Boole on Identity, Noncontradiction, and Excluded Middle

As the principles of identity and excluded middle...are true principles and are moreover either first principles or as consciousness informs us lie close to the very ground of the possibility of thought (it matters not here that they have been regarded by some as metaphysical and not logical and by others have been considered frivolous and trifling). A theory of Logic which does not both recognise them and give to them a very important place must be a very imperfect theory. It does not suffice that their existence should be casually noticed.

On the other hand it is very evident that the principles of identity, contradiction and excluded middle are rather principles which relate to conception and to judgment -- to the power by which [we] conceive of things as existing and as existing in relation expressible by propositions -- than to reasoning. To the latter they seem to belong only or chiefly in an implicit manner inasmuch as reasoning presupposes conception and judgment as the sources form which the materials upon which it operates are derived.

George Boole, Prolegomena, sects. 4 & 5, Selected Manuscripts on Logic and its Philosophy, Grattan-Guinness and Bornet, eds. Birkhäuser Verlag (Boston: 1997) 51-52.

A Poem Draft

Half Asleep in a Thunderstorm

I lie in bed at night,
a fan above my head;
my mind whirls round and round
and I dream that I am dead.

The darkness all around me
like a blanket on the brain,
my heartbeat in my ears
like the pounding of the rain,
I watch the world go by,
just leaves upon the gale,
seeing visions of lost time
and the lapse of every tale.

The darkness thunders softly
as I drift here in my bed,
half in the world and of it,
half out of it and dead.

Dark Satanic Mills

Mark Shea notes the oddity of the hymn "Jerusalem", and of its popularity. The hymn was fashioned from a poem in the preface to William Blake's Milton:

And did those feet in ancient time,
Walk upon England’s mountains green:
And was the holy Lamb of God,
On England’s pleasant pastures seen!

And did the Countenance Divine,
Shine forth upon our clouded hills?
And was Jerusalem builded here,
Among these dark Satanic Mills?

Bring me my Bow of burning gold;
Bring me my Arrows of desire:
Bring me my Spear: O clouds unfold:
Bring me my Chariot of fire!

I will not cease from Mental Fight,
Nor Shall my sword sleep in my hand:
Till we have built Jerusalem,
In England’s green & pleasant Land.

I think the popularity of the hymn has to do with its militancy. Militant hymns are striking and stirring in ways that many other hymns are not; they make you want to rise up and do something. And they invoke the sublime, and that is a rare quality in hymns, or, indeed, in any songs whatsoever. Most songs, of course, are better off not even attempting it; but a song that manages to do it without obviously descending into a sort of parody is a rare thing.

Of course, there are hymns that do these things much better than "Jerusalem" does. "The Battle Hymn of the Republic," for instance. But the Battle Hymn, for all its Unitarian provenance, can't be (as Shea notes "Jerusalem" is) a post-Christian hymn; it lacks, for instance, the neo-Pelagian view that progress is something you build by imposing your will on the world. In the Battle Hymn, it is not you who bring progress: it is God's truth that marches on, as inevitable and inexorable as the glory of the morning on the wave, it is He who looses the fateful lightning of His terrible swift sword, against which those who oppose the march of His truth cannot stand. And the only contribution the hymn exhorts people to make to this progress is this, that just as Christ died because that was what it took to make men holy, so we should be willing to die if that's what it takes to make men free, because God is marching on. So much easier to sing that you'll fight ceaselessly to destroy all of the effects of the Industrial Revolution on the basis of a story nobody believes....

Decisive Voting and Oxfam Alternatives

Harry Brighouse has some arguments that there is no strict obligation to vote. There are a few points in the post I agree with (e.g., I don't think anyone has a moral obligation to vote), but he also gives an argument that just gets on my nerves:

Finally, whereas campaigning really does matter in well structured institutions, voting is very strange – the chance that your vote will, in fact, be decisive is almost zero (usually). Suppose it takes you 30 minutes to vote. Even if you earn minimum wage, it would almost certainly be better to work that 30 minutes, and donate the proceeds to Oxfam. All I can say about this is that most people who don’t vote do not, in fact, spend the time they gain from not doing so working for a wage they donate to Oxfam.

I do agree that if you are the sort of person who is persuaded by this argument, you probably should not vote. Ever. It provides such an utterly ridiculous criterion for what would make a vote "matter" that you would think that people who give arguments like this would pause a moment and say, "Well, now that I say it, that doesn't sound quite right." Under what reasonable, rational conception of voting does voting only matter if your vote, in particular, stands a good chance of being decisive? So that's one part of the argument that gets on my nerves.

But the rest gets on my nerves, too; there is, I've found, a whole class of arguments (particularly popular among utilitarians, but not exclusively among them) which might be called "Oxfam alternative arguments", where an activity is compared to donating to Oxfam (or something similar), or working for a period of time and donating to Oxfam, and the comparison is always, of course, unfavorable to the first choice. But this is silly; there is no way to compare the two activities unless we know the field and standard of comparison. Suppose, for instance, that you value participation in the institutions and traditions of your nation. Then it would be utterly silly to say, in light of that value, that it would almost certainly be better to work to donate to Oxfam than to vote. Even if it were still better to work to donate to Oxfam, it would not 'almost certainly' be so; and it could only be so because some greater value took precedence over the value of participation. So such comparisons are meaningless. Which is better, throwing a birthday party for your daughter or giving all the money to Oxfam? Which is better, typing up a post about whether you should vote or spend that time working and donating the money to Oxfam? Which is better, getting eight hours of sleep, or only four while working the other four to donate to Oxfam? There is no meaning to such vague and indefinite comparisons.

Feast of St. Athanasius

Who, then, is this Christ and how great is He, Who by His Name and presence overshadows and confounds all things on every side, Who alone is strong against all and has filled the whole world with His teaching? Let the Greeks tell us, who mock at Him without stint or shame. If He is a man, how is it that one man has proved stronger than all those whom they themselves regard as gods, and by His own power has shown them to be nothing? If they call Him a magician, how is it that by a magician all magic is destroyed, instead of being rendered strong? Had He conquered certain magicians or proved Himself superior to one of them only, they might reasonably think that He excelled the rest only by His greater skill. But the fact is that His cross has vanquished all magic entirely and has conquered the very name of it. Obviously, therefore, the Savior is no magician, for the very demons whom the magicians invoke flee from Him as from their Master. Who is He, then? Let the Greeks tell us, whose only serious pursuit is mockery! Perhaps they will say that He, too, is a demon, and that is why He prevailed. But even so the laugh is still on our side. for we can confute them by the same proofs as before. How could He be a demon, Who drives demons out? If it were only certain ones that He drove out, then they might reasonably think that He prevailed against them through the power of their Chief, as the Jews, wishing to insult Him, actually said. But since the fact is, here again, that at the mere naming of His Name all madness of the demons is rooted out and put to flight, obviously the Greeks are wrong here, too, and our Lord and Savior Christ is not, as they maintain, some demonic power.

If, then, the Savior is neither a mere man nor a magician, nor one of the demons, but has by His Godhead confounded and overshadowed the opinions of the poets and the delusion of the demons and the wisdom of the Greeks, it must be manifest and will be owned by all that He is in truth Son of God, Existent Word and Wisdom and Power of the Father. This is the reason why His works are no mere human works, but, both intrinsically and by comparison with those of men, are recognized as being superhuman and truly the works of God.

From Athanasius, On the Incarnation (ch 8/sect. 48).

Indicative Conditionals and Material Conditionals

A nice little argument worth thinking about. The following is a valid inference.

(p → q) & (r → s), therefore (p → s) v (r → q)

But given this we can easily show that at least some cases of English indicative conditionals do not fit this scheme. Since they would if they were material conditionals, they are not material conditionals. Here's an example, taken from Graham Priest, who takes it from W. S. Cooper:

If John is in Paris he is in France & if John is in London he is in England.

From this we obviously cannot conclude

If John is in Paris he is in England or if John is in London he is France.

Another one. This is valid:

~(p → q), therefore p

But this is not:

It is not the case that if there is a good God the prayers of evil people will be answered. Therefore there is a good God.

Because, of course, it does not follow that there is a good God merely from the assumption that "if there is a good God the prayers of evil people will be answered" is false.

Malebranche on Mathematics

In a recent discussion of the philosophy of mathematics at "n-Category Cafe", Malebranche shows up in the comments, in the form of the following quotation:

L’étude des mathématiques est la plus pure application de l’esprit à Dieu.

I don't presently have the whole Malebranchean corpus at my fingertips, so although I suspected this is an abbreviated rather than exact quotation (such as one might pull from memory rather than directly from the text), I couldn't rule out an exact reference. But it would be a very Malebranchean thing to say (in a slightly more qualified form), and I did find something very similar to it in The Search after Truth, Book V, Chapter IV:

But very few know with certainty that to know the truth is to be joined to God as far as nature allows, that to contemplate the true idea of things is in a way to possess God Himself, and that the abstract perceptino of certain universal and immutable truths, which determine all particular truths, is achieved by the mind that attaches itself to God and rejects the body. Metaphysics, pure mathematics, and all the universal sciences that determine and contain the particular sciences as the universal being contains all particular beings seem chimerical to almost everyone--to the pious as well as to those who have no love for God. Consequently, I hardly dare claim that in applying itself to these sciences the mind applies itself to God in the purest and most perfect way of which it is capable, and that it is in perceiving the intelligible worlds that these sciences have as their object that God God knows and produces the sensible world that bodies depend on for their life as as minds depend on the intelligible. (Lennon-Olscamp translation, p. 367, my emphasis).

Malebranche says other interesting things about mathematics in the Search. For instance:

One can hardly do without at least a crude smattering and a genral knowledge of mathematics and nature. Everyone should have learned these sciences in his youth; they detach the mind from sensible things, and they prevent it from becoming soft and effeminate. The are rather useful in life, and they even direct our attention toward God; the knowledge of nature causes this in and of itself, and that of mathematics through the distaste that it inspires in us for the false impressions of our senses. (LO 292)

And of geometry:

Geometry, then, should be regarded as a kind of universal science that opens the mind, makes it attentive, and gives it the skill to control the imagination and to draw from it all the help it can give; for with the help of geometry the mind controls the imagination, and a controlled imagination sustains the mind's perception and attention. (LO 429)

And similarly, of the ancient practice of teaching mathematics to the young:

Apparently they knew that arithmetic and algebra extend the scope of the mind and give it a certain acuteness we cannot acquire from other studies, and that geometry rules the imagination so well that it does not easily grow confused. For this faculty of the soul, so necessary for the sciences, acquires through the practice of geometry a certain scope of accuracy that impels and preserves the mind's clear perception even in the most perplexing difficulties. (LO 483)

He then goes on to recommmend a course of study that would cover all the major mathematics known in his day, up to "the new differential and integral calculi, and to the methods drawn from them for the understanding of curved lines."

Examples could be multiplied; mathematics plays a very important role in Malebranche's theological rationalism, both on the rationalist side (since he uses it to mount a powerful challenge against any empiricist approach) and on the theological side (since on his view mathematics studies purely intelligible extension, which is found in God, being God's divine idea of body).

Blackburn at the THE

At THE they are starting a series in which academics talk about things "beyond their area of expertise." This is a somewhat dubious experiment, it seems to me; the idea behind it is that academics don't talk beyond their area of expertise, an idea that will not, I think, withstand close scrutiny. But I suppose it is something different. Those of us in philosophy are represented right off by Simon Blackburn, the first in the series, who gives us an attempt that can only be regarded as a bit of a bad omen for the series in general. The basic idea is interesting enough: Blackburn identifies 10 things that he regards as major modern myths. Unfortunately, only one of the points (the fifth) is a serious candidate for a myth, and the reasoning presented on several points is muddled. I suspect there is a mix of factors responsible for this: the speculative character of the series, the need to be concise, the need to be clever and funny and interesting, etc. But it's not a great list. Some thoughts on each of Blackburn's "myths".

(1) The myth of meaning. This is Blackburn's best attempt: "People think words mean things and that they know what they mean. Both claims are often untrue." That seems somewhat plausible at first, if not examined too closely; but reading on, we realize that what Blackburn really means is that there can be words with no clear ideas attached, and clear ideas are not a plausible account of meaning. Indeed, a more careful reading of Berkeley, whom Blackburn quotes, might have led Blackburn to this reflection, because Berkeley's point is not that there are words that have passions substituted for meanings, but that words often inspire passions rather than ideas. This does not mean that the words are meaningless; on a Berkeleyan account of meaning, words would still have a meaning from their use in syntax. But Blackburn muddles things up even further when he goes on to say:

The test of whether someone is talking like this is whether you can imagine successful action based specifically on what they say. When we cannot, Berkeley's process is under way.

But this is extraordinarily implausible, as Berkeley again could have told him. Words, when they directly inspire passions rather than ideas (that in turn go on to inspire passions), can shape action more directly than words that don't, because they skip the middleman. This is why politics, rabble-rousing, advertising, exhortation, and the like is so rife with words calculated to bypass ideas. If I say, "The bourgeois statesman oppresses the proletariat and thus should be killed," if this leads people to reflect on the ideas raised by these words, this has put matters in the field of speculation, and I will have led people to reflect on the death-worthiness, if any, of people meeting a certain description. But if my words are well-calculated to raise passions rather than ideas, I will have motivated people to a state where they might well engage in successful action based specifically on what I say.

And this makes sense: meaning and idea are not the same, as Berkeley saw. A word can have meaning even if I do not put an idea to it that can be examined. If I exhort bereaved people to take comfort in the fact that so-and-so lives on in his children, I have said something to which most people will not, under the circumstances, put a an idea, because they are too distraught. But that doesn't mean that they couldn't fix ideas to it under any circumstances, nor, even if they didn't, that there isn't a meaning of some other sort that could be analyzed from the usage of the words or their associations in such usage. All it means is that ideas are not essential to the many of the functions of language, especially many of the practical ones.

(2) The myth of religious belief. I appreciate the quotation from Hume's Natural History of Religion, but the argument here is simply too absurd to take seriously. Hume himself was well aware that the simple equation between belief and behavior that Blackburn attempts to make is untenable; that custom can have "an effect on the imagination in opposition to the judgment" (Treatise 1.3.13.9). Thus when Blackburn says,

People say they believe in life after death but still grieve when people die. Christians try to get rich and Muslims gamble. The state of mind here is unaccountable in the same way as that of the child who pretends that the tree stump is a bear and then becomes genuinely frightened of it, while knowing all the time that it is a tree stump.

he is simply being silly; the state of mind is no more unaccountable than the fact that someone grieves when their friend moves despite knowing that it is a great move for them, or the fact that people can simultaneously affirm the importance of obeying the law and still speed or jaywalk when in a hurry, or the fact that an alcoholic can insist that alcohol is something he detests and nonetheless in a moment of weakness fall of the wagon.

(3) The myth of British values. Much the same problem here. That the British often don't engage in fair play doesn't tell us anything about whether they value it, or do more to try to encourage it, or have a better conception of it than others. This is practical inconsistency; and surely Blackburn is well aware that human beings are not flawlessly consistent. For instance, you can have respectable philosophers writing silly things for Times Higher Education.

(4) The myth of the scientist. "This claims that there is an expertise, science, and that people who are good at it deserve a lot of attention. This is almost wholly false." But, of course, there is an expertise, science, and people who are good at it do deserve a lot of attention. There is no such thing as a scientist, says Blackburn, with a silly snipe at Whewell, just "biologists, chemists, physicists, mathematicians and so on," and being an expert in one field doesn't make you an expert in another.

By the same reasoning I can prove that there is no such thing as philosophy, or philosophers. There are just ethicists, logicians, historians of philosophy, etc., etc., and when people step outside their field of expertise "they are no better than the rest of us".

It is unclear why Blackburn thinks breaking it down to the level of "biologists, chemists, physicists, mathematicians and so on" is adequate. For obviously one can be an expert in, say, the physiology of newts and not in, say, the ethology of hyenas, and someone who is an expert in the one might well be at a bit of a loss in the other. So it turns out that there is no scientific expertise at all, and no scientific experts. Of course, this is absurd. What Blackburn should have argued is that there are, in fact, overlapping fields of expertise and the access from one field to another is not always equally easy. A physicist may struggle in moving from physics to some forms of paleontology, but be able eventually to find an 'in' by looking at methods for dating. It's simply false to say that outside their field "they are no better than the rest of us"; but it is true that no field of expertise provides the royal road to every other field of expertise. There is no universal method. Yet there is a complex set of overlapping fields, and collective these can be treated as forms of scientific expertise.

Nonetheless, this is better than some of the others; if we were to set aside the specifics of Blackburn's reasoning, we could get something like what he seems to want to get at; we do often talk about 'science' as if it were univocal and monolithic. So perhaps we could treat this one a bit more favorably than I have.

(5) The myth of management. I think this is Blackburn's best point, since it is actually a reasonable candidate for a myth. Again, some of the reasoning is a bit shaky; but some of it is clearly at least half-joking.

(6) The myth of democracy. I'm not even quite clear what Blackburn thinks the myth here is supposed to be. It sounds very much like he is claiming that people can't at all be trusted to govern themselves because they are easily manipulated, which is, again, silly; first, because Blackburn just pointed out that people can't be managed, so the manipulation has limits, and second, because when people put forward democracy as a value, they aren't claiming that people are saints and geniuses, but that there are moral reasons to support a set of rights related to self-governance. Which there are.

(7) The myth of culture. "As it occurs in phrases such as multiculturalism, working-class culture and the like, this is the myth that there is a definite, admirable, rooted traditional way of being, and that it must be valued and cosseted and, above all, respected. All this is poppycock." If by 'poppycock' (one of those words that tend to be associated more with a passion or sentiment than with an idea) we are referring to the claim that when people talk about "multiculturalism, working-class culture and the like" they are committed to saying "that there is a definite, admirable rooted traditional way of being, and that it must be valued and cosseted and, above all, respected," then, no doubt, it is all poppycock, because that's not what people are saying. What they are actually doing is something much closer to the opposite: denying that there is a monolithic, definite culture, and affirming that there is a diversity that needs to be recognized. Blackburn seems to be conflating a great many different contexts in which one might use the word 'culture'; one could, of course, use it to refer to something supposed to be monolithic and definite. Most people use it just as a rough term for a stable set of practices. For instance, part of the culture of Quebec is the use of the French language. This is verifiable fact. Nor do people use the term 'culture', as Blackburn seems to suggest, to convey something that does not change; if they did, there would be no one going around arguing that this or that aspect of culture needs to be preserved.

8. The myth of equal respect. Chris Bertram has tackled this one at "Crooked Timber".

9. The myth of choice and competition. Need I say that his whole description here is tendentious? But perhaps this is one, too, where something can be found analogous to what he is suggesting.

10. The myth of the public service ethos. I take it here that Blackburn is primarily using hyperbole to make a point, which is not something I would criticize him for doing.

I do appreciate the difficulty of what Blackburn is trying to do here; there are several demands, not all easily reconciled, that pull a piece like this in several directions. He's trying to be light; several times his attempt to be light comes across as mere shock-jockery, or whatever is the British equivalent. He's trying to make serious, thought-provoking points; he doesn't manage to meld this with the light touch very well, since it means that some of his jokes are going to be read as serious and some of his serious points are going to be read as jokes. It's scarcely decipherable. He's trying to be concise; sometimes accuracy and clarity get sacrificed. He's trying to be clear; nuance has in several places been lost. As one of the commenters says, it's "juvenile stuff," and as another says, it's "half-baked nonsense". It needn't have been, and a few times you can see that there is probably some more serious thought behind the silliness, but I don't think Blackburn has succeeded very well in presenting his points in a way that lets you see such serious thought.

Adversarial and Other Methods

Kenny has an interesting post on the adversarial method in philosophy; the occasion is the discussion of philosophy as bloodsport at Feminist Philosophers, which I noted here. In the post, Kenny argues for two major points:

(1) 'Blood sport' approaches are degenerations of adversarial method.
(2) Adversarial method is one of the best methods of philosophy.

His argument is interesting on both accounts. I think (1) is fairly clearly right; and one can in part see it by the fact that criticisms of bloodsport are often rejected on the basis that adversarial method or debate plays a key role in philosophical discussion -- that is, bloodsport gets a pass because it can masquerade as debate and argument. I'm much less inclined to agree with (2), though; I think there is a genuine place and a genuine value for adversarial method as Kenny understands it, but it is a secondary place and a limited value.

Kenny gives an analogy with adversarial method as found in law:

The adversarial method is best known from its use in law. The theory (which is at least as degenerate in law as it is in philosophy) is that if equally matched opponents argue opposite sides of a matter, the side of the truth will be at an advantage. For this reason, no matter how obvious a person's guilt seems, her trial is not judged to be valid unless she has adequate representation. She must have an attorney who has done a competent job of defending her.

Obviously this can only be analogy. For one thing, in the case of law you are not really so much interested in truth -- well, at least not immediately and directly. Your primary concern is not discovery of truth but adjudication, i.e., reasonable and orderly resolution of the dispute; and adversarial systems come into play when the sort of adjudication you want is the sort in which both sides should be given full rein (or as close to it as is genuinely feasible and reasonable) to present their side in what they deem to be the best light. Truth acts as a constraint on what's reasonably allowed, but it is not the primary interest. In matters where it isn't in everyone's interest to be allowed to do whatever it takes to present their side well, another method of resolving the dispute would have to be used. For instance, the usual view is that in matters of family law adversarial method is often contrary to everyone's interest; and, in our system at least, family law tends to be handled by collaborative approach, in which everyone agrees to reach an agreement if there is any reasonable way to do so, the adversarial approach being a last resort if the collaborative approach breaks down. In many systems, you have a so-called inquisitorial approach, where the two parties are relatively constrained in what they are allowed to do, and many of the burdens and responsibilities we place on the adversaries are placed instead on the adjudicating party.

I dwell on this somewhat because third-party judgment is a key difference between adversarial method in law and the sort of adversarial method Kenny has in mind in philosophy. We get a lovely illustration of this in Plato's Gorgias. Socrates and Polus, a Sophist, are arguing in front of an audience, and Polus keeps trying to play to the crowd. Socrates points out, however, that in the sort of argument they are having the only jury or judge that matters is the person with whom you are arguing. Thus in philosophical matters, the adjudicating party is not a third-party; in most cases, each of the two parties to the discussion has that responsibility. (I say 'in most cases' because in certain types of pedagogical discussion, e.g., a medieval disputation, the responsibility will fall chiefly on the teacher. Even there, however, there is a sense in which it falls on the students as well.) I think Kenny would agree with this, at least more or less, because I think it is this that is responsible for a key feature of adversarial philosophy as he understands it:

How do we ensure that the two sides are equally matched? Well, when your "opponent" is struggling to find a good argument for his position (or against yours), you have to help him out. I think (or at least I hope) philosophy professors do this for their undergrads all the time. We have to get the strongest form of the position, and the strongest arguments for it, in order to be able to evaluate whether our attacks against it succeed; otherwise, we are in danger of the strawman fallacy.

In law the relatively equal matching of the two sides is established by neutral procedural rules; but this is not operative here. If one side is struggling, and the other side is merely taking advantage of this weakness rather than allowing the fair consideration of arguments, the opportunistic side is not violating any procedures of disclosure, or anything like that. Rather, it is contrary to the spirit in which the discussion is supposed to be held: as a philosophical discussion, it has certain ends -- understanding, truth, wisdom, etc. -- and such a means will tend to be poorly proportioned to that end.

But I think in most cases, in fact, there will be better means to those ends than adversarial method, as Kenny understands it, can provide. Not every philosophical discussion is a dispute between sides; most, arguably, are not. Nor, even in a dispute between two sides is it always necessary to take an adversarial approach; there are approaches that forego ordinary adversarial opposition in favor of collaboration or investigation. I'm inclined to think, in fact, that the best place for such methods -- the place in which it can genuinely be considered one of the best methods available to philosophy -- is in arguing with sophists who can be argued with. (Plato's Gorgias again. Of course, if you are faced with having to argue with sophists who can't be argued with, you may well have no good method available save, in Boethius's phrase, victorious death.) You'll still need to raise the strongest points; but this can be done in circumstances that involve no opposition or adversarial character. I think philosophical blogging is often a good example of this, since I think that, contrary to Kenny's suggestion, it is usually investigative, not adversarial. On this issue, for instance, Kenny and I are in no direct opposition; we are simply conducting contrasting investigations into the same topic. These can then be compared and contrasted and critically examined in future investigations; but there is nothing really adversarial about it, and it really doesn't matter whether either of us is giving the strongest argument available.