Science as Religion

This is the claim made by opponents of public funding of science, recently and notably Simon Jenkins in The Guardian. This has garnered a hostile yet somewhat lighthearted response from science professionals: A Mammoth of Research by Jon Butterworth.

Jenkins’ article is not completely without value. It does however veer wildly between the indefensible and unsupported and the reasonable. It is not clear to me that he is aware of this.


“A ‘mammoth of research’ is about to rise behind London’s St Pancras station, a biomedical centre costing £600m and housing about 1,250 ‘cutting-edge’ scientists. Ask not its value. Science jeers at the idea.”

This is unfair. Scientists are aware that they have a duty to account for their use of public funds. They are sometimes wary about making that case with maximum force however because they are unsure whether the approach is correct. Certainly, civil servants ‘picking winners’ in science is as ineffective as having them do so in the wider economy. They lack the skills (numeracy) because they are often arts graduates, motivation because they do not get fired if they fail. I do not disparage arts graduates – notably because I am a philosophy student – I just do not think that person or indeed anyone can decide from proposals what science or manufacturing will produce an economic return. The situation is somewhat more clear in the case of economic decisions because by definition, the market has not pursued an opportunity that civil servants deem worthy of subsidy. The question as to why can be answered. But scientists themselves do not know which avenues will result in the next world wide web – they just know, that as in finance generally, risk diversification calls for a wide spread of angles of attack.

There is a detailed defence of the economic value of particle physics here.


Jenkins complains that there is excess reverence paid to science in the media: “Today programme science items, all reverential. No scepticism is admitted to this new orthodoxy”; the Reith lectures involve “safe, hand-picked questions”. This is bizarre. The commentary might apply very well to Thought for the Day, which can naturally endure no questioning as to evidence, but the idea that science coverage on the Today programme does not involve controversy and aggressive questioning is at variance with the facts. Many in fact have made the opposite complaint in relation to the BBC searching for ‘balance’. This involved it in considering both sides of the MMR debate, an approach which appeared excessively even handed when the doctor in question was merely alone in claiming that the vaccine caused autism and now appears foolish when he has been struck off. The climate change debate has a similar two-sided appearance in the media when there is only one side in the labs. And yet there is a way to attack scientists for orthodoxy which Jenkins has missed: ask them about evidence for string theory.


“It was too bad that the Icelandic ash clouds turned out to be not as bad as “the science” had claimed. It was too bad if science banned beef on the bone; too bad if science wasted £2bn on Tamiflu; too bad if science wrecked the case for nuclear power by its hypersafe radiation limits, or failed properly to defend GM foods.”

This is unfair. Science does not give advice. It tells you what the answer is if you ask questions like “what number of extra cancers can I expect with a 66% confidence level if I build a nuclear power station 5km away?”. Politicians decide what they can sell to the public, but since they and especially the public lack numerical ability and especially risk assessment skills (for example, people are frequently up in arms about lack of access to a particular drug on the NHS that improves their status for three months when they are happy to smoke which is extraordinarily more risk by orders of magnitude). And that approach just won’t work.


“Since science supplies its own “organised scepticism”, its claims on the public purse should be asserted as infallible.”

No scientists claim this. But consider the numbers. As I have pointed out several times here, we could build 41 LHC-scale science projects in the UK every year with the £231bn social security budget. Science funding through STFC, the relevant council, is something like £800m. Which of those numbers should you cut and which is likely to produce a return?

More real than finance

“In his lecture he insulted the financial sector as ‘not the real world’, as ‘faffing around with derivatives’ and as undeserving of any graduate’s respect. (Yet within minutes Rees was moaning that in Britain there was not enough ‘venture capital for startups’.)”

This is one place I agree with Jenkins. There aren’t many people who understand the value of derivatives or their very real value in the actual world, arising as they do from the desire of Japanese farmers several centuries ago to have a stable known future price for their crops. But it also ill behooves scientists to attack derivatives as in some way airy fairy because they sometimes employ mathematics and also employ many of the scientists who cannot find permanent jobs in labs or universities. And since the financial sector produces 31% of UK GDP, taxes on it will be needed to support science.

Supply of practitioners

” ‘Britain needs more scientists.’ Their canticle was: ‘More money for research.’ Other vocational subjects such as law, accountancy and finance were deplored, even as the jobs market screamed for them.”

This can’t be right. If any market anywhere is screaming for anything, then it gets it. That is how our system works. I am not aware that law, accountancy and finance are underpaid. New graduates in banking can still get close to £40k as a starting salary. If the system wants more of them, it pays them more and more are thereby trained, especially if the employers offer to pay off student loans as well. They will do so if the value to them justifies it.

We are not short of lawyers in this country and not short of them in Parliament either. And that’s fine. But can anyone name an MP with a science degree? Shouldn’t we have a few of them?

‘Both A Black Raven And A Red Herring Confirm The Claim That All Ravens Are Black.’

Examining the paradoxical yet true but possibly slightly misleading claim of the title.

1. Introduction

This question bears some similarity to Moore’s class of paradoxes of the form “P, but I do not believe that P”. The similarity relates to the fact that we have an intuitive reaction against both claims, though they may not in fact be logically contradictory. To be contradictory, a claim must violate the law of non-contradiction and assert P & ¬ P. Moore’s paradox does not actually do this, but it carries an impression that it does, because we assume that someone asserting P must believe it.

Similarly, the assertion made here contains no logical contradiction. There are no logical reasons why any observation P should not confirm any claim Q. However, we intuitively feel that any observation purporting to confirm P must have ‘something to do with’ P. Surely nothing can be learned about ravens by observing herring. This essay will argue that here intuition is wrong and logic is right in this case.

The problem originates with the logical equivalence of hypotheses, as illustrated by the pair below.

S1: All ravens are black
S2: All non-black objects are not ravens

It seems at first that the two claims i) and ii) are different because they have different subjects. But in fact they say the same thing. They are both made true by the blackness of all ravens, despite the appearance that i) is about ravens while ii) is about anything that is not black.

We now introduce what appears to be a basic rule of confirmation, the Equivalence Condition:

EC: Anything that confirms a hypothesis also confirms any logically equivalent hypothesis.

This simply means that hypotheses come together with any further claims they entail. If I have evidence, perhaps visual, that Pierre is in the café, then this is equally good evidence for the claim that he is not in the park, because the truth of the first claim entails the falsity of the latter and many other similar assertions. It would be strange if I could be certain that Pierre was in the café but unsure about whether he was also in the park.

Note that the strangeness is not related to the certainty here. If someone has secretly selected a ball from a box containing three white balls and one black ball, I know that there is a 75% chance that they have a white ball and equally a 75% chance that they do not have a black ball, because if it is white then it is (perhaps logically but certainly in some fashion) entailed that it is not black.

This leads to the paradox. For an observation of a red herring confirms b). So it must also confirm a). And how can that be?

2. Hempel

2.1. Origins of the Paradox

Hempel introduces Nicod’s Criterion, as below.

NC: A hypothesis can only be confirmed or dis-confirmed by one of its instances.

It can be seen that despite the fact that this criterion was widely accepted, it already has the appearance of being in conflict with A above. Hempel considers hypotheses i) and ii) in the light of a universe of four objects, as specified below:

a) a black raven;
b) a non-black raven;
c) a black non-raven;
d) a non-black non-raven.

By NC, these objects would have the following effects in relation to S1 and S2.

Object S1 S2
a Confirms Neutral
b Disconfirms Disconfirms
c Neutral Neutral
d Neutral Confirms

The different effects of a) and d) mean that Hempel is able to bring the apparently fatal objection that NC “makes confirmation depend not only on the content of the hypothesis, but also on its formulation”. It is therefore clear that in choosing between NC and EC, EC is to be preferred. This then leads directly to the paradox that a red herring confirms both S1 and S2.

Hempel has a further approach to argue that the intuitive conflict is purely a result of psychological factors, by using the well-known oddities in the behavior of the logical-IF statement. The relevant truth table allows for a material conditional to be false in only one circumstance: where the antecedent is true and the consequent is false. This has the unusual result that the conditional is true if the antecedent is false even if the consequent is also false.

Thus, the proposition ‘all mermaids are green’ is true. The logical explanation of this is that we could only falsify it by observing a non-green mermaid, and since we cannot observe any mermaids at all, this cannot be done. Hempel notes the Russellian point that we are probably subconsciously attaching existential import to the proposition and expanding it to ‘there is something which is a mermaid and it is green’. The first conjunct is false and so the proposition is false on that expansion. Similarly, we find it strange to say truly of someone that all their daughters are clever when that person has no daughters.

It is known that all sodium salts burn yellow. This may be phrased conditionally as if x is sodium then x burns yellow. Note that we do no expect this hypothesis to be confirmed by an observation of ice, which does not contain sodium, not burning yellow. Yet this is exactly the same fallacy. The proposition is still true and is confirmed by the ice observation because the antecedent is false.

Hempel seeks to illustrate this further by considering the order in which the observations are made or what background knowledge we are using. If an unknown substance is burned, we would interpret the results differently. If the unknown substance does not burn yellow, we would conclude that it did not contain sodium salts. If on the other hand we know already that it is ice, we would be tempted to conclude that its failure to burn yellow tells us nothing about the sodium salt hypothesis. But we need to note that this is still consistent with the hypothesis and thus confirms it.

If the flame has burned yellow, we could subsequently have determined otherwise that the material contained sodium salt and confirmed the hypothesis. If it did not, we could have determined otherwise that the material was ice and this confirmed the other formulation of the hypothesis – that anything that does not burn yellow is not a sodium salt. Hempel claims that this makes the paradoxes disappear but it can be noted that the strong temptation remains ignore the reasoning.

2.2. A Definition of Confirmation

Hempel notes that there had been two candidates for definitions of confirmation, NC and also predictive success. The latter would be primarily associated with A J Ayer and could take the plausible form that a hypothesis is confirmed to the extent that it is able to predict observations successfully.

He replaces EC with a more fundamental Consequence Condition:

CC: If observation confirms a class of propositions K then it also confirms all logical consequences of K.

This is argued for convincingly by noting that in fact the original hypothesis already includes all further statements entailed by the ones specified and thus an observation can only confirm or dis-confirm them as a group – a remark very suggestive of Quine’s later holism. CC has EC as a consequence and so Hempel is able to drop EC as a separate independent criterion, while of course retaining its import within the CC umbrella. CC has the further desirable result of excluding NC, which factor constitutes a further argument for CC.

Hempel now excludes Predictive Success (“PS”) as an element for confirmation by noting that PS, while allowed by EC, is not allowed by CC. If a hypothesis H allows successful prediction of B2 future findings from B1 existing findings, then any equivalent hypothesis to H will also allow this. A weaker hypothesis than H – i.e. one with less predictive power – would not do this.

Any hypothesis H2 that is stronger than H, so that H2 entails H, can also be used to make this prediction. This relates to the famous Under-determination of Theory by Evidence (“UTE”) problem, whereby an apple falling to the ground is equally good evidence for a) gravity and b) gravity plus the moon is made of cheese. So PS would mean that any stronger hypothesis is confirmed by observations while CC says that only weaker ones are. Since CC produces the independently argued for EC and avoids the UTE problem, CC is shown to be a better candidate for a definition of confirmation.

3. Mackie

3.1. Intuitive Explanation of Hempel’s Result

Mackie notes Hempel’s suggestion that there are psychological factors in play. He considers an alternative proposal that looks at the question from a probability angle.

The key element of this type of solution involves postulating a potential equivocation on ‘confirmation’. In ordinary language, the term refers to knowledge or strong enough levels of certainty. But here it becomes a term of art and should perhaps be understood as standing in for ‘tends to confirm’ or indeed ‘supports the hypothesis’. As is well known from the work of Popper and the general philosophy of induction, the current scientific paradigm says that observations can never prove a hypothesis. There always remains the possibility of finding a white raven. This is the case even though a single dis-confirmation can provide a falsification.

So perhaps the problem is that while it is true that a red herring confirms in this sense that all ravens are black, the degree of confirmation is less. However, it still remains to be explained how this can be. To see this, note that there are in principle two ways of confirming that all ravens are black. The first way is to observe all of the ravens.

The second way still exists: we could look at everything that is not black and see how many ravens are in that category. If the category of all non-black objects does not include any ravens, we have also shown S1. Since the second way is immensely impracticable, we would for all normal purposes ignore it: this is the source of our intuition against the red herring confirming S1.

In the world as it is, there are many fewer ravens than non-ravens. I have devised an example to make the above argument more intuitive; begin by considering a universe of discourse where these normal circumstances are reversed. It could be an aviary, since it contains many ravens. Imagine that it also contains a large number of non-descript items, all of which are black. These are hard to see and harder to describe. In addition, there are a white piece of chalk and a green leaf. These are the only non-black items. Under these circumstances, we would indeed conclude that all ravens are black by noting that everything that is not black is not a raven.

3.2. Further Cases Beyond Those Considered by Hempel

Mackie allows that Hempel has successfully argued for a consistent definition of confirmation within a limited set of universes of discourse. He then considers an extension he attributes to Watkins termed the Alternative Outcome Principle (“AOP”). This holds that if there are two potential outcomes of an observation, then they cannot both confirm the hypothesis under test. This seems plausible, because it would mean that the experiment or observation had been poorly designed. We must here as ever be on guard against equivocation on ‘confirmation’.

In practice, AOP has strange consequences. “If we inspect an object already known to be a raven and it turns out to be black, this confirms h, for the procedure might have turned out the other way and falsified h; but if we inspect an object already known to be black and it turns out to be a raven, this does not confirm h” and vice versa. The essential reason for this is that under the AOP, not both outcomes can confirm S1 even if they are both consistent with it, as they are – and in fact one outcome must deny the other or reduce its plausibility.

If the raven had not turned out to be black, then S1 would have been falsified. But if the black object had turned out not to be a raven, S1 would not have been falsified on this view – a crucial difference with Hempel – and so the reverse would not have been a confirmation of S1. The view is Popperian in that a test of a hypothesis can only be an attempt to falsify it.

But this cannot be right, because it means that the order of observation of characteristics is significant. A black raven with its species observed before its color confirms S1 but a black raven with its color observed before its species does not confirm S1. Surely a total observation of a black raven must have the same consequences independent of the order of consideration of its characteristics.

Mackie concludes that the paradox is to be resolved in different ways for different circumstances. In a limited Hempelian universe without background knowledge, we simply deny that observations of red herrings are irrelevant to S1 via a consideration of EC. We are simply wrong to think that this is the case.

Secondly, a numerical approach may be adopted to illustrate the equivocation of ‘confirms’. We are again wrong about the observation of red herrings, but we are wrong because we mistake ‘no confirmation’ for ‘minor confirmation’.

But thirdly, Mackie believes that the best form of confirmation should be on a Popperian basis where the outcome could have falsified the hypothesis. So observations of black ravens confirm S1 only in circumstances where they could have falsified it – we should specifically look out for non-black ravens as opposed to ignore anything not black. Also, “observations of non-black non-ravens confirm [S1] to a worthwhile degree only if they are made in genuine tests of this hypothesis.”

This is an echo of the example in section 3.1 above of the aviary containing mostly black items, many ravens and two non-black items. Counting the white chalk and the green leaf do constitute a good test of S1 in those circumstances. But in the actual world, containing as it does large numbers of ravens and herrings, and vast numbers of other objects of all kinds, there is no real test of S1. A negative outcome would not falsify S1 and so a positive one does not confirm it.

Written 23/03/10


  • C Hempel, Studies in the Logic of Confirmation (I.), Mind, New Series, Vol. 54, No. 213 (Jan., 1945), pp. 1-26 and (II.) Mind, New Series, Vol. 54, No. 214 (Apr., 1945), pp. 97-121
  • J. L. Mackie, The Paradox of Confirmation, British Journal for the Philosophy of Science, Vol. 13, No. 52 (Feb., 1963), p. 265, (“Mackie”)
    Cited as Philosophy, 1960, 10, 319

    How, if at all, can the traditional problem of induction be solved?

    1. Introduction

    Hume outlined the traditional problem; in sum it poses the question as to whether any justification of induction is possible that is not invalidated by being required to assume that induction is already valid.

    Inductive reasoning is less rigorous than deduction, because it does not entail its conclusions when its premises are correct. This is because it by definition involves an extrapolation from the observed to the unobserved. The latter may be distinct from the former in a number of ways, including being future examples of a previous observed kind of item, or future events of a similar type to previous events.

    The structure of an inductive argument will be as follows: All observed F’s are G, therefore All F’s are G. Note that there are few if any examples of all items of type F being observed, and even if they had been, there would probably remain epistemic doubt as to whether this was the case. So it is always possible that even if many thousands of white swans have been observed, a black swan will exist. And of course if all F’s had been observed, there would be no application of any inductive knowledge to any further F’s. We would always need a ‘uniformity of nature’ principle holding that the future will resemble the past, and arguments to show the principle would rely on it.

    One is naturally convinced that seeing that may F’s are G is excellent evidence for all of them being so, but this is a direct parallel to Hume’s sceptical problem and why he is also prominent in this area. The fact that we seem naturally to have no choice but to accept the existence of the external world and the validity of inductive reasoning does not mean we are ipso facto released from the question as to how these things are possible.

    2. Mellor

    Mellor appeals to Ramsey’s encapsulation of the reason for our belief in induction. This says that we use induction because it leads to true beliefs that we can then use with success to complete actions – this is a pragmatic theory of truth. He defines induction as “something that can warrant anticipating an observation” and then introduces a non-standard fallible definition of observation by noting that false beliefs can be acquired through sensory data. So on this line, observation “no more entails the truth of the beliefs it gives us than induction does. How then can it warrant them?”.

    Mellor also notes that observation is generally much more powerful than induction: if I observe something highly surprising, I do not dismiss the observation merely because I have never seen an elephant in Piccadilly Circus before. I assume on the other hand that something unusual is happening. Therefore observation must be able to meet any standard that induction can. Mellor will argue that since observation cannot pass what might be termed a ‘uniformity of observation’ test, neither can induction and we therefore need a different test of warranted inductive beliefs.

    It is frequently argued that there must be a KK principle viz. I can only know something if I know that I know it. Arguments for this would include the idea that I could only act successfully based on a piece of knowledge if I recognise that piece of knowledge as such. Yet there are strong counterarguments to KK including the myriad of unconsidered background conditions that I frequently assume to be the case without conscious consideration. For example, I will know there is an elephant in Piccadilly Circus if I see one even though I do not know that there is not a rare optic disorder that causes one to see illusory elephants and that I do not have it.

    Mellor combines this type of attack with the other idea that if KK, then the first K must be self-intimating. I should not have to consider whether I know that I know something: if I know it, that should already be enough to settle the higher orders. Yet there is an infinite regress here. If true warranted belief if enough for knowledge, as Mellor claims, then by KK I will need to have a true warranted belief that K in order to have K. And I will also need a true warranted belief that KK and so on. Even if these infinities are acceptable, the phenomenology does not allow the idea that they are self-intimating any plausibility.

    There is a nod in the direction of Sartre in Mellor’s observation that the attraction of the KK principle may lie in our strong but false intuitions that we know ourselves and that there is a fixed self to know. Abandoning KK permits the adoption of a pragmatic theory of truth; truth becomes “the attribute of beliefs which ensures that the actions they cause will succeed”. So a warrant will be anything that works as opposed to being KK. Note that these are not necessarily incompatible: I could have self-intimating KK that works – it is just that KK does not lead to beliefs that work. And Mellor also claims that KK produces the problem of induction because it introduces the regress.

    We can acquire a habit of inductive reasoning because it works. It then continues to work. Even if it evolves randomly, organisms that have it will be immensely more successful than those without. And the position would be so much the worse for those that draw counterinductive conclusions. So without KK, I can use induction because it works and I do not need the first K, and I cannot have it – I do not need to know the principle of induction to use inductive reasoning successfully and therefore I can in fact inductively reason.

    3. Dancy

    Dancy considers a number of responses in the literature to the problem.

    3.1. Circularity not Vicious

    Black states that the problematic argument takes the following form:

    “Inductive reasoning has proved reliable in the past. Therefore inductive reasoning is (generally reasonable).”

    This is an example of inductive reasoning. The conclusion is needed to move from the premise to the conclusion. However – it is not needed as a premise, but as a rule of procedure. If it were included as a premise, the argument would clearly be problematically circular. Yet we do not adopt that approach. There is no premise in deductive syllogisms to the effect that syllogisms entail their conclusions: this is taken as read. We should also bear in mind that inductive arguments are not required to be deductive and so neither is an inductive argument for induction.

    And in addition, insertion of such a premise leads to a regress in the familiar way: the premise would need support if explicitly included.

    However, the problem with this argument is that it only preaches to the converted. There is no reason to accept the premise unless one already does accept it. This can be illustrated by an inversion of the form ‘induction has succeeded in the past but it may not in the future, therefore induction is not an appropriate form of reasoning’. This seems equally persuasive, especially when one notes that the conclusion is doubly supported by argument from the premise and also by the premise considered alone.

    3.2. Argument Analytic

    Dancy cites Edwards and Strawson as arguing that solely the meanings of the term evidence can justify induction: the “statement that observation does constitute evidence is true because of what we mean by ‘evidence’ ”. This seems weak for a number of reasons; Quine indeed does not accept the notion of analyticity at all.

    But it also seems to load to much on stipulation. It is somewhat similar to Mellor’s redefinition of ‘observation’ to include what we might alternatively call ‘unsuccessful observation’ as discussed above. We can allow Mellor his stipulation because it does not represent an attempt to change the world by fiat. However, while it is clear that a definition of ‘evidence’ can be allowed to only refer to ‘successful evidence’, that does nothing to change the availability in the real world of such evidence.

    It is certainly the case on this definition that if we have evidence, we have good grounds for believing the thesis supported by that evidence. But how would we know when we had evidence?

    There is a further argument due to Urmson which notes that we learn what is good evidence from approved specialists or those with more experience, but that we can later form different views that are totally at variance with those we have learnt. In fact, this is not just possible, it seems to frequently be the case. And simply posing the problem of induction as Hume did is an example. Thus it seems hard to allow that the notion of evidence is analytic.

    3.3. Coherentism

    Coherentism is one of three possible exits from Agrippa’s trilemma. The justification for a belief will normally be an appeal to another belief. There are three ways this process can develop: there may (i) be a final core of beliefs that do not have and do not require similar justification (foundationalism); there may (ii) be no end to the chain of beliefs (infinitism) or the best picture may be obtained by (iii) allowing that the chains can loop back into themselves (coherentism).

    Here the key idea is that the beliefs all cohere together and make each other more plausible. The extension to the problem of induction is simply to claim that use of a working principle of induction is justified because it leads to a more coherent set of beliefs. This approach of course relies on the truth of coherentism for its effectiveness.

    Hume’s problem of induction stems from his views on causation: there is no necessary connection between events. We just come to expect them by constant observation. Realists about the future who hold that we can have knowledge about future events can deny this and insist that there must be a necessary connection. We could not know that the brick will break the window when it is flying towards it and is an inch away unless there is in fact a necessary connection between the two events of the brick hitting the window and the window breaking.

    Again, this line of reasoning may succeed in answering the problem of induction, but again it requires coherentism. It also requires realism about the future when anti-realism is appealing in that context; the most natural statement in relation to statements about the future is that there are no facts of the matter yet and so no truth values so far for such statements.

    If anti-realism about the future is true, then there is a reduction in the scope of the problem of induction because there is no knowledge about the future in any case. But some variants might remain. If I have myself observed 90% of the swans in the world and found them all to be white, I may well use an inductive approach to decide what my Australian colleague, who has observed the remaining 10% but not yet reported his results, has already found.

    4. Reichenbach

    Reichenbach has a further pragmatic approach to the problem. His paper is somewhat redolent of Valberg on scepticism, in that it notes the contrast between some problematic reasoning (purporting to show that there is no justification for induction) and our everyday behaviour of use of induction. This contrast is just as relevant to those familiar with the reasoning as to those not.

    Since Reichenbach has a probabilistic view of causation, whereby causes make their effects more probable as opposed to necessitating them, he states the target formulation of the aim of induction as being to “find series of events whose frequency of occurrence converges towards a limit”. Note that the limit is not supposed to be 1.0. The idea is that if a fair coin is thrown, and there is a 50% chance of heads, the percentage difference between the proportion of heads will approach 50% as more throws are made. This is good enough to defeat the problem for Reichenbach: with sufficient observations to confirm that the coin is landing on heads 50% of the time, I can make that statement abut future throws.

    It is admitted that the world must be predictable for this to be the case. If the world is destroyed, there will be no truth-values in relation to coins thereafter. Equally, if the laws of physics may fluctuate dramatically, we would not be able to observe the limits of series. But Reichenbach insists that while we cannot know if there can be success, if any method will permit the determination of the limit of the series, then induction will be one such method. An analogy is given of a doctor who justifies an operation without knowing whether it will work on the basis that if anything will work, then it is an operation.

    This seems plausible because if the world is predictable, induction is fine – the argument so far has been that we cannot know non-inductively that the world is predictable.

    So under these circumstances, induction is the best bet because it minimises risk. The risk that the world is unpredictable cannot be addressed. But using induction at least minimises what might be termed ‘estimation risk’. If I see a coin landing on heads approximately 50% of the time, there are two ways I can be in error in using that as my estimate of future results. The first way is that I depart from induction and choose 75% as my estimate. The second way is that I choose 50% but the world is not predictable.

    This is the only justification of induction that can be given. Hume’s objections succeed in showing that no full proof is available as a justification. The only remaining approach is to do what works, and Reichenbach has shown that nothing works better than induction.

    D Hume, An Enquiry Concerning Human Understanding, eds L A Selby-Bigge, P H Nidditch, Clarendon Press, 1975, s4.
    D H Mellor, Matters of Metaphysics, Cambridge University Press, 1991, ch. 15
    op. cit. p. 263
    J Dancy, Introduction to Contemporary Epistemology, Blackwell Publishing, 1985, ch.13 (“ICE”)
    Cited by Dancy as M Black, Problems of Analysis, Routledge, 1954
    Dancy’s formulation of Black’s position.
    Cited by Dancy as P Edwards, Russell’s Doubts About Induction, Mind 68
    Cited by Dancy as P Strawson, Introduction to Logical Theory, Methuen, 1952
    ICE, p. 203
    Cited by Dancy as J Urmson, Some Questions Concerning Validity, Revue Internationale de Philosophie, 25
    H Reichenbach, The Pragmatic Justification of Induction, edited selection in S Bernecker & F Drestske (eds), Knowledge: readings in contemporary epistemology, Oxford University Press, 2000, (“BD”)
    J Valberg, The puzzle of experience, in T Crane (ed), The contents of experience, Cambridge University Press, 1992

    Does the observation that knowledge ascriptions are context-sensitive provide the basis for a satisfactory response to scepticism?


    1. Introduction

    There are several prior questions here, including the following. Is it the case i). that knowledge ascriptions are in fact context sensitive, ii). that contextualism is therefore true and iii). that a satisfactory response to skepticism is thereby derived? This also assumes that a response to skepticism is needed; it is also open to hold simply that if a theory is true, but it appears to open the door to skepticism, that this is just the way things are. I will begin with the first two questions before considering the last one.

    2. The Case for Contextualism

    2.1. DeRose

    DeRose begins his most recent defense of contextualism by noting the support it derives from ordinary language. The main thesis of contextualism is that standards for knowledge are sensitive to context, and DeRose contends that we can observe these shifting standards in the way people commonly describe the epistemic status of themselves and others. He believes that whether we ascribe knowledge to ourselves and others can change because the relevant standards or the strength of the criteria for knowledge can change.

    It is not sufficient to make this case by noting that the knowledge status of subjects changes. This change clearly occurs when the relevant circumstances including perceptual orientation of the subject change or when in fact the situation alters: these changes can give the subject new knowledge. If we are assessing whether subject S knows that there is a sheep in the meadow, the presence of a rock occluding the sheep for S will lead us to say no; if S moves such that this is no longer the case, we will be more likely to agree that S now knows there is a sheep present. This type of case is one in which knowledge changes because truth-relevant factors change; contextualism holds that knowledge changes when non-truth relevant factors change.

    DeRose’s canonical example of how this might work is known as the Bank Case , but it also might be termed a ‘stakes-change’ case. There are two scenarios, LOW and HIGH. These denote two situations where a subject has the same information relating to a question, but different levels of interest in the answer. We are two assess in both cases whether S has knowledge of the answer.

    In LOW, S and his wife are outside the bank on a Friday evening wishing to deposit their paycheques, but note there are large queues. S was present at the bank in the last couple of weeks on a Saturday morning and it was open. S therefore says “I know the bank is open on Saturday morning” and suggests they return then.

    In HIGH, the situation is the same as above with the exception that the couple have written a large check and if they do not deposit their cheques before Monday (we are to assume that the bank is closed on Sunday) there will be severe consequences. S will probably therefore say on Friday words to the effect of “I don’t know the bank is open on Saturday morning” and proposes to go and check. This DeRose claims means that S has altered his epistemic status in relation to the proposition even though no truth-relevant factors have changed. S still remembers seeing that the bank was open two weeks previously. What has changed is the risk assessment S makes of the consequences of error; conceivably the bank has changed its opening hours recently or even was only open on a Saturday for special reasons. It will be immediately apparent that one type of objection to this argument will claim that was has changed in HIGH is not the relevant epistemic standards, but warranted assertibility. It has not become appropriate to check the hours because the knowledge status of S has changed.

    2.2. Lewis

    David Lewis argues for a different variety of contextualism in which knowledge is defined as follows: “Subject S knows proposition P iff P holds in every possibility left uneliminated by S’s evidence”. This is modified with the caveat that ‘every possibility’ excludes those possibilities that S is properly ignoring. We do not claim that someone fails to know that it is daylight because they have failed to check whether someone has placed a set of lights outside their bedroom window overnight.

    Assessing which possibilities may be properly ignored in this way is central to Lewis’s account. He proposes a set of rules to do this, including rules requiring that the actual situation and the one believed to obtain by the subject cannot be ignored; additionally any possibility being attended to is not properly ignored because it is not ignored at all – setting aside whether it should be, it needs to be considered because it involves the key concept of what is salient for S. These rules are context-sensitive and therefore represent a contextualist approach because different ranges of possibilities will become relevant in different contexts.

    Which context is the relevant one is important. If A and B are discussing S, then there are two possible contextual sources of variation in knowledge ascription of S: the context of S and the context of A and B.

    Lewis’s primary motivation in proposing this line is to defeat various skeptical lines including Gettier problems, lottery cases and skepticism in general. He views his claimed success in doing this as the primary commendation of his method. Since discussing this requires consideration of the skeptical angles, I will defer it to the final section on whether contextualism, if true, can defeat skeptical arguments.

    3. Objections to Contextualism

    3.1. Knowledge Destruction by Attention and Remote Conversations

    The most significant type of problem with contextualism for many observers is apparently due to what might be termed ‘friendly fire’ from Lewis. DeRose discusses whether the salience line or attention can destroy knowledge, in that the more closely we consider a proposition, the more likely we are to cease to properly ignore a defeating alternative. This seems highly implausible; for one thing it would mean that the most careless and inattentive observers are the most knowledgeable. Yet Lewis seems to leave the door open to this: “Maybe epistemology is the culprit [that] robs us of our knowledge […] when we look hard at our knowledge, it goes away”.

    There is a closely related objection that considers a scenario in which A and B are discussing whether S knows that P. The context changes for A and B in a way which means that they become much more epistemically demanding for S in relation to P. It seems extremely unappealing to now assert that S has ceased to know P, because S may have no knowledge of the conversation, and there may in fact be many such conversations taking place about S with wildly variant epistemic standards and in many distant locations.

    DeRose may not be being entirely fair to Lewis here in that Lewis explains later he has been using some ellipsis for simplification; Lewis may wish to run an as if line here. However, DeRose avoids these problems by the incisive expedient of restricting the change in the epistemic status of S to whether S counts as knowing. This subtle but far-reaching change solves the A & B problem because it is entirely possible that different observers will have different views on whether S knows P.

    It also solves the knowledge destruction by attention problem by denying it. In the Bank Case, one view would be that what has happened is not S previously knew P, where P is the proposition that the bank is open on Saturday mornings, and has now ceased to know it because S has now considered it more closely. DeRose can simply claim that in fact contextualism should hold that there are varying standards for knowledge in LOW and HIGH. S has knowledge sufficient for LOW in both scenarios and knowledge insufficient for HIGH in both scenarios: no knowledge has been destroyed. This response succeeds, but we should note how it restricts the theory, and also that the consideration of Lewis as the major proponent of contextualism requires modulation.

    3.2. Why Privilege Ordinary Subjects?

    DeRose clearly attached great importance to what people say. While some of his phraseology is strained, he can be allowed to be at least in the general vicinity of the way people talk. Yet why should we pay attention to this? We know that people are mistaken about an enormous variety of things on frequent occasions, and also that language is an evolving tool of imprecise nature and fundamentally pragmatic value. We say what works. Often what works well enough is shorter than a full description that would be tedious and unnecessary: “I knew it was daylight, provided no-one had set-up a lighting rig outside my bedroom” would needlessly eliminate one of an infinite number of irrelevant possibilities.

    This weakens the idea that studying language can lead to epistemological insight because there may not be much there. DeRose will respond to this by saying that the structures of language reflect deeper structures based on knowledge, and the evolution of language is indeed a survival of the fittest terminology that can only drive increased accuracy. However, this seems questionable particularly when seen in light of the objection considered in the next section, where DeRose is content to accept limited speaker competence.

    3.3. Semantic Blindness

    Some words, termed ‘core indexicals’, are very obviously contextual in behavior. They include “I”, “here” and “now”. The proposition “It is raining now” is false as I write; it may well be true for the reader. “Tall” exhibits similar behavior; a man may be tall on a tube train and not tall on a basketball pitch. Contextualism seeks to place “knows” in this category while its opponents, adherents of invariantism, deny this.

    DeRose admits that since everyone agrees that “now” behaves contextually, but not everyone agrees that “knows” does so, some people must be insensitive to the true behavior of “knows” if contextualism is true. He attempts to defuse this by saying that invariantism has the same problem, because there are also some contextualists who suffer from semantic blindness in relation to the behavior of “knows” if invariantism is true: they falsely believe it reflects varying epistemic standards. This seems like a slightly over-clever maneuver and in any case inconsistent with the previous appeal to speaker competence.

    4. How Does Contextualism Help With Skeptical Arguments?

    Certainly all of the leading contextualists take themselves to be engaged in attacking skeptical arguments. DeRose bases his approach on a post-Nozick analysis, while Cohen attacks elements of Lewis’s line while supporting the overall approach.

    4.1. DeRose

    DeRose outlines an argument from ignorance that derives from Putnam’s Brain-in-a-Vat (“BIV”) scenario. This involves a modernized version of Descarte’s skeptical evil demon argument in which the subject is actually an envatted brain being fed with experiences identical to the ones that the subject apparently has in the real world. The argument runs as follows.

    I). I do not know that not-H
    II). If I, then I do not know that O
    III). I do not know that O

    H is a skeptical hypothesis, such as “I am not a BIV”, and O is an ordinary claim such as “I have hands”. Thus if knowledge is closed under known logical entailment, then I can only know that I have hands if I also know the heavyweight implication that I am not a BIV.

    Nozick’s response is to attack the skeptical line by denying closure. DeRose wishes to retain Nozick’s Subjunctive Conditional Analysis (“SCA”) of knowledge, but also retain closure. He notes that the mention of the BIV hypothesis in the skeptical argument means that it has become salient, is being attended to and therefore by Lewis’s criteria, may no longer be properly ignored. The power of the argument then derives from the fact that actually, we cannot be 100.0% certain that BIV is false.

    One advantage of SCA is that it correctly denies knowledge in this case, as DeRose points out. This is because the belief not-BIV would still be maintained even were BIV the case. In using SCA, Nozick will consider close and remote possible worlds in order to examine the counterfactuals. DeRose rightly notes that the selection of exactly which possible worlds constitute relevant alternatives is both central to SCA and potentially highly contextual.

    DeRose will then contend that his modified Nozickean scheme retains closure, an intuitively plausible principle, and also avoids holding the abominable conjunction: ‘I know that I have hands and I do not know not-BIV’. DeRose does this by introducing comparative conditions, such as ‘tall’, and in the way previously mentioned. He thereby supports (II) by observing that even if we do not know whether A is tall or B is, if A is taller than B, we can assert that if B is tall then A is tall, in all contexts. Since contextualism holds that ‘knows’ behaves in the same way, this allows DeRose to retain the advantages of Nozick’s account without the claimed drawbacks.

    4.2. Cohen

    Cohen does not support Lewis’s attempt to solve all three of skepticism, the Lottery problem and the Gettier cases via his brand of contextualism. Kyburg’s Lottery problem relates how we are reluctant to say we ever know a particular lottery ticket will not win even though the number of tickets can be arbitrarily chosen; it can be so immense that the probability of it winning is less than the probability of the radio announcer reading out the wrong numbers – yet we still do not accept we know it is a losing ticket because there is no relevant difference between all the tickets and one of them will win. By Lewis’s rules of actuality and resemblance, that possibility may not be properly ignored.

    Lewis also requires resemblances to be salient. Cohen makes the crucial inquiry of to whom the salience is relevant: the speaker ascribing knowledge to S or to S? And Cohen believes that this can avoid some skeptical issues with Lewis’s approach: Lewis should use the salience qualification to exclude the extreme skeptical possibilities. BIV cannot become salient because it is does not sufficiently resemble reality. It will be apparent that this is another benefit of the flexibility Nozick has built in to his account to allow for discussion as to which are the relevant possible worlds to consider in examining counter-factuals.

    K DeRose, The Case for Contextualism, Oxford University Press, 2009
    D Lewis, Elusive Knowledge, Australasian Journal of Philosophy, Vol. 74, No. 4; December 1996
    K DeRose, Solving the Skeptical Problem, The Philosophical Review, Vol. 104, No. 1 (Jan., 1995), pp. 1-52
    R Nozick, Philosophical Explanations, Harvard University Press, 1981
    S Cohen, Contextualist solutions to epistemological problems: Skepticism, Gettier, and the Lottery, Australasian Journal of Philosophy, 76: 2, 289 — 306

    Assess The View That The Primary Objects Of Perceptual Awareness Are Sense Data


    1. Introduction

    There are two pre-theoretic claims made by ordinary people who have not studied philosophy; absent that event, most people tend to be direct realists. The two claims are as follows.

    (A): The direct objects of perception are typically mind-independent external objects.

    (B): Perception involves a direct relationship to its objects.

    Few philosophers defend direct realism. So they will deny one of the claims. Claim (B) is denied by intentional theories. Claim (A) is denied by sense data theories.

    This essay will outline the arguments in general for sense data or equivalently against (A), and then consider in detail the related positions of Valberg and Snowdon.

    2. General Arguments For Sense Data

    2.1. Argument From Commonality of Stimuli

    Many observers deny claim (A) without denying the sub-claim that mind-independent external objects exist. There seem to be commonalities in our perceptions of the same object at different times and for different observers. While we cannot rule out possibilities such as inverted spectra for different observers, we can observe that everyone leaves a room by the door that therefore appears to be perceived as having the same location for all observers.

    The inverted spectrum possibility does however raise the prospect of a mismatch between what different observers perceive in detail: I may see an object as red with an experience that would be described as green by another observer. This would not be detectable in behavior because we would both have acculturated.

    If two people can perceive the same object differently, then they must directly perceive sense data to allow for the difference to exist. This may be objected to in a transcendentally idealistic vein by claiming that in fact our sensory modalities create much of what an object appears to be is created by the observer in any case. However there would still be scope for different observers to ‘create’ different objects and this difference must be accommodated somewhere.

    2.2. Argument From Illusion/Hallucination

    It is possible for people to perceive objects incorrectly to have properties they do not have or indeed to perceive objects that are in fact not there at all. Examples of the former would include looking at a white wall under a red light that is not itself seen. Subjects may incorrectly believe that the wall is red. Examples of the latter include afterimages that are caused by looking at a bright light source. These persist after the subject is no longer looking at the source and thus the perceived object is not related to a currently existing physical object at that location.

    In both of these cases, the information that the perception is false – i.e. does not relate to an actual physical object present at that location at that time with those properties perceived – will typically not be available to the subject purely through perceptual channels. They may be able to reason from prior experience of afterimages and the unlikelihood of a reddish circular diaphanous object appearing soon after accidentally viewing the sun to the truth of the matter. But perceptually all that will be available is the illusory percepts. It is therefore held that there will be no relevant difference in the perceiver in the case of a veridical perception of an external object and a hallucinatory perception of a non-present external object.

    Subjects must have internal representations of their percepts in the case of non-veridical perceptions because there is no external object to allow for the supply of perceptual data from outside. Since there is no difference accessible to the subject in veridical cases and illusory ones, these internal representations – or sense data – must also operate in normal cases and in fact all cases of perception. Direct realists and any others who wish to retain claim (A) must accept that different types of situation are occurring in veridical and hallucinatory perception; this is perhaps unpalatable and I would not endorse it but it is certainly not ruled out by the absence of differential phenomenology.

    2.3. Neuroscience

    As this experimental field develops, few things are clearer than that the brain is immensely complex and has an extremely large number of processes; visual processing drives a major part of this complexity. This is taken to be an argument against claim (A) in that these manifold processes must be having significant effects on the raw input – this is in some ways another transcendental idealism line. Dancy dismisses this by asking in what way these processes are intermediaries between the perceiver and the object. However his main argument for this is lack of relevant phenomenology. This seems inadequate because I also have no phenomenology in respect of photons as such travelling to me from distant stars and those must be intermediaries. In sum, it seems improbable that immense amounts of processing in the primary visual cortex V1, containing 140m neurons though only one of five visual areas, leaves the input untouched.

    2.4. Time Lag Argument

    The speed of light is finite and the light from distant objects may take appreciable time to arrive at the retina of a perceiver. In the case of very distant objects such as stars, this time lag may be a thousand years. The star itself may have ceased to exist five hundred years previously to the light from it being perceived. Thus, claim (A) must be false because no external object corresponding to the perception exists at the time of the perception.

    This argument is then extended to all objects of perception by observing that given a finite speed of light, there will always be some lag for all objects at a non-zero displacement to the perceiver.

    This argument seems weak because it may be objected that claim (A) does not mention time lag effects. There cannot now be a direct relationship with an object that is no longer present; but there can be one with an object that was present when it emitted the light. Or perhaps the direct relationship is with the light that is in fact now present. Though the counter to this counter is to note that claim (A) was not supposed to be arguing for a direct relationship to light but to external objects.

    3. Valberg

    Valberg’s paper falls into two parts; he discusses an ‘antinomy’ between reasoning about visual experience and the relevant phenomenology. The reasoning is essentially that discussed above in favor of sense data while the opposition is that if there are in fact sense data, they must be transparent because we do not experience them: all we experience is the world. This line is somewhat redolent of Hume’s discussion of finding skeptical arguments convincing until he returns to company and backgammon; and Valberg’s conclusion has a Wittgensteinian air: ordinary life is the cure for philosophy.

    3.1. Arguments For Sense Data

    Valberg’s main line involves defining ‘demonstrative reference’, by which he means the ability to speak of that book which is an object of his experience. He deliberately leaves open the ambiguity initially as to whether that book as an object of experiences is external or internal because this is precisely the point at issue. Whichever way that question is resolved, it still makes sense to talk in this way.

    Valberg then runs a detailed version of the Argument From Hallucination, noting that it is logically possible for an external object to be eliminated and yet the brain activity of the perceiver remain unaltered. Therefore “it would in some sense be true that ‘how things are in my experience would remain the same’ ”. Note that Valberg continues to leave open the key question: he wishes to restrict ‘experience’ to the brain activity. If experience of the book extended to the external object, he would have begged the question.

    The final stage of what Valberg terms the ‘problematic reasoning’ uses the demonstrative reference previously introduced. He now uses the term this to refer to an object present to him in his experience. He is “focused on whatever it is that is present in his experience while I am looking at the book”. He notes that it is possible for him to hold his attention focused in this way and yet also possible that the book was eliminated say half way through a five second period without his experience changing. Despite the unchanging experience, there has been a significant rupture in the world with a book popping out of existence. So this object is not the book in the external world and claim (A) is false. While this argument seems strong, it is not clear what Valberg has added to the canonical formulations beyond a certain time slicing.

    3.2. Openness To Experience

    The second half of the antinomy results from the conflict between the problematic reasoning and the fact that in experience, there is only one object present. The book is this object and it is on the table and not in the mind. So indirectly, argument suggests that this is sense data while, directly, being open to our experience suggests the opposite.

    Valberg then takes a phenomenological/existentialist line. Sartre’s concept of bad faith is mentioned; this is to refer to the fact that we are not really surprised when we see a book in the world as an external object. This is because while we in some way know or accept the problematic reasoning, we do not or are unable to follow such beliefs: our dispositions to behave will inevitably be based on the idea that the book is out there to be read and handled. But the possibility of bad faith arises only for people who have considered the idea of sense data because only those persons can lie to themselves. Everyone else is simply engaged with the world. This talk of engagement and handling naturally sets the scene for the introduction of Heidegger, who is cited paradoxically referring to the need to “first leap onto the soil on which we really stand”.

    The key point is that we have to ask the question as to what mechanism will allow us to adjudicate between competing frameworks for judgement. There seems to be no actual arena in which the two halves meet; worse, both are supreme in their own spheres. Surely we cannot use reasoning to judge whether the problematic reasoning is correct: on the basis of reason it surely is because experience does not enter the arena. However, if we care about how it seems to us, and more, importantly how it appears inevitably and unchangeably to appear to us, we obtain the opposite result. Can we on the other hand use experience to privilege experience over reasoning? Not without solving this particular version of a problem of induction. Valberg concludes on the rather aporetic note that he has failed to solve the conflict and also does not believe it can be dismissed as illegitimate.

    4. Snowdon

    Snowdon wishes to examine the term ‘direct perception’ which he abbreviates by considering a subject who d-perceives an object. He introduces two constraints on his theory. Firstly, it should account for the fact that everyone pre-theoretically supports claim (A). Secondly, since the denial of claim (A) amounts to a claim that there is no direct relationship to external objects, the theory must make this possible. So there must be sufficient conceptual space to allow for the truth of the relationship claim because otherwise it has effectively been stipulated as false rather than investigated. So x d-perceives y should be an extensional two-place relation and the question is whether x can be an observer and y an external object.

    Snowdon first considers epistemological interpretations of d-perception, citing Russell’s claim that the table must be an inference from what is immediately known. This cannot mean that we can see different things when we use inference than otherwise. The difference is that I can know immediately that something is green but I must then additionally infer that it is an apple.

    Snowdon then dismisses these epistemological interpretations on two bases. First, they fail to satisfy the second constraint listed above in that they produce a relationship between the perceiver and some facts and not the perceiver and some objects. Second, it produces an intensional context because the question (X) ‘do I d-perceive that thing?’ has no unique answer; the answer will change depending on what other facts and relationships the observer commands. An intensional context is an unhelpful element in a theory of d-perception because these related but separate facts will alter the truth conditions of the question (X).

    The alternative non-epistemological interpretation of d-perceives introduced by Snowdon relies on a similar demonstrative concept to the one discussed by Valberg: Snowdon claims that x d-perceives y if the relationship between x and y is such that x could make the true demonstrative judgment that ‘that is y’. Sense data theories will then go on to deny this via claim (A) that holds that y can only be filled by internal objects.

    This rather subtly fulfills the first constraint because it is effective whether claim (A) is correct or false. If it is false, people are making correct judgments about sense data; otherwise they are making correct judgements about external objects. It also fulfills the second constraint because it is a two-place extensional relation.

    The objection that this would deny perception to non-cognitively adept entities such as non-human animals is met by pointing out that the d-perception description merely describes the subject-object relation that would allow for true demonstrative thoughts when sufficient cognitive ability existed.

    Snowdon’s picture has up to this point deferred the question on claim (A) and is consistent with its falsity and its truth. He now considers Hume’s version of the Argument From Illusion, which relates to a table apparently diminishing as we move. Clearly that table has properties not possessed by any mind-independent table and so they are not identical. Snowdon also covers the time lag argument by holding that the finite speed of light means it is possible for us to demonstratively think about that star even though it may no longer exist. The weight of his position is predominantly for claim (A).

    These arguments are outlined in Dancy, Introduction to Contemporary Epistemology, Blackwell Publishing, p. 152
    G Leuba, R Kraftsik, Changes in volume, surface estimate, three-dimensional shape and total number of neurons of the human primary visual cortex from midgestation until old age, Anat Embryol (1994) 190:351-366
    J Valberg, The puzzle of experience, in T Crane (ed), The contents of experience, Cambridge University Press, 1992
    Ibid, p. 42, Valberg refers to M Heidegger, What is Called Thinking, Harper and Row, 1968, p. 41
    P Snowdon, How to interpret ‘direct perception’, in T Crane (ed), The contents of experience, Cambridge University Press, 1992

    Critically Evaluate The Thesis That Knowledge Is Truth-tracking

    1. Nozick’s Analysis of Knowledge

    1.1. Introduction

    Nozick is responding to Gettier’s claim that the traditional tripartite definition of knowledge as justified true belief is inadequate. Nozick’s analysis is specified by the following four conditions, which together are necessary and sufficient for knowledge:

    1. p
    2. Bap
    3. ¬ (1) → ¬ (2)
    4. (1) → (2).

    The symbol → is non-standard: Nozick uses it for his relation of subjunctive conditionality. A → B means that if A were the case, then B would also B the case. This differs from logical implication ⊃. If it is true that A ⊃ B, then in all possible worlds in which A is true, so is B. Nozick uses A → B to mean the much more restricted case in which in the closest group of possible worlds in which A is the case, so is B. We are also using the following symbols: p is a proposition, a is a subject, B is the relation of belief so that Bap means that a believes p; ¬ is negation and → is Nozick’s subjunctive conditional.

    Dancy gives an illustration for which he cites Lewis of this crucial distinction. Lewis considers the conditional ‘if kangaroos had no tails, they would topple over’. This is a good illustration of A → B and not of A ⊃ B. In some possible worlds, the Australian tourist board gives the kangaroos crutches. This group of possible worlds is certainly more remote than the nearest possible world in which kangaroos have no tails and are unstable. So A → B is true but A ⊃ B is false because A does not entail B.

    One of the terms for this analysis is ‘truth-tracking’ because the subject’s belief is co-variant with the truth of p; if it were the case that p then the subject would believe it and if it were not the case that p then a would not believe it. It has also been known as a counter-factual analysis because of the way in which it discusses near possible worlds distinct to the actual world in order to assess knowledge claims in the actual world.

    1.2. Motivation

    Nozick introduces his two new conditions (3) and (4) in order to handle cases which had not been soluble on the previous bases. Gettier cases involve erroneously scoped referencing in which the subject appears to have a justification for believing p and p is true and yet the situations appear to fall short of knowledge. For example: “Two other people are in my office and I am justified on the basis of much evidence in believing the first owns a Ford car; though he (now) does not, the second person (a stranger to me) owns one. I believe truly and justifiably that someone (or other) in my office owns a Ford car, but I do not know someone does.” Condition (3) eliminates this type of case as an instance of knowledge, which is a point in favor of Nozick’s analysis.

    Nozick’s introduction of condition (4) occurs in the context of a skeptical scenario termed ‘Brain in a Vat’ (“BIV”) by Putnam. The subject is in fact a disembodied brain being stimulated by electrochemical means to have experiences; these being in the base case scenario all of the same experiences as in the current world. This skeptical hypothesis will produce important implications for Nozick’s analysis, to be discussed in the next section. The power of the hypothesis lies in the fact that while it is doxically identical to the actual world, almost everything believed in it is false.

    As Nozick points out, his subjunctive analysis is related to but more restricted than the prior causal analysis. Under BIV, the subject can be brought to believe that BIV is true by being given appropriate stimulation. There is a good causal link between the event and the belief formation, but this cannot count as knowledge because it is fortuitous. Nozick can exclude this type of counterexample because it fails condition (4): in the close world to that of the BIV subject where he is not given the relevant stimulation, he no longer believes BIV although it is still true.

    1.3. Skeptical Implications and Non-Closure

    There is a major ‘heavyweight implication’ of Nozick’s analysis that is highly counter-intuitive. It will be instructive to see how he resolves it. The following principle, termed the closure principle, seems valid:

    (CP): Kap & Ka(p -∃ q) → Kq.

    The symbol -∃ is used to signify entailment, and so CP may be expressed as ‘if it were the case both that a knows that p and a knows that p entails q, then it would be the case that a knows q’; K is the two-place relation of belief used similar to B for belief previously.

    This seems entirely plausible but Nozick uses BIV to argue that it is false. Let p be any everyday proposition such as ‘a is in London’. Let q be the negation of BIV. It is clear that p entails q, that a knows this entailment and that p is true and so under CP, a knows that BIV is false. Yet this is exactly the skeptical scenario that appears difficult to defeat.

    Nozick’s dramatic response to this is to deny CP: “Knowledge is not closed under known logical implication”. He explains this by deriving it from the non-closure of (3): “That you were born in a certain city entails that you were born on earth. Yet contemplating what (actually) would be the situation if you were not born in that city is very different from contemplating what situation would hold if you weren’t born on earth.”

    1.4. Methods

    Nozick introduces a further refinement to handle what he terms the grandmother case. A grandmother comes to know that her grandson is healthy by seeing him. Were he not however, she would nevertheless be told that he was, in order to spare her distress. Nozick wishes to preserve this as a case of knowledge even though it fails condition (3).

    This he does by adding the requirement ‘via method M’ to (2), (3) and (4). For a case to represent knowledge, M must not change in the relevant possible counter-factual situations. This means that the grandmother has knowledge in all the possible worlds in which she learns her grandson is healthy by seeing him, and does not in the possible worlds in which she relies on inaccurate testimony. This appears to be the correct result.

    2. Objections to Nozick

    2.1. Forbes

    Forbes defends CP by putting pressure on Nozick’s line that the same method M must be used in (2), (3) and (4) in order to avoid incorrect knowledge ascriptions in the grandmother case. Forbes points out that M being reliable in the actual world where p is true does not entail that M is reliable in even the closest possible worlds where p is false.

    The example given is of a reliable computer that can also check its own status. The proposition p is that the computer is functioning normally. The question is whether a subject can acquire knowledge that p by asking the computer to report its own status. If p, then this method M is reliable. However, if not p, then method M is by hypothesis no longer reliable. Thus there is no way to hold M constant while varying the truth value of p in order to assess whether the belief of the subject is co-variant with p.

    Forbes allows that Nozick may have a response along lines similar to those used in an example that Nozick himself gives. This is of a vase in a box that is pressing a switch. The switch activates a holographic projector set to show a vase in the box. An observer passes all of (1) – (4) in respect of p, there is a vase in the box, and yet this is not a knowledge case. But Forbes holds that Nozick would then need to concede that the counter-factual analysis was inappropriate for all inferences and this would be arbitrary and severe for Nozick’s analysis. Perhaps Nozick here can instead adopt in some form Harman’s suggestion that all the lemmas be true.

    2.2. Wright

    Wright also attacks Nozick’s claim to have defeated the sceptical argument by introducing non-closure. He notes that using Nozick’s standard p and q (p = ‘I have a hand’; q = ¬ BIV) produces a problem for the ¬q scenario. Here, BIV is true and so p is false. We can assume that BIV is one of the relevant ¬p scenarios to be considered in assessing whether Kap. But if so, then subject a fails condition (3) because, even though p is false, Bap.

    So Wright argues that Nozick must assume that BIV is not one of the relevant ¬p scenarios. And he further uses Nozick’s own argumentation against him with the following line, in which (I) represents ‘had it not been the case that I have a hand, then it would still not have been the case that BIV’.

    (I): ¬p → q
    (II): ¬q → ¬p
    (III): ¬q → q

    (II) is simply the statement that in BIV, I do not have a hand and then the reductio (III) follows by modus ponens from (I) and (II). As Wright points out, this could be seen as a refutation of the skeptic, but that line is not open to Nozick who wishes to agree that BIV is logically possible.

    Wright allows Nozick the response of denying that transitivity holds for counter-factual conditionals. This would break the step to (III).

    2.3. Garrett

    Garrett defends Nozick against a purported counterexample given by Martin. Martin’s example considers a subject a placing a bet that pays if either of two horses wins. Subject a uses the unreliable method of finding out whether his horse won in the first race of simply cashing in his slip after the second race while avoiding any information about the first race. If his slip pays, he assumes that the first horse won whereas in fact it could have been the horse in the second race.

    Assume that the first horse did in fact win, and this is proposition p. The horse in the second race did not win. Condition (3) seems satisfied because ¬p → ¬Bap. Also, (4) seems satisfied. And yet this surely cannot be a case of knowledge because of the good fortune of a that the second horse did not win; a has failed to consider a relevant alternative.

    Nozick’s response will be that in fact the possible worlds in which the first horse loses and the second wins are close enough that they have to be included in the assessment of whether Kap, whereas some possible worlds do not, such as one in which the betting machine has malfunctioned and is paying all slips. And then it is precisely the failure of Kap to track p in those close worlds that means (3) is not satisfied and this is not a knowledge case.

    But Garrett has a refined version of this counterexample that he thinks is more dangerous to Nozick. Proposition q is that the father of person A is a philosopher; q is true. Proposition p is that the father of person B is a philosopher. Subject a uses the unreliable method M of forming Bap if a understands that q. It transpires unbeknownst to a that A and B are brothers, so in fact p. This fulfills conditions (1) – (4) but cannot be knowledge because it relied on the random unknown fact of A and B being brothers.

    2.4. Gordon’s Response to Garrett

    Gordon replies to Garrett’s objection by narrowing the scope of the problem of the father of A being a philosopher. Gordon notes that Nozick can appeal to his insistence that method M be held constant across the counter-factual scenarios. If method M means that a can legitimately infer facts about the father of A from knowing facts about the father of B and knowing that A and B are brothers, then M is reliable. It only becomes unreliable if extended to the general unrelated population. So can Nozick argue that this is in fact no longer M? For Garrett, the question becomes “why is it a requirement of knowledge that one have good grounds for thinking one’s method reliable?”

    Gordon holds that Nozick has in fact replaced the tripartite analysis of knowledge as justified true belief (“JTB”) with his four conditions. Nozick is not therefore committed to JTB, and “even if Garrett can show a case in which one can meet Nozick’s conditions while using an unreliable method, he won’t have arrived at a clear counterexample to Nozick”.

    2.5. Garrett’s Rejoinder to Gordon

    Garrett responds by insisting “it is no presupposition of my counterexamples that it is necessary for knowledge that one have good grounds for thinking one’s method reliable if it is reliable”. Garrett agrees that if his counterexample shows unjustified true beliefs that meet all of Nozick’s conditions, and if JTB is required for knowledge, then he has found cases where Nozick ascribes knowledge incorrectly. However Garrett further claims that his counterexamples are valid against Nozick whether or not JTB is required. This seems strange however.

    Garrett seeks to draw an analogy with the standard Gettier cases, saying that it is possible to explain why his father of A case is a counterexample to Nozick by showing the presence of unjustified true beliefs without insisting that justification is essential to knowledge. The idea seems to be that there is no entailment here. This seems true, but Garrett does not specify what alternate method he has to show that Nozick has falsely ascribed knowledge. Or alternatively Garrett may be thinking of a negative condition. Lack of justification is sufficient to disprove a knowledge claim, while the presence of justification is insufficient to prove a knowledge claim. This separation seems somewhat arbitrary though. In summary, Gordon’s defense of Nozick appears successful.


  • R Nozick, Philosophical Explanations, Harvard University Press, 1981, (“PE”), p. 167 et seq.
  • J Dancy, Introduction to Contemporary Epistemology, Blackwell Publishing, 1985, p. 42
  • G Forbes, Nozick On Skepticism, The Philosophical Quarterly, Vol. 34, No. 134 (Jan., 1984), pp. 43-52, Blackwell Publishing
  • C Wright, Keeping Track of Nozick, Analysis, Vol. 43, No. 3 (Jun., 1983), pp. 134-140
  • B Garrett, Nozick on Knowledge, Analysis, Vol. 43, No. 4 (Oct., 1983), pp. 181-184
  • R Martin, Tracking Nozick’s Skeptic: A Better Method, Analysis, (Jan., 1983), pp. 28-33
  • D Gordon, Knowledge, Reliable Methods, and Nozick, Analysis, Vol. 44, No. 1 (Jan., 1984), pp. 30-33
  • B Garrett, Nozick and Knowledge: A Rejoinder, Analysis, Vol. 44, No. 4 (Oct., 1984), pp. 194-196
  • Written 19/01/10

    A Comparison Of Nietzsche And Dennett In Relation To Error


    Dennett has recently modified his position in respect of whether error can ever be beneficial. His initial line had been that truth as a component of knowledge is always the primary epistemic goal. While not abandoning truth altogether, he now argues that there are many situations in which truth and usefulness are not coextensive. This argument features prominently in the writings of Nietzsche. In this paper I will examine the extent to which Nietzsche is precursor of Dennett in this respect.

    The central question that prima facie appears to require no consideration is whether we should seek the truth. It seems obvious that in our daily progress, anything other than an unswerving devotion to truth seeking would have the most severe and immediate consequences for all of our pragmatic aims. This seems to be just as much the case across the animal kingdom.

    McKay and Dennett (“M&D”) argue that truth seeking may not constitute the entirety of the goals of a well-adapted organism. This argument is based on an evolutionary perspective. If the most adaptive beliefs are always the true ones, then the belief-forming mechanisms that we have will be the ones that have found the truth most often. Nietzsche’s line is more appropriately characterized by the phrase ‘one goal among many’ rather than ‘a major goal with some exceptions’ which would be more appropriate for M&D. First I will discuss the latest line of M&D and then I will consider Nietzsche’s views while at the same time covering the parallels with M&D.

    1. The M&D Argument

    1.1. Design Feature Argument

    The central view of M&D is that if there are adaptive goals other than truth, then we should expect these also to figure in the relevant belief forming mechanisms. This means simply that if there are benefits to false belief under certain circumstances, then we should now be such that those circumstances will produce false belief.

    This may be for negative or positive reasons: I may wish to avoid some truths because they are damaging or otherwise unhelpful. Alternatively, if I benefit from believing some propositions falsely, because for example they assist me in forming a self-image that directly or indirectly enhances my reproductive success, then I ‘should’ so believe. The ‘should’ here is not normative; it merely indicates that if adaptive false belief mechanisms exist and are evolutionarily accessible to human cognition, then we will have them.

    M&D begin by dividing false belief into two categories. The first category simply relates to situations where the subject has incomplete or inaccurate data. This is unavoidable and not philosophically interesting. The focus of the paper is entirely on the second category: scenarios in which the subject could have formed a correct belief. These deviations might be termed ‘design features’.

    1.2. Biological ‘Design Faults’ Not Always Faults

    Transferring to the biological domain, potentially beneficial faults are illustrated in the context of error management theory. This relies on asymmetries between the adaptive costs of false positives and false negatives. Where the cost of error is much higher in one direction, evolution will favour estimation in the direction of the less costly error. Note that this is not to abandon truth as an objective; merely to acknowledge that where there is unavoidable error, it may be better to err on the side of caution.

    A familiar example of cost asymmetry from philosophy would be Pascal’s wager. He argues that the costs of error are very much larger in one direction (failure to believe when there is a deity) than the other (false belief when there is not).

    A biological example of error management theory and how this cost asymmetry could play out is as follows. If an animal is in conflict for resources with others, it will need to assess its relative ability to prevail by force amongst the likely competitors. If it overestimates its own strength, it is likely to suffer severe adverse consequences in combat. The opposite error means that it avoids some combats it could have won, and thus does not gain some resources that were in fact available to it, but this outcome is much less severe. Thus in this case, the belief that animal A could not overcome animal B is both false and adaptive for animal A.

    There is also an asymmetry with respect to ‘agent detection’; it is better to misidentify a rock as a bear than vice versa. So M&D have made out their case that there are many natural examples of cost asymmetries influencing systems away from a total adherence to truth.

    An explanation of the imperfect nature of evolution is needed, to allow M&D to claim that the results of lengthy and intensive selective pressure on humans have not eliminated all real and apparent flaws in truth mapping. This is found by noting that selection can become trapped in local minima in design space; each incremental adaptation must itself be adaptive and there is no long-term perspective allowing penalties to be paid now in order to reach an optimal solution later.

    1.3. Beneficial ‘Design Faults’ In The Context Of Beliefs About The Self

    M&D extend these ideas into self-deception, by considering whether there are circumstances in which inaccurate beliefs about the self could be beneficial. The well-known ‘better-than-average’ effect is cited, where most people hold that view of themselves across many parameters, despite the fact that it is impossible in the context of the population and extremely unlikely in individual cases. Examples include AIDS patients who lived longer if they had unrealistic expectations of likely remaining lifespan or further, complete ignored or denied their status. In addition, various forms of the placebo effect are well documented, even in relation to surgery.

    The important qualification is made that it is not to be expected that adaptive false beliefs be generated by a mechanism that is ‘designed’ to produce false beliefs, because such a mechanism could not itself be adaptive. Rather, adaptive false beliefs will be by-products of normally reliable systems operating out of their usual domain or fast heuristics evolved to deal with the many situations where a quick semi-accurate decision is better than a slow and more accurate one. The latter example represents an evolutionary mechanism that would produce ungrounded beliefs. To the extent these are harmless, they will not be selected out; even less so if they happen to be beneficial.

    Once a mechanism like this has been made plausible, a self-limiting device must be found in order to avoid predicting that humans would be fantasists convinced of their own abilities to leap tall buildings. M&D therefore observe that once the delusions of self-performance grow too distant from reality, they will become dangerous.

    1.4. Genetic Fallacy In Relation To The Eye

    There is an ironically false claim in the M&D paper that I believe makes an error of a type in which Nietzsche was most interested. M&D criticise Fodor for his objection that an understanding of evolution would not allow us to distinguish evolved features from accidental by-products. Fodor is committed to saying that it is not true to say that eyes are for seeing and bird wings are for flying, although it is true to say this of aeroplane wings.

    But Fodor is exactly right to say that the eye is not for seeing in the sense that the first step in its evolution, thought to be development of a light-sensitive area of skin, did not occur with the eventual aim of vision in mind. This is true a fortiori because there is no such mind, but additionally, no evolutionary mechanism exists to allow this. Each evolved step must pay its own way. The response of M&D fails for this reason; moreover their line is in conflict with their stated line elsewhere that false beliefs can arise as side effects only. That the eye is now used for seeing is irrelevant; Fodor and M&D are using the word for in different senses.

    This is an example of what Nietzsche called the genetic fallacy, most prominently considered in On the Genealogy of Morality . He means that there is no reason to believe that the original cause for the emergence of a particular biological or cultural feature must be the same as its current use, and in fact given the elapsed time, this is unlikely.

    2. Nietzsche’s Views And Their Similarities To M&D

    Origin Of Knowledge

    Nietzsche’s most clear statement of his overall position in this respect comes in an eponymous section: “throughout immense stretches of time the intellect produced nothing but errors; some of them proved to be useful and preservative of the species: he who fell in with them, or inherited them, waged the battle for himself and his offspring with better success.” Nietzsche does not put the word ‘knowledge’ in quotation marks; so he may be seen as accepting the non-standard view that ‘knowledge’ can be false. We can most easily comprehend him here to be referring to ‘knowledge’ as commonly understood; i.e. some of what people think of as true and as being part of knowledge is in fact false.

    It is important to note that Nietzsche identifies two mechanisms by which this could happen. One might fall into error culturally by picking up the habits of others. One might also inherit errors. This biological term could be understood culturally, but it also provides a clear link to the M&D claim that false belief mechanisms can be adaptive.

    Useful Blindness About Oneself

    Nietzsche is sympathetic to the view that the world of perception is an illusory flux hiding an unchangeable invisible interior; the Eleatics, Schopenhauer and Kant held similar views. In particular, Nietzsche claims that in order to avoid succumbing to the error of believing in fixed objects, the Eleatics needed to “deceive themselves concerning their own condition: they had to attribute to themselves impersonality and unchanging permanence, they had to mistake the nature of the philosophic individual, deny the force of the impulses in cognition, and conceive of reason generally as an entirely free and self-originating activity”.

    There is a Sartrean feel to this argument, which holds as he did that we pretend that our characters are fixed and that our choices are limited to as not to be overwhelmed by the ‘nausea’ resulting from the realisation of the fact that we have absolute freedom at every moment. There is nothing in reality that gives us a fixed identity or requires us to do what we have previously decided to do. There is also a very clear recognition by Nietzsche that a denial of the truth that reasoning has partisan ends is necessary to allow one to pursue it in the belief that it will produce impartial results.

    The existence of a self is a pre-requisite to the idea of self-deception; though of course there is a further Sartre/Freud paradox in the vicinity of the question as to who is deceiving whom in such circumstances. M&D’s related discussions extend beyond the delusional and yet healthier AIDS patients to those who gain from self-deception about themselves: college lecturers, students and drivers who think that they are better than average. They even note that people think of themselves as less prone to self-deception than others! There is perhaps an echo in Nietzsche of the various placebo errors when he writes of “a melancholy invalid, who, in order to forget his present condition, writes the history of his youth”.

    Alchemy As Prelude To Science

    Nietzsche notes the importance of beginning from falsely conceived projects in order to motivate more realistic approaches: “Prelude to Science. Do you believe then that the sciences would have arisen and grown up if the sorcerers, alchemists, astrologers and witches had not been their fore-runners[?]”. This means that the desire for power could have arisen before the means of satisfying it could be properly constructed and the failed attempts motivated the better ones and facilitated them by the nature of their falsity. M&D touch on Dawkins’ meme idea , whereby a natural selection mechanism for cultural items is posited. Those beliefs including fitness enhancing elements such as religions including punishment for non-belief would survive; alchemy and similar pre-sciences would fail via lack of predictive power.

    Nietzsche later discusses the role of hypotheses in science, which are of necessity not true at the time they are selected, the impossibility of a pre-suppositionless science, which must nevertheless be assumed possible and how the value of truth must be affirmed without warrant: “the question whether truth is necessary, must not merely be affirmed beforehand, but must be affirmed to such an extent that the principle, belief, or conviction finds expression, that ‘there is nothing more necessary than truth, and in comparison with it everything else has only secondary value.’ ”

    Necessary Error

    Nietzsche praises criticism and the illusion that we change our minds for impartial reasons: “something now appears to thee as an error which thou formerly lovedst as a truth, or as a probability: thou pushest it from thee and imaginest that thy reason has there gained a victory”. The biblical flavour of the terminology immediately suggests here that Nietzsche has religion in mind as a candidate for a beneficial false belief, though we should note that this may be a translation artefact: the Nauckhoff translation modernises this section. M&D discuss at length the various arguments that may be summarised as ‘no atheists in foxholes’; they also consider the idea that supernatural beliefs may be exaptations of theory of mind capabilities, themselves extremely adaptive.

    Monkeys And Error Asymmetry

    In the context of discussing how people wish to be prophets without understanding the concomitant difficulties, Nietzsche retails a parable concerning monkeys before a storm: “these animals then behave as if an enemy were approaching them, and prepare for defence, or flight: they generally hide themselves, they do not think of the bad weather as weather, but as an enemy whose hand they already feel”.

    While one should not make too much of the biological nature of this example, it does indicate that Nietzsche has a good understanding of how in the natural world, it may be better to behave as if. The parallel to M&D would be to their argument on error management theory and asymmetry when it is better to mistake a boulder for a bear than vice versa. The monkeys are better off by behaving as if the storm were a physical enemy approaching.

    R McKay, University of Zurich and D Dennett, Tufts University, The Evolution of Misbelief, Behavioral and Brain Sciences (in press), Cambridge University Press 2009
    F Nietzsche, On the Genealogy of Morality, Tr. M Clark & A Swensen, Hackett Publishing Co. Inc., 1998
    F Nietzsche, The Gay Science,, (“GS”) III, s110
    GS III, s110
    R Dawkins, The Selfish Gene: 30th Anniversary Edition, Oxford University Press 2006