Random Musing on Politics

In The Mind of the Maker, Dorothy Sayers suggests that every work of art or craft should be seen as exhibiting three aspects, analogous to the Father, the Son, and the Holy Spirit in Christian theology. Elsewhere she refers to these three aspects as the Idea, the Energy, and the Power. The Idea is what is unfolded in the work of art; the Energy is what we would often call the execution; and the Power is roughly its ability to initiate a response. In principle every artist aims to find the perfect proportion and balance among these three. In practice no one succeeds: everyone's triangle is scalene, sometimes slightly, sometimes severely.

Vico regarded government as a factibile, something made, and I think one can, as a rough but interesting exercise, think of governments as exhibiting these three. And as with works of art, every triangle is at least slightly scalene, and sometimes severely so.

I was somehow put in mind of this by a side comment in Arsen's post on archaism and futurism:

The French Revolution serves as a classical and large-scale example of a real try at futurism. Its henchmen even changed the names of the months on the calendar. The current Tea Party movement serves as a minor example of an archaist reaction to the initiatives of the Obama administration. That administration is wrongly seen as futurist in its intentions. Alas, it’s merely rational—but unfortunately also inept. Its futurist coloration is a very pale shade of pink and derives from the illusion that change can be made almost entirely by magical PR gestures intended to influence public opinion.

This does seem to be a besetting sin -- an artistic heresy, to use Sayers's phrase -- of the Obama administration, one that was actually foreshadowed, I think, by some of Obama's approach to campaigning. The administration takes an Idea, often a very interesting Idea worth developing, but then goes directly for the Power, as if the Idea itself would overwhelm all opposition by a kind of intrinsic magic. This was much the way Obama campaigned, too: ideas robed in a cloud of BOMFOG and glitter.

One is tempted to contrast this with the Bush administration, with all its emphasis on energy and forcefulness and decision and changing the world, and say that that administration was all Energy and no Idea. But this is not right, I think, and would come from accepting too uncritically the administration's own view of itself. In fact, the Bush administration was pretty thoroughly inept, as well: it, too, was an Idea-ridden administration (Spread Democracy! Go to Mars!) that expected Ideas magically to glide directly into Power without the difficult, careful, intricate work -- the actual act of administration -- required to make it happen; it just happens that one of the Ideas with which the Bush administration was enamored was the Idea of what Hamilton called an "energetic magistrate". But that Idea, too, was an Idea that they simply expected to overwhelm with its own intrinsic force; the attempt actually to put it into practice was slipshod, confused, and inept. Their Idea of Energy had no Energy.

I suspect that you might actually find this to be a common problem among American administrations. The degree to which it is a problem no doubt varies from administration to administration -- no government is scalene in exactly the same way. But American-style campaigning, especially at the Presidential level, gives almost no room for making a choice of the President that takes Energy into account. We do not test out administrative competence on the campaign trail; it is not part of our run-up to the election that each candidate is required to spend a week as Acting President so we can see how they handle the day-to-day details. At most we look at their record, and even there we don't look at the day-to-day but at the big things they did. Nobody runs on a campaign platform of quiet and tidy management that slowly and carefully refines and improves what we have; they run on some big idea which they insist will change the way we do things forever. After all, what would be stirring about someone who said that his goal as President would be to improve government accounting practices, reorganize the executive branch to improve efficiency, and to initiate a more systematic ethics review system in order to reduce corruption? It often seems like the last time that this sort of thing was a campaign issue was in the struggle over the spoils system, and like the last time that a President made a name doing this sort of thing was Chester A. Arthur, who put an end to all sorts of corruption by pushing forward a regular civil service -- and that, beneficial as it was, still only got people's attention by being a big, flashy idea.

So perhaps democracies and republics are plagued by the problem of Energy-deficiency. That is indeed very close to how some theorists of democratic government have seen them. Montesquieu's solution (found encapsulated for American's in George Washington's Farewell address) was that this sort of problem could only be remedied by virtue among the people. So perhaps we are doomed, and our good intentions, piling up without the care and craft to put them to good effect, are paving the road into our inevitable future.

Sommers Notation, Part II

(Part I)

Singular Terms

It's easy enough to see how Sommers notation handles universal quantity, like 'All dogs are canines' or 'No dogs are felines':

-D+C
-D-F

It's also easy enough to see how Sommers notation handles particular quantity, like 'Some dogs are tame' or 'Some dogs are not housebroken':

+D+T
+D-H

But what if we have a singular term, like, 'Fido is a dog'? Every singular subject can be treated as having a 'wild quantity', because as far as the term itself goes it doesn’t matter whether you treat it as universal or as particular. Thus 'Fido is a dog' would be symbolized as:

±F+D

In an argument you can treat the singular proposition as universal or particular, as you need; the only tricky thing is that you sometimes need to keep track of what you are doing with it. Sometimes, to help keep track, it’s useful to mark a term with a star to indicate that it is singular, e.g.,

±F*+D*

It would be possible to handle singular terms without this convention, however; one could treat singular propositions as always universal, but as implicitly paired with corresponding particular propositions. This would, in effect, be treating every singular proposition as a noncategorical proposition, but for practical purposes it would amount to the same thing.

Relations

Take the proposition, "All sophists take money from some fools". This is called a relational proposition because it has a term that relates other terms to each other. The basic format of this proposition is:

-S+P

But the P term is a complex term consisting of other terms, and sometimes these terms play a role in inference. What can we do? Wecan expand the predicate in this way:

-S+(T+M+F)

Then we can do all sorts of things with this. For instance, suppose we add to it the proposition, "All money is gold." The conclusion is:

-S+(T+G+F) [All sophists take gold from some fools]

Sometimes it is useful to use subscripts, when the direction of the relation is important. So, we could symbolize this proposition as:

-S1+(T123+G2+F3)

The 1, 2, 3, indicates that the action of the term, T, is going from S to F through G.This, however, is just a convenience to help us keep track of what the terms mean in complex relational predicates. (Subscripts can do a little more than this, since we can use them as pronouns, for which see below. But for the most part we don’t need them to do so.)

On this basis we can translate any relational proposition you could want. Here are some examples and their translations.

Every boy loves every girl. -B1+(L12-G2)
Every boy loves some girl. -B1+(L12+G2)
Some boy loves every girl. +B1+(L12-G2)
Some boy loves some girl. +B1+(L12+G2)
No boy loves every girl. -B1-(L12-G2)
Every boy sends a rose to some girl. -B1+(S123+R2+G3)
Some girl was sent a rose by every boy. +G3+(S123+R2-B1)

Note that the last two are logically equivalent, which is precisely the result you should get. There are more complicated terms that can't be handled so easily, for instance,

Some girls who think that all love is easy are unhappy.

To do this one must introduce propositional nominalization, which we will get to later. But even without this we can do a lot.

Pronouns

Suppose we have a sentence like: "Some boy kissed some girl and she clobbered him."

The first conjunct is easy: +B1+(K12+G2). The second conjunct has a pronoun, however. How will we handle this? Given this, we can represent the whole sentence as:

(+B1+(K12+G2))+(±2+(C21±1)

Singular pronouns are just singular terms, and are treated as such. Nonsingular pronouns act like normal terms. But the use of the subscripts in this way is just a matter of convenience, to keep track of the fact that we are dealing with pronouns.

(Singular) Identity and Existence

Because singular terms are indifferent to quantity and can be qualified, we can handle identities between singular terms very easily. 'Socrates is Socrates' becomes:

±S+S or
±S*+S*

Thus there is no need to bring in any special way of handling identity in order to handle singular identity statements. (Identity between variables is more difficult, and we will not discuss it here.)

Just as identity is handled by normal predication in Sommers notation, so, too, are existential statements: existence is a predicate in Sommers notation. If I say, “Socrates exists,” I can represent it as:

±S+E

There are other ways to handle this, as well, but we won’t get into them here.

Having looked at some of these we will get into actual arguments, starting with some simple ones. Then we will look at how Sommers can handle whole propositions as terms.

Fallacies and Invalid Argument Forms

At AskPhilosophers.org, someone asked the question:

How do you prove that a certain logical fallacy is a fallacy indeed? Are there "fallacies" about which there is a controversy if it is a fallacy or not? And if in the future, a new fallacy will be discovered, what will be the outline of the proof that one will have to use to prove that it exists? (Just an application of the first question.)

Nicholas Smith provides an answer that I think is dubious:

From the point of view of deductive logic, your question is very easily answered: a fallacy is an argument form in which the premises may all be true, but the conclusion false. To prove this, one provides what is called a "counterexample," which is simply a substitution instance that has the above characteristics.

We need to distinguish between two kinds of deductive systems. In a monotonic system, which is deductive in the strict sense, something like this answer is at least plausible, but in a nonmonotonic system it certainly would not. I suspect that Smith would classify nonmonotonic systems under 'inductive logic'; this would not be unheard of, although it is misleading given that nonmonotonic systems generally have nothing to do with induction, or at least no more to do with it than monotonic systems do.

But more than this, even with a monotonic system, the plausible answer is not right if we are not merely operating within the system but applying it to actual arguments. For to apply formal systems to actual arguments we must allow for implicit premises and enthymemes, and once this is recognized there turns out to be no good way to answer the first question. In particular cases you can show that there is no way to salvage an argument with implicit premises that would not be either unreasonable or provably wrong. But Smith's argument conflates 'invalid argument form' with 'fallacy' and this is untenable as a practical matter. Even a formal fallacy as straightforward as the one Smith gives (affirming the consequent) can be salvaged in particular applications with implicit premises, e.g., premises that combined with the other premises make the relation between p and q to be one of mutual implication (equivalence). Counterexamples are not generally useful for analyzing enthymemes; and nobody commits a fallacy simply by not stating all of the premises and assumptions of the argument. At least, if we identified fallacies with formally invalid argument forms, we make the label 'fallacy' completely useless in practice. What counts as invalid is relative to the formal system we use; whenever we apply formal systems to actual arguments we have to allow ourselves so much room for the implicit and assumed that merely identifying the explicit form as invalid tells us virtually nothing about whether it is a good argument or not. (As I always tell my students, it is very, very useful to know that an argument is valid. It is at best only somewhat useful to know that it is invalid.) We can prove that particular arguments are fallacies; there appear, however, to be no generally applicable methods for doing this, because an invalid argument form that is fallacious in one context may not be in another because the second context is, so to speak, 'rigged' so that the invalid argument form, despite not being generally truth-preserving, is so in contexts like that one.

A straightforward example of this is found with fallacies of composition. An argument form like this is both formally invalid as it stands (the explicit premise does not require the conclusion) and admits of many, many counterexamples:

Each part of the wall is red; therefore the wall is red.

But we all know that under particular conditions this type of inference is not only good but certain. But pinning down these conditions is always extraordinarily tricky; what you are really trying to do is to prove something by division of possibilities, and as Aristotle pointed out long ago, even when arguments by division are certainly right they are not rigorously demonstrative.

My own view is that in the strictest sense you can't have a fallacy without an application -- that is, no argument form is fallacious as such. Rather, there are only fallacious and non-fallacious applications of argument forms. There are, of course, argument forms that are especially subject to abuse because they are not usually reliable but look superficially like argument forms that are -- the fallacy of affirming the consequent is a good example -- and we can, by a sort of metonymy, call these fallacies because their non-fallacious applications are rare enough that we can usually neglect them. But this is a metonymy; and a 'fallacy' in this sense may admit of rare cases in which an argument of exactly that form would be a perfectly good argument, and thus by definition not a fallacy at all.

Moreover, one has only to look at disputes raised by paraconsistent logical systems to see that there are problems with the counterexample approach even if the above points are set aside. Disjunctive syllogism, for instance, is valid in some formal systems and invalid in others; what counts as a counterexample to it in one system will not count as one in another. We are left with the question of whether disjunctive syllogism is really best modeled as strictly valid, or as valid only under limited conditions, like the inferences from composition; and the method of counterexamples is necessarily useless for this question.

Thus I would suggest the proper answers to the questions are, in order:

Except in a formal system there is no general method to prove that a logical fallacy is a fallacy indeed.

There are indeed argument forms whose status as fallacious is open to dispute; indeed, even disjunctive syllogism and modus ponens, which are standard inference forms, have been questioned in ways that would imply that at least some of their applications are fallacious.

It may genuinely be possible to prove that the new fallacy really is a fallacy, but without a general method for doing so, it is impossible to forecast how one would do it.

Craig Ferguson on Moral Philosophers

Jonathan Dancy gets a mention on Craig Ferguson's Late Late Show (ht):

Sommers Notation, Part I

For my students I'm putting together a new guide for using Sommers-Englebretsen Term-Functor Logic, also known as Sommers-Englebretsen Term Logic, and which I will call here, for simplicity, Sommers notation. I thought I would put up a draft version.

Parts of a Categorical Proposition

If we want to talk about categorical propositions, it’s helpful to break them down into six parts which may be briefly described as follows:

(1) Subject Term: This is what the proposition is directly about.
(2) Predicate Term: This is what is being said about the subject term.
(3) Universe (or domain) of discourse: This is something the subject and predicate term share that allows them to be compared in the proposition.
(4) Quantity of subject: how much of the subject the predicate covers.
(5) Quality of predication: how the predicate term applies to the subject term.
(6) Judgment: how the whole proposition is being put forward.

There is much more that could be said about each of these things, both separately and in their relations, but this will do for our purposes. Because the universe of discourse is already implicit in the subject term and the predicate term, we don’t usually need to include it specifically in a notation, although (as we shall see) it can be useful to have a way to do it if we need it. But, in general, we want a notation that allows us to keep track of all these parts.

Sommers notation starts from the basic idea that every categorical proposition is the affirmation or denial of a simple or complex predicate of all or some of a subject. When you look at categorical propositions in this way, we can see that they admit of three basic kinds of oppositions.

1. Term Valence. Every term has either a positive or a negative term quality. 'Red' would be an example of a term with positive term quality; 'Nonred' would be an example of a term with negative term quality.

2. Opposition of Quality. Likewise, every predicate has either a positive or a negative predicate quality. 'Is red' has a positive predicate quality; 'Isn't red' has a negative predicate quality. (One of the features of Sommers notation is that there is no practically significant distinction between term quality and predicate quality; 'S is non-P' is not significantly different from 'S isn't P'. But when starting out is useful to treat them as distinct.)

3. Opposition of Quantity. Every predicate is predicated of at least some or definitely all of a subject. This sort of opposition is an opposition between a universal subject and a particular subject. So 'Some S is P' is opposite in quantity to 'All S is P'.

3. Opposition of Judgment. Every proposition is put forward as true or false, that is, it is asserted or denied. 'It is not the case that S is P' is opposed in judgment to '(It is the case that) S is P'.

The upshot is as follows.

(a) Every categorical proposition has a subject (S) and a predicate (P).
(b) Every term, independently of its role in the proposition, has a mark indicating term valence.
(c) Every P as a complete term has a mark indicating opposition of quality.
(d) Every S is a term with a mark indicating opposition of quantity.
(e) The entire proposition linking S and P is itself a term with a mark indicating opposition of judgment.

Given these four basics, which I will not argue for here, we can develop the basic format of Sommers notation.

Plus and Minus

We have three oppositions. Sommers's great idea was to take these oppositions and note them down as plus and minus in a subject-predicate proposition. So we have (on the basis of (a) above)

S...P

as our assertion. However, we know from (b) that every term has its own valence. Thus:

(±S)...(±P)

We know from (d) that we want every subject to have its mark of quantity. Thus:

±(±S)...(±P)

And since each predicate may be itself a complex term, it has as predicate a mark of quality, which allows us to take (c) into account. Thus:

±(±S)±(±P)

And we know from (e) that every proposition has a judgment that (so to speak)links the predicate and subject together so that the proposition either asserts something or denies something. This we can symbolize, putting the mark of judgment at the beginning, as:

±(±(±S)±(±P))

Of course, this is just a general format. Let's take a basic assertion: All S is P. This can be symbolized by:

+(-(+S)+(+P))

S and P are both of positive quality, so the sign linked to each term is positive. P is affirmed of S and so there is a plus sign linking (+S) and (+P); S is of universal quantity, which we indicate with the minus in front of (+S); and the whole proposition is being asserted as true, so we have a plus sign in front of the whole proposition. This is pretty intuitive, except, perhaps, for the reason why the universal quantity is given a minus and the particular quantity is given a plus. The reason for this is (if you want the crude and read version) is that if we do it this way the whole thing works. If you want a more technical answer, however, we make the universal minus and the particular plus in order to preserve the contraposition of the A categorical (All S is P) and the conversion of the I categorical (Some S is P). That is, we want these two equivalences:

+(-(+S)+(+P)) = + (-(-P)+(-S)) [i.e., Every S is P is equivalent by contraposition to Every nonP is nonS]

+(+(+S)+(+P)) = +(+(+P)+(+S)) [i.e., Some S is P is equivalent by conversion to Some P is S]

It's easy to recognize these equivalences if we give the universal a minus and the particular a plus. Another way to put the same point in technical terms would be to say that the minus for quantity tracks what the traditional theory of the syllogism calls distribution. But quantity's the only tricky thing about this basic format: + and - simply indicate an opposition, and '-' in particular shouldn't be confused with negation, which it only sometimes has.

In the above format, all we've marked are the terms and their oppositions. Which opposition is relevant is entirely a matter of where it is positioned in the assertion, so we don't have to worry about distinguishing them in any other way; + and - will do for everything. The really neat stuff we'll get to later. For now, we'll note just one neat feature that this way of symbolizing yields us. If we treat +'s as we usually treat +'s (e.g., in math), we can contract a string of plus signs. Thus

+(+(+S)+(+P))

can be written as

+S+P

without any loss of logical function. Likewise, we can treat -'s in a complementary way, such that two minuses together become a plus, and a minus and plus contract to a minus. Thus

-(+S)-(-P)

can be written as

-S+P without any loss of logical function. They are always logically equivalent, although in their expanded forms they may look different. We can then give a simplifed form to all the basic Aristotelian categoricals:

A (All S is P) -S+P
E (No S is P) -S-P
I (Some S is P) +S+P
O (Some S is not P) +S-P

But, given that we can do all Aristotelian syllogisms. A syllogism works when it can be formulated as a true equation and both sides are similar. Take the famous Barbara (AAA-1) syllogism:

All S is M
All M is P
Therefore, All S is P.

This has the equation:

(-S+M) + (-M+P) = -S+P

Just treat it as you would treat it if it were an algebra equation. You'll see that the left side is indeed equal to the right. All we have to do in order to be certain that it is a valid syllogism is to make sure that the two sides are similar. The two sides are said to be similar if (a) they have the same extremes (i.e., terms that are not arithmetically eliminable); and (b) they have the same quantity (the conjunction including a particular always being particular). In the Barbara case, the sides are clearly similar. Therefore it is valid. We can even handle 'weakened syllogisms' (syllogisms with universal premises that have particular conclusions) if we assume that they have the hidden premise +S+S (which, as we'll see, is a tautology and can be introduced at will). Thus Camestrop (AEO-2) would be:

(-S-M) + (-P+M) + (+S+S) = +S-P

It is useful to summarize this in a procedure that will help us to determine validity in any categorical syllogism using Sommers notation:

(1) Check to see if the argument is algebraically acceptable – that the premises add up to the conclusion.
(2) Check to see if the argument is regular. There are two, and only two, ways an argument can be regular. Either it has only universal propositions, or, if it has a particular proposition, it has one (and only one) particular proposition in the premises and a particular conclusion.
(3) To handle weakened syllogisms, if an argument fails at (1) and (2), check to see if it can pass if we add (+S+S) to the premises, where S is the subject term of the conclusion,

That is, a syllogism is valid if its premises add up to the conclusion and it is regular, either in itself or with the premise ‘Some S is S’ is added.

This is all quite cool. But I'm partly getting ahead of myself here. Sommers notation is more powerful than I've suggested so far, and we need to introduce a few additional tools if we are to see this and handle all the kinds of argument Sommers notation is capable of handling. So now we'll go on to look at how Sommers notation handles various key issues (singular terms, relations, identities, meta-propositions, existence). Then we'll handle arguments.

(Part II)

Three Poem Drafts

Cliché

Lady love, my darling dear,
my honeyed life, my angel's tear,
my doggerel verse will light the way
along your path the live-long day,
and though its speech is trite and worn
it shall upon bright wings be borne;
for each cliché was turned to such
by being truth used overmuch,
and (though these words are tired speech)
when used of you, the truth they teach.

Pythagorean

The lilting light on its lyre
makes melodies of mercy
and I, strange as it seems,
am the music, am the light's song,
a Pythagorean harmony.

Participations

The first creating one
in infinity dwells,
for the created infinite
participates the first,
and so also simple goods,
life, light, beauty,
that cause all things that have these,
for as the first cause of all
must be infinite itself
(all else follows from it)
so then life, light, beauty,
these it must then be,
and from it life and light
and beauty too
commingle and flow down
to cause mind to be.

The Sight of a Bear or a Fox

Father Stephen Freeman has a good quotation from Elder Paisios:

Elder Paisios said: Often we see a person and we say a couple spiritual words to him and he converts. 
Later we say, “Ah, I saved someone.” I believe that the person who has the disposition and goodness 
within him, if he doesn’t convert from what we say, would convert from the sight of a bear or a fox or from anything else. Let 
us beware of false evangelization.

(Paisios (also known as Eznepidis) was a twentieth-century monk at Athos, who spent much of his life at the Panagouda hermitage.)

I Strain My Heart, I Stretch My Hands

De Profundis
Christina Rossetti

Oh why is heaven built so far,
Oh why is earth set so remote?
I cannot reach the nearest star
That hangs afloat.

I would not care to reach the moon,
One round monotonous of change;
Yet even she repeats her tune
Beyond my range.

I never watch the scatter'd fire
Of stars, or sun's far-trailing train,
But all my heart is one desire,
And all in vain:

For I am bound with fleshly bands,
Joy, beauty, lie beyond my scope;
I strain my heart, I stretch my hands,
And catch at hope.

Friday Random Ten

1. Sufjan Stevens, In the Words of the Governor
2. Animals, Please Don't Let Me Be Misunderstood
3. Jonathon Coulton, re: Your Brains
4. Alphaville, Forever Young
5. Jana Mashonee, O Holy Night (Hodiyin Tl'ee'go)
6. Sufjan Stevens, You Are the Blood
7. America, Sister Golden Hair
8. Jann Arden, Never Mind
9. Wainotar, Kihlaus
10. Madison Park, Opus One

Jana Mashonee's "O Holy Night" is from her American Indian Christmas album; the song is a Navajo version of the carol, if I remember correctly. You can hear a sample here.

Nostalgia is a curious thing, because it is so very rooted in particulars. The Alphaville song is pretty sappy, but I like it because I remember hearing it on a mix tape that was playing while I was chatting with Adrienne about existentialism -- and that conveys nothing to anybody else, but it is the full explanation.

Doing Ethics

In the past when I've taught Ethics, I've taught virtue ethics last; but this term I am teaching it first. It's already begun to give a different flavor to the course; today this passage from Aristotle was a big part of the class discussion:

The many, however, do not do these actions but take refuge in arguments, thinking that they are doing philosophy, and that this is the way to become excellent people. In this they are like a sick person who listens attentively to the doctor, but acts on none of his instructions. Such a course of treatment will not improve the state of his body; any more than will the many's way of doing philosophy improve the state of their souls.

[from Louis Pojman, Moral Philosophy: A Reader, 3rd edition, Hackett Press, p. 254]

And despite the fact that I think Aristotle is quite right here, it felt odd as an early part of an Ethics course: the insistence that the way to learn ethics -- the way to do ethics at all -- is not so much to listen to arguments but to go out and start practicing good deeds. Starting out with this sort of standard makes much of the rest of a college course seem a little odd.

My Ethics course has a service learning component, which is the tiny pittance I, as a college professor teaching ethics, am able to throw Aristotle's way on this point. But even that is sometimes awkward to integrate into the course, for reasons that have nothing to do with ethics itself.

Last term I had a student who was asked by a supervisor of a local charitable organization, during his service learning hours, why he was doing volunteer service, and who responded that he was doing it as part of a course on ethics.

"Really?" said the supervisor. "What does volunteering have to do with ethics?"

Many Validities

When we talk about validity in logic classes, we typically frame it as truth-preservation: a valid argument is one in which, if the premises are true, the conclusion must be true. And most of what is taught in such classes concerns truth-preservation, either directly or indirectly. However, as I've noted before, there is no fundamental distinction to be made between truth values and modal operators; the latter can be treated as a particular kind of truth value and the former as a particular kind of modal operator. Thus there is no good reason why logic can't concern itself with other kinds of preservation.

In a sense one can say that it has from the beginning. The centrality of demonstration in Aristotle's logical work can be said to make his primary concern not truth-preservation but necessity-preservation: he wants to know the preconditions for saying of an argument that if its premises are necessary the conclusion will also be necessary. Aristotle's famous definition of a syllogism ("A syllogism is a logos in which, certain things having been supposed, something different from these necessarily results because of their being so") has sometimes been taken to indicate that the premises and conclusion have to be relevant to each other, and that therefore Aristotle's logic is a kind of relevance logic; I am not sure that this is so, but it is clear enough that if you are interested in how arguments be necessity-preserving when the premises are different from the conclusion, you will be interested in something that can broadly be called 'relevance', because irrelevance is an impediment to necessity-preservation. One could also cash out the distinction between perfect and imperfect syllogisms in these terms: perfect syllogisms, those of the first figure, are those which make it obvious that if the premises are necessary the conclusion must be necessary; thus it makes sense to regard them as a sort of 'normal form' for demonstration. In any case, for purely structural purposes the distinction between truth-preservation and necessity-preservation is not one that makes a difference: every necessity-preserving inference, for any standard notion of necessity, will also be truth-preserving. But, since not every truth-preserving inference is necessity-preserving, if you are especially interested in getting necessary conclusions from necessary premises, it's a distinction that can support some logical weight.

If you can distinguish necessity-preservation from truth-preservation, you can also go in the opposite modal direction and distinguish truth-preservation from possibility-preservation. Indeed, the preservation of any sort of modality -- obligation, pastness, knownness -- can be investigated in its own right. Preservationist approaches to paraconsistency are essentially doing this: preservationism is the investigation of consistency-level-preservation in arguments, or, to put it in other terms, preservationism is the investigation of a particular sort of possibility-preservation. I'm not fully familiar with preservationism, but my guess is that the form of possibility it preserves is the capability for being true or, in other terms, degree of coherence.

In short, there are plenty of other things on the table besides truth-preservation: many validities beside the standard one.

Cyrano and Determinate and Indeterminate Ways of Taking Terms

In Edmond Rostand's classic play, Cyrano de Bergerac, a very fictionalized tale about the seventeenth-century duelist and playwright of that name, we find an interesting case of a love triangle based on muddled identity. Cyrano de Bergerac is a brilliant swordsman who has an extraordinarily large nose, about which he is rather sensitive. He is in love with Roxane; but he learns that Roxane is in love with the soldier, Christian. She asks him to befriend him and protect him, and because Cyrano loves her he agrees to do it, even after a not-very-auspicious first meeting with Christian in which Christian can't help but remark loudly and with great astonishment, several times, about the size of Cyrano's nose (a very famous scene -- C'est un roc! C'est un pic! C'est un cap! -- Que dis-je, c'est un cap! C'est une péninsule!). Cyrano tells Christian that Roxane wishes a letter from him and Christian is depressed by this because he has a very poor way with words (as might have been guessed from the nose incident). Cyrano gives Christian a letter he himself had written to express his love for Roxane. The letter floors Roxane -- it is extraordinarily beautiful and eloquent. Christian tries to do it on his own for a brief while, but it is a disaster -- he is so ineloquent that he almost loses her; fortunately for Christian, Cyrano saves the day by giving him words to say that reverse her sudden disappointment and win Christian a kiss. Then Christian and Cyrano go off to war together. Cyrano meanwhile, unbeknownst to Christian, continues to write love letters to Roxane under Christian's name. Roxane is so smitten by the letters that she visits Christian at the front, at great risk to herself. She tells him before she was attracted by his beauty, but because of his letters she has come to love him for his soul alone, and would love him even if he is ugly. Christian, who despite his dullness is trully a good man, is too honorable to leave it at that; he goes to Cyrano and says that they must make a clean break of it -- if he, Christian, is not loved as "the fool that he is," he is not truly loved. Cyrano does not believe Christian until a little while later, after talking a bit with Roxane, when she tells him personally. He is about to tell all when Christian is suddenly brought back to camp -- he has been shot, and fatally so. And then Cyrano is too honorable, and too much in love, to shatter Roxane's illusions about a brilliantly witty and romantic Christian. Roxane goes into mourning for fifteen years, living in a convent, but Cyrano comes by regularly to tell her of the world. Then one day, Cyrano is mortally wounded; but he still comes by to say farewell to Roxane, without telling her of the injury. He begs to read her Christian's last letter to her. As he reads, it grows dark, and listening to Cyrano's voice read the letter in the dark, she suddenly realizes that the letter itself is very Cyrano-like, and that all of Christian's letters had always been Cyrano's. Cyrano grows delirious from his injury as Roxane tells him that she loves him. He dies in her arms.

The ending deliberately strengthens the sense of muddled identity rather than resolving it. Roxane says, "I loved but once, yet twice I lose my love!" And Cyrano tells her,

I would not bid you mourn less faithfully
That good, brave Christian: I would only ask
That when my body shall be cold in clay
You wear those sable mourning weeds for two,
And mourn awhile for me, in mourning him.

The point is quite deliberately not that Roxane had really loved only Cyrano all along, nor that she had really loved them both all along, but that she had loved Christian, and yet she loved Christian only in part for being Christian; in part she loved him for being Cyrano. She really did love Christian, for his beauty and for his courage; she really did love Cyrano under Christian's name, for his wit and passionate eloquence; and she had no way of distinguishing the two in the love itself. There was only one object of Roxane's love; she just didn't know that that one object was two persons.

That's the story and the idea. I want to raise it in order to raise a point about how words, like names, apply to things. We can start with asking the question: Is the implication of Cyrano de Bergerac, that the one object of Roxane's love was two people, logically coherent. One could argue in this way. If Cyrano and Christian are one object of love, they must be either a single object that is Cyrano or a single object that is Christian, because Cyrano and Christian are not the same thing. But either assumption yields a contradictory conclusion: either Cyrano is something that is not Cyrano or Christian is something that is not Christian. We could put it in other terms. Cyrano is not Christian. The single object of Roxane's love is Cyrano. And the single object of Roxane's love is Christian. Thus the single object of Roxane's love is Cyrano and not Cyrano, Christian and not Christian, a contradiction. Or again: if Cyrano is the object of Roxane's love, and Christian is the object of Roxane's love, and Cyrano and Christian are not a single thing, the object of Roxane's love cannot be a single object: there must be as many things loved as there are things that are loved.

This cold conclusion, according to which Roxane's own view of her love is irrational and incoherent, would perhaps be something we would have to accept with regret if it were really as thoroughly logical as it seems to be at first glance. In fact, however, these arguments commit the age-old fallacy of figura dictionis -- they make the mistake of assuming that the same words means the same underlying logical structures. In fact, 'the object of Roxane's love' is capable of applying to things in at least two distinct ways: it could be applied determinately or it could be applied confusedly. Taken determinately, there are two objects of Roxane's love: the individual Christian and the individual Cyrano. Taken confusedly, there is only one: Christian and Cyrano insofar as they are not distinguished (or distinguishable, as the case may be). All the arguments treat a term that obviously should be taken confusedly as if it should be taken determinately.

To see that this is not ad hoc, we need to recognize just how essential this distinction is to much of our reasoning. Suppose I say, "At least one of these soldiers is not a lieutenant." In this case, I am taking the common noun, 'soldier', determinately. Since it is a common noun, it leaves open the possibility of there being more than one soldier, but for the subject term to work as it must for this sentence to make sense, we can't be taking soldiers indeterminately: if at least one soldier is not a lieutenant, then there is some soldier, namely, this individual soldier, who is not a lieutenant; and if there are two, then this soldier is not a lieutenant and that soldier is not a lieutenant; and so on if there are three or more. But 'a lieutenant' here is not taken determinately here: it is not a claim that at least one soldier is this or that lieutenant. The term is taken confusedly. If I did take the term determinately, saying, "At least one soldier is not at least one of these lieutenants," that would be a very different claim. Likewise, if I say that "Every good dog is an animal that goes to heaven," I am not taking 'good dog' determinately. I am taking good dogs indeterminately or confusedly, making no distinction among individuals. Likewise, 'an animal that goes to heaven' is taken confusedly and not determinately: I am not saying that every good dog is this animal that goes to heaven; nor am I saying that every good dog is this or that or that other animal that goes to heaven.

In Roxane's case the confused application of the term is due literally to confusion; this is what makes relatively plausible what is the genuinely unusual (but not impossible) logical feature of the predicament, namely, that it forces a proper name ('Christian') to be taken determinately and indeterminately depending on the circumstances and that one of the major players, namely Roxane, is not in a position (until the very end) to say when it should be taken one way and when it should be taken the other way (indeed, she doesn't know until the end that it can be taken both ways, and that many things that she said of Christian, taking the name determinately for Christian, are really only true of Christian if we take the name indeterminately for Christian and Cyrano). But cases of the distinction doing real logical work in a context not depending on psychological confusion lie ready at hand in practically everything we say.

Thus Roxane's final assessment of the situation is not logically confused; and, indeed, it is exactly right.