Phil 2511: Paradoxes

Lecture 7:  Sorites III: The Epistemicist Solution (continued) and the `No Philosophical Solution’ Solution


1.      To ask whether phenol-thio-urea is bitter -- yes or no -- is to commit what I have called `the Fallacy of the Simple Question', the sort of question to which the proper response is to refuse to give the sort of simple answer that the questioner demands.  If I like playing tennis against strong opponents, but really dislike playing against weak opponents, then there is no `Yes' or `No' answer to the question `Do you like playing tennis (simpliciter) ?' It is neither true nor false that I enjoy playing tennis (simpliciter).  It is likewise neither true nor false that phenol is bitter, nor is it true or false that the color patch Q is red.  Since Q lies in the border area, some competent observers will say that it is red (i.e. will classify it as red rather than orange), others that it is orange.  Given that we know this fact, it would be unfair to demand answers to crude questions such as `Is Q red or is it not ?'.  (See also O. Hanfling, `What is wrong with Sorites arguments?’, Analysis 61 (2001), pp.29-35.)

2.      By contrast, a perfectly legitimate question is `Does phenol-thio-urea taste bitter to you?'.  To say that I judge phenol bitter is to say that bitter is how phenol tastes to me.  On this construal, `bitter' is an adverbial qualification of tasting, How something tastes to me may be quite different from how it tastes to you, just as how grass looks to me is quite different from how it looks to a person with the kind of abnormal photoreceptor cones that give rise to red-green blindness. And a particular off-red shade may divide observers in their judgments about whether it is red.  The statement `Q is red' does not admit of a simple `true' or `false' evaluation.  What we can say, truly or falsely, is that Q looks red to some individual, that Q appears redly to that individual.

3.      Epistemicists might accept this conclusion with equanimity.  They could say that, truistically, the Principle of Bivalence applies only to statements to which the ascription of truth or falsity is appropriate, not to utterances to which, for whatever reason, such ascription is inappropriate.  And that, if indeed it is a mistake to ascribe truth-value to some color ascriptions, all that means is that the CPS and its non-standard variant are ill-formulated versions of the Sorites; they do not create any problem peculiar to Epistemicism.  This is correct.  But, of course, the Sorites is not to be dismissed by pointing the finger at one or two poor formulations of one version of the paradox.  Paradoxes have a habit of taking revenge on arrogant solvers by re-emerging in stronger, more virulent strains.  And it is one such strain that poses real difficulty for the Epistemicist.  Bennett's `phenol' argument suggests a double strengthening of the CPS.  First, replace `is red' by `looks red'; and, second, consider how samples look to just one individual --  to me, say.  If some sample looks red to me then (so the reasoning goes) an adjacent sample which I find visually indistinguishable from it must also look red to me; so the next adjacent sample must also look red to me ... etc.  The paradoxical conclusion is that a sample which in fact looks orange to me must, by the above reasoning, look red to me.  This is a tough variant of the Sorites.

4.      How would Epistemicists handle this version of the paradox ?  Their official position would be that, for some particular sample Xn of which I say `It looks red to me', what I say is true, but when I say `Xn+1 looks red to me', what I say is false.  There is, however, an immediate problem with this.  How can I be wrong in my judgment of how something looks to me -- do I not have first-person authority?  A possible reply is that, although someone cannot be mistaken about how something looks to him, he can be mistaken about whether some word, e.g. `red' is the right one to describe how it looks.  This reply, however, takes us no further than the Strengthened-Pigeon version of the CPS, in which Gregory, a pigeon is trained to peck to the right on being presented with paradigm samples of red, to the left for paradigm samples of orange, with dire consequences for non-bivalent behaviour (doing neither or doing both).  Show Gregory successive samples in a series of colour patches running from paradigm red to paradigm orange (ensuring that the visual difference between neighbours is less than the threshold of pigeon discrimination) and one will conclude, in the usual way, that, wordlessly, he will end up making the `red' response to a sample he recognizes as orange.

5.      All the above moves made on the CPS can be duplicated for the Thin Tim version of the Sorites.  Tim Williamson writes, "No one knows whether I am thin.  I am not clearly thin; I am not clearly not thin...  I am a borderline case for `thin'" (See Williamson, p.185, footnote 3).  Well, he would definitely be classified as not thin by a peasant in Northern China, where most people are thinner than Tim, so, in order to avoid the Fallacy of the Simple Question, we had better strengthen the paradox, and work with the predicate `looks thin to Jowett'.  The Epistemicist is faced with the awkward prospect of having to say that, for some particular girth of Tim, when, not seen by Jowett, Tim swallows a snowflake, it is true that he looks thin to Jowett before the swallowing, but not after, even though Jowett cannot notice any difference.  And that thereafter, assuming no change in girth, Tim continues not to look thin to Jowett.  So when Jowett says to Tim `You're looking thin, same as you looked last week', an omniscient being (who knows the difference a snowflake makes) could overrule Jowett, and inform him (to his great surprise) that Tim really does not look thin to him now.  Surely not.

6.      Here’s a variant on the objection just discussed.   Consider the predicate `is known by me to be red’.  I am shown a red patch, and I say `That is known by me to be red’ (or `I know that patch is red’).  I am shown the next patch (visually indistinguishable from the first, even though it is fractionally yellower) and say `That is known by me to be red’.  And so on.  Obviously, by the time I get to the last patch, which I can see clearly is orange, not red, I will NOT say `That is known by me to be red’.  Therefore at some point in the series, I will say of one patch `That is known by me to be red’, but will decline to say that of the next patch.  So here we have a definite cut-off point.  Now, the Epistemicist agrees that there is a cut-off point, but he insists that where this cut-off point occurs is unknowable.  But didn’t I just identify the cut-off point?  Can the Epistemicist reasonably reply: `You identified a cut-off point, but you don’t know that it is the correct cut-off point between what you know to be red and what you do not know to be red?’  So the Epistemicist would be telling me `Yes, you think that you know that that patch is red, but you don’t know that you know it’. 

7.      For replies to these objections, see Williamson, Identity and Discrimination, Chap.6.

8.       Let us now move on to a solution to the Sorites Paradox that I favour – to the effect that solving the Sorites is not a philosophical project.  I call this the `No philosophical solution solution.  What does that mean?  A philosophical solution is one that advocates a revision to accepted logical or semantical principles, or which seeks to expose some conceptual confusion.  I shall argue that nothing of this sort is required – that basically the problem is one for science to resolve.  This is the theme of my paper `How to Boil a Live Frog’, Analysis 60 (2000), pp.170-178, on which the following is drawn.

9.       There are three types of person that we must distinguish when considering the Sorites.  The first is the Sorites subject (real or hypothetical) -- the person on whom a Sorites experiment is performed.  The rôle of the subject is to make a series of honest observational judgments, as does the subject of the Colour Patch Sorites.  What is required of such subjects is only integrity -- they cannot, qua subjects, be faulted for poor reasoning, for no reasoning is involved in their task.  The second type of person is the Sorites reasoner, the person who goes through the Sorites reasoning, starting off with plausible premises and ending with a false conclusion.  This reasoning concerns observational judgments -- judgments made by a subject.  The third type of person is a Sorites theoretician, a person like you and me who is trying to work out what goes wrong in the Sorites reasoning.  Of course, these are idealized types; in practice it is rare to find an individual who is not a mongrel.  But it is important for us (theoreticians) to have a clear view of these three quite distinct types of rôle.

10.   A predicate such as `red' is Sorites-susceptible, while a predicate such as `triangular' is not.  Although both redness and triangularity have prototypical and peripheral exemplars, the reason why `triangular' is not Sorites-susceptible is that triangles -- at least, pure Euclidean triangles -- do not shade off into non-triangles. Two triangles may be somewhat different with respect to angles and length of sides, but they cannot but be similar with respect to three-sidedness.  So it is a definition, not a judgment of similarity, that determines whether or not a given shape is a triangle.  This is what distinguishes members of the Sorites family from other paradoxes -- the former trade exclusively in those predicates the applicability of which depend essentially on our judgments:  I judge that Bill Gates is rich, concede that, if he had one penny less, he would remain rich, so, by iterating this concession, I conclude that a penniless Bill Gates is rich.  The reasoning leads from a clearly true premise, via a series of steps each sanctioned by the plausible thought that taking one penny off a rich man won't make him a not rich man, to a clearly false conclusion.  All Sorites-type arguments are of (or can be moulded into) this pattern.

11.   Jastrow's duck-rabbit is an ambiguous drawing -- it can be seen either as a duck or as a rabbit.  A Necker Cube is the outline drawing of a cube set skew; which face is at the front is ambiguous.  The visual experience one has with each of these drawings can be described as follows: an object judged F on one occasion may be judged not-F on the next even though the object has not changed at all.  Normal observers experience this switching of judgments; Wittgenstein has an epithet -- `aspect-blind' -- for those people who don't.  Both the duck-rabbit and the Necker Cube are examples of visual judgment-switching but similar effects afflict the other senses.  Duke Orsino, at the beginning of Twelfth Night suffers an aural judgment-switch.  The music stays the same but, after a short while, Orsino's appetite for it disappears ("'Tis not so sweet now as it was before").  It happens in love too -- you stay the same but, for no reason, your fickle lover stops loving you.

12.   Now, consider the general form of Sorites-type paradoxes: A series of instances is such that, if a subject judges ai to be F, he has no good reason to withold the judgment `F' from ai+1.  Yet a1 certainly is F and the subject judges it to be so, while an is certainly not F, and the subject judges this to be so.  It follows that, at at least one step along the series, the subject must switch F-judgments from one object to the next for no good reason.  But this should occasion no surprise for, as we have seen, subjects may switch judgments about an object that has not changed at all.  It would, of course, be absurd to maintain that, if an observer judges that X is a duck-picture, then logic demands that the subject must, at every future time, or even at the next instant, not judge X to be not a duck-picture (but a rabbit-picture).  Switching between duck- and rabbit- judgments is just what observers do.  This is an empirical fact requiring an empirical explanation.  As is the empirical fact that subjects switch (non-uniformly) from `red' to `orange' judgments between two colour shades that are visually indistinguishable to that observer.  (And an observer might revise his judgment about a single patch of colour from one instant to the next.)

13.   It might be tempting, at this stage, to insist that judgments are made at particular points in time, and that a subject's judgment-switch about an object that does not change in the interval between the two judgments is to be explained as stemming from some change in the subject during that interval.  That that, while possibly true, cannot be the whole story, is revealed by considering an ingenious counterfactual version of the Sorites, due to Michael Morreau: if an observer judges that ai looks red at time t, then if that observer were to view the visually indistinguishable ai+1 at t, then the observer would judge ai+1 to be red at t.  This is a particularly tough variant of the Sorites: one seems irresistibly drawn to the false conclusion that, with a series of patches each one of which is imperceptibly yellower than the next, if an observer judges a1 (a primary red patch) to be red, then he would judge an (obviously orange) to be red too if the latter judgment were made at the same time as the first.

14.   There is, however, a way out, but, again, it turns on empirical considerations.  Wittgenstein, in the course of a discussion on `kinaesthetic sensations', pointed out that we can locate the direction of a sound source in virtue of a stereoscopic effect -- the two ears are (slightly) differentially affected -- but, of course, the hearer does not sense being so affected.  In his words, "I may be able to tell the direction from which a sound comes only because it affects one ear more strongly than the other, but I don't feel this in my ears; yet it has its effect: I know the direction from which the sound comes" (Wittgenstein, Philosophical Investigations, p.185).  There are thus two importantly different senses of the verb `sense'.  For an individual to sense1 something is for him to be aware of it, but for an individual's organs (e.g., his ears, his brain) to sense2 something is for them to be affected when the individual may be quite unaware of this affect.

15.   A well known example of sensing2 without sensing1 is blindsight.  A blindsighted subject is unaware of objects on his `blind' side, yet, if asked to make a wild guess, he will accurately describe the colour and shape of those objects.  So the subject has `picked up' or sensed2 the presence of the objects.  The blindsighted subject is visually affected on the `blind' side without actually seeing what is there.  Similarly, the difference of colour between two patches may be beneath the threshold of discriminability of a subject, yet the subject (here, the subject's visual system) may sense2 the difference.

16.   So it is with judgments made in Sorites experiments.  The subject is subject to the influence of at least two types of neurological process.  The first -- Type A -- are changes that occur in the subject's head, unprovoked by any change in the external environment, during a time interval -- it is this type of process that is responsible for Orsino's change of verdict, from `sweet' to `not so sweet', and for our flip-flopping judgments about which face of the Necker Cube is to the front.  The second -- Type B -- which we have just been discussing, are changes wrought by some environmental elements of which the subject is unaware, yet which affect his judgments (as in blindsight).  It is through a combination of these processes that subjects make their `for no good reason' switches (and backsliding judgments) in Sorites-type experiments.  There is no right (though unknown) moment to switch (contrary to what epistemicists claim).  Naturally, the neurological processes within each Type that underlie such switches of visual judgment will differ from the neurological processes within each Type that underlie switches of aural judgment.  And the processes (or mix of processes) that underlie judgment switches from `rich' to `not rich', from `large number' to `not large number' etc., will be different again.