Ottoline sat there, closing her eyes. I feel so stupid, so miserably stupid.
Don't, he said, smoothing her arm. Consider it another way. You can say a man is part of the class of men. But the
class
of men is not itself a
man
.
She blinked. Rightâ¦
So: the class of men is not itself a man. Thus, it's a class that does not belong to itself, just as the Cretan is a liar telling the truth, or vice versa. It was this problem with classes that undermined Frege's mathematics. Well, I was reading Frege's
Foundations of Arithmetic
when I realized this. So I sent Frege a letter telling him how much I admired his work, and what a great influence it had had on me and so forth â
Here Ottoline made a sudden leap. And you told him his classes were all wrong?
Russell looked at her with surprise. Well, not so bluntly. But yes, I told him about the paradox, certainly.
But how vile of you! Ottoline jumped up and stared at him. First you praise the poor man, then you tell him his work is all wrong?
Not
all
wrong. But very much eroded by this paradox â at least with regard to this theory of classes.
Ottoline continued staring at him. But didn't you feel dreadful, ruining his work like that?
Russell was at something of a loss. Well, I wouldn't say
ruin
. But, yes, I suppose I felt sorry, somewhat. Not that Frege blamed me, you understand. Oh, he was most gracious about it â more than gracious. There was something very noble in his reaction. He sent me a letter that went on for several paragraphs with mundane business about offprints and such â and then, almost by the bye, he said my discovery left him beyond words â left him quite thunderstruck, in fact. Yes, said Russell, looking up musingly. Those were almost his exact words. He said he felt thunderstruck because my discovery had undermined the basis on which he had hoped to build his mathematics â especially as his next volume was just ready for publication.
Ottoline dropped her arms in stupefaction. And you
knew
that?
No! No, I didn't know that â But as I say, Frege was extraordinarily dignified about it. There was something superhuman about it, really. He reacted almost with pleasure, intellectual pleasure at my discovery.
Oh, please! Ottoline winced. It couldn't have been that pleasurable!
Nervously fingering his mustache, Russell asked, Well, what would you have had me do? Not to have told him would be unthinkable. Was Copernicus to hide his contention that the earth revolved around the sun out of respect for Ptolemy?
Well, he didn't write Ptolemy in the guise of a friendly letter and say, Oh, by the way, old boy, everything you think is wrong! And wait! Before you even say a word, I'm aware they weren't contemporaries.
Standing there with his hands hanging limp and a pleading look, Russell said, Please, understand this. If I overlooked something in my work, I certainly wouldn't wish to persist in my delusions. I would very much want to be told about it.
You would? she asked skeptically.
Oh, absolutely. Not that I'd enjoy it, of course.
Not enjoy it? But you just said Frege reacted with pleasure.
Frege, I said â not me.
But it must have given you great pleasure, didn't it? Getting the old general to surrender his sword to you like that?
Why, no! That wasn't the spirit at all. With a look of pain, he asked, Why are you suddenly attacking me like this â and here on my last day! I thought we were talking about logic.
We were â are. It's just that you say the most extraordinary things sometimes. I mean, for you to say that Frege would not have been devastated. Or that you, a young man hardly launched in his career, would not have been gratified to upset his applecart. Why can't you admit it?
Admit what? he asked, hedging. I've always thought I would want to behave as Frege did when it happens to me. And someday, no doubt, it will happen. I know that. It's the natural order of things. I owe a great debt to Frege.
So you do, said Ottoline with a faint edge of smile. But then Frege owes you a great debt, too.
They walked on after that, a little bruised and gloomy. Climbing the hill, they could see the sea rippling in the distance like a flying rug. The sea was only water, and the sky was less than the sea. Russell felt cut adrift. It was all he could do to believe in their love or compatibility, let alone be sanguine about the future. Ottoline didn't share his fears. If Ottoline was not worried about the future, that was because she wasn't thinking of it, or at least not with him.
I'm ready to eat, she said, and so, on a lofting hill above the sea, they spread their blanket, then opened their basket filled with cold poached chicken, wine and other good things. Uncorking the bottle, Russell told himself not to be so dour. He told himself that he and Ottoline were, in the main,
happy
, and that with time they would be even happier, rising higher and higher in their happiness, like a tire being pumped with air. Kissing him, Ottoline said they would quarrel no more, and they clinked their glasses. But then as they were eating, she said he must finish his story about the round square and the present king of France.
Do you really want to go into this? he asked, a little wearily.
Ummm, she said, wiping her lips. If it's not too terribly complicated.
No, it's not too complicated. Really, the problem with the round square and the present king of France is rather apparent. As I said, the problem here is of denoting statements that have a sense but no reference: you can't point to the present king of France in the way you can the king. The problem, then, is how a nonexistent thing or person can be the subject of a true or at least grammatically orthodox proposition. And you see, this curiosity can easily lead to metaphysical misadventures. Thus we had Meinong arguing that because we can say “the round square does not exist,” there must be such an object as the round square, but that it must be a nonexistent object, dwelling, one must suppose, in that Platonic realm where nonexistent kings confer with round squares.
Russell took a bite and finished chewing. But first let me complete my earlier discussion. For the paradox suggested by the Cretan, I developed my theory of types. What this did was to break such statements down into smaller classes that, in effect, avoided this paradox of a class that wasn't a member of itself. This way I was able to avoid the trap of having to pronounce a statement like the Cretan's to be either true or false. Instead, I could say that the statement was not true or false but
meaningless
. Ah, you smile! Well, this may sound arbitrary, just a logician's trick, but I think it is a truly great advance in sheer common sense. At least it doesn't leave logic at the same impasse.
Umm, minced Ottoline, as if to say that for her these weren't problems at all.
But Russell ignored this. Magisterially holding his half-eaten drumstick, he pushed on:
Now, as to the round square and the present king of France, these gave rise to my theory of descriptions. In a way, the theory of descriptions is analogous to the theory of types, in that it recasts a problem into terms in which it can more readily be understood. Essentially, the theory of descriptions is a method of descriptive translation: it casts the troublesome phrase into a form that doesn't contain the original confusions. Hence, I can translate “The present king of France is married” into “
Exactly one thing reigns over France and nothing that reigns over France is not married
.” This says what the first statement does. True, it requires more words, but it does so without the more or less direct suggestion of some entity presently sitting on a nonexistent throne. It also shows that we cannot assume that each separate word or phrase has significance on its own account.
But wait, said Ottoline, laying down her fork. I don't see what you changed with the second statement. You merely said only one person presently reigns over France. Isn't that tantamount to saying he's the present king?
It's a subtle distinction. But it's a distinction just the same. I'm not saying “the king” in the confident way I say “George the Fifth, by the grace of God!” It also helps me better see what I am saying. I can see the grammar of it while making these other confusions more or less disappear.
But here again, for some reason, he felt himself inwardly sag. Closing his eyes then, he asked, Might we continue this lesson some other time? We're both a bit tired now. At least I am.
Of course, darling, she said solicitously. Putting her hand on his, she said with a look of alarm, Was I horrid talking about Frege? I was horrid, wasn't I?
No. He put his hand on her knee. Really, you weren't. If we'd been alone these past two days, I'm sure it wouldn't have happened. I'm convinced of that, aren't you?
I don't know ⦠She canted her head from side to side, thinking. We might have quarreled a little. About sex, most likely.
Do you really think so? he asked, brightening a bit. About sex?
She saw he was looking at her strangely, and before he could even ask she said with mock vehemence, Don't you dare think of it! Twice is quite enough for one day.
He grinned. Did you like it back there, against the tree?
Ummm. Most novel â¦
He was still smiling at her funny.
And the answer is still no!
Why, my darling, he demurred, with a foolish grin. I wasn't even asking.
He was feeling so much better as they walked home. He didn't know why, in the midst of such good feelings, he should have thought of his wife.
But then Russell realized it was the present king of France that had reminded him of Alys. This was the problem he had been grappling with that day ten years before while out riding his bicycle.
The king of France is bald ⦠The king of France is married â¦
Riding along that afternoon, the young logician was fully as unreal and abstract an entity as the nonexistent monarch. But then in the midst of this otherwise logical process, his mind substituted for the king the equally troublesome phrase:
The husband who loves his wife pedals up Chertnam Road
.
And then as he puffed along under the greening trees, he heard, like an echo, his voice call back in translation:
Exactly one thing is on that bicycle on Chertnam Road, and on that bicycle there is
no one
and
no thing
that loves his wife
.
Grasping the handlebars, with his pipe clenched in his teeth and legs revolving so uselessly, the logician felt upside-down. He was fairly suspended in air as he sailed over the rise, then dipped down that ditchy lane into the coming kingdom. Indeed, the Cycling Husband then saw that he was not one man but two: the one who had loved, and the one for whom the word “love” now had a sense but no apparent reference â a fraud and a fiction like the hollow king.
Walking along with Ottoline now, Russell was thinking hard about that earlier, humbug self who had fallen from grace that day in 1902. Like cows returning from pasture, he and Ottoline were being driven home from that Eden of their one day together. They were holding hands, yet they were somehow separate, just as he himself was cut in two, one foot in this new land, the other in that place where Alienated Affections consort with Nonexistent Kings. These two Russells, then, were walking abreast of their mistress, who was herself a being of opposite minds, like a child with an ice cream in each hand. And so, all of them were walking home that summer day, not long before the Messrs. Russell were to meet that other illogical assemblage, the Messrs. Ludwig Wittgenstein.
L
IKE A GUILTY CONSCIENCE
, Karl Wittgenstein's letter was waiting in Cambridge when Wittgenstein arrived there in late September for the start of Michaelmas term. His work had not even begun, thought Wittgenstein, yet here it was â the next shot and probably the deadliest now that his father was taking deliberate aim.
23. September 1912
My son,
Your last letter offers little but artful evasions. Let me offer you, if I may, something more in the way of
provender
.
Families are not static things, and when you have lived as long as I have, you will note in them a certain progression, especially in those of Hebrew lineage. In the latter case, they begin, as we ourselves did, as peddlers and artisans; they accumulate money, which is like a stream of water that eventually grooves its own bed to the noble sea, wherein power resides; and there, in that sea, they acquire influence and visibility until, at length, the children do not have to work and indeed have to do precious little of anything. Freed of the burden of securing the requisite material comforts, the spoiled heirs feel the mercantile is no longer good enough; they think it grubby and pedestrian, and they crave the life of art (or philosophy, which amounts to the same thing). Again, I say, in the Jew, there is the dual tendency to understand and even crave art
in more or less direct proportion to his own inability to express himself as an artist
. Mahler is a good practitioner, with sometimes wonderful effects, but he has not, it seems to me, the depths of Christian artists. I would not presume to tell you why this is, but all the same â
it is
. It is quite empirically true, as you will readily see by simply asking yourself how many of our greatest artists have been Jews. Few. Precious few. And fewer still philosophers.
But I have veered off the track. As I say, for these heirs, they suffer from a kind of spiritual hemophilia, increasingly seduced by art and other fancies, which, I again emphasize,
did not bring their people to that succès d'estime.
And then begins the downward motion, just as one sees in certain degraded countries, such as France and Italy. The farmer divides his fields among his sons, whilst the merchant or industrialist divides his holdings, until the family's power declines and comes to nothing, whereupon the cycle begins again, as do those other cycles of weal, woe and war that the stockbroker senses in the way a farmer does fluctuations in the weather. Evolution thus begets dilettantes â cows who give no milk, beget neither true art nor commerce but only vanity books, vain thrashings, debauchings and worse.
Now, it is quite true that we Wittgensteins are not what we once were, nor will we be, in fifty years' time, what we are now. My enemies have accused me of trying to found a house of Rothschild â apparently in reaction to certain admittedly shrewd speculations I have made. This, as surely you know, is absurd. What concerns me is OBLIGATION. No doubt you think your work is an obligation, if one patently self-proclaimed. But if you truly had such a vocation, I am convinced,
the world already would have found you.
This has not been the case, as is evinced by your own telling lack of conviction; or perhaps by a fear that, beneath it all, you may only be
ordinary
. (You are not, and will never be,
ordinary.)
Please understand that I am trying not to be harsh. But, I beg you, please ask yourself what you will do to advance the dreadnought of culture? She needs steam, not pretty streamers and whirligigs. For all its manifold guises and disguises, progress is quite fearfully simple: it goes FORWARD, just as I ask you, as my son, to go FORWARD.
Let me leave you with a little story of my own patrimony that I do not believe I have ever shared with you. My father once asked, “Do you like me? I mean, on a purely human basis, as one man to another?” This was a difficult pass. Certainly, I did not want to hurt my poor father; yet I saw I must be truthful. A minute passed before I offered tentatively, “I respect you.” Father drew up his lips and said, “I thought you would say that. But that is quite all right. As a man, I don't like you, either.”
Please don't suppose I am “fishing” if I mention this trifle. I would not presume to put to you this hard question, because I know, and have always known, the answer. Moreover, I am convinced that it is like this with all sons and fathers. All the same, you ought to listen to me. I was once a latecomer like you, but I now know more of the story.
Father