PHILOSOPHY PATHWAYS Issue 164

I. 'Does the Snake Really Exist in the Rope? An Exposition of the Advaita Vada's view on Error' by Arup Jyoti Sarma

The theme of this issue of Philosophy Pathways could be broadly described as Epistemology, or the Theory of Knowledge. However, each of the three articles connects its epistemological theme with another equally foundational area in philosophy.

Arup Jyoti Sarma examines Samkara's theory of error in the context of the metaphysical theory of 'Advaita' ('non-duality'). In Western philosophy, the theory which most closely resembles the Advaita is the Absolute Idealism espoused by F.H. Bradley in Appearance and Reality (1893). As in Bradley, the notion of individual 'things' -- or in a subtly different way the notion of individual 'selves' -- is an illusion generated by the process of discursive thought. Yet, as the realist critics of Sankara argued, what is the point of calling this an 'illusion' if we never get to see the way things really are? Or as J.L. Austin famously quipped, 'There's the bit where you say it and the bit where you take it back.'

Zoltan Vecsey focuses on Timothy Williamson's theory -- highly controversial when it first appeared -- that the vagueness in a statement like, 'this is a heap of sand' or 'that man is bald' is merely a form of ignorance. According to Williamson, there is always a truth of the matter in borderline cases even though we can never access that truth. Williamson's case is based on the admittedly urgent need to save logic, in the face of the threat of paradox. Yet as Vecsey argues there comes a point when talk of 'truth' becomes merely otiose. What can it mean to state 'there IS a truth', when no means exist to express or access that truth?

Raam Gokhale, in his second dialogue published in the e-journal, offers a useful exposition of the debate in the philosophy of science between proponents of the view that scientific laws express regularities, and proponents of the view that they state necessary connections, a question which David Hume first examined in his Treatise of Human Nature. How can we ever know of the existence of necessary connections in nature, when all we can ever experience or describe are regularities, or 'lawlike' generalizations? Near the end, Raam Gokhale offers a solution to Nelson Goodman's 'New Riddle of Induction'.

I. 'DOES THE SNAKE REALLY EXIST IN THE ROPE? AN EXPOSITION OF THE ADVAITA VADA'S VIEW ON ERROR' BY ARUP JYOTI SARMA

In this article, I have made an attempt to discuss critically Advaitavada's Theory of Error. The Advaita as a distinct philosophical tradition owes its origin mainly to the celebrated writings of Samkara (788-820 AD). There are of course, other scholars, such as Gaudapada, Suresvara, Padmapada, to name a few beside Samkara. But Samkara has extensively dealt with the theory of error, which is commonly as Anirvacaniya khyativada. This article strict its limit mainly to the writings of Samkara, and some of the criticisms associated with this theory.

Any discussion of error in the context of Indian philosophy cannot be said to be comprehensive unless one takes deep into the Advaita Vada's account of error (khyati). In fact, it is Advaita alone, which is found to have given plenty of importance to the discussion of error for the construction of its own philosophical positions. Maya, the popular expression for error has been so elaborately analysed and discussed in the entire Advaita literature that the whole system is called by many as Maya Vada.[1]

The Advaita as a distinct philosophical tradition owes its origin mainly to the celebrated writings of Samkara (788-820 AD). Samkara not only mentions the topic of error in his different works but devotes a full chapter on error which is added ab extra to his famous commentary on Brahma Sutra. Samkara emphasises that any enquiry into the knowledge of Brahman must necessarily be pre-supposed by a clear analysis of the concept of error, which he regards as Adhyasa or superimposition. Samkara's definition of adhyasa, 'Smrtirupah paratra purvadrstababhasah,' has been usually translated as 'the apparent presentation, in the form of remembrance to consciousness of something previously observed, in some other thing.'[2] According to T.M.P. Mahadevan,

     Superimposition is erroneous cognition (mithya-jnana),
     illusory appearance (avabhasa): It is the cognition of
     'that' in what is not-that.' The stock examples are the
     rope-snake and the nacre-silver. Snake is not rope; and yet
     a piece of rope is mistaken for a snake. Nacre is not
     silver; and yet the one who sees a shining object which is
     nacre lying on the sea-shore and imagines it to be silver,
     picks it up out of greed. These are cases of delusion,
     superimposition.[3]

The Advaita Vedanta School advocates the theory of Anirvacaniya khyati of error. The term anirvacaniya is used by Samkara in several places in the Vedanta Sutras.[4] This school holds that the object of illusion is neither real (sat) nor unreal (asat) nor both real and unreal (sadasat). It is different from both existence and non-existence (sadasadvilaksana). It is not existent or real because it is sublated or contradicted. The error is immediately rectified, when we get true knowledge of the object, for example, when we truly know that it is shell and not silver. Thus, the knowledge of silver vanishes when the knowledge of shell arrives. This sublating experience shows that the object of illusion is not existent or real. Had it been existent or real, it would not have been sublated and contradicted. Moreover, it is also not unreal or non-existent because it appears in experience. And what is totally non-existent, nothing, like a barren woman's son can never appear in experience to anyone. The immediately perceived presence of the illusory object can never be dismissed as a void or nullity. Again, it cannot be said to be both real and unreal because it is a contradiction in terms to speak of a thing as both real and unreal. Therefore, the silver in illusion is really indeterminable as real or unreal. It means that the object of illusion cannot be logically defined as real or unreal.

The whole of Samkara's philosophy may be summed up as follows: (1) the Brahman of the Upanisad is the only reality. According to him, the reality or the essence of a thing is that which persists through all its states.[5] And as such, anything which is changeable and perishable becomes virtually unreal. If the self is ultimately real, the necessary conclusion is that all else is mere illusion or maya.[6] (2) The world is unreal and it is an illusory appearance; Brahman itself under the limitations which form part of that illusory universe and (3) the individual soul (Jiva) is non-different from Brahman, the one without a second, which the scripture defines as Existence-Consciousness-Bliss. The non-duality of Brahman, the non-reality of the world, and the non-difference of the soul from Brahman -- these constitute the teachings of Advaita.[7]

The distinction between this dual relationship of Brahman with the world and with the individual soul or jiva must be clarified in order to avoid confusion. The confusion arises because the manner in which Samkara identifies the universe with Brahman is different from the manner in which he identifies the jiva with Brahman.[8] This confusion is due to two diversities of views -- the diversity displayed by the various objects of the universe and the diversity displayed by the various individual subjects, who are also part and parcel of this universe. The manner in which the diversity of the objects of the universe is negated is somewhat different from the manner in which the diversity of the individual subjects is negated, although the two negations are not unrelated. According to Arvind Sharma, 'The issue might appear as one of only dry intellectual interest, when presented in this way. It is, however, also loaded with deep philosophical significance, or is at least often viewed in that perspective.'[9]

     Samkara recognises... that there are two streams of thought
     in which the Upanisads; but he thinks that one of them, viz.
     that which affirms the reality of diversity, is only a
     concession to empirical modes of thought. All diversity
     being thus only conditionally true, the only teaching of
     the Upanisads, according to him, is that of unity. Since,
     however, there can be no unity apart from variety, he does
     not describe his teaching as monism but only as
     'non-dualism' (advaita). Strictly speaking, it is therefore
     wrong to say, as it is now too common to do, that Samkara
     teaches bare unity. If he did, his Absolute would be 'pure
     nothing'. But as Vacaspati says, he only denies the many
     but does not affirm the one.[10]

The question then naturally arises, if truth is one, why arises this many, which we experience through the senses? Truth can not contradict experience. Therefore, Samkara has to explain this apparent contradiction between truth and our everyday experience. He says that this plurality is an illusion (Maya). It has no reality, for it disappears when the knowledge of the true nature of Brahman is realized. It is just like seeing a snake in a rope in the dark. This wrong perception is brought about by ignorance (Avidya), which is beginning less (anadi). It is the ignorance which is the cause of all this duality, Brahman being mistaken for the world. On account of this ignorance, the individual soul (jiva) identifies itself with its adjuncts (upadhis) that is, the body, the senses etc., which are only superimposed on it. This identification makes the soul think that it is the doer, enjoyer etc., though the truth is that it is none of these and thereby it comes under the influence of birth, death, happiness , misery etc. It becomes bound down to this world (samsara). In the case of the relationship between Brahman and individual self, however, 'the jiva is not false or illusory as the world.'[11] According to Arvind Sharma, 'It is Brahman itself appearing through media or limiting adjuncts (Updhi), but these limitations which are really of its empirical adjuncts, appear transferred to it.'[12]

When Samkara says that the world is false, he does not mean that it is absolutely nothing, but that our experience is liable to be stultified by means of knowledge of things as they are. The world has a relative existence; it is true for the time being, but disappears when true knowledge dawns. It is not real from the absolute standpoint. Maya or ignorance is not a real entity. We can neither say that it exists, nor that it does not exist. It is a mystery, which is beyond our understanding. It is unspeakable (anirvacaniya). As maya is not real, it cannot be related to Brahman, the ultimate reality in any way, for any relation between truth and falsehood is impossible. The relation is only apparent, and therefore Brahman is not affected by this illusion, which is superimposed (adhyasa) upon it. Even as the rope is not affected by the snake, that is assumed to exist in it.

Therefore, the only way to liberate from this earthly existence (samsara) is to get rid of this wrong notion through the real knowledge of Brahman. Just as in the case of the rope and the snake, it is the knowledge of the rope alone that removes the illusion of the snake, so also it is the knowledge of Brahman alone that brings about the cessation of this relative existence (samsara). Knowledge of Brahman being thus the only way of liberation, an inquiry into Brahman through the study of the Brahma-sutra is absolutely necessary.

Samkara's explanation of the world as an illusion has given his philosophy the name of Mayavada or Anirvacniya khyativada. It is also known as Vivartavada. Vivartavada is a doctrine of the apparent modification of Brahman into this phenomenal world, as opposed to Parinama vada or the doctrine of the actual modification of Brahman into the phenomenal mode of existence, as held by some other schools of Vedanta like the Visistadvaita of Ramanuja.[13]

If the world phenomena are a case of superimposition like the snake in a rope, then the question naturally arises to our mind -- what is superimposed upon what? Is the world superimposed upon Brahman? Or, is the Brahman superimposed upon the world? In the latter case, the world, which is the substratum, like the rope in the example would be a reality. If it is in the former case, the world superimposed upon Brahman, then it is not possible, because, Brahman is not an object, which can be perceived by the senses like the rope. A thing becomes an object when it is limited by space, time and causation. Since, Brahman is unlimited, it is beyond these, and therefore, Brahman cannot be an object of perception. As such, Brahman cannot be the substratum of a superimposition. However, it should be noted that while the world may be a superimposition on Brahman, the statement cannot be reversed and Brahman cannot be considered a superimposition on the world. The impossibility of such mutual superimposition in relation to the Brahman and the world and its plausibility in relation to the jiva and the world are two facts which stand out in sharp contrast.[14]

Mutual superimposition involves superimposing, for instance, the features of antahkarana on the atman and of the atman on antahkarana. Thereby the antahkarana which is not spiritual in nature appears conscious and the atman, although infinite in nature, appears limited to the antahkarana. When the reality Brahman is realized in one's own experience, what is denied is not jiva as a spiritual entity, but only certain aspects of it, such as its finitude and its separateness from other selves.

Neither can Brahman be both subject and object of the thinking process, for one and the same being cannot both be the agent and the object of its activity at the same time. An object is that on which is concentrated the activity of the agent and hence it must be different from the agent. Again, if Brahman is manifested by some other knowledge and thus becomes an object, it ceases to be self-luminous and becomes limited, and therefore, the scripture will not accept it. Furthermore, in all cases of superimposition, there is an antecedent real knowledge of the object which is superimposed, as of the snake in the example. Therefore, to superimpose the world on Brahman, a real knowledge of the world is necessary, and this would make the world a reality, with the result that the cessation of the world phenomena would be an impossibility and liberation would be impossible. Thus, in whatever way we may try to establish the theory of superimposition, we are failed to establish it.

However, Samkara says that it is natural on the part of man, because of ignorance, not to distinguish between the two entities (the subject and the object), which are quite contradictory, and to superimpose the one on the other, and their attributes as well, and thereby mixing up the real and the unreal to use such phrases as 'That is I' or 'This is Mine'. The self again is not altogether a non-object, for it is the object of the notion of the ego. The self again, is not altogether entirely avoiding our grasp. Though the inner self is not an object and is also without parts, yet due to ignorance, which is unspeakable and without a beginning, attributes like mind, body, senses etc., which are products of ignorance are superimposed on the self. Because of this superimposition, the inner-self behaves as if it is an agent, enjoyer, possessor of parts. But in reality, it is none of these. The real self can never be an object of knowledge. Self-consciousness is possible only with respect to a self already qualified by these adjuncts (Upadhis).

This sounds like arguing in a circle, for to establish superimposition, we have to accept the self to be an object and the self can be an object only through the superimposition of adjuncts; but actually it is not so. It is a case like the seed and the tree. The seed gives rise to tree, which again produces the seed, the cause of the future tree and so on. Therefore, in this series of illusions without a beginning, the self, which is the substratum of the present superimposition, is an object on account of a past superimposition and that one has for its substratum the self, which has become an object of a still earlier superimposition, and so on ad infinitum. The pure-self without limiting adjuncts is never the substratum of a superimposition. It is the difference in the limiting adjuncts that makes it possible for the self to be at the same time an agent and the object of action.

Superimposition again is due to ignorance (avidya), and hence it can be removed only by right knowledge. Samkara admits the reality of an intuitional consciousness (anubhava), where the distinction of the subject and object are superseded and the truth of the supreme self is realized. It is the ineffable experience beyond thought and speech, which transforms our whole life and yields the centrality of a divine presence. It is the state of consciousness, which is induced when the individual strips himself of all finite conditions, indulging his intelligence. It is saksatkara or direct perception, which is manifested when the ignorance (avidya) is destroyed and the individual knows that the Atman and the Jiva are one. It is also called perfect knowledge (samyogjnana) or perfect intuition (samyogdarsana). While samyagjnana insists on the reflective preparation necessary for it, samyagdarsana points to the immediacy of intuition, where the ultimate reality is the object of direct apprehension (iksana) as well as meditation (dhyana).

However, the realist schools of the Nyaya and the Bhatta Mimamsa refute the Advaita view. The Advaitin holds that object of illusion is indefinable. The object of illusion is neither real, nor unreal nor both. A snake is perceived in illusion and later on, it is sublated. An object, which is perceived and sublated cannot be definable. The Nyaya School urges that the Anirvacaniyakhyati cannot explain the sublation. They pointed out that the silver exists somewhere else but is sublated here and now when we realize that 'this is not silver'. It is not the knowledge of the silver, which is sublated here. On the other hand, it is the silver itself. If the knowledge of silver, too is sublated then the knower and the fruit of knowledge, too would have to be taken as non-existent, the sublating cognition will be without any basis. As a result, nothing will be sublated. Therefore, only what is obtained through is sublated.

The Advaitin holds that the illusion is indefinable, because it is neither real nor unreal. The illusory snake is neither absolutely real nor absolutely unreal because it is perceived for the time being and is sublated later on. But this cannot provide sufficient ground for the illusion to be inexplicable. Even if this theory is accepted, the inexplicability remains as it is. That which is different from the absolutely real, for example, hare's horn, cannot be perceived and that which is different from the absolutely unreal, example, the self, cannot be sublated. Hence, the illusory snake, which is different from absolutely real and the absolutely unreal, can neither be perceived nor sublated. Whereas, it is actually perceived and sublated. Moreover, the theory of Anirvacaniyakhyati is not different from Anyathakyati. The assumption of an inexplicable silver in illusion implies that one thing appears as another. If this illusory object is inexplicable, there is no illusion at all.

Hiriyanna, M., (1949), The Essentials of Indian Philosophy (London: George Allen and Unwin).

Kar, Bijayananda, (1978), The Theories of Error in Indian Philosophy: An Analytical Study (New Delhi: Ajanta Publications).

Mahadevan, T.M.P., (1985), Superimposition in Advaita Vedanta (New Delhi: Sterling Publishers Pvt. Limited).

Samkaracarya, (1962), Vedanta Sutras, translated by G. Thibaut (Banaras: Motilal Banarsidass Publication).

Sharma, Arvind, (2006), Sea-shell as Silver (New Delhi: D.K. Printworld (p) Ltd.)

Sharma, Arvind, (2007), Advaita Vedanta: An Introduction (New Delhi: Motilal Banarsidass).

1. Kar, Bijayananda, (1978), The Theories of Error in Indian Philosophy: An Analytical Study (New Delhi: Ajanta Publications), p.102.

2. Samkaracarya, (1962), Vedanta Sutras, translated by G. Thibaut (Banaras: Motilal Banarsidass Publication), p.4.

3. Mahadevan, T.M.P., (1985), Superimposition in Advaita Vedanta (New Delhi: Sterling Publishers Pvt. Limited), p. 1.

6. Dasgupta, S.N., (1933), Indian Idealism (London: Cambridge University Press), p.163.

7. Slokardhena pravaksyami
   Yadukatam granthakotibhih
   Brahma satyam jaganmithya
   Jivo brahmaiva naparah

(Mahadevan, T.M.P., (1971), Outlines of Hinduism (Bombay: Chetana Limited), p.141.)

8. Sharma, Arvind, (2006), Sea-shell as Silver (New Delhi: D.K. Printworld (p) Ltd.), p.5.

10. Hiriyanna, M., (1949), The Essentials of Indian Philosophy (London: George Allen and Unwin), p.154.

13. Hiriyanna, M., (1949), The Essentials of Indian Philosophy, op. cit., pp.159-60.

Dr. Arup Jyoti Sarma Assistant Professor Department of Philosophy Tripura University Tripura

Vagueness, as Timothy Williamson (1994, 2007) conceives it, is an epistemic phenomenon that can be characterized in terms of absence of knowledge. The phrase 'absence of knowledge' means something stronger than mere lack of epistemically relevant information: it means the in-principle unknowability of the semantic boundaries of vague predicates. According to Williamson's theory, there is a sharp boundary between the extension and anti-extension of vague predicates, but because of our conceptual limitations we are unable to figure out the exact location of this boundary. If F is vague, then some objects may be classified as clear cases of F, some objects may be classified as clear cases of not-F, and there are also intermediate cases where our classificatory capacities turn out to be insufficient. This is tantamount to saying that vague predicates give rise to epistemic borderline cases.

One of the primary challenges of epistemicism is to provide an explanation of why we are doomed to ignorance in the borderline area. Williamson's proposed explanation consists of two parts:

The first part elaborates and defends a reliabilist thesis according to which a belief constitutes knowledge only if it is reliable in an appropriate way (see e.g. Williamson 1994, 226-230; 1997, 926-27). The idea, succinctly stated, is that beliefs may be considered reliable when statements based on them express knowledge in all sufficiently similar cases. What counts as sufficiently similar is supposed to vary across contexts and believing agents.

The second part formulates a supervenience principle about the meaning of vague predicates. The principle states that (i) the extension of vague predicates supervenes on the overall use of those predicates in such a way that a small change in our use of a particular vague F would induce a small change in the extension of that F, and that (ii) we do not have appropriate conceptual resources to detect such small changes (cf. Williamson 1994, 231; 1997, 948).

The reliability thesis and the supervenience principle can be taken as being intended, jointly, to entail the unknowability of the boundary between the extension and anti-extension of vague Fs. Borderline cases should then be thought of as incompatible with knowledge. But as Williamson points out, our irremediable ignorance does not prevent us from making true judgements about objects that are neither clearly Fs nor clearly not-Fs (see e.g. Williamson 2003, 709). So conceived, borderline cases appear to be compatible with true judgements. I argue below that Williamson's view on the epistemic status of borderline cases is incorrect.

2. An Argument against the Existence of True Judgements about Borderline Cases

The crucial point in Williamson's explanatory model can be best brought out by an example. Suppose that, in accordance with the sharp boundary hypothesis, a borderline bald man with 3,831 hairs on his head belongs to the extension of 'bald' and a borderline bald man with 3,832 hairs on his head belongs to the anti-extension of 'bald'.[1] So someone whose beliefs are consistent with this supposition may judge truly that a man with 3,831 hairs on his head is bald. But the statement 'A man with 3,831 hairs on his head is bald', though unquestionably true, does not express knowledge since the belief on which it rests is not reliable enough. Had things been very slightly different in our overall use of 'bald', then though we had the same belief it might not have produced the same statement. For instance, if our overall use had been slightly shifted in such a way that a man with 3,831 hairs on his head would already belong to the anti-extension of 'bald', then the statement 'A man with 3,831 hairs on his head is bald' would have been false. Such shifts in use are so small that they must remain undetectable to us. We are not able to track all the relevant factors that might influence the use of a certain predicate. But then we cannot detect shifts in truth value either: no one can ascertain whether the borderline statement 'A man with 3,831 hairs on his head is bald' expresses a true or a false proposition. The final consequence, obtained by semantic descent, is that it cannot be known whether a man with 3,831 hairs on his head is bald or not bald.

As has already been recognised, the epistemicists' explanatory model incorporates a number of hidden assumptions concerning the existence of sharply bounded extensions. It has been pointed out, for instance, that the linkage between our non-linguistic beliefs and the extensions of vague predicates is not quite as simple as the epistemicists' model assumes (see Ray 2004). It is also often remarked that the epistemicist accepts without further proof that the externalist semantics of predication is the correct one (see e.g. Schiffer 1999; Wright 2003). Instead of reconsidering the sustainability of these assumptions one by one, I will try to pinpoint a hitherto overlooked difficulty in Williamson's argument.

The difficulty begins with the non-triviality of the first supposition outlined above. Let n and n+1 be the numbers of hairs between which the sharp boundary for 'bald' is supposed to lie. Then, according to Williamson, one may judge truly that a man with n hairs on his head is bald. And similarly, one may judge truly that a man with n+1 hairs on his head is not bald. But given that having n or n+1 hairs are both borderline cases of baldness, one can make judgements like these only by mere luck or happy accident. Neither the agent who makes the judgement, nor the epistemicist who investigates the agent's act, nor anyone else with normal human abilities seems to be in a position to come to know that the judgement is in fact true. This kind of ignorance is irremediable and unalterable.

If this is so, we may presume that the possibility of making true judgements about borderline cases remains doubtful even under lucky circumstances. For consider an agent who judges truly by sheer luck that a man with n hairs on his head is bald.[2] At first sight, the conditions for obtaining such a judgement seem to be coherently conceivable. Under closer inspection, however, the coherence of the conceived situation becomes dubious. The problem arises from the fact that in order to establish that the judgement based on the lucky guess is true, we should already know that someone who has n hairs on his head belongs to the extension of bald. But this is something we obviously cannot know. An important consequence is the following. Where there are no competent agents who are, at least in principle, able to determine the epistemic status of certain judgements, there is little point in using the truth predicate. Thus, to say that a particular judgement is true in the borderline area seems to be a mere verbal manoeuvre without any theoretical weight.

The difficulty increases when we recall that Williamson explained the unknowability of the sharp boundary for 'bald' with recourse to the basic epistemic difference between true judgements and knowledge. True judgements about borderline cases were declared not to be reliable enough to constitute knowledge. Of course, we may judge truly that a man with n (or n+1) hairs on his head is neither clearly bald nor clearly not bald. To do so would require no more than recognizing the presence of intermediate statuses between clear cases of baldness and clear cases of not-baldness. Moreover, without the truthfulness of such judgements we would not be able at all to think of someone as borderline bald. This does not entail, however, that a man who has n hairs on his head may be judged truly to be bald, or that a man who has n+1 hairs on his head may be judged truly to be not bald.[3] It is hard to imagine how we could have any chance of validating or disproving judgements of this latter sort. Even if all the relevant non-semantic facts about baldness were available, and all the semantic facts about 'bald' known, our epistemic situation would hardly be improved.

But if there are good reasons to deny that we can make true judgements about borderline cases, then it could no longer be plausibly maintained that the unknowability of sharp boundaries results from lack of reliability. In this respect, it does not much matter that our overall use of 'bald' might have been slightly different from what it actually is. What is of primary importance is the defectiveness of our judging situation concerning borderline cases: contrary to Williamson's model, borderline cases must be thought of as incompatible with true judgements. Thus, once we see that the proposed distinction between true judgements and knowledge proves to be pointless in the borderline area, it becomes reasonable to think that Williamson's reliability thesis is also incorrect.

Does all of this mean that the epistemic status of borderline cases is incompatible both with true judgements and knowledge? Yes, and no. If we agree with the traditional epistemological approach and construe knowledge as a factive concept, then the incompatibility becomes evident (cf. Williamson 2000: 95). Suppose, in accordance with the alleged factivity of knowledge, that if we are in a position to know a statement about a man who has a particular number of hairs on his head, then the statement in question is true. Suppose also that excluded middle and bivalence holds even in the borderline area. Then it is either true that a man with n hairs on his head is bald or true that he is not bald. But it is a robust phenomenon of human knowledge that such things are not knowable. In this sense, we are ignorant of a truth. Borderline cases must be seen, thus, as incompatible with knowledge.

As an alternative, we may advocate a somewhat more liberal approach to knowledge. According to the alternative view, it is epistemically possible for us to know that a man with n hairs on his head is bald, and it is also epistemically possible for us to know that he is not bald. We are not thereby involved in a truth value contradiction, for the epistemic possibility that a man with n hairs on his head might be known to be bald (or not bald) does not imply that it is in fact true that he is bald (not bald). The existence of these possibilities reflects only how things might turn out to be in the borderline area (cf. Chalmers 2010).[4]

This can provide an interesting new perspective for the analysis of the knowability of borderline statements. In the possibilist approach at hand, we are not conceptually or a priori prevented from making knowable statements about borderline cases.[5] Quite the contrary, there seems to be nothing wrong in forming beliefs which aim to express our cognitive relation to borderlineness. Given that some of our vagueness-related beliefs might turn out to be true, it is not irrational or epistemically irresponsible to think that we have the right to claim knowledge even in borderline cases. We might call this phenomenon weak epistemic entitlement, since the statements that result from these belief-forming processes do not require full-blooded factual justification. In such circumstances, it is sufficient for us to be convinced that the resulting statements are not in direct conflict with what we already know about clear cases. Two considerations follow. First, our knowledge in clear cases remains unexceptionally factual. But when we make statements about borderline cases, the constraints on factuality are weakened: borderline statements do not serve to describe the world, they express cognitive relations rather than facts.[6] Second, conflicting statements -- for example, 'a is F and a is not-F' -- lead unavoidably to epistemic contradictions in clear cases. In the borderline area, however, such conflicts become rationally acceptable.

Now back to our example. If it is not excluded by any existing piece of knowledge that a man with n hairs on his head is bald, then we are weakly entitled to say that he is known to be bald; and similarly for not bald. Thus, we may conclude that in this more liberal sense, and in this sense alone, the epistemic status of borderline cases is compatible with knowledge.

Chalmers, D. 2010. The Nature of Epistemic Space. Forthcoming in Andy, E.; Weatherson, B. (eds.) Epistemic Modality. Oxford: Oxford University Press

Ray, G. 2004. Williamson's Master Argument on Vagueness. Synthese 138: 175-206

Schiffer, S. 1999. The Epistemic Theory of Vagueness. Philosophical Perspectives 13: 481- 50

Williamson, T. 1997. Reply to Commentators. Philosophy and Phenomenological Research 57: 945-953

Williamson, T. 2000. Knowledge and its Limits. Oxford: Oxford University Press

Williamson, T. 2003. Vagueness in Reality. In Loux, M.; Zimmerman, D. (eds.) The Oxford Handbook of Metaphysics. Oxford: Oxford University Press, 690-715

Wright, C. 2003. Rosenkranz on Quandary, Vagueness and Intuitionism. Mind 112: 465-474

1. In order for the example to work we should also suppose that 'hairs' and 'head' can be used precisely and thus do not give rise to further complications.

2. It is important to note that in the present context 'luck' should not be interpreted as 'epistemic luck'. From an epistemic point of view, these are different expressions. While the latter functions usually as a potential indicator of knowledge, the former is neutral in that respect.

3. Or, to put it more generally, if x is recognized as having an intermediate status between being F and not-F, then x may be judged truly to be a borderline case of F. But it does not follow from this that we can judge truly that x is F or that x is not-F.

4. I do not want to suggest that to refer to the idea of epistemic possibility is entirely unproblematic in the theory of vagueness. But I think one key feature of the idea can be invoked here without any need of deeper justification. It may simply be contended that in using the notion of 'epistemic possibility' we do not aim to extend our analysis to include counterfactual circumstances or possible worlds. Because epistemic possibilities concern only the way things might actually be, we should not directly deal with the additional issues of metaphysical modality.

5. Note that though some parts of the the epistemicists' explanatory model is invalidated by the possibilist approach, neither excluded middle nor the principle of bivalence need be given up.

6. In this regard, the present view has a certain affinity with Seth Yalcin's non-factive theory of epistemic modals (see Yalcin 2007).

     'If knowledge is my God, doubt would be my religion.'
     - Kedar Joshi

     'Everything should be made as simple as possible but no
     simpler.' - Einstein

Scene: Kedar's flat in Pune, India.

Ram: So when we left off the other day, you wanted to talk about justification?

Kedar: Yeah, I was intrigued by your comment that justification being more technical is a more promising concept to investigate philosophically than knowledge.

Ram: That's right. But before plunging into the epistemological sense of justification, I think we should consider one other sense of it as it may shed light on the sense we want to investigate.

Ram: We give justifications for our beliefs but we also give justifications for our actions. Justification has an ethical sense as well as an epistemological one.

Kedar: Interesting. It must be because decisions are made in both cases, a verdict handed down whether it's to believe a proposition or perform an action. And decisions, verdicts are the hallmarks of justice, hence just-ification.

Ram: I would even say just-if-ication, since it consists of giving just ifs or reasons in support of our beliefs or actions.

Ram: Yeah, I guess I was being punny rather than funny. Philosophers are disposed to make bad puns.

Ram: Anyway, you're right. Justice is probably the etymological root of justification in epistemology as it is more obviously in ethics, though there's an important difference: ignoring three-valued logic, beliefs are either true or false. Actions on the other hand are three-valued, being good, bad, or as indifferent as scratching an itch. That's why we don't demand justifications for every action as we do for beliefs.

Kedar: This is interesting but you suggested the parallel with ethics could shed light on the epistemological sense of justification?

Ram: I did. Justice is a virtue of reasonableness, whether in the way people are treated or decisions are made. So we should be reasonable in the demands we make of justification. If we don't demand justifications for every action, perhaps we should be less demanding in assessing epistemic justifications.

Kedar: I disagree. If the only alternative to good actions were bad actions, we would demand justifications for every action to avoid bad ones just the way we demand justifications to avoid false beliefs. Because beliefs are two-valued, we have the right to demand the highest standards in the justifications people offer. I for one don't think we're ever fully justified about anything because we never know the true underlying reasons that make our beliefs true. This is certainly the case in our inductively justified beliefs, but even in the case of deductive reasoning we are not justified because we can never know either the premises that go into our deductions or know that our deductive capacities are working properly.

Ram: Of course, you can be as demanding as you want about justification. I can even concede that we're never 'fully justified' in any of our beliefs, whatever that means. But I would point out that if we're never fully justified, we are often what you might call partially justified and that is a philosophically interesting phenomenon -- what characterizes what you'd call partial justification.

Kedar: Could you give an example of what 'I'd call' partial justification? I use scare-quotes because I don't think there is any such thing as partial justification. Only God has full justification which we can't even approach.

Ram: Well, the ideal, God's eye justification for believing it's 5:00pm may be that the sun is exactly at a certain position in the sky given where you are on earth and what date it is. Now looking at your watch may not be justification enough, but we can approach the ideal, reasoning on the basis of physics/ cosmology that it's about 5:00pm because the sun is in roughly the right position in the sky. The philosophically interesting issue is what makes the rough reasoning in some sense more scientific than simply looking at your watch which might be wrong, and for that matter what difference in degree makes the rough reasoning less than it could be.

Kedar: OK, if you can concede we're never fully justified, I can concede we're sometimes partially justified. And I have to admit investigating why some forms of justification rank higher than others is philosophically interesting. Perhaps we can rank different types of justifications by considering the hierarchy of the sciences, investigating why we think there's a hierarchy. For example, physics is more basic than chemistry, which is more basic than biology, which is more basic than psychology. The phenomena of the more basic and more justified sciences constitute the phenomena of the less basic.

Ram: That's certainly how it's commonly conceived, but in philosophy we should get at the root of the issue. It's not constitution that makes some laws more justified. It's which laws are more truth-preserving. Constitutive phenomena generally permit more truth-preserving inferences but that needn't always be the case. Consider Mendel's genetics. Its subject matter is constituted by chemistry but as far as justification is concerned, Mendel's laws concerning the distribution of dominant and recessive traits in the propagation of pea plants permit inferences as truth-preserving as chemistry's law about the distribution of C12 and C14 atoms in a carbon compound. That's why they're as reliable in justifications.

Kedar: Yes, the more truth-preserving the law the more reliable the justification that uses it. That's why I think only the laws of logic approach full justification. I say approach because even there we may be flawed in our deductive capacities.

Ram: Hold on. I think admitting the possibility that our reasoning faculties may be flawed is good philosophical humility. But that's all it is. Nothing interesting can be said further on the subject. So in exploring different kinds of justification we might as well put the limitations of our faculties aside.

Now let's turn to logic. I think we shouldn't lose sight of the fact that laws of logic -- like modus ponens -- are justification schemas or rules of inference not actual justifications or inferences themselves. Nobody believes q on the basis of p and p implies q. We believe genuine propositions not proposition variables That's why I think it's somewhat confused to say that only the laws of logic are fully justified.

Still, all forms of reasoning can be put into a deductive format by putting in implicit premises. That's why axiomatic systems have provided theorists since Aristotle a good model to study justification. Being guided by their example, we can say there are really only three things that can be justified: the theorems, the axioms and the rules of inference. Within the deductive system, the theorems are justified by the axioms using the rules of inference. The axioms and rules of inference are justified by their capacity to generate the truths that we want to come out as theorems. But we don't construct deductive systems in a vacuum: they're constructed so that some statements we independently want to count as theorems come out as theorems. The independent justification we have for them is inductive, reasoning from the particular to the general. These inductive truths may become so compelling that we are willing to preserve them even at the cost of abandoning cherished axioms and rules of inference when they come into conflict.

Kedar: I guess a good example of our reconsidering cherished axioms and rules of inference is the development of three-valued logic in response to indeterminacy in quantum mechanics.

Ram: That's right. Another may be the greater legitimacy non-Euclidean geometry enjoyed after the discovery that space is curved. In both cases, alternative deductive systems were given greater legitimacy by emerging inductive discoveries.

To sum up, there are three kinds of justification: deductive justification of theorems, justifications of axioms and rules of inference by considerations of strength and simplicity and inductive justification.

Kedar: Whew that's quite a summation but I'll be damned if I can think of any exceptions. Now how do you propose to rank these three forms of justification?

Ram: Well, each has something to recommend it. The theorems are the result of truth-preserving inferences, the axioms have to be believed because they're the basis of everything else and the inductive truths are the raison-d'etre of the whole deductive system in the first place. Given your preference for deductive reasoning, you'd probably prefer conditional statements like if the axioms are true the theorems have to be true. I on the other hand think some inductive truths are the most certain. To make them come out as theorems is the reason we formulate deductive systems in the first place.

But we don't have to rank them. Our next course should be to investigate any problems that are associated with each.

Kedar: I've studied enough philosophy to know the chief problems are with induction, the method inductive truths are first justified.

Ram: You're right again. But before we examine the old and new riddles of induction, we should consider what form inductively justified truths take. It may give us insight into the type of justifications that are appropriate for them.

Kedar: Don't inductively justified truths take the form of generalizations like, 'All men are mortal'?

Ram: To consider that, let's examine a simpler, more basic inductive truth. Suppose you're taking coins out of an urn. You've withdrawn 5 coins and they've all been dimes. As you keep drawing dimes, at some point it'll become reasonable to assume that if you were to draw another coin from the urn, it would be a dime. The belief that it would be a dime would be justified because the set-up is just sufficiently law-like to support that counterfactual -- though not all counterfactuals would be supported... for example it's not true that if I were to drop a penny into the urn it would become a dime. The question is what happens when you first entertain the proposition that all the coins in the urn are dimes.

Kedar: I don't know if this is what you have in mind but what would happen for me would be that I'd entertain some story about how only dimes came to be in that urn, like maybe someone is sorting the change in his pocket... maybe the laws of nature are God sorting the change in his pockets.

Ram: Interesting analogy, especially if in the case of God devising the laws of nature, you mean 'change' in both senses. Hmm maybe I'm being punny again... Anyway, a story is essential because it explains why all the coins in the urn are dimes. Without the story there is at most the generalization -- that all the coins in the urn are dimes -- which may be only accidentally true. Without the story, there is no reason to think future draws from the urn will yield dimes and we have no explanation why the draws to date have all yielded dimes.

Kedar: But different stories could be given which make the generalization not accidentally true. So any given story is not essential.

Ram: You're right. But some story or theory might be thought essential because it establishes a connection between properties, the property of being one of the coins in that urn and the property of being a dime. So inductively justified truths could be said to take the form of connections between properties, as philosophers like Dretske and Armstrong have argued, connections that vary in strength depending on how compelling is the story doing the connecting. Inductively justified truths are not generalizations of individuals, on this reading; they are not about individuals but about properties. All men are mortal not simply because each individual human is mortal but because being human is connected with being mortal.

Kedar: Just to play devils advocate, maybe they could be generalizations -- they just are non-accidental because they play a part in a larger story, one that contains only other generalizations... like 'all men are mortal' being subsumed under 'all organisms are mortal'.

Ram: That's another theory about laws of nature or LON's. Lewis for example has argued that LON's are elements of systems that optimize the opposing desiderata of strength and simplicity. As we alluded to before, the LON's, which serve as premises in our justifications, should be strong enough to explain the wide variety of phenomena but simple enough in the sense that they don't assume more than is necessary. LON's on this view are generalizations that appear in our best, most optimal true theories.

Kedar: Doesn't optimizing between strength and simplicity make LON's too dependent on our subjective preferences? Couldn't LON's be what we would rightly or wrongly consider suboptimal?

Ram: That's indeed one of the chief objections to views like Lewis' which are collectively called the systems view of LON's, the other being the universals or properties view. The criticism is evident in our dimes example.

Ram: The story in our dimes example is like the theoretical system. It gives us a reason to think the generalization that all the coins in the urn are dimes is non-accidentally true. But before we think of the story, it's a fact that there is a law-like connection between drawing dimes and drawing coins from that urn. The fact may be better explained by a different story -- for example, there could be other coins in the urn but because someone's vigorously shaken the urn, the heavier coins are at the bottom. Still whatever the explanation, there is a connection between our drawing dimes and the setup of that urn; it's a connection between properties not mere individuals. The story makes the generalization non-accidentally true by establishing a connection between the relevant properties, but the connection exists before the story.

Kedar: Your modified dime example where there are other coins in the urn is illuminating. It suggests that the connection between properties in a LON may be only a probable connection not always a necessary one.

Ram: In fact that reminds me of the standard problem with the properties view: how do we characterize the connective connecting the properties? Whatever it is, it's capable of connecting individuals with individuals, individuals with properties and properties with properties. It also can be a necessary connection or a probabilistic one. Material implication as used in generalizations, being not so diffused, is on a sounder footing.

Kedar: Well as usual you've summarized both views and the problems with each. Are you going to indicate which one you prefer?

Ram: As usual you're going to be disappointed because as usual I'm going to straddle both positions.

Laws of Nature, like the concept of God, has several satisfaction conditions. We might be willing to consider a being as God if it possessed the three omni's, or failing that some of the three omni's or failing that was perfect or failing that had created the world, etc. The point is it's not like searching for the 'God' particle where physicists have clear ideas of the particle's properties before they discover it. LON's and other pre-theoretic concepts like God, could have one of several 'essential' characteristics. One characteristic may be that they make connections between universal properties another may be that they are a part of our most optimum theories about the world.

Kedar: What I'm interested in is when these intuitions come into conflict, which one wins out?

Ram: Since interest in that kind of conflict is commendable philosophically, I'll try to oblige. But first let's draw a sharper distinction between the two camps. Allied with the systems view of what LON's are is the Regularists' view of what LON's do. If laws are generalizations then they serve to describe the world.

Kedar: That seems fairly uncontroversial. What's the view of the other camp?

Ram: Well if laws are necessary connections between properties they, according to the Necessitarians, govern real world phenomena; they are a necessary feature of the world. So the issue is whether LON's merely describe the world or do they in some sense govern it as well.

Kedar: Well, being opposed to any sense of necessity other than logical necessity, I don't much care for the necessitarians' label. But I have to say, I think the view that LON's govern phenomena seems more plausible. After all, even if there were no sentient beings to describe the world, the LON's would still be there governing it.

Ram: I'm afraid it's not that simple. They could still be said to just describe the world even if there were no beings to do the actual describing. To say they govern the world has to mean something more, like the phenomena that come under their scope behave the way they do because the relevant LON's are true.

Kedar: You know, now that you put it that way, I'm struck by something odd about the necessitarians' view: statements are made true by things being a certain way; the necessitarians seem to invert that, committed as they are to things being a certain way because some statements are true. Is that odd enough to be damning?

Ram: Interesting. That cart-before-the-horse argument is indeed one of the criticisms of the necessitarians view. But I don't find it all that compelling: necessitarians could always hold that LON's, though they can be described as any other feature of the world, are states of affairs not statements. Saying that the law of gravity being true causes the proverbial apple to fall on Newton's head may be no more odd than saying that the apple falling on Newton's head being true makes Newton's head hurt. In both cases you have states of affairs causing other states of affairs. It's just that in case of the law of gravity causing the apple to fall you have a state of affairs connecting properties causing a physical event. Just because the properties state of affairs can be described by a proposition doesn't mean that the proposition being true causes the event except in an elliptical sense.

Kedar: I think I follow that. But what then is the best case for highlighting the difference between the two positions?

Ram: Here's one. Suppose that gravity doesn't follow an inverse square law, that there is an inverse cube term as well. It just so happens that there is an inverse cube law of repulsion that in every case cancels out the inverse cube term in the gravity law. Would we say that there are two LON's operating in that case or just one?

Kedar: Being an idealist I would say there are two, though you, being a pragmatist would probably say there is only one.

Ram: I don't know if there is an 'ism' for straddling the fence but I find both views have their merits. I think we'd say there is just one law of gravity -- the inverse square law -- that describes the phenomena we observe but if there really are features of the world -- albeit undiscoverable features -- that make there be two opposing forces... I don't know... I can be brought to say there are two laws operating in that case.

Ram: I'm saying I'm confused beyond all hope. But seriously, I think the confusion is like admitting humility and boldness, as opposed as they are, are both virtues. Admitting some features of the world are undiscoverable is humility but we don't stop with the admitting; we imagine scenarios of how some things could be undiscoverable and imagining them is like the beginning of the thought experiment that could lead to eventually discovering them. The admission is like humility, the imagining like boldness.

Kedar: That's profound man. I'm myself almost tempted to straddle the fence as you say. But not to spoil your poetic moment, wouldn't Hume have something to say about the view that there are necessary connections in nature?

Ram: He certainly would though even there the answer is not clear-cut. Hume's point that we observe no necessary connections between events, that all we observe are constant conjunctions, certainly bears on the issue at hand... though recent exegesis of Hume tends to support the interpretation that he was making a purely epistemological point. He allowed there to be necessary connections between events. His point was simply that we can never have any evidence for them, that only habit leads us to suppose a billiard ball struck directly will move in the opposite direction to where it was struck from.

Kedar: Yeah I guess Hume being Scottish wouldn't be sympathetic to there being any 'English' on the ball.

Kedar: I guess it is. But seriously if we can't ever know there are necessary connections why should we ever assert them?

Ram: The same reason that despite the fact that all we have are sense impressions, we nevertheless assert -- our science asserts -- there are physical objects. There may be no justification for our belief beyond the fact that we're just constituted to believe so, but our constitution has served us well in the past and maybe that's justification enough. (pause)

Or maybe not... you see, my straddling the fence is at least consistent. And I'm not just being cagey: beliefs like there are physical objects and that there is a necessary connection between causes and effects seem to play some role in how we understand the world but they don't neatly fit into any of the tripartite division of justifications we made earlier: They are not deductively justified as are the theorems of our science, nor are they justified by considerations of strength and simplicity as are the axioms, nor are they inductively justified as are the truths we independently want to come out as theorems.

Kedar: You were a bit quick. Why couldn't we say they are justified as axioms based on considerations of strength and simplicity?

Ram: That's the usual move but the skeptic can always say, 'What additional theorems are you purchasing with these as axioms?' For example, the supposition that there are necessary connections between causes and effects supports no scientific laws as far as I know. Same with the supposition that there are physical objects. So considerations of simplicity would seem to demand that we drop these from our set of axioms.

Kedar: OK, you've convinced me: maybe fence-straddling is the best position on this issue. Let's see if we can make any progress on the New Riddle of Induction.

Ram: You won't find me straddling the fence on that one. The new riddle has been around since the 1950's so maybe, like grue, it too is past time t when it should be called something else -- like maybe the 'Solved Riddle of Induction.' (snicker, snicker)

Kedar: I don't get it. I confess I don't know anything about the new riddle.

Ram: Oh I see. Before I give my solution to the new riddle, I have to explain it. As Goodman argued, Hume's solution to the problem of induction leaves open the conditions under which regularities get habituated. Not all regularities get habituated: for example, while it's true that the evidence to date has supported the claim that all emeralds are green, it's also true that the same evidence is consistent with the claim that all emeralds are grue, where an emerald is grue if examined before some future time t and found to be green or otherwise is blue. The riddle is to give criteria under which the first regularity is supported by the evidence to date but the second regularity is not.

Kedar: Can't we disqualify the second hypothesis on the grounds that it employs a disjunctive predicate and refers to a particular time instant? Proper scientific predicates shouldn't have such characteristics.

Ram: Goodman has a nice response to such an objection. Analogous to grue, he defines another predicate, bleen such that an object is bleen if examined before t and found to be blue and green otherwise. If we adopt grue and bleen as our primitive predicates then green and blue turn out to have disjunctive definitions which refer to a time instant. The moral Goodman wants us to draw is that preferring one set of predicates over the other is purely a matter of practice, practice conditioned by which predicates have been used successfully in past projections.

Kedar: Couldn't we again appeal to our constitutions, saying we're so constituted as to key-in on green things rather than grue things?

Ram: That's another response to Goodman's riddle, to point out that green things are a 'natural kind' for us, that the reason we favor green is not simply practice which could've just as easily favored grue. Our physical nature predisposes us to pick out green things rather than grue things.

But both practice, or entrenchment as Goodman calls it, and the constitution argument make it a little arbitrary that 'all emeralds are green' is better supported by the emeralds we've actually seen than 'all emeralds are grue'. Science should be on a sounder footing.

Kedar: I presume your solution to Goodman's riddle puts it on a sounder footing?

Ram: It does. My argument, which is detailed in a paper called 'Resolution of Grue Using a Support Measure' published in PhilSci Archive, is essentially as follows: denying 'all emeralds are green' lowers the likelihood of having found green emeralds more than denying 'all emeralds are grue' lowers the likelihood of having found grue emeralds. This is because when we deny all emeralds are grue we're casting doubt on emeralds after t being blue, which is consistent with them being green like in our sample. Mathematically it can be shown that if some evidence is less likely given the denial of a hypothesis than given the denial of a second hypothesis, then the evidence supports the first hypothesis more than the second hypothesis. In other words, the evidence to date supports 'all emeralds are green' more than it supports 'all emeralds are grue'.

Kedar: I'll have to check out the PhilSci Archive paper, but it does sound intriguing. It is refreshing to see you not straddling the fence on an issue.

Ram: You could say I saved the best for last since I think we've covered about all the bases on the topic of justification.

Kedar: Say, now that we're at the end, what would you make of our talk, not only this discussion but our philosophical discussions in general? Good, bad or indifferent as scratching an itch? I fear it's the last, which may still be a little bad since there is so much other good things we could be doing.

Ram: Oh it's not so bad. Philosophy is not just our itch to scratch. We'll just have to see to it that other people's inquisitive itches are scratched by our philosophizing as well.

www.geoffreyklempner.net

klempner@fastmail.net

International Society for Philosophers

Wisdom begins with wonder