil is the all-devouring maw.

We lose sight of this if we try to identify fascism by collecting specimens of corruption and failure. Anyone who knows human nature can see exactly where such an approach will lead: there will be plenty of cases of pareidolia, seeing things that aren't there due to vaguely similar shapes from one particular perspective; there will be plenty of cases of putting the fascist-color lens on the camera to make one's political opponents seem a little more fascist-like; there will be a lot of caricature-versions of fascism blended with caricature-versions of current events; and there will, of course, be lots of genuine evils that will be misclassified on the principle that if it is this or that it must be fascism. You'll get the kinds of the things you got from some Marxists in the Cold War, in which every corruption and failing of the Western powers was a sign that those powers were fascist. What will certainly not happen is that anyone will have a genuinely better understanding of the situation at large, or even, in many cases, the specimens. And what will even more certainly not happen is anything that would actually stand in the way of anything like fascism.

Wednesday, May 06, 2020

Pagnan Notation

As I've noted before, Ruggero Pagnan in a handful of articles* has introduced an interesting semi-diagrammatic method for handling syllogisms. He calls it SYLL (or SYLL+ when subalternation is added, or SYLL++ when both subalternation and an identity rule are added); I'll call it Pagnan Notation, since I'm less interested in logical systems qua systems than qua instruments for reasoning. Pagnan Notation has terms, represented by letters, and the following symbols:

← left arrow
→ right arrow
• bullet

Arrows must link terms or bullets; they cannot stand on their own. The basic categorical propositions are as follows:

All A is B
A → B

No A is B
A → • ← B

Some A is B
A ← • → B

Some A is not B
A ← • → • ← B

In addition, for purposes of manipulation, these each has a reversed form that is equivalent to it, but switches the positions of the terms:

All A is B
B ← A

No A is B
B → • ← A

Some A is B
B ← • → A

Some A is not B
B → • ← • → A

Because I and E are symmetrical diagrams, allowing reversals directly gives us two rules of immediate inference:

(1) I-Conversion: From A ← • → B, you can conclude B ← • → A, and vice versa.
(2) E-Conversion: From A → • ← B, you can conclude B → • ← A, and vice versa.

For obvious reasons, we can likewise recognize,

(3) Identity: You may at any time add A → A

which is equivalent to "All A is A"; and we can also have,

(4) Subalternation: You may at any time add A ← • → A

which is equivalent to "Some A is A". Combining reversal with Subalternation lets us have conversion per accidens for A propositions.

When two propositions share terms at the extremes, they can be concatenated. So, for instance, A → B and B → C can be superposed at the 'B' in order to get A → B → C. And we can delete any term (but not a bullet) if it occurs between two arrows going the same way. This is enough to start getting syllogisms.

All B is C: B → C
All A is B: A → B
concatenate to get A → B → C
delete to get A → C, All A is C.

No B is C: B → • ← C
All A is B: A → B
concatenate to get A → B → • ← C
delete to get A → • ← C, No A is C.

All B is C: B → C.
Some A is B: A ← • → B
concatenate to get A ← • → B → C
delete to get A ← • → C, Some A is C

No B is C: B → • ← C
Some A is B: A ← • → B
concatentate to get A ← • → B → • ← C
delete to get A ← • → • ← C, Some A is not C.

Thus all the First Figure syllogisms are simple cases of concatenation and deletion. For other figures we will sometimes need to use the equivalent reverses (once for Second Figure and Third Figure, twice for Fourth Figure); for all weakened syllogisms, we will need also to use our Subalternation rule. Subalternation effectively functions as a bullet-introduction rule.

The notation tracks distribution of terms. If a term is at the tail of an arrow, it is distributed; if it is at the head of an arrow, it is not. Thus if we look at one of the standard distribution rules for syllogisms, The middle term must be distributed at least once, we see immediately that a middle term allows concatenation; but it needs to have an arrow proceeding away from it if it is to be deleted and not show up in the conclusion. The second distribution rule, Terms distributed in the conclusion must be distributed in the premises, forbids just flipping arrows on their own. Pagnan notes that it's thus also possible to look at the syllogisms within the system by considering the facts that bullets cannot be deleted and that any bullets in the conclusion have to come from the premises. Then:

(a) You can only get S → P, which has no bullets, if there are no bullets in the premises; only the universal affirmative categorical proposition has no bullets. Therefore a universal affirmative conclusion requires universal affirmative premises.
(b) A universal negative conclusion, S → • ← P, is only possible if our premises have one bullet total and both arrows directed toward it. So one premise has to be universal affirmative, and the other has to be universal negative.
(c) A particular affirmative conclusion, S ← • → P, is only possible if our premises have one bullet total and both arrows directed away from it. So one premise has to be universal affirmative, and the other has to be particular affirmative.
(d) A particular negative conclusion, S ← • → • ← P, is a little trickier. But it will require two bullets that get us the arrows pointing the right alternating way. If each bullet in the conclusion comes from a different premise, one has to be universal negative and the other has to be particular affirmative to get two bullets and alternating arrows. If the two bullets come from one premise, that premise has to be particular negative (the only categorical proposition with two bullets) and the other premise has to be universal affirmative (which has none).

From (a), (b), (c), and (d) together we can see that every possible combination has one affirmative premise; none of the possibilities has two negative premises. Likewise, every possible combination has one universal proposition; none of them has two particular propositions. Every possibility with a negative premise has a negative conclusion. This is enough to get us the standard 'rules for syllogisms' in any of the usual forms that you find.

Pagnan also notes that you can build the square of opposition with what we have, if you add one additional consideration, namely,

(5) Noncontradiction: A ← • → • ← A may never be either a premise or a conclusion.

This, of course, reads as "Some A is not A". Any propositions that put together would yield a proposition of this form cannot be combined. So let's take

A → B
A ← • → • ← B

Concatenating gives us the contradiction (with B instead of A). The same will happen with

A → • ← B
A ← • → B

That's enough to get us a Boolean square of opposition; adding our Subalternation rule gets us the rest of the classical square of opposition.

Given that, we could also prove the validity of the Second, Third, and Fourth Figures by Aristotelian reduction to First Figure syllogisms. Take Datisi:

M → P
M ← • → S
Therefore S ← • → P

It's a Third Figure in which we can reverse the minor, concatenate, and delete; it is valid on the grounds we've noted. But, of course, by reversing the minor, we have turned it into a Darii syllogism. They're usually not that easy, of course. Let's take a Baroco syllogism:

P → M
S ← • → • ← M
Therefore, S ← • → • ← P

Baroco is converted to Barbara by contradiction, as the nasty little 'c' in its mnemonic tells us. Assume the contradictory of the conclusion, which would thus be S → P, since putting that with the actual conclusion would violate Noncontradiction. If you concatenate this with the major premise, P → M, we get S → P → M, which is equivalent to S → M, which is the contradictory of the minor premise (S ← • → • ← M), since if you put those together you violate Noncontradiction. So when we assume the opposite of the conclusion and use it for a Barbara syllogism, we get a conclusion that is inconsistent with the other premise; from which we can know that the conclusion does follow from the premises and Baroco is valid.

We have not considered two immediate inference rules, obversion and contraposition. Obversion of E and of O are extremely easy. "No S is P" is:

S → • ← P

The obverse is "All S is non-P"; but you can get this if you see • ← P as a negative and then read it all as one term. Using parentheses to make it a bit easier to see:

S → (• ← P)

Moving from "Some S is not P" to "Some S is non-P" works exactly the same way -- the obverses of the negative are already built in. Obversion of A and I require a new rule:

(6) Double Negation: → A and → • ← • ← A are equivalent.

Then we can see that "All S is P", S → P, is equivalent to S → (• ← • ← P), and that "Some S is P", S ← • → P is just like S ← • → (• ← • ← P).

Double Negation also allows us to do contraposition for A, since contraposition is the conversion of the obverse. S → P becomes S → • ← • ← P this is then reversed to get P → • → • ← S, "No non-P is S". With contraposition for O, we don't need Double Negation, we just reverse: "Some S are not P", S ← • → • ← P becomes P → • ← • → S, "Some nonP is S".

On this basis we can give translations for propositions with complemented terms:

All nonA is B
A → • → B

All nonA is nonB
A → • → • ← B

Some nonA is B
A → • ← • → B

Some nonA is nonB
A → • ← • → • ← B

No nonA is B
A → • → • ← B

No nonA is nonB
A → • → • ← • ← B

Some nonA is not B
A → • ← • → • ← B

Some nonA is not nonB
A → • ← • → • ← • ← B

If we wanted to, we could add parentheses to make the negated terms easier to pick out, but this wouldn't affect anything.


Since we can do complemented terms, it also follows that we could use Pagnan notation to do propositional logic that can be simulated by syllogism (although we have to drop Subalternation). For instance, "All A is B" is like "If p, q", so the latter can be p → q, and then a hypothetical syllogism would work exactly like a Barbara syllogism. For something like modus ponens or modus tollens, we would need to allow bullets to be terminal; that is p → • is "It is not true that p" and • → p is "It is true that p". Given this, we can always turn p into • → p; that is to say,

Assertion: p and • → p are equivalent.

Then modus ponens is:

p → q
• → p
by concatenation and deletion we get • → q.

Disjunction 'p v q' would be p → • → • ← • ← q. Disjunctive syllogism would be

p → • → • ← • ← q
p → •
Reversing the first premise and concatenating, we get q → • → • ← • ← p → •
But by Double Negation, → • ← • ← p is equivalent to → p, so
q → • → p → •
But then p can be deleted to get
q → • → •
But then by Assertion we have, • → q → • → •
but then by double negation that is equivalent to • → q.

And so it goes. In any case, this is all just a side effect of the fact that syllogisms can simulate propositional logic; we could do the same with any other logical fragment that can be simulated by syllogisms, like basic mereology (A → B for "A is part of B" and A ← • → B for "A overlaps B"), or binary modal logic (e.g., we could take A ← • → B to mean "A is compossible with B"), or (as Pagnan does in one of his articles) rudimentary linear logic. Syllogistic is an extraordinarily powerful thing, so a notation that can handle syllogistic fairly easily can do a lot with only minor modifications.


* Ruggero Pagnan, "A Diagrammatic Calculus of Syllogisms", Journal of Logic, Language, and Information, Vol. 21, No. 3 (Summer 2012), pp. 347-364; "Syllogisms in Rudimentary Linear Logic, Diagrammatically", Journal of Logic, Language, and Information, Vol. 22, No. 1 (Winter 2013), pp. 71-113; see also "Ologisms", Logical Methods in Computer Science, Volume 14, Issue 3 (August 31, 2018), arXiv:1701.05408.

Common Good and Public Good

The common good must be distinguished from the public good. These two matters are confused with consequent serious harm to the science of public Right and to humanity which, because of this confusion of concepts, searches in vain for a suitable social constitution. The common good is the good of all individuals who make up the social body and are subjects of rights; the public good is the good of the social body taken as a whole or, according to some opinions, taken in its organisation.

[Antonio Rosmini, The Philosophy of Right, Volume 6; Rights in Civil Society, Cleary & Watson, trs., Rosmini House (Durham: 1996), p.33 (sect. 1644).]

Tuesday, May 05, 2020

Cinco de Mayo


Zaragoza looks out on the fields wet with rain,
the mud that flows over the trampled terrain.
The wind in the face is now humid and hot.
He sighs, for he knows that his army is caught;
though at Puebla is safety, at least for a while,
defense on defense to weather the trial,
two forts newly linked by a trench laid in haste,
yet the French are now coming to lay all to waste.
Of the greatness of France, no word need be said,
the might of its force writ in soldiers now dead;
but here -- draw a line for its ruthless demand,
and let it be bitten as it stretches its hand.

Now hearken -- artillery booms out its cry;
insistent with tremor, the cannons let fly.
Too quick and too late have the French made advance,
and, seeking swift winning, they lost their best chance.
Their horses now turn in the sigh of retreat,
but soon are they met by hooves steady and fleet
as the Mexican cavalry swoops on their flanks
and troops in their ambush pour out their ranks.
The rain is now falling like heavenly grace
and all the French army is sliding in place,
and, frantic in flight, slip here and now there
as blood like to rust is incensing the air.

Zaragoza looks out on the field, lost in thought,
and sighs, for he knows that his army is caught,
and speaks the words hardest for commanders to say,
and tells his sure troops to stop now and stay:
Defeat may be birthed by a win stretched too far;
repair and look well on the night filled with stars
that fortune with favor has made you to see
with eyes yet alive and spirits yet free.
The French are defeated, at least for a breath,
and now is the time to retreat from more death.
'The national arms have been covered with fame';
immortal shall be Zaragoza's own name.

Zaragoza looks out on the fields he has won.
Perhaps he thinks back on the course he has run.
Perhaps he hears pipers rejoicing in tune.
Perhaps he foresees that his death will be soon.

Monday, May 04, 2020

Four Species and Metonymic Symbolism

Brown Judaic Studies is putting up open access versions of its monographs. They are on all sorts of different topics. I can highly, highly recommend Jeffrey L. Rubinstein's A History of Sukkot in the Second Temple and Rabbinic Periods; if the Feast of Tabernacles is a topic that interests you, this is definitely a book to read.

I did have a thought about one thing he says. In Chapter 7 (Sukkot in the Amoraic Midrashim), starting on p. 305, Rubinstein has a discussion of the Four Species (arba'at ha-minim), which are used in Sukkot celebrations. The Four Species come from a rabbinical interpretation of Leviticus 23:40, which says that should take something from four things:

es hadar, goodly trees, which rabbis usually interpret as the etrog
temarim, palm trees, usually interpreted as the date palm
es abot, leafy trees, usually interpreted as the myrtle
arbe nahal, willows of the brook

Rubinstein considers a brief discussion by Rabbi Akiba of these:

Rabbi Akiba says:

[A1] Fruit of goodly (hadar) trees (Lev. 23:40). This is the Holy One blessed be He, since it says about Him, You are clothed in glory and majesty (hadar) (Ps. 104:1).

[A2] Palm branches. This is the Holy One blessed be He, since it says about Him, The righteous bloom like a palm (Ps. 92:12).

[A3] Branches of leafy trees. This is the Holy One blessed be He, And He stood among the myrtles (Zech. 1:8).

[A4] Willows ('arvei) of the brook. This is the Holy One blessed be He, since it says about Him, Extol Him who rides the clouds ('aravot) (Ps. 68:4).

Rubinstein summarizes this, reasonably, as "R. Akiba proposes the mystical notion that each of the four species symbolizes God" (p. 306). Given things that he says elsewhere, though, it seems that he takes this to mean that R. Akiba literally thinks that each of the Four Species stands for God in some way. But, thinking through the actual verses to which Rabbi Akiba appeals, I don't think this can be quite right. It seems much more likely that R. Akiba is taking the link to be more indirect than this suggests. What the Four Species represent are four things that are closely associated with God, what we might call His appurtenances, rather than (directly) God Himself; they symbolize God not by direct symbolism but by symbolic metonymy.

Psalm 104, for instance, talks about God by associating Him with several things -- light, heavens, wind, fire, earth -- and thus is taking an indirect approach to description of God. What the hadar trees, the trees of splendor, directly symbolize is the hadar, splendor, that God wears as a vestment. Your vestments or clothes are things very closely associated with you that are nonetheless not you; splendor is not the divine being but something very closely associated with it. Likewise, Psalm 92:12-13 does not directly talk about God but about how the righteous are palm trees in the divine court. Looking at Zechariah 1, the one standing among the myrtles of the ravine is literally the Angel of the Lord -- again, closely associated with God as His messenger, but distinct. Psalm 68 does talk directly about God, but 'willows' only comes in because the word for 'willow' and the word for 'cloud' is the same word. And the clouds here are the divine chariot. So in each case what is directly symbolized is not God but something closely associated with God: the divine vestment, the divine court, the divine messenger, the divine chariot. However, because of this close association these things can in turn be used as a metonymic description for "the Holy One blessed be He" and thus can symbolize God indirectly.

This fits, of course, with a common pattern in how the rabbis tended to talk about God. We could indeed say, allowing for the fact that there are obviously many exceptions, that Christian discourse about God tends to diverge from Jewish discourse about God because Christians usually have preferred to talk about God by metaphor whereas Jews usually have preferre to talk about God by metonymy. One can think of the difference between, say, Philo of Alexandria and Dionysus. But in any case, it's worth keeping in mind that metaphoric symbolism and metonymic symbolism are distinct, and can sometimes operate in very different ways.

Sunday, May 03, 2020

And Worthy of the Sunlight and the Stars

by Paul Elmer More

Right often as I gazed upon the sea
And over all the billows far and wide,
Meseemed each passing wave but rose and died,
To murmur in the air some mystery
Learned in the solemn depths where such may be;
And once when the broad wind rose from the tide
And with the gathered burden louder sighed,
Meseemed I caught their utterance thus to me:--
Live in the heart of things where warnings sleep
That tears and laughter are not idle farce;
Live, not ashamed for honest pain to weep,
Still conqueror through sorrow's many wars,
Glad in the universal joys that keep,
And worthy of the sunlight and the stars.