art by Morton Meskin

I believe that my first encounter with the works of Ayn Rand was in seeing as a child some of The Fountainhead (1949) on television. All that I really remember seeing of it then were the final two scenes, which may indeed be all that I saw. I would have been unable to tell anyone very much about the movie (I didn't even know its name), and unaware of there being a book whose ideas were behind it.

Later, I read some distinctive stories by Steve Ditko in Charlton Comics. I was not a fan of Ditko's graphic work (which combines spareness of detail with an a propensity to put figures in ape-like positions and to present an abundance of wildly exaggerated facial expression), but the stories were written from an unflinching, and seemingly grim yet ultimately optimistic belief in straight-forward good and beauty. I wouldn't have been able to tell anyone whose prior work had informed his.

My next encounter was as a teenager, in a Midwestern drug store. Some of Rand's books were in a rack there; on the backs of the volumes were remarkable claims about Rand's popularity and about her significance to many people. I was skeptical, as I'd not otherwise heard of her. In any event, I didn't buy any of the books, but a mental note was made.

When I became more politically active over the next few years, I began to encounter frequent reference to Rand from people with whom I had some ideological allegiance. So I decided to read one of her books.

I tend to read authors' works in the order in which they were written, and the earliest of Rand's works that I found when I looked at a book-store was The Fountainhead (1943); and I had begun to think that I'd seen part of a movie based upon it; so that was the book that I first read. It was rather a while before I read any more.

Reading The Fountainhead was not the transformative experience for me that it has been for some people. There weren't any notions in it that were new to me (albeït perhaps in part due to my prior exposure to Ditko), and Rand seemed to confuse egoism with egotism. In a preface, she blamed a use of egotism for egoism on a poor dictionary (English was not her first language), but it seemed and seems that the confusion at the time that she wrote that novel was not merely one of words but of ideas.

I think that Rand suffered from mind-blindness of a sort, such that she could not use ordinary intuïtions as most people do to understand other people. That is not to say that she could not use some other means; and being compelled to use other means sometimes even caused her to have insights that other people would miss. But it was a struggle, her understanding could be imperfect, and it left her treating empathy as if it were an unfair demand. (It surely didn't help that she'd been forced to live under a regime that willfully confused coërcive redistribution with brotherhood in order to license a considerable amount of repression and brutality.)

One sees this lack and rejection of empathy somewhat reflected through-out her writing. Its expression diminished over time, but at its worst it embraced sociopathy. In some of her journal notes of 1928, a young Ayn Rand seriously planned to have a hero modelled on William Edward Hickman, who in late 1927 had kidnapped a 12-year-old girl, and then delivered her grotesquely mutilated corpse when her father paid for her return. Hickman, as Rand saw him, had acted without concern for others, with the supposed motto What is good for me is right. In The Night of January 16th (1934), the protagonist is a woman whose heroic love is for a man whom she knows to be a conscienceless swindler (inspired by Ivar Kreuger). In We the Living (1936), the heroine at one point thrills in response to a depiction of a man whipping serfs, and her truest love, Leo, lives only for himself. In The Fountainhead, that has largely been left behind, but it has a very ugly echo.[1]

In The Fountainhead, the hero rapes the heroine. I put rapes in quotation marks because, even though it is called as much in the book, it (as Susan Brownmiller noted in an moment of lucidity) isn't a genuine rape; rather, it is a confrontation, pretty literally by engraved invitation, between two individuals over whether they will have sex on her terms or on his, which he wins largely by physical force. It was enough like a real rape that I was deeply appalled. Bearing in mind the historical context, that this was written in a time when rape was still widely romanticized, did not help much.

Thereäfter, the relationship between the two remains perverse, with the heroine marrying a couple of other men, whom she certainly does not love, simply to hurt the hero, whom she does love — in her own, Randian way.

Additionally, this was a book without much salvation. In particular, no one saves Catherine, a woman crushed by abandonment, who is then drawn into a life of soul-less self-lessness, and Gail Wynand's redemption is in suïcide. If anyone is actually saved in the book, it is Mallory, who fell so far as to have made a private attempt at popular sculpture, before Roark summons him to reälize his true vision. I would note that salvation was something that I had seen in at least one of Ditko's stories, in which the hero and heroine reach out to pull a fellow doing an imitation of Ellsworth Toohey (Rand's principal villain in The Fountainhead) back into a world-view of truly humanistic possibility.[2]

I finished reading The Fountainhead with little desire to read anything more by Rand.

But she continued to be referenced, positively and negatively, by friends and by allies, and I was ultimately moved to read her magnum opus, Atlas Shrugged (1957).

Atlas Shrugged was not so unpleasant as had been The Fountainhead. Rand again manages to toss her heroine into bed with two men other than the hero, the second much to the distress of the hero (and to that of some hapless other fellow), but this time she isn't out to cause anguish; she isn't even aware of him as a person. The descriptions of sex between the principal hero and heroine seem a little peculiar, but markèdly different from the confrontational initial sex of the previous book.

There's salvation of one sort in the book — the main hero is persuading the most genuinely productive members of society to withdraw, in order to bring an end to a social order of unreason that demands self-sacrifice and becomes ever-more totalitarian. But none of these people are in danger of being lost to the unreason itself. The two characters who are in such danger, Cherryl and Tony, are basically left by the heroes to sink or swim. Cherryl literally drowns, unable to cope (with no one helping her) when she begins to grasp the prevailing social order. Tony figures it out, with little help, and is shot dead for trying by himself to stop a group of thugs from the other side; by the time that a hero could be bothered to help him, Tony was really past help.

As well as the lack of empathy expressed in the treatment of such characters, there's something else that I take to be a manifestation of Rand's mind-blindness. Some of the villains demand to be understood; the heroes reject the idea that they must understand such people. And understand is the recurring word, without the heroes asserting that there is a difference between understanding and acceptance. Personally, I very much want to understand my opponents, without any expectation that this will cause me to think much better of them. In fact, having a working model of what makes them tick often intensifies my rejection, but it allows me to anticipate their behavior. However, Rand seems truly to object to a demand of understanding. I think that it was because understanding did not come intuïtively to her.

Atlas Shrugged is often criticized for the fact that its characters are archetypal, and apt to present long philosophical monologues in the context of extemporaneous discourse. I think that such criticism is actively ridiculous (especially when it comes from people who haven't directed the same criticism at the works of Shakespeare, or at various ostensibly classic works by Russian novelists,[3] whose characters are like-wise archetypal and like-wise given to unlikely speeches). Atlas Shrugged is a novel of archetypes and of monologues because it seeks to present a fairly comprehensive philosophical statement. Even with the device of archetypes and monologues, it is a very long book, and without those devices it would be less clear and probably much longer. It is also, somewhat more reasonably, criticized as belaboring ideas, but Rand was plainly concerned not to allow a point to be treated as obvious when presented and then repeatedly ignored in application; I think that such concern is quite well-founded.

As with The Fountainhead, reading Atlas Shrugged was not a transformative experience for me. There were only three philosophical novelties for me. The first was simply interesting; the second and third were not clear to me.

It used the word justice in reference to something inexorable. I'm not sure that I would use that term in that way, though it does seem useful to me to recognize that a natural law that says that one should or shouldn't do X is founded on one that says what obtains from doing X.

What I didn't understand, but wanted to pursue, were her claims about causality being necessitated by logic and that Logic is the art of non-contradictory identification.

I came away from Atlas Shrugged more willing to read other things by Rand, especially to understand what was meant by those last two assertions. The book in which the last was answered (she was cryptic on the other, and I had to figure that one out largely on my own) is also the book by Rand that most affected me philosophically, Introduction to Objectivist Epistemology (1979). I didn't agree with everything in it, and have since come to reject more in it than I did at first. I also came to recognize that a considerable amount of it is unacknowledgedly borrowed from Locke and from others. But I believe that there is a core to it that is an original synthesis and a genuine advancement in epistemology, more properly conceptualizing logic in terms of a Lockean notion of concepts.

As well as Introduction to Objectivist Epistemology, I got and read We the Living, Anthem (1938), various anthologies derived from The Objectivist Newsletter and from its successor, The Objectivist, and a few interviews. I also found and watched a movie whose screen-play she wrote, Love Letters (1945). (And, somewhere along the line, I watched the movie The Fountainhead from start to finish.)

In the fictional work, I perceived a recurring theme. As Rand herself essentially says in a later introduction, The Night of January 16th is about how Rand felt people ought to have reäcted to Ivar Kreuger's selfishness. Anthem is an unacknowledged re-write of We (1921), by Yevgeny Zamyatin; it is the novella that she thought that he ought to have written. I think that The Fountainhead is about the sort of man whom she felt Frank Lloyd Wright ought to have been. Love Letters is supposedly based on a book, Pity My Simplicity, by Christopher Massie, but when I skimmed through that I book, I found it hard to recognize the one in the other; meanwhile the screen-play bears a significant resemblance to Rostand's Cyrano De Bergerac, except that it ends with the true author of the love letters getting the girl; it is Rand again setting things as she feels that they ought to be. And Atlas Shrugged is, of course, about the strike that really ought to be held (and, on the side, with a pirate of the sort who ought to be out there plundering and sinking the ships that ought to be sunk). As to We the Living, well, I think that it's about the man whom Rand felt ought to have loved her.[4]

The non-fiction was often insightful or amusing; and, my objections to aspects of the sexuality in her novels not-withstanding, I also thought that some of the claims concerned love and sexuality were important insights. But, at some point, I just didn't think that I was likely to get much more value out of her work. Before Rand had died, I had stopped reading her work, except occasionally to read an excerpt here-or-there.

While she was alive, I didn't encounter many people who could admit both that Rand was right in some of her unpopular assertions and that she was wrong in others. Instead, the vast majority of people who recognized her name either denounced her as having had nothing to say that were both unusual and correct, or endorsed her every claim without exception, and each group was condescending and curtly dismissive of anyone who would say otherwise. (The preëmption, whatever its motive, insulated them from potential correction.) But, over time, I have increasingly noted people who self-identify with her philosophy, but not without their own criticism, and not without a willingness to entertain the thought that further criticism might be neither knavish nor foolish.

My own philosophical position is removed from Rand's in some very important ways, and I would simply not count myself as a subscriber.

For example, Rand treated existence as a property of things; I would join with various philosophers who would assert that existence is not a property of the thing considered, but of the consideration. When one says something such as that unicorns do not exist, one is really saying something about the idea of unicorns. (And to say that the idea of unicorns does exist is really to say something about the idea of the idea of unicorns, &c.) The reason that existence seems to be a property of things is that our natural discourse isn't clearly distinguishing between things and ideas of those things. If unicorns do not exist, then it is absurd to talk about the unicorn itself as having a property of non-existence, because there is nothing to have the property. Rand objected to Reification of the Zero, but if we treat existence as a property of elephants themselves, then its contradiction, non-existence, becomes a property, which can only be held by, um, nothing; the Zero would then be reïfied. Rand's formula existence exists isn't particularly helpful, and its invocation seems to be nothing more than an artefact of confusing a crudity of grammar with a metaphysical insight.

By the way, I want to mention a book by another author, The Watcher (1981) by Kay Nolte Smith. Smith was at one time amongst those personally associated with Rand, but (like many) eventually left. The Watcher is a novel that successfully fused much of what virtue is to be found in Randian fiction with a deep sense of empathy. And its heroes don't simply march relentlessly towards triumph, but reach back to save people who ought not to be lost.

[1] I wasn't at all positioned to write that paragraph until years after I read The Fountainhead.

[2] However, Ditko certainly does not present all of his characters as saveable; and, in particular, those characters of his who step across the line between Good and Evil with the thought that they will later redeem themselves are inevitably morally destroyed.

As to such crossings, Ditko's villains are more likely than those of Rand to be conscious of when they are crossing the line or that they have crossed the line. While both Rand and Ditko would declare wickedness to be founded in a choice not to think; Ditko's villains are more likely to be in fact thinking.

[3] It is certainly worth noting that Rand was a novelist from Russia.

[4] And thence I would explain much of the sexual dynamic across her fiction.

There is a passage[1] in Locke's Essay Concerning Humane Understanding of which I took special note from the first time that I read it:

5. That men should keep their compacts is certainly a great and undeniable rule in morality. But yet, if a Christian, who has the view of happiness and misery in another life, be asked why a man must keep his word, he will give this as a reason:—Because God, who has the power of eternal life and death, requires it of us. But if a Hobbist be asked why? he will answer:—Because the public requires it, and the Leviathan will punish you if you do not. And if one of the old philosophers had been asked, he would have answered:—Because it was dishonest, below the dignity of a man, and opposite to virtue, the highest perfection of human nature, to do otherwise.

The reason that this passage stood-out and stands-out for me is that it contains a fundamentally sympathetic statement of a godless morality, and indeed fairly clearly exhibits the parallel between the might of G_d making ostensible right for the Christian, and the might of the State making ostensible right for the Hobbsean.[2] Locke's philosophy, epistemological and ethical, is heavily informed by a belief in a loving G_d, yet here Locke seems to reveal sufficient subtlety to do rather well without that G_d.

There's another striking passage[3] in that same work:

50. If we look upon those superior beings above us, who enjoy perfect happiness, we shall have reason to judge that they are more steadily determined in their choice of good than we; and yet we have no reason to think they are less happy, or less free, than we are. And if it were fit for such poor finite creatures as we are to pronounce what infinite wisdom and goodness could do, I think we might say, that God himself cannot choose what is not good; the freedom of the Almighty hinders not his being determined by what is best.

51. A constant determination to a pursuit of happiness no abridgment of liberty. But to give a right view of this mistaken part of liberty let me ask,—Would any one be a changeling, because he is less determined by wise considerations than a wise man? Is it worth the name of freedom to be at liberty to play the fool, and draw shame and misery upon a man's self? If to break loose from the conduct of reason, and to want that restraint of examination and judgment which keeps us from choosing or doing the worse, be liberty, true liberty, madmen and fools are the only freemen: but yet, I think, nobody would choose to be mad for the sake of such liberty, but he that is mad already. The constant desire of happiness, and the constraint it puts upon us to act for it, nobody, I think, accounts an abridgment of liberty, or at least an abridgment of liberty to be complained of. God Almighty himself is under the necessity of being happy; and the more any intelligent being is so, the nearer is its approach to infinite perfection and happiness. That, in this state of ignorance, we short-sighted creatures might not mistake true felicity, we are endowed with a power to suspend any particular desire, and keep it from determining the will, and engaging us in action. This is standing still, where we are not sufficiently assured of the way: examination is consulting a guide. The determination of the will upon inquiry, is following the direction of that guide: and he that has a power to act or not to act, according as such determination directs, is a free agent: such determination abridges not that power wherein liberty consists. He that has his chains knocked off, and the prison doors set open to him, is perfectly at liberty, because he may either go or stay, as he best likes; though his preference be determined to stay, by the darkness of the night, or illness of the weather, or want of other lodging. He ceases not to be free; though the desire of some convenience to be had there absolutely determines his preference, and makes him stay in his prison.

Now, regardless of whether we agree that a being can be free and yet determined by something (not, as I believe, a contradiction if that something is internalized in the determined being), the fact remains that a G_d of this sort is more law-driven than many would conceive G_d to be.

Anyway, what brings all this to mind is that, lately, I have been reading (albeït in somewhat desultory manner) The Courtier and the Heretic: Leibniz, Spinoza, and the Fate of God in the Modern World by Matthew Stewart. Chapter 15 (The Haunting) contains a section entitled Stopping Locke, which ends thus

Locke's vague conjecture that matter might be able to think, of course, is Spinoza's avowed doctrine. […] Leibniz's magesterial refutation of the founder of British empiricism, in brief, is a covert assault [Spinoza]. Furthermore, [in Leibniz's mind] Locke — like Descartes before him — is really just a feeble imitation of Spinoza: he leaves in doubt that which his dark master pitilessly destroys.

[…]

Leibniz's unstated intuition that Locke was something of a Spinozist, incidentally, is probably more insightful than is generally allowed in modern interpretations of the great empiricist's work. Locke wrote much of his Essay while living in exile in Holland from 1683 to 1688, during which time he purchased all of Spinoza's works and mingled in circles that included some suspiciously freethinking characters. Furthermore, the parallels between his work and that of Spinoza extend well beyond those suggested by Leibniz. To be sure, as a conciliation-minded member of the Christian establishment, Locke toned down or obfuscated some of the more radical implications of his Spinozism — a task for which his inimitably wobbly prose was particularly well suited.

I would hardly agree that Locke's prose were wobbly, let alone that it were inimitably so; in fact, I don't think that a person given to wobbly writing would be capable of the sort of perspicacious thinking that got Locke as far along as his did. But the point remains that some of what I noted in Locke, such as in the two paragraphs of the Essay that I quoted, demonstrates that Locke represented some of the same tendencies as did Spinoza. Any notion that Locke borrowed heavily from Spinoza would have to confront what was already indicated by Locke's background and writings before he fled to Holland (and, earlier, before Spinoza had published anything); none-the-less, it would hardly be surprising if Leibniz indeed feared that Locke were in effect an agent of Spinoza's philosophy.

[1] Book I Chapter II ¶5, in the 1894 edition edited by Alexander Campbell Fraser (which is the edition that I read).

[2] The Hobbsean will assert that the State makes possible a manner of living whose goodness is not itself derived from the dictates of the State. Many Christians would want to make a similar claim for the goodness of the manner of living made possible by G_d. However, if pressed, most of them would not answer as did Ευθύφρων in the fable by the old philosopher Πλάτων; rather, they would feel compelled to hold that not simply instances of goodness but the distinction of goodness were creäted by the power of G_d. But Locke himself proves an apparent exception to my characterization. (See above.)

[3] Book II Chapter XXI ¶50-1.

As noted earlier, I've been reading Subjective Probability: The Real Thing by Richard C. Jeffrey. It's a short book, but I've been distracted by other things, and I've also been slowed by the condition of the book; it's full of errors. For example,

It seems evident that black ravens confirm (H) All ravens are black and that nonblack nonravens do not. Yet H is equivalent to All nonravens are nonblack.

Uhm, no: (X ⇒ Y) ≡ (¬X ∨ Y) = (Y ∨ ¬X) = (¬¬Y ∨ ¬X) = [¬(¬Y) ∨ ¬X] ≡ (¬Y ⇒ ¬X) In words, that all ravens are black is equivalent to that all non-black things are non-ravens.[1]

The bobbled expressions and at least one expositional omission sometimes had me wondering if he and his felllows were barking mad. Some of the notational errors have really thrown me, as my first reäction was to wonder if I'd missed something.

Authors make mistakes. That's principally why there are editors. But it appears that Cambridge University Press did little or no real editting of this book. (A link to a PDF file of the manuscript may be found at Jeffrey's website, and used for comparison.) Granted that the book is posthumous, and that Jeffrey was dead more than a year before publication, so they couldn't ask him about various things. But someone should have read this thing carefully enough to spot all these errors. In most of the cases that I've seen, I can identify the appropriate correction. Perhaps in some cases the best that could be done would be to alert the reader that there was a problem. In any case, it seems that Cambridge University Press wouldn't be bothered.

[1]The question, then, is of why, say, a red flower (a non-black non-raven) isn't taken as confirmation that all ravens are black. The answer, of course, lies principally in the difference between reasoning from plausibility versus reasoning from certainty.

The Classic Monty Hall Problem

Andy is a contestant in a game. In this game, each contestant makes a choice amongst three tags. Each tag is committed to an outcome, with the commitment concealed from each contestant. Two outcomes are undesirable; one is desirable. Nothing reveals a pattern to assignments.

After Andy makes his choice, it is revealed to him that a specific tag that he did not choose is committed to an undesirable outcome. Andy is offered a chance to change his selection. Should he change?

Three Contestants

Andy, Barb, and Pat are contestants in a game. In this game, each contestant makes an independent choice amongst three tags. Each tag is committed to an outcome, with the commitment concealed from each contestant. Two outcomes are undesirable; one is desirable. Nothing reveals a pattern to assignments. In the event that multiple players select the same tag, outcomes are duplicated.

After all contestants make their choices, it is revealed that Andy, Barb, and Pat have selected tags each different from those of the other two contestants. And it is revealed that Pat's tag is associated with an undesirable outcome. Andy and Barb are each offerd a chance to change their selections. What should each do?

3-Player Monty Hall

• Neither should change.
• Andy should stick, but Barb should change.
• Andy should change, but Barb should stick.
• Andy and Barb should exchange choices.

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I've been taking another run at Subjective Probability: The Real Thing (2004) by Richard C. Jeffrey. I'd started reading it a while back, but got distracted. Anyway, Jeffrey was an important subjectivist — someone who argued that probability is a measure of belief, and that any degree of belief that does not violate certain rationality constraints is permitted. (As I have noted earlier, the subjectivism here is in the assignment of quantities not specifically required by objective criteria. The subjectivists believe either that quantity by reason must be assigned, albeït often arbitrarily, or that Ockham's Razor is not a binding constraint.) And the posthumous Subjective Probability was his final statement.

At some point, I encountered the following entry in the index:

Nozick, Robert, 119, 123

which entry was almost immediately annoying. Page 119 is in the References section, and indeed has the references for Nozick, but that's a pretty punk thing to drop in an index. Even more punk would be an index entry that refers to itself; and, indeed, page 123 is in the index, and it is on that page that one finds Nozick, Robert, 119, 123.

Well, actually, I'd forgot something about this book, which is probably an artefact of its being posthumous: Most or all of the index entries are off by ten pages, such that one ought to translate Nozick, Robert, 119, 123 to Nozick, Robert, 109, 113. And, yes, there are references to Nozick on those pages (which are part of a discussion of Newcomb's Problem and of related puzzles). It was just chance-coïncidence that ten pages later one found the listings in the references and in the index.

In decision theory, there are propositions call independence axiomata. The first such proposition to be explicitly advanced for discussion (in an article by Paul Anthony Samuelson) is the Strong Independence Axiom, the gist of which is that the value of a reälized outcome is independent of the probability that it had before it was reälized. Say that we had a lottery of possible outcomes X₁, X₂,… X_n, each X_i having associated probability p_i. If we assert that the expected value of this lottery were

Σ[p_i · u(X_i)]

where u( ) is some utility function, then (amongst other things) we've accepted an independence proposition. Otherwise, we may have to assert something such as that the expect value were

Σ[p_i · u(X_i,p_i)]

to account for such things as people taking an unlikely million dollars to be somehow better than a likely million dollars.

Anyway, there's another proposition which to most of us doesn't look like the Strong Independence Axiom, and yet is pretty much the same thing, the Sure Thing Principle, which is associated with Leonard Jimmie Savage (an important subjectivist, whom I much admire, and with whom I markèdly disagree). Formally, it's thus:

{[(A ∧ B) pref C] ∧ [(A ∧ ¬B) pref C]} ⇒ (A pref C)

Less formally,

If the combination of A and B is preferred to C, and the combination of A without B is preferred to C, then A is just plain preferred to C, regardless of B.

Savage gives us the example of a businessman trying to decide whether to buy a piece of property with an election coming-up. He thinks-through whether he would be better off with the property if a Democrat is elected, and decides that he would prefer that he had bought the property in that case. He thinks-through whether he would be better off with the property if a Republican is elected, and decides that he would prefer that he had bought the property in that case. So he buys the property. This seems very reasonable.

But there is a famous class of counter-examples, presented by Jeffrey in the form of the case of the Marlboro Man. The hypothetical Marlboro Man is trying to decide whether to smoke. He considers that, if he should live a long life, he would wish at its end that he had enjoyed the pleasure of smoking. He considers that, if he should live a short life, he would wish at its end that he had enjoyed the pleasure of smoking. So he smokes. That doesn't seem nearly so reasonable.

There is an underlying difference between our two examples. The businessman would not normally expect his choice to affect the outcome of the election; the Marlboro Man ought to expect his choice to affect the length of his life. Jeffrey asserts that Savage only meant the Sure Thing Principle to hold in cases where the probability of B were independent of A.

But what makes the discussion poignant is this: Jeffrey, dying of surfeit of Pall Malls, wrote this book as his last, and passed-away from lung cancer on 9 November 2002.

While I was doing some research to-day, I ran across yet another article that classified John Maynard Keynes as a subjectivist when it came to probability theory. I feel moved to explain why this is incorrect.

First, let me explain something about the general issue. There is an outstanding question about just what a probability is. One could take many courses about probability without ever being alerted to the question. The textbook and lecturer might not ever touch on that basic question, or might present a definition of probability as if it is universally accepted by all Wise People. But Wise People are not in agreement. When it comes to answers to the basic question, the two dominant answers are very different one from another.

One answer is provided by the frequentists, who say that a probability is some sort of frequency of occurrence. They don't agree amongst themselves as to the precise answer, but the gist of their answers is that if a process is repeated m times, where m is satisfactorily large, and results in some particular outcome n of those times, then the probability of that outcome is n/m.

One problem with this notion of probability is that it is only useful in cases where we are concerned with a sufficiently large sample. If one is concerned only with a single instance, then there is actually no logic to get us from a mere probability to a course of action. A single patient won't have average mortality; she will either live or die.

Another answer is provided by the subjectivists, who assert that a probability is a degree of belief, formed subject to certain rationality constraints. These constraints can be largely motivated in terms of avoiding probability assignments under which believers would accept gambles that they are sure to lose. The rationality constraints themselves are ostensibly objective — rules that should hold for everyone; amongst other things, these rules are to constrain the evolution of one's degrees of belief, as new information is introduced. The subjectivism is present in that one supposedly gets to start with any degrees of belief that don't violate these rules.

One immediate consequence of this notion of probability is that probabilities become largely unarguable. There is no real contradiction in Tim claiming that there is an 80% chance of rain and Bob claiming that there is a 20% chance; each is describing his respective belief per se. (The rationality constraints force a convergence of belief at the limit, but that could take forever.)

The subjectivist notion is often defined in terms such as degree of rational belief or rational degree of belief; it's best to be wary of such terms. The rationality constraints themselves only preclude certain sorts of irrationality; aspects of the degrees of belief permitted are at best not irrational. And if we are not somehow required to assign some quantity to that belief, then the assignment violates Ockham's Razor.

Now, Keynes's position is that we can make meaningful statements about the plausibility of uncertain outcomes for which frequencies are unknown or otherwise inapplicable. And he certainly wants to impose rationality constraints much like those of the subjectivists. But he sees no requirement that one always assign a quantity to belief. Indeed, he sees no reason to treat the set of possible outcomes as even necessarily totally ordered; that is to say that he holds that, when asked to compare the likelihood of two events, sometimes one can only shrug, rather than making claims that one event is more likely or that the two are equally likely.

Under Keynes's theory, a rational person says no more about the probability of an event than the application of objective rules to the information set yields, and any other rational person with the same information set would reach exactly the same conclusions about probabilities (except, perhaps, where one person halted consideration where the other continued). Keynes rejects the very thing that is subjective in the subjectivist framework.