The Sleep of Reason Produces Monsters: A review of a review by Tim Maudlin of two books in the philosophy of science

Can one review a review? Well, perhaps one can if  the review is over 7,000 words long and has a wide focus. Tim Maudlin’s review of two books, Adam Becker’s What is Real?: the Unfinished Quest for the Meaning of Quantum Physics, and Errol Morris’ The Ashtray: (or the Man who Denied Reality) is the basis for an extended look at two, alleged, sources of modern irrationalism — one says ‘alleged’ because there is no attempt to make a causal connection from the figures under discussion, Neils Bohr and Thomas S. Kuhn, to the modern “post-Truth” world, and even a cursory look at discussions on social media would suggest that the sources are quite distant from quantum mechanics and Bohr’s idea of complementarity. (Kuhn, however, is another story, as I will argue.) Still, as one who is as worried at the furious irrationalisms of the modern world as I think Maudlin is, this is a discussion worth having.

I must begin by saying that Maudlin writes so well and so persuasively and the areas of agreement are so large that any small matter of disagreement or addition is likely to mislead.  Nevertheless, some disagreements are worth recording — because I want to indicate that there are interconnections that have been overlooked.

With respect to Bohr there is no doubt of his Kantian education, nor of his creating an almost religious sense of mystification about Quantum Mechanics. His response to the Einstein, Podolsky, Rosen paper of 1935 is a staggering example of throwing up meaningless Kantian phrases to hide the vacuity of his response. He seems not even to grasp the significance of non-locality, nor of its potential for being in conflict with Special Relativity. And yet, as Maudlin notes, physicists bought it, hook, line and sinker; the Kantian phraseology was sufficient to allow them to resume their dogmatic slumbers. The EPR argument was ignored, as was Schrödinger’s contemporaneous paper that introduced entanglement. Here was a tremendous opportunity that went begging — for decades. And all because physicists were lulled by a philosophical gibberish by which philosophers would not have been fooled. 

Modern physicists today like to disparage their philosophical colleagues — they appear to think that philosophy is an easy subject and something they can turn their hands to with no training whatsoever. Yet most of their forays into philosophy are staggeringly naive, embarrassing even. And this naivety was fully in evidence in the disputes with Einstein and Schrödinger in the 1930’s and 40’s, and the consequent attempts, in the 1950’s, to undermine their reputations. But it was not Bohr who was most to blame for this outrage — Bohr managed to maintain cordial relations with Einstein throughout his life. The real culprits in this were Heisenberg and Robert Oppenheimer — and despite being German, Heisenberg showed less allegiance to Kant than did Bohr. Oppenheimer was another story.

By the late 1950’s Oppenheimer was, in the minds of many, the epitome of the distinguished scientist. Yet he had harassed Einstein while the head of the Institute of Advanced Study, and he was, as Maudlin notes, the person responsible for setting the FBI on David Bohm — to cover up, it has been said, the fact that he himself was, all along, a secret member of the Communist Party. Then, during the war, Oppenheimer’s secret lover, the ardent Communist Jean Tatlock, died under suspicious circumstances — some months after he visited her, without security clearance, while leading the Manhattan Project. She was found drugged and drowned in her bath. Coincidentally, earlier, in the 1930’s, Oppenheimer had attempted to murder his PhD supervisor at Cambridge, by poisoned apple — an event that was hushed up only with the intervention of his parents. Then he attempted to strangle his best friend when the latter announced his engagement.

And yet he became — was allowed to become — the representative for many of the distinguished intellectual-scientist. It was under his stewardship that the negative picture of Einstein hardened: he was a dinosaur, out of touch with modern physics, had done nothing for the last 20 years of his life. When the idea was mooted that there should be a publication of Einstein’s collected works, it was Oppenheimer who personally intervened to stop it. Bohr and Heisenberg may have crafted and weaponised the Copenhagen Interpretation but it was Oppenheimer who used it to the lethal administrative effect.

Kuhn enters the story at this point. What is omitted from Maudlin’s review is that Kuhn was very influenced by the Copenhagen Interpretation and by Bohr’s philosophy in particular. Kuhn’s denial of truth and his denial of the idea that science progresses toward the truth, are really his application of Bohr’s philosophy to science as a whole. One can tell this only by the fact that to a large extent Kuhn leaves Bohr out of his exposition and instead uses as his example that of Einstein’s theory of gravitation replacing Newton’s. This is baffling until one realises that this is yet another hit at Einstein. When Einstein’s theory replaced the Newtonian theory of gravitation this was not progress, this was one paradigm replacing another, but the paradigms were just different ways of seeing the same facts. It was as though one fashion had been replaced by another fashion: flares are no more a progress to the truth than is a straight leg. 

So why was Quantum Mechanics not his prime example, why was that also not one fashion replacing another? The reason is that the Copenhagenists had enshrined the One True Philosophy into their account of physics — in fact this is where Kuhn probably had learned the philosophy in the first place — and the One True Philosophy was that there was no truth, there was only ‘perspective’, of complementary (i.e mutually incompatible) kinds: complementary, that is, in just the way Kuhn’s paradigms were.

The one who was supposed not to have understood all of this, who was too much of a dinosaur to get it, was Einstein. So Einstein’s pretensions of saying something about the real world, of there being an objective world of which something could be said, had to be punctured. If he couldn’t be refuted then he had to be ridiculed. Einstein was wrong that Quantum Mechanics wasn’t perfected by Bohr and Heisenberg because he didn’t understand the truth about truth that Bohr preached; he was wrong even where he might most have seemed to be right, in his theory of General Relativity. But it was just a fashion choice.

This “no progress” picture of scientific progress needed one element to be complete: it needed to be married to an inductive scepticism. Fortunately for Kuhn this had already been made popular by Karl Popper, who endlessly repeated the falsehood that David Hume had proven inductive scepticism in the 18th Century — endlessly repeated and endlessly refuted, this canard lives on to this day. 

But whereas America — at least in its philosophy of science departments — had a strong probabilistic tradition and could therefore resist these arguments of Popper and Kuhn, other places with a weak background in mathematical probability crumbled. Thus it was that there were “philosophy of science” departments that grew up in Britain and Australia, in the latter case without exception, that taught this anti-truth, anti-science credo, with a dogmatic fervour. And once it is in place it takes no leap to join it with “social theory” and SJW rhetoric to condemn science as imperialistic, patriarchal — or any of the other ready-made jibes that fit comfortably on a placard or in a twitter post. 

The modern world was baked in the oven provided by Kuhn, and ultimately Kant — or perhaps one could say “half-baked”.

Kant’s role in all this was far more than providing a framework for Bohr’s or Kuhn’s self-contradictions. He created an environment in which to speak an unintelligible nonsense could — like the Emperor’s New Clothes — be made to pass for the profoundest speech: Kant as Cant. Whereas philosophers before this had striven to be clear and where to write unclearly was a sign of failure, Kant reversed it. Kant wrote as though he could only be understood by the initiate, the one who had earned the right to kneel in the presence of his Mysteries. Kant replaced the task of making sense of the world with that of making sense of him. Good anglophone philosophers like Bertrand Russell were able to see though the pretensions, but only one who knew German culture intimately was able to properly skewer Kant. That was Nietzsche. Here is part of his denunciation, in The Antichrist, section 10.

Among Germans I am immediately understand when I say that philosophy has been corrupted by theologian blood. The protestant pastor is the grandfather of German philosophy. Protestantism itself is its peccatum originale. Definition of philosophy: the half-sided paralysis of Christianity — and of reason. . . One has only to say the words ‘College of Tubingen’ to grasp what German philosophy is at bottom — a cunning theology. . . The Swabians are the best liars in Germany, they lie innocently. . . .  Why the rejoicing heard throughout the German academic world — three-quarters composed of the sons of pastors and school-masters — at the appearance of Kant? Why the German’s conviction, which still finds an echo even today, that with Kant things were taking a turn for the better? The theologian instinct in the German scholar divined what was henceforth possible once again. . . . A back staircase to the old ideal stood revealed, the concept “true world”, the concept of morality as the essence of the world (— these two most vicious errors in existence!) were once more, thanks to a crafty-sly scepticism, if not demonstrable, yet no longer refutable. . . . Reason, the prerogative of reason, does not extend so far. . . . One had made of reality an ‘appearance’; one had made a completely unintelligible world of beings into a reality. . . . Kant’s success was merely a theologian’s success: German integrity was far from firm, and Kant, like Luther, like Leibniz, was one more load upon it. — — 

This idea, that Kant’s obscurantism was theology for people who felt that they’d gotten beyond religion explains so much of the worst parts of what is called “Continental Philosophy”, where practitioners act like members of a Pentecostal church speaking and writing in tongues. The effort is entirely to write so that one may not be understood, but to use select phrases so there is a something that teases the listener’s understanding, to make them think that something important is being said.  It’s a sham performance. University lecturers get away with this only by first making sure that their students are so browbeaten and intimidated that they won’t — and by the end of it can’t — speak up against it. (And it only adds to the shamefulness of this situation that the students are actually paying to be bullied thus into a cognitive paralysis, paying to the point of long term bankruptcy — even in the Soviet Union students were not required to pay for their own mental hobbling.)

Kantian philosophy is called “critical” and the word itself has spread like a virus. It is a word that presents a deceptively positive image: it suggests that here is a philosophy that is open to logical argument, reason, and criticism, that it will consider all positions fairly. But that is the opposite of the truth. In fact “critical philosophers” write and act as though they are contemptuous of logic and reason — in fact of all that “analytical philosophers” do. “Critical” in fact means to be closed to logical persuasion — just as Bohr’s notion of complementary meant exactly the opposite of what it seems to mean. Instead the critical philosopher is one who sees through things like logic, to its “presuppositions” — a very Kantian term — and who, having seen through them is instantly beyond them. This works with any and all social institutions: to apply a “critique”, and to question presuppositions is all that is required for the institution to be instantly up for replacement. The game of issuing social critiques is easy because it brooks no back-and-forth questioning of the value of what is being questioned. One repeats the magic incantation, rolls one’s eyes back in one’s head, and the job is done. Nor can it be undone with the same method of critique — one could not, for example, question Feminism with the same naively simplistic trick. The method is inherently asymmetric — a door that you can go through but cannot return through.

However it would be quite wrong to lay all of the blame for the modern world’s irrationalism at Kant’s door; this would be to overlook a far more insidious culprit much closer to home. As Nietzsche said: opening up a back staircase for religion may have been Kant’s underlying purpose, but he was not alone in having that purpose. William James, with his Pragmatism — as expressed in his essay ‘The Will to Believe’ — was attempting to make it reasonable to believe in a God under the very loose conditions of there being no definitive proof against the existence of God, and of that belief “working” for the believer. (This was much to the horror of his friend, the philosopher C. S. Peirce, who could see the disaster looming in such a permissive criteria, and it caused Peirce to dissociate himself from James’ Pragmatism and to call his own view Pragmaticism.)

Nothing placed lying so at the heart of American Letters as effectively as James’s Pragmatism. Eventually, once it had sunk in,  the criterion of believability would become the simple does it work for you? Of course it would have been naive to think otherwise: of course lies work for liars, that is why they tell them. But to have James’s personal blessing — that was more than could have been wished for! Of course this was not James’s intention, and no one could have suggested that it was — but philosophical ideas can have unintended consequences just as much as actions do. 

William James was a distinguished psychologist, a man who had the ear of presidents, but he could not have created this disaster alone. Help came to him from John Dewey, who had done his PhD on Kant, considered himself a follower of Hegel — he wrote like Kant-from-Vermont — and who was an indefatigable promulgator of Pragmatist-like ideas. (One has to say “Pragmatist-like” because Pragmatists were very unclear what this idea of ‘beliefs working’ actually amounted to — but one can say that it was Dewey who emphasised that this “working” meant in a social context, in the furtherance of liberal democracy.)

Dewey had very little effect outside America but within America his influence was profound — in part simply from his having lived so long a life and written such an extraordinary number of books.  He became America’s leading public intellectual. Yet it was through his disciples that he exerted his greatest influence very near the time of his death in the 1950s. The idea that beliefs can be maintained come what may — that is, despite the fact that they are manifestly false — was held by W.V.O Quine (in his essay ‘Two Dogmas of Empiricism’) in one of the most notorious passages of contemporary philosophy: ‘Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system. Even a statement very close to the [sensory] periphery can be held true in the face of recalcitrant experience by pleading hallucination or by amending certain statements of the kind called logical laws.’  And also later in the same essay:

But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conception only as cultural posits. 

The phrase can be held true is a devious alternative to speaking of what is true — but it really just means believed to be true. However the point is clear: beliefs about the gods can be held true if one is prepared to be pig-headed in the assessment of evidence. The delusional, the liars, the conspiracy-theorists, can take great comfort in all of this. Pragmatism is a gift of irresponsibility that was set as a curse upon an entire nation.

One may object that these words are too severe, too unkind to American philosophers, who for the most part have used their irresponsibility fairly responsibly. (It has to be stressed that there are many, many analytic philosophers who have not succumbed to this view and who work to maintain high standards.) But the Pragmatists were themselves very adept at mud-slinging with a distinctly militaristic tenor. William James likened those who didn’t believe in his religious beliefs to cowards — according to him it was cowardice in the face of the enemy not to risk your cognitive life by refusing to believe ridiculous things. (Yet who on earth was the enemy in this case?) F. C. S. Schiller, the Columbia and Oxford-based Pragmatist, likened his opponents to defenders of the city of Jericho, for whom it self-crumbled without even the need of a trumpet.  Having described his own view in glowing terms we have, on the other hand

… opposed to it on every point, an old metaphysic of tried and tested sterility, which is condemned to eternal failure by the fundamental perversity of its logical method.  

And this was Naturalism!

Pragmatism won whatever following it had by insult and denigration — and that is how it has continued to the present day. It declared the correspondence theory of truth refuted with not a single non-question begging argument anywhere in sight. And that lie also has continued to be told — repeated in one classroom after another across America.

But it was this philosophy that, in a sense, became the Copenhagen interpretation in physics. When Feynman issued his declaration: just shut up and calculate! it was because all that mattered were the empirical predictions that could be wrung out of quantum theory. Who cared whether the theory had two dynamical processes and no clear rule as to when one takes over from the other? American physicists did not repeat Bohr’s Kantian obfuscations, they ignored them — they repeated Pragmatism’s injunctions to just look at whether the theory worked — and they are still doing that to this day. 

But because they were in this Pragmatist coma, physicists missed what may be the greatest discovery of the last two thousand years: entanglement. And they only began to take notice of this when money began to be thrown at anything that could be called quantum computing. In effect, yet more Pragmatism — more of that same dull mixing of the businessman’s idea of things working — of a theory paying off — and a more commonplace empiricism.

In doing all of this the Pragmatist may well have come close to enshrining a logical fallacy as a central tenet of American intellectual life: from, if p then q, and q, infer p. Dewey and F. C. S. Schiller often seemed to be committed to something even more dangerous: from if p then q, and q is unknown, infer p is unknown and in fact meaningless. (What is often taken to be Wittgenstein’s signature doctrine that meaning is use is in fact a commonplace Pragmatist idea, attributable originally to Sidgwick.) The corollary of Pragmatism’s emphasis on the importance of things working — for someone, somewhere, in whatever dubious way — is that if they don’t work they are meaningless. 

The wreckage that is America’s current political and social discourse — on both the left and the right — possesses a toxicity that has spread itself around the world, due in no small part to the philosophical doctrines that are so peculiarly American: Protagorean relativism, Pragmatism, and the concept of a uni-directional, unanswerable, social “critique”: all a kind of political midden that has replaced rational discussion and an openness of debate with a rancorous hatred at even the smallest trace of disagreement. In this one can see the signs of a timidity that is afraid that its convictions will not stand up under scrutiny — that the lie that keeps one drugged and unable to see things as they are will wear off, that it will no longer work. 

What will happen to America, and the Western world in general, if these trends continue unabated? Chaos of belief is the precondition for, and the first step towards, a true chaos. One cannot have a country where the people cannot think, cannot discuss, and cannot disagree without violence and mutual hatred, and it is a disgrace — and that word cannot encompass the true magnitude of the offence — that this situation should have been abetted and the groundwork laid by philosophers.

Pragmatism in the development of America’s intellectual life — if such a life deserves that adjective — shows the truth of the old proverb: Crooked logs make straight fires. And large fires at that.

Russell and the Stopped Clock

Many philosophers today appear to regard Russell’s example of the stopped clock as the really hard Gettier counterexample, the one to beat — or believe that it can be tweaked slightly to defeat most current solutions. In the last post I sought to counter this view by describing my own truthmaker solution and showing that it defuses this example in the same way as the others. Here I want to say a little bit more about this example in the context of Russell’s writing on epistemology.

The first thing that needs repeating is that Russell himself did not put up the stopped clock example as a Gettier counterexample — i.e. he did not see it as an example of a justified true belief that yet wasn’t knowledge. Rather he saw it as an example of a true belief that yet wasn’t knowledge because the proper justification was here lacking. Here is the full quote from Human Knowledge: Its Scope and Limits, pp. 170—1.

It is clear that knowledge is a sub-class of true beliefs: every case of knowledge is a case of true belief, but not vice versa. It is very easy to give examples of true beliefs that are not knowledge. There is the man who looks at a clock which is not going, though he thinks it is, and who happens to look at it at the moment when it is right; this man acquires a true belief as to the time of day, but cannot be said to have knowledge. There is the man who believes, truly, that the last name of the Prime Minister in 1906 began with a B, but who believes this because he thinks that Balfour was Prime Minister then, whereas in fact it was Campbell-Bannerman. There is the lucky optimist who, having bought a ticket for a lottery, has an unshakeable conviction that he will win, and, being lucky, does win. Such instances can be multiplied indefinitely, and show that you cannot claim to have known merely because you turned out to be right.

If you have a true belief just from dumb luck you do not have knowledge: knowledge requires that you have come by your belief legitimately, as the result of honest toil. That was Russell’s point. But Gettier went further: his idea was that you could have acquired the belief as the result of toil and yet still have been merely lucky that it was true, because its truth wasn’t guaranteed by the evidence that you obtained and that provided you your justification. But would Russell have agreed with this? Or would he have thought that this was a pseudo-problem, generated by a false view of how beliefs are justified? I think, the latter.

First let us note that, for Russell, it is, in the first instance, beliefs that are true or false, and that sentences only become true or false derivatively in expressing beliefs. Also — and most importantly — beliefs are far richer for Russell than simple sentential reports. One can have beliefs without language; Russell notes that many animals have beliefs, but no language. But even for us: beliefs may go far beyond what we are able to express, or ever actually express. As he says: ‘the belief is richer in detail and context than the sentence, which picks out only certain salient features’.

You say “I shall see him soon”, but you think “I shall see him smiling, but looking older, friendly, but shy, with his hair untidy and his shoes muddy” — and so on, through the endless variety of details of which you may be only half aware.

Given this, I think we can see that Russell would have had very little patience with Gettier’s first counterexample, about Smith and his belief that the man who will get the job has six coins in his pocket. For Russell, the content of this belief fixes the referent as Jones, because it is Jones who Smith believes will get the job. Thus, since it is Smith who ends up getting the job, Smith’s belief is simply false. It is irrelevant that Smith happens to have six coins in his own pocket — that is just dumb luck — what matters is that Smith’s belief was a belief about Jones. Thus, for Russell, this would be merely a case of a false belief — and not knowledge simply because it is false.

What Gettier did — his trick, as it were — was to make beliefs thin: delimited by the content of a proposition. But then there was a second trick: the believed proposition was expressed in words (as though the belief was merely a string of words in Smith’s head) and thus was capable of implying other sentences and of being treated as separate from Smith’s intentions — in fact capable of being ambiguous as to its referent. Thus, in the proposition the man who will get the job has six coins in his pocket, Gettier can construe the referent of the descriptive term the man who will the job as whomever is picked out by that description, as a matter of objective fact. And that man is Smith himself, since, unbeknownst to himself, he will get the job.

But the two steps that Gettier takes are steps that Russell explicitly warned against. Beliefs are thick, for Russell, and it is they that are true or false. And it is also they that have evidential support. There is no reason to believe that the evidential support for a thick belief will descend to a proposition believed in Gettier’s thin sense — because so much content is removed. Thus, for Russell, Gettier’s target proposition the man who will get the job has six coins in his pocket has no evidential support if the descriptive phrase the man who will get the job does not specifically refer to Jones. It is void.
For Russell, Gettier’s first counterexample would simply be a mistake in analysis.

But in fact the second counterexample would fail for similar, though not exactly the same, reasons.

By treating Jones’s belief (remember that was Brown owns a Ford) as a proposition in a thin sense — one that has the structure of a sentence — Gettier is able to use the elementary Propositional Calculus to form another proposition that will be true if that original proposition is true (remember: that new proposition is Either Brown owns a Ford or he is in Brest-Litovsk). If Jones is going to believe this disjunctive proposition it would be because he has additional beliefs about the truth functional character of the inclusive disjunction and the validity of the rule of Addition (Or-Introduction). His evidence that Brown owns a Ford would not be enough, alone, for him to believe the disjunction. But the situation is even worse than this.

Truth functional implications apply to propositions in logical derivations — not to beliefs. It isn’t the Belief-Functional Calculus. From the belief Brown owns a Ford Jones could not move to the disjunctive proposition but only to the more complex conditional proposition

If Brown owns a Ford then either Brown owns a Ford or he is in Brest-Litovsk.

With his beliefs about truth-functionality, Jones could well believe this conditional. He should. But one cannot say, on Jones’s behalf, that since Jones believes Brown owns a Ford he must then believe that either Brown owns a Ford or Brown is in Brest-Litovsk. Because Jones should protest: Only if my belief is true will that disjunction be guaranteed to be true; if it is false there is no such guarantee, and my evidence must then be misleading; and my believing something to be true does not mean that it is true. So I do not, as a matter of fact, believe the disjunction: my belief in this case is void. (This argument seems to me to be very similar to an argument that John Broome has given in Ratio — but I don’t have the reference available.)

In other words Jones should believe

  1. If p is true then p or q is true for all q,

but there is no good reason for him to believe

2.    If I believe p then I must believe p or q for all q.

One can see this perhaps more clearly if we note that Jones, believing p, may give up p when it is pointed out to him that it implies some other proposition r.

The upshot is that there is no reason to suppose that Jones should believe Gettier’s disjunctive proposition. And I think — though of course one cannot be sure — that this is what Russell would say about the example. For Russell evidence and belief are fused together rather like parts of a single organic process. The evidence once received is turned into the belief; the thickness of the belief is a function of the thickness of the evidence. The belief is a mental state in a rich sense, more resembling, in its complexity, a painting than it resembles a thin proposition. This suggests that evidence need not be transferable — from a belief to a proposition that is logically implied by it (in Gettier’s sense). And if it is not transferable then Gettier’s disjunction need have no evidential support. In the case of the stopped clock I think Russell would say that merely glancing at a clock does not give you sufficient evidence to believe that it is accurate. (But I emphasise that with respect to Russell, I am speculating as to what he would say to Gettier.)

It is this transferability of evidence that does the heavy lifting in Gettier’s argument and opens up the gap between a justified true belief and knowledge. Once we allow it we must find a way to close it again. This is where the truthmaker account comes in. By insisting that the state of affairs that is the truthmaker be the same as the state of affairs that the evidence is evidence of, the gap is closed.

It is worth noting that, in Human Knowledge, Russell describes a truthmaker theory. I think that most students of philosophy do not understand this — almost certainly because they have never been taught it. They might be aware that Russell outlines something resembling a truthmaker account in the Lectures on Logical Atomism, from 1918. But there seems to be a general idea that this is something he gave up. He didn’t. In his works of the 1940’s — An Enquiry into Meaning and Truth and Human Knowledge — he holds to it. It is true that Russell doesn’t use the word ‘truthmaker’ but he does certainly speak of facts making beliefs and sentences true. Thus he says

In like manner we want a description of the fact or facts which, if they exist, make a belief true. Such fact or facts I call the “verifier” of the belief. (p. 166)

So a verifier is a truthmaker. The whole theory of truthmakers is just the development and continuation of the view initiated by Russell and Wittgenstein before and during WWI. It is a great shame — and a lost opportunity that lasted for nearly a full century — that this view was not taken up and developed as it needed to be. And even today the theory is treated as something odd and unfashionable — as though philosophers were peacocks that can only stand to be seen in the latest dress!


Postscript for bibliophiles.

The copy of Human Knowledge that I have is a first edition — I bought the book second hand many years ago. It comes from the library of T. D. Kellaway, who was Professor of Pathology at Cambridge University. But what is particularly interesting is that the dust jacket of the book is printed on the back of a WWII map — since paper was still in short supply in Britain through the 1940s and rationing was still firmly in place. Images below.


The Truthmaking Solution to the Gettier Problem

In 2003 I set out a new solution to the Gettier problem that had bedevilled the theory of knowledge. Here I want to describe that solution and make some personal remarks as to its genesis and subsequent history. (All the relevant papers can be found on

The idea is easily described. Let us take the second of Gettier’s own counterexamples to the idea that knowledge is justified true belief (and no more than that) — that is, the idea that in having a justified true belief one has satisfied the sufficient conditions for knowledge. Jones has good reasons to believe that Brown drives a Ford, in the form of Brown’s own testimony and his (Jones’s) own observations. Jones picks a set of cities that begin with the letter ‘B’: Barcelona, Brest-Litovsk, Boston, say, and then forms propositions for each such city, of the kind:

Either Brown owns a Ford or he is in Barcelona,

Either Brown owns a Ford or he is in Brest-Litovsk…

Jones believes each of these propositions simply because he believes on good evidence that Brown owns a Ford, and this is the first disjunct of each of these sentences. (It must be emphasised that the disjunction here must be understood as inclusive disjunction.) It turns out however that Brown does not own a Ford but that he is in Brest-Litovsk. Thus this sentence is true and believed on good grounds, and hence is justified — despite the fact that Jones has no reason at all to believe that Brown is in Brest-Litovsk. It must be emphasised that this problem rests on us sharing Gettier’s intuition that under this circumstance Jones does not know that Either Brown owns a Ford or he is in Brest-Litovsk but that his belief is both true and justified. Most people have shared this intuition — but if one doesn’t then one will not see a problem here. At any rate I do share Gettier’s intuition.

The truthmaker solution to this and similar Gettier problems is that the truthmaker for the sentence — the state of affairs that makes it true — is not, as it normally would be, the state of affairs of which Jones has evidence. Instead we have two different states of affairs, one of which is the truthmaker, and the other of which the evidence for the belief is evidence of. Thus all of these classical Gettier cases involve a doubling of the states of affairs that are involved. Thus I proposed an analysis of knowledge that goes as follows:

The Knowledge-conditions. X knows A iff  X believes A; X is justified in believing A; A is true; and the evidence that X has which constitutes the justification is evidence of the very state of affairs that makes A true.

In addition to what I would call the classic Gettier problems — an example of which is above — there is another set called the Ginet-Goldman cases, also called the fake barn cases. An example is as follows. Along a particular stretch of road there are many fake barn facades so skilfully done as to be indistinguishable, to the casual motorist, from the real thing. Driving along the road you form a sequence of beliefs that this is a barn, that is a barn, this next one is a barn and so on. However, one of these barn facades, call it R, is the facade of a real barn. Passing R you form the belief that is a barn. This is a true belief. Moreover you have good evidence that it is true. So it would seem that you know it is a barn. Some distinguished philosophers however have wanted to claim that it is not knowledge — simply because you also formed similar beliefs when driving past all of the fake barn facades — and in those cases your belief was false. One might say that your belief about R was true, but so embedded in a series of false beliefs that you cannot take credit for it. So it is not knowledge.

This also depends on our sharing the intuition — that the motorist here has a justified true belief but does not have knowledge. But how plausible is that intuition in this case? Certainly it must be agreed that the motorist has many beliefs that are false and that therefore do not count as knowledge. But in the case where the motorists belief is true, where the evidence is of a genuine barn nothing has gone wrong. Thus my intuition in these cases is that the motorist does have knowledge after all. And note that in this case there is no doubling of the states of affairs that are responsible for the attribution of knowledge to the motorist. So my truthmaker account deals with this view automatically.

I put this solution forward in 2003 at a conference on epistemology — in fact at the last session of the conference, when many had gone home. However the attendance at the paper was still respectable, and the conference had attracted most of the people in Australia who were centrally concerned with the theory of knowledge: Tim Oakley, John Bigelow, Anne Newstead, Michaelis Michael, etc. Along with these there were many overseas visitors. The paper was finalised by the time of the conference because I had been testing out this solution and refining it for two years, 2000 and 2001, in my epistemology classes — lectures which were then written up as the first four chapters of my book A Primer on Knowledge. It’s also worth noting that I’d been working on truthmaker theory itself, on and off, since 1995 when Kevin Mulligan was visiting the Sydney department — one result of which came out in Logique et Analyse in 2003. (It was this visit by Mulligan that propelled David Armstrong’s interest in truthmaker theory.) The point of saying this is to note that this solution did not just come out of nowhere — there was a prepared ground.

The paper, ‘Truthmaking and the Gettier Problem’ came out in 2006 in a volume of papers from the conference: Aspects of Knowing: Epistemology Essays, published by Elsevier, edited by Stephen Hetherington, who had also been the conference organiser.

In the original paper I took the view that Russell’s stopped clock example — which, historically was the first classic Gettier counterexample in the literature, published in 1948 in Human Knowledge: Its Scope and Limits — was dealt with by my account: it involves a doubling of the relevant states of affairs: the evidence is of a clock which stopped 12 (or some multiple of 12) hours earlier, whereas the truthmaker is the time that actually obtains. However an email from Gonzalo Rodriguez-Pereyra raised a doubt about this. In reply I repeated my belief that it required no more than had already been given. Over time however it seemed to me that the case was interesting enough, and complex enough, that it required further comment — and after all, what matters in philosophy is whether one has said enough to convince everyone, and not simply whether one has convinced oneself: I felt that I had done Rodriguez-Pereyra a disservice by not attempting to make the case in more detail. And so I wrote a short paper for Analysis in which I tried to lay this problem to rest — once and for all (so I hoped). (This was ‘Gettier and the Stopped Clock’, Analysis, 72, 2, 2012. See here)

The solution was this: Firstly the actual time depends on governmental stipulations and decisions, so the truthmaker in this case is partially constituted by such decisions. This does not make such facts any the less objective. Once the stipulations are in place it is an objective fact that the time is now 11.10 am. Clocks represent the correct time to us by being synchronised causally with an authoritative original clock, and with being constructed so as to “keep time”. But when you look at a clock (in keeping with Russell I am assuming that clocks are the usual 12 hour analog clocks) you do not know the time just from that looking, you use a wealth of contextual information — the position of the sun in the sky, the sound of traffic, the sounds of birds and people — to check whether the  clock is accurate or no longer running. Merely glancing at clock in the absence of this contextual information is not sufficient for forming a justified belief. Neverthelesss when the clock is running and has been properly set the evidence you acquire from looking at the clock plus this contextual information is evidence of the correct time. When the clock is stopped or slow (or fast) the evidence you acquire is of a different state of affairs — even if it happened to stop 12, or a multiple of 12, hours earlier. There is a doubling of the relevant states of affairs — so my account deals with it by adding the extra condition, as above. All is good.

Thus let us suppose that a clock stopped at 2.00 am but then suddenly started working properly at 2.00 pm of the next day — and let us suppose that no one looked at the clock in the 12 hours during which it was stopped. Then, I say, it is still not giving one a knowledge of the correct time — instead it is indicating a time that is 12 hours earlier. No one may be aware of this: but still it is so, ex hypothesi.

It should be noted that Russell himself did not claim that in looking at the stopped clock you acquired a justified true belief (that yet wasn’t knowledge). His example was meant to show merely that this was an example of a true belief that wasn’t knowledge. So my view about the stopped clock case is consistent with Russell’s own view, whereas those who believe that merely looking at a clock is enough to give you a justified belief as to the time go considerably beyond what Russell was prepared to assert. The onus is on them to make their case.

As a personal aside I might note that my grandmother worked for Russell at the end of the 1940’s and through the 1950’s — and thus through the time when he was writing Human Knowledge: Its Scope and Limits. (In fact she claimed to have saved Russell’s then wife, Patricia Spence, from committing suicide by jumping off the balcony: they were going through a particularly unpleasant divorce at the time. My aunt was Conrad Russell’s best friend in childhood — indeed one has to say his only friend.)

It should be noted that Russell not only gave the stopped clock example he also gave an example that is logically equivalent to Gettier’s first counterexample (the one not given above). He is given scant credit for his contributions to the theory of knowledge, particularly those found in his later works. The recent treatment of Russell amounts to a scandalous neglect, in my opinion.

I’ve been asked a few times how David Armstrong reacted to my solution to the Gettier problem. After all, it could be said to vindicate his idea — expressed in many later books — that truthmakers were the key to understanding Truth and many metaphysical problems. The answer is that he didn’t know of it — as far as I know. During 2003 and the time around it Armstrong was teaching in America and even when he returned I didn’t bump into him until much later. By that time the Gettier paper was old news for me and I was thinking about other things. So I don’t ever remember mentioning it to him. Which is a pity: I think he would have been chuffed.

Since the Analysis paper I’ve written a number of other papers on the topic, which are here here and here — which were all attempts at stopping the view from being misunderstood. But the misunderstandings, though unpleasant and unnecessary, were the least unpleasant aspect of a rather unpleasant subsequent development. A number of unscrupulous philosophers — four to my certain knowledge, but there may be more that I haven’t been alerted to — have attempted to take my work, reword it slightly, and claim it as their own. They have wanted to claim that they have solved the Gettier problem — though years later, in fact.  Plagiarism is NOT too strong a word for this. I think this speaks volumes about the current state of academic philosophy — but such plagiarism requires a blog post of its own.

Review of Jeff Bub’s Bananaworld: Quantum mechanics for Primates

Jeffrey Bub is one of the most distinguished philosophers of quantum mechanics writing today. His first book on the subject, The Interpretation of Quantum Mechanics, was published more than forty years ago, and he has written many works on the subject since, including the Lakatos Prize winning Interpreting the Quantum World in 1997. His latest book presents a wealth of material that has emerged in the last fifteen years related to the explanation of the central aspect of quantum mechanics as we understand it today: entanglement. A novel pedagogic device in the book is provided by an analogy to two different ways of peeling a banana, with a consequent difference in how it tastes. On the basis of this analogy there are some wonderful illustrations of a Carrollian bent — Tenniel himself would have been proud! I’ll come back to the analogy in the course of the essay.

There are two properties that quantum mechanics (henceforth QM) satisfies: 1) there is no superluminal signalling (NS); and 2) the observables can be contextual (C). Combined with the well known fact — a result of Bell’s theorem — that the predictions of QM cannot be reproduced by a non-contextual hidden variable theory (NCHV) and it follows that QM is non-local. From non-locality and (NS) it follows that QM cannot be fully deterministic. But — and this is the first surprise — principles (NS) and (C) do not uniquely delimit the set of correlations to just those predicted by QM. There are supra-quantal non-local correlations that are non-physical (as far as we know) which satisfy (some neutrally formulated) version of (NS) and (C). Thus (NS) and (C) are necessary but not sufficient for QM. The task then, as it is now formulated, is to find the underlying principles that distinguish QM not just from classical physics, but also from supra-quantal ‘physics’.

The upper bound of QM has been known for a long time, since 1980: it is called the Tsirelson bound (from Cirel’son (1980)). In 1994 Sandu Popescu and Daniel Rohrlich devised a set of correlations that exceed the Tsirelson bound but that satisfy (NS) and non-locality (Popescu and Rohrlich  (1994)). This showed that what was above the Tsirelson bound was at least something that could be described consistently. But were there principles that would naturally rule out such supra-quantal correlations as unphysical, and does any of this shine a brighter light on QM itself? Why is our world not more non-local than it is? Or more indeterministic? These are the questions with which Bub’s book is concerned….

[To read the rest go to the full text on ]

Who discovered entanglement I

One answer to this question — probably a common one — is that entanglement was discovered by Einstein in the Einstein-Podolsky-Rosen paper of the 15th of May, 1935: `Can Quantum-Mechanical Description of Physical Reality be Considered Complete?’. It was discovered only to be instantly repudiated! The non-locality implicit in a change in a wave function at place A leading to a change in a wave function at place B seemed to Einstein to be inconsistent with relativity and the assumption that A was separable from B was one of his assumptions of reality.

That definition of separability was:

Separability: Whatever we regard as existing (real) should be localised in time and space (space-time). Or, more weakly, if two dynamical systems are space-like separated then each system can be characterised by its own properties, independently of the properties of the other system.

Since this separability was the denial of entanglement and so EPR discovered entanglement — or so the story might go — by denying its possibility.

However, even though Einstein et al were the first to publish on this the better answer as to who discovered entanglement was Schrödinger. Schrödinger published the paper `Discussion of probability relations between separated systems’ in the Proceedings of the Cambridge Philosophical Society for 1935, in fact in August of that year, only a few months after the Einstein et al paper, and he and Einstein had been in correspondence on this for several years, both with the idea that the measurement process suggested something deeply problematic about quantum theory. But Schrödinger is better at drawing out the consequences and indicating that it arose from the nature of the tensor product itself. What he says on this is far clearer than what is in the Einstein et al paper — and Einstein would probably have agreed, as he was known to have disliked how Rosen and Podolsky (mostly the latter) wrote up the idea after their talks together.

Whereas, by 1935 Einstein was well-settled in Princeton, Schrödinger was unsettled in Oxford. He had just had a baby daughter by his mistress, Hilde March, and he had just won the Nobel Prize (in 1933), but he had no permanent position and he was unhappy with the home he had been given by ICI who were paying his stipend — a stipend that he also didn’t feel was enough. Nor did Oxford take entirely to Schrödinger: Frederick Lindemann, the head of physics, strongly objected to Schrödinger’s ménage à trois and wanted to get rid of `this bounder’. And yet out of this chaos Schrödinger managed to write, in lucid prose, an account of the characteristic trait of quantum mechanics.

Here is Schrödinger’s conclusion:

When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives (or $\psi$-functions) have become entangled. To disentangle them we must gather further information by experiment, although we know as much as anyone could know about all that happened. Of either system, taken separately, all previous knowledge may be entirely lost, leaving us but one privilege: to restrict experiments to one only of the two systems. After reestablishing one representative by observation, the other one can be inferred simultaneously. In what follows the whole of this procedure will be called \textit{disentanglement}. Its sinister importance is due to its being involved in every measuring process and therefore forming the basis of the quantum theory of measurement, threatening us thereby with at least a regressus in infinitum, since it will be noticed that the procedure itself involves measurement.

We might note that Schrödinger distinguishes between the state and its representative; why does he do this? The reason is that the state is not Lorentz invariant, so it changes as we change Lorentz frames. So Schrödinger is careful not to speak of the state, as though it were something absolute — which would be as bad a mistake as speaking of the velocity of an object in the light of Galilean relativity. For Schrödinger the quantum state is something rather mysterious, and he thought that others were far too free with the notion, and too incurious as to what lay behind it. But though we cannot speak of the state we can speak of its \textit{representative} in a frame. It should be noted that this frame relativity does not mean that entanglement is also relative: it is frame invariant (because the fact that the state for the joint system is a pure state is an invariant).

The entanglement that we have here was called, by Schrödinger, in his German publications, Verschränkung — cross-linking.

He continues:

Another way of expressing the peculiar situation is: the best possible knowledge of a whole does not necessarily include the best possible knowledge of all its parts, even though they may be entirely separated and therefore virtually capable of being “best possibly known”, i.e. of possessing, each of them, a representative of its own. The lack of knowledge is by no means due to the interaction being insufficiently known — at least not in the way that it could possibly be known more completely — it is due to the interaction itself.

Attention has recently been called to the obvious but disconcerting fact that even though we restrict the disentangling measurements to one system, the representative obtained for the other system is by no means independent of the particular choice of observations which we select for that purpose and which by the way are entirely arbitrary. It is rather discomforting that the theory should allow a system to be steered or piloted into one or the other type of state at the experimenter’s mercy in spite of his having no access to it. — Schrödinger 1935, p. 556.


It might seem as though everyone would pay attention to this startling prediction. But as it happened, it was almost universally ignored. For decades it lay dormant.


The purpose of this blog is to say some things that don’t fit into the format of a traditional academic paper. There are many such things, and they would, in the past, have gone unsaid, or have been said only in the context of a discussion among academics over coffee. To the outside world such things are invisible — but they constitute the living world in which academic debates and disagreements exist and they constitute the invisible 0.9 iceberg as compared to the published tip (as it were). It is the existence of this larger context that makes it virtually impossible for anyone who is not within a University to understand what is going on in a particular discipline — and I would say this is especially true for philosophy. For example, just browsing a philosophy bookshelf in your local bookstore would give you no idea what it is philosophers do or what they are interested in — and this would be true even if the bookstore is well-stocked with recent publications. But this has the consequence that no one who is not in philosophy can really understand the subject, though many people will be deceived into thinking that they can and do.

This is a great pity. But it is more than that — it has divorced philosophy from the culture that surrounds it and consequently left that culture philosophy-less, clutching on to fragments of misunderstood eastern mysticism and wisdom literature, blended together with cat-memes and the saloon-bar sawdust of political outrage. I can’t possibly hope to reverse the damage that has already been done. But it may do something (an epsilon of something) to say a few things that are fragments of that wider philosophical discussion, not behind closed doors but out in the open. However I can only do that from within my own areas of interest, which are Philosophy of Physics, Philosophy of Mathematics, Epistemology and Metaphysics. Perhaps the best that could be hoped for is that people will understand their debt to Plato or Aristotle — or have a little more knowledge of what they were saying, rather than at present, where it is vanishing to zero.

As you can see, I’m a pessimist even in my optimism.