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Saturday, 8 April 2017

A brief response to Dr Eugene Earnshaw

In a recent article in Philosophy Now, 'How I Solved Hume’s Problem and Why Nobody Will Believe Me', Dr Eugene Earnshaw of Seneca College claims, as evidenced by the title of his article, to have solved Hume's problem of induction. If true, this would be no small feat. However, Earnshaw has not solved Hume's problem of induction. In fact, Earnshaw fails to address the already extant literature responding to the purported solution.


1. Earnshaw's argument


I will assume that Earnshaw, contrary to his claims, sets out to justify only P: 'some inferences from the observed to the unobserved are justified'. This is strictly weaker than the claim that all inferences from the observed to the unobserved are justified, or even that inferences of a particular type are justified. If P is accepted, the skeptical thesis about induction--there are no grounds to make any inference from the observed to the unobserved--is false.

In order to justify P, Earnshaw first sets out the distinction between deductive and inductive arguments, and shows how with the introduction of a premise an inductive argument is transformed into a deductive argument; similarly, by the elimination of a premise, a deductive argument may be transformed into an inductive argument. Thus, so Earnshaw claims, 'one can deductively justify various types of inductive arguments'.

As an illustration, the following inductive argument,

P1. All observed X are Y.

C. The next observed X will be Y.

is transformed into a deductive argument with the introduction of P2: 'All X are Y'. While P2 is question-begging, modifying P2 and C will produce a deductively valid argument as follows: consider P2*: 'If it is an X it is probably Y' and C*: 'The next observed X will be probably Y'. By introducing the implicit premise P2*, C* is necessarily entailed. Furthermore, as Earnshaw notes, 'it is necessarily the case that if those premises are true, the conclusion [C] is probably true. Therefore we have justified inductions of that general form'.

Earnshaw's argument is a variation of statistical sampling arguments, a deductive argument Earnshaw attributes to D.C. Williams (1947) and David C. Stove (1986). Statistical sampling arguments rest on the sampling principle: 'when a simple is drawn randomly from a population, the probability that the sample is representative of the population is very high provided that the sample is "reasonably large"' (Indurkhya, 1990, 101). In fact, Williams considers this principle 'self-evident' (1947, 8).

Since the 'reasonably large' size of the sample drawn is not contingent on its relation to the total population, but merely on the 'largeness' of the sample size drawn, statistical inferences can be made from a sample considered relatively small compared to the total population. In fact, the total population can be of several factors larger than the sample.

With the sampling principle in hand, we reason as follows: if we have a representative sample of a population, an inductive inference based on the representative sample is probably true. The sampling principle makes it highly probable that a 'reasonably large' sample is representative of the population (Williams, 1947). Therefore, at least one inference from past events to future predictions is justified. Thus the negation of P, 'inferences from past events to future predictions are not justified' is false. In short, as Ernest Nagel (1947, 691) notes in his review of Williams' book, '... the argument is simply a restatement of Bernoulli's theorem and the statistical syllogism'. Williams (1947, 165), however, maintained 'the discovery of truth to be the natural and almost inevitable thing, and persistent error the merest residuum of coincidence and accident'.

Earnshaw concludes, 'More broadly, any valid deductive argument that has as its conclusion "it is probable that waddle-waddle is the case" justifies the corresponding inductive argument that argues from the same premises to the conclusion "waddle-waddle is the case"'. However, even assuming that Earnshaw has argued for the weaker position P, 'some inferences from the observed to the unobserved are justified', rather than argue that some inductive inferences of a particular type are justified, Earnshaw's argument is fundamentally flawed.

2. Goodman's new riddle of induction


Unfortunately for Earnshaw, rejoinders to Williams and Stove's statistical sampling arguments were made not long after the publication of Williams' The Ground of Induction (1947) and Stove's The Rationality of Induction (1986): the argument proves too much (cf. Nagel, 1947; Black, 1947; Will, 1948; Miller, 1988, 287; Griffin, 1988; Maher, 1996). Sentences that include disjunctive or ill-behaved predicates like 'grue' are equally justified as well-behaved predicates like 'green'. Thus 'it does not imply or make probable that most of the samples we select will match the population' (Nelson, 1948, 141).

Take for example the inductive inference, 'All observed emeralds have been grue, therefore the next observed emerald will be probably grue': it is identical in form to statistical sampling arguments that produce the inductive inference, 'All observed emeralds have been green, therefore the next observed emerald will be probably green'. Indurkhya (1990, 102) notes this fatal flaw, with an intuition pump bearing similarities to Goodman's initial formulation of his new riddle of induction (1946, 1983). I will reproduce the relevant section from Goodman's 1946 paper below:

'Suppose we had drawn a marble from a certain bowl on each of the ninety-nine days up to and including VE day, and each marble drawn was red. We would also expect that the marble drawn on the following day would also be red. ... Our evidence may be expressed by the conjunction "Ra * Ra₂ * ... * Ra₉₉," which well confirms the prediction "Ra₁₀₀." ... Let "S" be the predicate "is drawn by VE day and is red, or is drawn later and is non-red." The evidence of the same drawings above assumed by be expressed by the conjunction "Sa * Sa₂ * ... * Sa₉₉." By the theories of confirmation in question this well confirms the prediction "Sa₁₀₀"... It is clear that "S" and "R" can not both be projected here, for that would mean that we expect that a₁₀₀ will and will not be red' (Goodman, 1946, 383).

The problem is, as Indurkhya (1990), Miller (1988), Griffin (1988) and Goodman (1946, 1983) note, if the differences between the inductive inference that the next observed emerald is probably green and the inductive inference that the next observed emerald is probably grue hinges on the distribution of emeralds being random; yet the sample is not random if it is restricted to a given time span. It is always possible to introduce a disjunctive predicate like 'grue' that applies to objects observed within the given time span that is as equally supported as the predicate 'green'.

Furthermore, Goodman's observation can be generalised to different dimensions besides time, such as location (Indurkhya, 1990). For example, the inductive inference, 'All ravens observed within a space-time region are black, therefore ravens observed outside the space-time region k are probably black' is as justified as the inductive inference, 'all ravens observed within a space-time region k are black, therefore ravens observed outside the space-time region k are probably bright', where 'bright' is the disjunctive predicate, 'black observed within space-time region k and white outside space-time region k'.

As an illustration of the failure of the statistical sampling argument, consider Tappan Square in Oberlin, Ohio. If a resident of Oberlin or a student at Oberlin College were to count the squirrels in Tappan Square and record their colour, they would observe that a disproportionate number of squirrels in Tappan Square are white. This is due to a number of environmental factors, specifically that the Square is relatively isolated from surrounding forests, lack of predation and a large incidence of inbreeding. Were the number of squirrels 'reasonably large', a natural inference would be that the next observed squirrel outside Tappan Square would probably be white. However, this is not so.

Further absurdities follow from this form of reasoning, even if ill-behaved predicates are disallowed. Nagel (1947, 692) notes, 'Were his proof cogent, it would be reasonable to maintain the absence of other evidence that since a man of 65 has lived through about 24,000 revolutions of the earth around its axis, it is highly probable that he would not fail to be alive during every future revolution of the earth. To put it mildly, such consequences of Mr. Williams's thesis are not plausible, and hardly add persuasive force to his argument'.

Reviewers of The Ground of Induction conclude, '... the probability syllogism is highly misleading, since its form suggests that some significant claim can be made concerning the probability of the single case, but the interpretation of the conclusion has to be such that it does not exceed the information provided in the premises. Thus it has to be a compact statement which when expanded merely summarizes the information provided in the premises' (Mayberry, 1968, 211), to wit, the statistical sampling argument, if valid, is trivial; however, if the argument were nontrivial, 'The acceptance of inductive conclusions on the grounds presented herein, however, involves the acceptance of a way of interpreting and assessing probabilities which ... now seems, in spite of Williams' spirited contrary contentions, to be pretty thoroughly discredited' (Will, 1948, 99); 'the theory must be set aside as incoherent, if not positively self-contradictory' (Black, 1947, 143)

In sum, the sampling principle cannot be used to justify any inductive inference, for there must be further assumptions made about randomness and uniform distribution of the total population (Nagel, 1947). This would, however, be question-begging, since the distribution of the total population is unknown a priori.

3. Earnshaw, Stove and Williams' psychological explanation for the unpopularity of their arguments


Earnshaw does not address any of these rejoinders in his article for Philosophy Now. In fact, there is no mention of the extent of the relevant literature responding to statistical sampling arguments. Of course, Earnshaw's article is presumably written with tongue planted firmly in cheek, and for a popular audience, but since it is written for a popular audience, they will be unaware of the existing literature that finds fault with this form of argument.

Rather than engage with the literature on statistical sampling arguments, a substantial portion of Earnshaw's article is dedicated to a psychological explanation for why inductive sceptics do not accept Stove and Williams' arguments: 'That Hume was wrong must be almost the most obvious thing that anybody every said'. However, 'judging arguments on their logical merits', presumably, including judging of Earnshaw's argument, is 'not something that human reason is especially well suited to do'.

Earnshaw continues: 'you could show people just how wrong they were [in the natural sciences] by waving the facts in their faces. But that is not an option in philosophy: you have to wave logical arguments in their faces, which is only possible metaphorically. And being convinced by a metaphor (or a logical argument) requires a certain attitude of co-operation. People have to keep an open mind'. Earnshaw leaves it open to the reader to infer that philosophers that do not accept his argument are universally blind to the strength of his argument, uncoöperative and close-minded.

Earnshaw concludes, 'the intellectual community of philosophers is just not set up to solve intellectual problems'. The outcome for philosophy is grim: 'Maybe this means that the progress of philosophy can't just rely on logic; it must resort to rhetoric. The arguments have to be dressed up prettily, or the objectively confused must be socially shamed and pressured'.

3.1 Willaims and inductive sceptics


The established style of discourse in philosophy calls for avoidance of personal attacks whenever possible. Consider, however, if we were to follow Earnshaw's advice and abandon the established style. This is easily done by examining how (to Earnshaw) the 'objectively confused' inductive sceptics have been 'socially shamed and pressured' by Williams and Stove.

After the publication of Williams' book, he was silent on this matter until 1953: Williams claimed W.C. Kneale noted an issue with a different argument in his book, however 'no other logical fault has been charged against' his statistical sampling argument. In fact, 'Other reviewers and commentators, to be sure, were not won round by my argument, but their objections were on other than logical grounds. They complained, for example, that ... a predominance of chances such as is provided by the classical theory and the bagful of balls, is not really a rational incentive to believe not ever, or anyhow not when part of the bagful is in the future' (1953, 468). This is the extent of Williams' reply: other than Kneale's reply, all responses given were not made on 'logical grounds', and are summarily dismissed. Williams concludes (ibid. 475), 'I have found neither the patience nor the capacity to ascertain whatever complex and qualified law' governs disjunctive predicates. So much for Goodman's new riddle of induction. While there may be an appropriate response to Goodman's new riddle, dismissal alone is not sufficient.

An examination of some choice passages from Williams shows this attempt at shaming the inductive sceptic, rather than engage in addressing the arguments from the sceptic on their merits. They include Williams asserting, 'To dispute the rational validity of induction, however, is to deny that reason and good-will have a purchase on reality'; for the inductive sceptic 'the relativity of ethical judgment becomes irremediable'; 'the confidence in democracy is a confidence in the inductive method in political action'; 'Skepticism [of induction] need not lead directly to cruelty, but it can apologize for a cruel regime'; the sceptic of inductive inference 'has invited positive unreason to invade the citadel' (1947, 15-20). It would not be overstating Williams to conclude that he sincerely believes inductive sceptics legitimate moral and political evil, and he reaffirms this later in his career (1953, 468, ft.1).

Earnshaw approves of Williams' analysis that the reasons for not accepting statistical sampling argument: 'the reasons he [Williams] discusses are rhetorical and psychological'. Philosophical orthodoxy 'ignores Williams' and Stoves' refutation [sic] of Hume's argument', thus (presumably) they must be shamed until they reverse course.

3.2 Stove and inductive sceptics


David Stove's output on the evils of inductive scepticism is far more voluminous than Donald Williams', and his attempts at shaming the inductive sceptic are too many to mention. In fact, Stove made much of his career out of detailing the perceived failings of philosophers that accepted inductive scepticism or deductivism (to Stove they amount to the same thesis). He primarily directs his bile at four philosophers of science that advocate inductive scepticism: Sir Karl Popper, Imre Lakatos, Paul Feyerabend and Thomas Kuhn.

Metaphors and allusions are necessary to make Stove's worries urgent: without hyperbole, Stove believes inductive scepticism is a cold adder lurking in the grass. It is an insidious plot, a conspiracy to kill philosophy. These four philosophers--Popper, Lakatos, Feyerabend and Kuhn-- are the tip of the spear of inductive scepticism. The tip pierced the side of the philosophical body, and Stove believes the blade was first poisoned by David Hume.

(As an aside, Stove reconstructs Hume's argument for inductive scepticism with fifteen premises, many of which are implicit; John Watkins (1985, 260) calls this complex reconstruction otiose and reconstructs Hume's argument with three. So much for adhering to the principle of charity.)

In Stove's words, these four philosophers 'have no clothes at all, except such as are woven out of Hume's scepticism about induction' (1982, 55). In fact, Stove claims in Popper and After: Four Modern Irrationalists that the extent of their work is the repeated neutralisation of 'success words' by the use of quotation marks (cf. Stove, 1999, 1982, ch. 2). This neutralisation is conducted in an attempt at 'sabotage' (ibid.)

What follows from Stove is a collection of insults, interspersed with an attempt at textual psychoanalysis: Stove says Popper's writings are 'insufferable' (1999, 15) and his work 'nihilist or irrationalist' (ibid., 16). Popper was, so Stove claims, 'in the grip' of a delusion over the irrationalism within his work, and Popper intentionally deceived other philosophers through 'a certain abuse of language', viz. the use of quotation marks (ibid.).

Stove conjectures 'the main emotional source of Popper's philosophy was horror victorianorum', horror at 'Victorian writing about science' (1985, 73-4). Stove continues: horror victorianorum ... springs from a fundamental levity... his wish is nothing more than a young man's adolescent urge to escape the burden of adult knowledge and responsibilities' (ibid., 74). Popper is, in addition, a 'parlour-pink' irrationalist that displays 'levity or enfant-terriblisme' (1982, 98). To Stove, levity is a mortal sin.

Philosophers are not the only ones to suffer the charge of levity--Stove levees the accusation at theoretical physicists as well: 'these scientists are distinguished from all others by their degree of levity' (1985, 74). Evidence for this conclusion is that theoretical physicists borrowed the word 'quark' from the 'anti-Victorian' James Joyce (ibid). The writings of philosophers that reject inductive scepticism (that is, in Stove's eyes, identical to the rejection of deducticivism), on the other hand, 'are entirely free from levity' (1982, 99).

Stove's comments about Lakatos, Kuhn and Feyerabend, although not as prevalent as his comments about Popper, are equally choleric: while 'Popperism is almost exclusively a, or rather the, British disease in philosophy', Kuhn 'picked up from the surrounding air a sufficiently lethal dose of Popperite radiation' (1999, 12, emphasis removed). Stove believes the 'philosophy of Lakatos, Kuhn, and Feyerabend' should be regarded 'with hatred, ridicule, and contempt' (ibid., 15).

This is but a small part of David Stove's social shaming of inductive scepticism (or deductivisim). He does not, however, limit his wrath to these four philosophers of science and all theoretical physicists. In fact, he claims the broader philosophical community has been infected with deducticism: 'Inductive scepticism ... is, of course, so irrationalist a thesis that it could hardly be a starting-point of any argument advanced by a sane person' (1982, 61). Inductive scepticism is, however, not the true cause, but only a feature of an underlying sickness: 'recent irrationalist philosophy of science is therefore to be ascribed (insofar as it can be ascribed to intellectual causes at all) to acceptance of the thesis of deductivism' (ibid., 86).

Deductivism is the thesis that amounts to 'P is a reason to believe Q only if the argument from P to Q is valid, or there is a validator of it which is either a necessary truth or a proposition about the observed' (ibid., 84). Stove concludes, 'any empiricist who is also a deductivist... condemns himself, not just to irrationalism, but to unseriousness, about science' (ibid., 90). Ergo, any philosopher that insists that only deductive arguments are valid and remains sceptical whether probabilistic arguments for provide a reason to believe Q is, so Stove believes, incurably insane and frivolous.

The concluding paragraph of Popper and After is as follows: 'If it is true that any philosopher who was once a deductivist will carry at least some tincture of deductivism to his grave, then the prospects are so much the worse for there being any future philosophy of science... For there can scarcely be any contemporary philosopher of science who is not either a deductivist or an ex-deductivist' (ibid., 104, emphasis added). In sum, inductive scepticism is but a symptom of moral and intellectual degeneracy in philosophy: all but a few philosophers are infected with the irrational belief that only deductive arguments are valid.

4. Conclusion


Stove and Williams assert inductive sceptics are apologisers for cruel political regimes, insane, suffer from a case of horror victorianorum, are promulgators of an intellectual disease in philosophy and philosophical saboteurs that produce ideas deserving of 'hatred, ridicule and contempt'. Williams said, 'It would be pointless to caricature modes of thought whose boldness has long since caught up with any possible burlesque' (1959, 157). How apropos, for we have not been presented with a caricature, but an accurate list of examples of this longstanding mode of thought in action.

Furthermore, few contemporary philosophers can be said to not be in the thrall of such pernicious ideas as inductive scepticism. It is no surprise that Stove declares, 'Genetic engineering aside, given a large aggregation of human beings, and a long time, you cannot reasonably expect rational thought to win' (1991, ch. 7). Only the instantiation of a longstanding eugenics movement could possibly sway the collective opinion of the philosophical community, who are, presumably, all irrational idiots. If true, no wonder no other philosopher accepts Stove and Williams' statistical sampling argument.

However, all that being said, all rejoinders to Stove and Williams' arguments for induction remain unaddressed by Earnshaw, much less acknowledged. Earnshaw seems unconcerned with mentioning the readily available literature that relays the deficiencies in his version of the statistical sampling argument.

While, as I must note for a second time, the article published in Philosophy Now is not an academic article, published in a peer-reviewed journal, and it would not be expected for Earnshaw to address at length the criticisms against the arguments, Earnshaw is silent. Instead of mentioning the extant literature on deficiencies in the statistical sampling argument, Earnshaw brings up Stove and Williams' modus operandi: insult the intellectual faculties of individuals that do not accept the argument.

Assume, just for the moment, that Earnshaw, Stove and Williams are correct in their psychological analysis of the inductive sceptic. Assume, just for the moment, that Stove and Williams are correct, and inductive sceptics are morally blameworthy, irrational golems, stupid and insane sheep that follow the herd. Assume inductive sceptics all have the worst possible motives, and smell like burning rubber.

Assume, just for the moment, that Stove and Williams are paragons of moral virtue, intellectual titans and have only the best intentions to save philosophers from themselves. Assume, just for the moment, those few, those happy, those band of brothers, are not tilting at windmills, but rightfully railing against the irrational, immoral teeming masses of philosophers.

If all these faults of inductive sceptics were true, and Stove and Williams have correctly diagnosed a psychological cancer at the heart of philosophical disputation, this would not make the objections to statistical sampling arguments disappear. Here is a modest suggestion: rather than allude to methods used by Stove and Williams to denigrate philosophers, Earnshaw should find a better argument.

Bibliography


Agassi, J. 1985. Review of 'Popper and After: Four Modern Irrationalists' Philosophy of the Social Sciences. 15(3): 368-369.

Black, M. 1947. Review of 'The Ground of Induction'. The Journal of Symbolic Logic. 12(4): 141-144.

Earnshaw, E. 2017. How I solved Hume's problem and why nobody will believe me. Philosophy Now. 119.

Goodman, N. 1946. A query on confirmation. The Journal of Philosophy, 43(14): 383-385.

______. 1983. Fact, Fiction and Forecast. Cambridge, Mass.: Harvard University Press. Fourth Edition.

Gower, B. 1990. Stove on inductive scepticism. Asutralasian Journal of Philosophy. 68(1): 109-112.

Griffin, N. 1988. Review of 'The Rationality of Induction'. Dialogue: Canadian Philosophical Review. 26(1): 178-181.

Indurkhya, B. 1990. Some remarks on the rationality of induction. Synthese 85: 95-114.

Lange, M. 2011. Hume and the problem of induction. In Gabbay, D.M., S. Hartmann and J. Woods (eds). Handbook of The History of Logic, Vol. 10: Inductive Logic. Kidington, Oxford: North-Holland: 83-86.

Maher, P. 1996. The hole in the ground of induction. Australasian Journal of Philosophy. 74(3).

Mayberry, T.C. 1968. Donald Williams on Induction. Journal of Thought. 3(3): 204-211.

Miller, D. 1988. Review of 'The Rationality of Induction'. Philosophy 63: 286-288.

Nagel, E. 1947. Review of 'The Ground of Induction'. The Journal of Philosophy. 44(25): 685-693.

Nelson, E.J. 1948. Review of 'The Ground of Induction'. Philosophy and Phenomenological Research. 9(1): 139-143.

Stove, D.C. 1982. Popper and After: Four Modern Irrationalists. New York: Pergamon Press.

______. 1985. Karl Popper and the Jazz Age. Encounter 65(1): 65-73. Reprinted in Stove, D.C. 1999.

______. 1986. The Rationality of Induction. Oxford: The Clarendon Press.

______. 1991. What is wrong with our thoughts?: a neo-positivist credo. In The Plato Cult and Other Philosophical Follies. Oxford: Blackwell.

______. 1999. Cole Porter and Karl Popper: The Jazz age in the philosophy of science. In Against the Idols of the Age. New Brunswick, New Jersey: Transaction Publishers.

Watkins, J.N. 1985. On Stove's book, by a fifth 'irrationalist'. Australasian Journal of Philosophy. 63(3): 259-268.

Will, F.L. 1948. Review of 'The Ground of Induction'. The Philosophical Review. 57(1): 98-100.

Williams, D.S. 1947. The Ground of Induction. Cambridge, Mass.: Harvard University Press.

______. 1953. On the direct probability of inductions. Mind. 62(248): 465-483.

______. 1959. Philosophy and Psychoanalysis. In Psychoanalysis, Scientific Method, and Philosophy; a symposium. S. Hook (ed), New York: New York University Press: 157-179.

8/4/17

10 comments:

  1. (broken into 2 for length)
    Hi Nathan,

    Thanks for the response to my article!

    So, here's the thing: your response isn't really to my article. It's a response to Williams and Stove. I place my own view in the lineage of their approach to Hume's problem, but I (deliberately) don't say that we have the same views.

    Let me start with what, to me, is the most glaring problem with your response: it misunderstands what my article's main goal was. The main goal was to explain why one SPECIFIC argument for inductive skepticism is flawed. This is the argument that goes: a justification must be either inductive or deductive, but it can't be either, so there can't be one. I note you (much like the Stanford Encyclopedia of Philosophy) make no mention of this argument, which despite your apparent lack of interest, is fairly widely disseminated -- much more well known and influential (for good reasons) than Goodman's grue stuff. Now, you may not especially care about that particular argument. But unless you can show why THAT ARGUMENT is not, contra what I claim, flawed, you are missing the point. You can argue for inductive skepticism using as many DIFFERENT arguments as you like, but you have not shown that the rebuttal of Hume's argument (distinct from Hume's conclusion) is incorrect.

    Okay, what about the positive case for inductive arguments? You'll notice I said absolutely nothing in the article about justifying 'inference from the observed to the unobserved'. So your long discussion of this in your response has what relevance to my piece? What I claimed to show was that non-demonstrative inference can be justified. That might not be what you are interested in, but it is not my fault that you wanted me to (and misread me as) doing something I wasn't. I mean, to spell things out a little, doesn't my deductive justification of induction seem a little... tautological? Why yes, yes it is. Of course it is. Sorry.

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    1. Dear Dr Earnshaw,

      I apologise for the lateness of my reply. Yesterday was far busier than I had anticipated.

      I must note that there is a minor mistake in your article: you say, 'D.C. Williams felt himself to be in this unfortunate position. ... His [Williams'] book includes a chapter entitled "Why these arguments do not convince"'. There is no such chapter in Williams' book, 'The Ground of Induction'. Your article mistakenly attributes a section of Stove's book, 'The Rationality of Induction', to Williams' book. See: Stove's 'The Rationality of Induction', Ch. VIII: Why These Arguments Do not Convince, 99-109. I suggest contacting the editors of Philosophy Now to make the necessary revisions to the online version of the article.

      (cont. below)

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    2. (cont.)

      Continuing on to the substance of your reply, if you believe I have only addressed Williams' and Stove's arguments, and not your own, I am then confused, since one of two things must be true: either (1) your argument is not a variation of their statistical sampling argument (the only argument they both advocate that plausibly fits the structure of your own argument), in which the suppressed premise is made explicit or (2) their statistical sampling arguments are merely more refined versions of your argument.

      You say, 'such arguments show that it is necessarily the case that the conclusion of an argument follows with probability from its premises'. You claim further that your argument was 'beaten to the punch' by Williams and Stove, and 'the substance of [your] argument can be found' in their respective books. If 1, why claim your argument is a variation of their argument when it is not? If the latter, your argument is a variation on Williams and Stove's, and is shown to prove too much on similar grounds. If it proves too much, it addresses your rebuttal.

      Furthermore, your claim that your argument is tautological is in line with Mayberry's reply to Williams: '... the probability syllogism is highly misleading, since its form suggests that some significant claim can be made concerning the probability of the single case, but the interpretation of the conclusion has to be such that it does not exceed the information provided in the premises. Thus it has to be a compact statement which when expanded merely summarizes the information provided in the premises' (Mayberry, 1968, 211), that is, the statistical sampling argument, if valid, is trivial. Or, in your words, 'tautological'. Of course it is.

      In addition, I do not understand why you believe the arguments I address are not relevant to your argument, since it is in a generally accepted form and applies to your argument. If it bothers you so much, other formulations can be made about the likelihood of a member of a population having a property based on the distribution of the property within the population without any substantive difference or about the past being like the future in important respects. See my formulation of P1, P2* and C* and compare it to your example of bugle blowers.

      With these issues out of the way, if you would like to respond to the second section of my post, 'Goodman's new riddle of induction', I would be happy to amicably have a discussion about the substance of your article.

      Lastly, I'm sure you're quite busy, so I would like to thank you once more for taking the time to respond to my post, as well as clarify your position and address any issues of offensive material in the post. I hope you have an enjoyable Easter weekend.

      Warmest regards,

      Nathan

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  2. Kind of a broader point: I find it a little bizarre that you're responding to an article that is written for a popular audience in such a... I'm searching for a word here... uncharitable way. This article had to be accessible to lay people. The point of it was not to actually solve inductive skepticism. I mean, wasn't it at least kind of obvious by the tone that I was making fun of myself a little? I couldn't lay out all the details about the broad topic of inductive skepticism, and most of them weren't relevant to the purpose anyway. In writing a popular piece, you have to make compromises everywhere, sacrificing precision for clarity. But I don't think it is really so hard for a trained philosopher to read between the lines of the article to see what I am leaving out, and why, if they approach it with a co-operative attitude, or at least make an effort to read clearly what is and what is not being said. You will notice that your blog post has about 20 more sources than my article. Perhaps that is NOT because I have read only two books on inductive skepticism -- a more charitable hypothesis might be that since the piece was not academic writing, I elided all the discussion that was not relevant to the purpose of the piece. But then, you seem to have missed the purpose of the piece, so the logic behind what was included vs. left out could hardly have been clear.

    Okay, a final substantive point: I'm sorry that Stove was such a jerk, but _I_ wasn't actually advocating virulent anti-inductive skeptic propaganda. I was speculating a bit about how one could break an intellectual deadlock in philosophy. If logical arguments are insufficient, what else could work? I didn't go so far as advocating a particular approach, but since you assumed I favor calumny, social shaming, and ad hominem attacks, let me take the opportunity to say: no, that is not how I think we should break an intellectual deadlock, if for some reason we really need to. I would prefer the carrot to the stick: seductive, amusing and entertaining persuasion, if we are to use rhetorical methods. Really, what I was interested in was the _intellectual possibility_ of deadlock in philosophy due to the failure to grasp decisive arguments. I am NOT especially interested in actually breaking the deadlock so that I win the war over Hume's argument (or free will and determinism, or whatever else), and the fact that what you took away from my article was so different again suggests that you rather missed the point.

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    1. Dear Dr Eugene,

      I thank you for taking the time to respond with your two comments. Due to the time difference, I believe I have time for only one reply this evening, but will attempt to respond to the other comment sometime tomorrow.

      Charges of uncharitability are fairly strong, but I believe that I read between the lines of your article quite fairly.

      By way of illustration, this is a short reconstruction of how the non-academic, having finished your article, would have reasoned: in short,
      a mental image of the philosophical playing field that was more of a fun-house mirror than an accurate reflection. Their mental image may not correspond with your intended paper, but I believe it is a mental image that, while false, is drawn from what you wrote (even if you did not intend it to be so).

      (As a peace offering, just this afternoon I picked up a used copy of Williams' 'The Ground of Induction', and plan on reading it tomorrow, time permitting.)

      If you are interested in charitable reading, I suggest you read in between the lines I wrote as well. It was an attempt to grind down the angles of the mirror to properly reflect the philosophical situation: from what research I did into what Williams and Stove wrote in response to reviews of their respective books that argued for statistical sampling arguments, I could find no cogent response from Williams or Stove that addressed the deficiencies in their argument.

      Instead, as you can see above, what I found was an overwhelming number of insults from Stove and silence from Williams.

      What are we to infer by your reference to Stove and Williams, especially in light of their response to criticism and your pessimistic conclusion, 'Maybe this means that the progress of philosophy can't just rely on logic; it must resort to rhetoric. The arguments have to be dressed up prettily, or the objectively confused must be socially shamed and pressured'?

      I do not think such an action would be appropriate from anyone, not the inductive sceptic nor the inductivist. Yet they were your parting words, and fully in line with the 'social shaming' from Williams and Stove.

      Thus, the innocent reader, would 'fun-house mirror' your article (to verb a noun, as one does) as follows: your argument is (secretly) quite good; here are two philosophers (Stove and Williams) that dealt with similar arguments; now comes a section on how they dealt with disagreement: the best explanation for the inductive sceptic's refusal to accept induction is due to matters of psychology, not philosophical reasons; on a related note, more generally, philosophical disputes cannot be resolved without engaging in a bit of mean-spirited repartee. This fun-house reading, I hope you can agree, is concerning.

      On this note, I sincerely thank you for clarifying that you do not mean to imply that social shaming involves, well... social shaming; instead you repudiate it.

      Instead, you favour the 'carrot', which is, if I remember the idiom correctly, the complete opposite form of the 'stick'--that is, not social shaming at all.

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    2. 'Reading between the lines' of my post, I hoped it would be seen as a cautionary warning for anyone that should take 'social shaming' to involve any shaming in a social setting.

      I fully accept that either you simply misspoke (something we all do) or I misunderstood what your intent was in using such language (again, a price we pay for communication).

      My greatest concern (and therefore, the greatest amount of space dedicated in the blog post) was due to the fear that cavalierly advocating 'social shaming' in a publication meant for non-academics (even though you meant to catch the flies with honey, not vinegar), in which, one presumes, any intent you may have would likely not be read between the lines by non-academics, would lead to reading words plainly.

      In short, the reader may take you seriously. This is a responsibility every writer has, especially when writing for the public. Several layers of irony may be appropriate, but given the audience, I imagine more than a few readers may take what you say to have been what you meant.



      On the subject of sources: this is a blog post on my website, and your article article is published in a popular magazine. The two have different standards, and I decided that dredging up as many relevant reviews of Stove and Williams was appropriate. I also decided to provide sources for all of Stove's incendiary comments if one were interested in seeing how an attempt at social shaming worked out in real life: it was not pretty.

      I also thought it relevant to include sources for the consensus in philosophy, and show how the consensus responded to the two of them.

      (By the bye, if I should find any sections in 'The Ground of Induction' tomorrow in which Williams makes similar claims or calls the inductive sceptic malicious or someone who legitimates evil, I may edit my post to include the relevant quotations as well. Williams' work on induction is, for better or worse, almost nonexistent on the internet.)

      Lastly, I would not want anyone to infer from my writings that I believe that you have read nothing but their two books; far from it. Rather, I wanted to make it clear that the dialectic did not end at the publication of their books: it was an interesting (but ultimately flawed) idea was brought up, and then summarily shot down twice, and nothing more.

      Warmest regards,

      Nathan

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  3. "Earnshaw follows Stove and Williams' modus operandi: insult the intellectual and cognitive faculties of individuals that do not accept his argument."

    This is the sort of thing that I mean when I said you are being uncharitable. Where do I insult anyone in the article? Where do I recommend insulting anyone? Your concerns about social shaming are drawn from one very short section, which I quote in full:

    "Maybe this means that the progress of philosophy can’t just rely on logic; it must resort to rhetoric. The arguments have to be dressed up prettily, or the objectively confused must be socially shamed and pressured. Or something: I don’t really know."

    Not only is that nothing remotely like an insult to anyone, to read that and conclude, as you do, that my modus operandi is to insult the intellectual and cognitive faculties of anyone who doesn't accept my argument, is, frankly, incredible. And yes, uncharitable.

    Regarding sources: yes, a popular philosophy article and a blog post have different standards. My point was indeed that your long discussion of responses to Stove and Williams, and your assertion that "Earnshaw does not address any of these rejoinders in his article for Philosophy Now. In fact, he does not appear to be familiar with the relevant literature responding to statistical sampling arguments" would have been an appropriate rejoinder for an academic article, but not for a popular one.

    Also, I say this not because I am offended (I try not to get offended on the internet), but it is a pretty harsh charge to make in any intellectual context that the other guy "does not appear to be familiar with the relevant literature". Rhetorically, it is a slightly more polite way of saying 'this guy is bullshit and he has no idea what he is talking about'. Now, again, if I had published an academic paper that didn't discuss any criticisms of Stove and Williams, fine, complain I'm ignoring the subsequent debate. But for you to then say, as you just did "I would not want anyone to infer from my writings that I believe you have read nothing but their two books', well, what else does "does not appear to be familiar with the relevant literature" mean in context?

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    1. Dear Dr Earnshaw,

      If you are offended, and believe I have misrepresented you, I will edit the post to reflect your recent comments.

      Furthermore, I think you are due an apology for any implication that you are 'bullshit and ... [have] no idea what [you are] talking about'. I apologise if I misrepresented your familiarity with the problem of induction.

      Best wishes and thank you for your comments,

      Nathan

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    2. Hi Nathan,

      No need to edit the post on account of my feelings: as I said, I try not to take criticisms personally. I do think that maybe your responses come across as more dismissive than intended -- if so, maybe editing is in order. But that's your call. I'd rather have a critical response to my stuff, than be ignored -- at least if someone explains why they don't agree with me, I have an opportunity to try and set them straight!

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  4. I'm not a professional philosopher, but in reading Earnshaw's original at Massimo Pigliucci's site, Goodman immediately jumped into my mind. And, I assumed that, even though Earnshaw was tongue-in-cheek, even a bit snarky at points, he was ultimately making a serious argument — one that's been shown to be, er, invalid, by Oseroff.

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