VAGUENESS: A CRASH COURSE
Type of course: Advanced Undergraduate/Postgraduate.
Prerequisites: None, but some knowledge of the philosophy of language and logic would be useful.
Place: Room 222, Department of Philosophy (S20A), University of Helsinki.
Date: May 12th-16th 2003.
Format: 5 x (1hr lecture + 1hr seminar).
Lecturer: Dr. Patrick Greenough, University of St. Andrews, Scotland, UK.
Touching your mother's foot is incest because all the rest is a matter of degree (or so said Diogenes). That's just one expression of the puzzle of vagueness. Here's another: the passage of one second cannot mark the transition from being a pupa to being a butterfly--if something is a pupa at one time then in all close instants it remains a pupa; alas, it follows from this, via trivial logic, that there are no butterflies. Or again: it's vague where the Highlands of Scotland begin and end, so, a small step in the direction of London cannot mark the boundary between the Lowlands and the Highlands. But then it follows, via trivial logic, that one is unable to leave the Highlands (even when in London). What's driving these paradoxical arguments seems to be the very vagueness of the terms involved: such terms as 'incest', 'butterfly', 'pupa', 'The Highlands' are all vague and such vagueness seems to make them tolerant to marginal change. The puzzles of vagueness are not only deep (in that they admit of no uncontroversial and entirely satisfactory solution), they are also broad, for vague language is everywhere. In this course, you will be introduced to the various puzzles of vagueness and whether and how we might best address them. We will tackle such as questions as: Does the possibility of vagueness entail that there simply cannot be a logic of natural language? Does it entail that language is governed by inconsistent rules? Or does vagueness require some special or deviant logic? Is vagueness a special species of ignorance? Is the world, in some sense, vague? Is there an uncontroversial definition of vagueness or can we only isolate the phenomenon from within some substantive and controversial conception? What is higher-order vagueness and why is it considered to be such a puzzling phenomenon? Must the truth about vagueness be so strange? In what exact way are vague expressions tolerant?
The course will consist of five lecture-seminars of two hours each. During the first hour I will give a lecture on the topic in hand while during the second hour we shall convert to a seminar in order to discuss issues raised in the lecture and the set reading. No specialist knowledge is presupposed, though it might be useful if you have done some basic logic and some philosophy of logic and language before.
Seminar 1. What is Vagueness and Why is it a Problem?
Seminar 2. Fuzzy Logic and Degrees of Truth: the Cool Wind of Sanity Fanning our Brow?
Seminar 3. Closing the Curtains on Incompleteness: is Super-Truth Really so Super?
Seminar 4. Dreaming of a Precise Meta-language: the Problem of Higher-order Vagueness.
Seminar 5. How to be an Epistemicist: Must the Truth about Vagueness be so Strange?
The set text is:
Keefe, R. & Smith, P., eds. (1996): Vagueness: A Reader, Cambridge, MA: MIT Press.
- This text is a superb collection of many of the most important writings on vagueness from the early 20th Century (Russell, Black, and Hempel) to a selection of the most important papers written after the explosion of interest in vagueness post 1970. It also contains a comprehensive introduction which gives an excellent overview of the vagueness debate and the puzzles to which vagueness gives rise, together with a discussion of the leading theories of vagueness. This introduction is well worth reading several times throughout the course. (Please bring the set text and previous handouts to each seminar.)
ASSESSMENT AND CREDIT
This is a 2 credit course.
To gain credit you must (a) attend all the seminars having done the set reading and answered any set questions, and (b) submit a coursework essay of between 2500-3000 words (including footnotes and references but excluding bibliography).
The exact deadline for submitting essays will be agreed at the seminars themselves, but it will be about two weeks after the course finishes.
- Choose one of the following questions:
1) What is the puzzle of vagueness? Does this puzzle show us that natural language is intrinsically incoherent?
2) Critically evaluate the virtues and vices of the supervaluational conception of vagueness.
3) ‘The truth about vagueness must be strange.’ Critically assess this claim.
4) Is vagueness a species of ignorance?
5) ‘Truth admits of degrees.’ Can we exploit this thesis to completely resolve the puzzle of vagueness?
Below are details of the general reading, set reading and additional reading on the topic of vagueness. In many cases, I have given some 'handrails' in the form of brief comments on the content and/or relevance of some of the books and articles mentioned. These handrails should help you to focus your reading and get some sense of how the debates pan out. More detailed bibliographies for the course can be found in many of the books mentioned below.
RECOMMENDED WORKS ON VAGUENESS
- Williamson, T. (1994): Vagueness, London/New York: Routledge. (This is THE book on vagueness. A modern classic. It's a critical appraisal of conceptions of vagueness from the stoic logicians through to the views of Russell, Frege, Wittgenstein, Peirce, Black and Hempel, to the modern discussion of vagueness post 1970. The chapters on many-valued logics, supervaluation, and nihilism are particularly valuable. Added to that, Williamson offers the most thorough defence of the epistemic conception of vagueness to date. Highly recommended. If you want to read beyond the set reading then this is the book to buy and digest. Invaluable.)
- Keefe, R. (2000): Theories of Vagueness, Cambridge: Cambridge University Press. (Well worth reading. Keefe's main aim is to defend a supervaluational conception of vagueness from the many criticisms that view has received--particularly from Williamson. But there is also a very useful introductory chapter (similar in content to the introductory article in Keefe and Smith 1996), a useful chapter on what we should expect from a theory of vagueness, a great chapter on epistemicism, and useful chapters on many-valued approaches, plus a chapter on the neglected pragmatic approach of Lewis and Burns.)
- Sorenson, R. (2001): Vagueness and Contradiction, Oxford University Press. (A quirky and highly readable book that, in my view at least, concedes too much ground to the nihilistic conception of vagueness from within the perspective of epistemicism. Well worth a read at the end of the course when you have digested what is at stake. Read Williamson and Keefe first.)
- Sainsbury, R. M. and Williamson, T. (1997): 'Sorites', in the Blackwells Companion to the Philosophy of Language, edited by Hale and Wright. (A superb short survey, well worth reading.)
- Tye, M. (1995): ‘Vagueness: welcome to the quicksand’, Southern Journal of Philosophy, 33, (supplement), pp. 1–22. (Well worth reading. I have a photocopy if you need to borrow it.)
- Hyde, D. (2000): 'Recent Work on Vagueness', Philosophical Books. (A useful survey article. Highly recommended.)
- Greenough, P. (2003): Vagueness: A Minimal Theory, Mind 112. (Not exactly an introductory article, but the author does attempt to say what vagueness is from a perspective which is as neutral as possible on matters both logical and philosophical.)
RECOMMENDED WORKS ON THE PHILOSOPHY OF LOGIC IN GENERAL
Sainsbury, R. M. (1995): Paradoxes, 2nd edition, CUP (This is a pretty introductory text so if you find yourself stuck with some of the other reading then this is the text for you. Contains an excellent chapter on the sorites paradox. Highly recommended.)
Read, S. (1995): Thinking about Logic, OUP. (An excellent book with a chapter on vagueness.)
Haack, S. (1978): Philosophy of Logics, Cambridge: Cambridge University Press. (Still going strong after all these years. There's useful stuff on alternative logics, and some, but not much, stuff on vagueness.)
Haack, S. (1996): Deviant Logic, Fuzzy Logic. (Overlaps somewhat with the above but still to be recommended, particularly for its discussion of fuzzy logic.)
Clark, M. (2002): Paradoxes from A to Z, London: Routledge. (Comprehensive discussion of all the well known logical and philosophical paradoxes. Short essays on each paradox, useful short guides for further reading.)
Goble, L. (2001): The Blackwells Guide to the Philosophy of Logic. (Has an article on many-valued logic and an article on intuitionistic logic.)
- Sainsbury, R. M. (1996): 'Philosophical Logic', in A. C. Grayling (ed.) Philosophy: A Guide Through the Subject, OUP. (Useful background reading or in order to brush up on the philosophy of language and philosophical logic.)
READING WEEK BY WEEK
Note: I've tried to rank the additional reading in a descending order of usefulness (for the purposes of this course). So, if you are having some trouble with the set reading have a look at one or two of the additional readings. Equally, if you'd like to know more, read, read, and read, again the additional texts.
SEMINAR 1: WHAT IS VAGUENESS AND WHY IS IT A PROBLEM?
Dummett, M. A. E. (1975): ‘Wang’s paradox’, Synthese, 30, pp. 301–24, and reprinted in the set text. (This is THE text which put vagueness firmly back on the philosophical agenda (firstly in Britain, then in the USA). After toying with a so-called supervaluational conception of vagueness, Dummett concludes that such a conception makes vagueness easily eliminable. Since vagueness is an essential feature of language--we couldn't possibly employ a sharp language--and since vague language appears to be governed by rules which issue in contradictory instructions then Dummett concludes that natural language is essentially inconsistent. It's for this reason that Dummett has been said to defend a nihilistic conception of vagueness--mostly notably in the local case of phenomenal predicates, predicates whose application is determined just by how things appear.)
Additional Reading on the question 'what is vagueness?':
- Sainsbury, R. M. and Williamson, T. (1997): 'Sorites', in the Blackwells Companion to the Philosophy of Language, edited by Hale and Wright. (A superb short survey, well worth reading to get a general overview of the various positions.)
- The introduction of the set text: Keefe, R. & Smith, P., eds. (1996): Vagueness: A Reader, Cambridge, MA: MIT Press. (Here you will find Keefe and Smith make the important distinction between the three facets of vagueness outlined in the first lecture: vagueness qua sorites-susceptibility, vagueness qua tolerance (vagueness qua fuzzy boundaries), and vagueness qua borderline cases. However do note that these authors betray a tendency to offer a initial characterisation of vagueness in non-epistemic terms. Hence their minimal theory of vagueness prejudices the case against the epistemic conception of vagueness--hence this theory is what Wright calls a 'proto-theory' of vagueness and not really a minimal theory at all.)
- Sorenson, Roy: 'Vagueness', Stanford On-Line Encyclopaedia (Link).
- Hyde, D. : 'Sorites Paradox', Stanford On-Line Encyclopaedia (Link).
- Merricks, T. (2001): 'Varieties of Vagueness', Philosophical and Phenomenological Research, 62, pp. 145-157. (Merricks disputes the traditional tripartite division of theories of vagueness into semantic, ontic, and epistemic. In particular, he argues that semantic theories of vagueness (vagueness is a reflection of semantic incompleteness) is really at bottom either an ontic or an epistemic conception of vagueness.)
- Greenough, P. (2003): Vagueness: A Minimal Theory, Mind 112. (Here various ways of defining vagueness are mooted. It is concluded that, as we experience it at least, vagueness is epistemic tolerance.)
Additional Reading on the Nihilistic Conception of Vagueness:
- Williamson, T. (1994); Vagueness, ch. 6 for a superb discussion of what he calls global nihilism and local nihilism.
- Wright, C: (1976): ‘Language mastery and the sorites paradox’, in G. Evans and J. McDowell (eds), Truth and Meaning: Essays in Semantics, Oxford: Clarendon Press, pp. 223–47. (Wright defends a conditional form of nihilism: if a certain rule-governed picture of language is correct then language is indeed governed by rules which issue in contradictory instructions as Dummett suggests. Wright takes this to show that we should reject the rule-governed picture of language in favour of something more behaviouristic.)
- Wright, C. (1987): ‘Further reflections on the sorites paradox’, Philosophical Topics, 15, pp. 227–90. (This is a development and qualification of Wright's earlier paper, particularly in response to the tachometer paradox given by Peacocke (1981). Wright offers a number of ideas in this paper: that there might not be a uniform solution to each type of sorites paradox, that higher-order vagueness but not first-order vagueness is intrinsically paradoxical, and the thought that vagueness is essentially bound up with Wittgenstein's famous rule-following considerations. To a large degree, Wright has now modified his views--see Wright (2001))
- Rolf, B (1984): 'Sorites', Synthese 58, pp.219-50. (Rolf defends a form of nihilism in this paper.)
- Unger, P. (1979): ‘There are no ordinary things’, Synthese, 41, pp. 117–54. (This is the nihilist view par excellence. Unger thinks that we should take the sorites paradox as showing that there are no heaps, no bald men, no red colour patches. Vague predicates are empty. See Williamson ch.6 and Keefe and Smith 1996 pp. 12-13 for some relevant discussion.)
- Tye, M. (1990): ‘Vague objects’, Mind, 99, pp. 535–57. (Tye defends the view that there are vague objects and endeavours to show how this thesis can be expressed using Kleene's strong three-valued logic which also contains a 'definitely' operator. Such a view is mildly nihilistic in the sense that it entails that vague concepts do not determine sets. See Sainsbury and Williamson (1997) for a brief account and criticism of this view.)
- Russell, B. (1923): 'Vagueness', Australasian Journal of Philosophy, and reprinted in the set text. (Russell famously says in this paper that logic habitually assumes that our symbols are precise--thus logic can only really apply to an imagined celestial existence.)
- Eklund, M. (2002): 'Inconsistent Languages', Philosophical and Phenomenological Research, 64. (Excellent stuff.)
- Eklund, M. (in draft): 'What Vagueness Consists in', (Link).
- Graff, D. (2001): 'Phenomenal Continua and The Sories', Mind 110. (Graff argues that phenomenal sorites are different than standard sorites and that we should accept the inference from x looks red and x looks the same as x to y looks red (when x and y are distinct but phenomenally indistinguishable). Hence, phenomenal indistinguishability is transitive.)
- Sider, T. & Braun, D. (in draft): 'Vague, so Untrue', (Link). (A Fregean approach--intriguing!)
SEMINAR 2: FUZZY LOGIC AND DEGREES OF TRUTH: THE COOL WIND OF SANITY FANNING OUR BROW?
Machina, K. (1976): ‘Truth, belief, and vagueness’, Journal of Philosophical Logic, 5, pp. 47–78 and reprinted in the set text. (This might be a bit dry in parts, but if you find this a bit hard-going have a look at Keefe and Smith's summary in their introduction, or the article 'Sorites' by Sainsbury and Williamson (1997) where there is a brief discussion of this proposal, or indeed you might like to look at Sainsbury (1989) or Lakoff (1973)).
- Sainsbury, R. M. Paradoxes, Chapter Two, (a pretty easy read).
- Sainsbury, M. (1989): ‘Tolerating vagueness’, Proceedings of the Aristotelian Society, 89, pp. 33–48. (This is a clear and engaging defense of a many-valued conception of vagueness. Much of this article is spent trying to rebut the criticisms of such a proposal given by Wright (1987). Sainsbury concedes that the approach sketched here does not as it stands handle higher-order vagueness. It is for just this reason that he later came to reject this proposal in favour of the approach in Sainsbury (1990, 1991). Nonetheless, well worth looking at.)
- Lakoff (1973): 'Hedges: A Study in Meaning Criteria', Journal of Philosophical Logic 2, pp. 458-508. (Written by a leading linguist, this is a highly readable paper on the basics of one form of fuzzy logic and the semantics of modifier term such as 'very', 'sort of', 'rather'. Lakoff seems unaware of the problem of higher-order vagueness and there is some evidence to suggest that he accepts a hybrid many-valued theory in which the degree of truth of a vague sentence is perfectly definite but unknown.)
- Sanford, D. (1976): ‘Competing semantics of vagueness: many values versus super-truth’, Synthese 33, pp. 195–210. (Sanford attempts to defend the validity of the so-called 'penumbral connections' from within the framework of a many-valued approach to vagueness.)
- Edgington, D. (1996): ‘Vagueness by degrees’, in the set text, pp. 294–316 (Edgington offers a novel and intriguing version of a degree-theoretic response to vagueness--one where the truth-functionality of disjunction and conjunction is not preserved. Certainly worth looking at.)
- C. Peacocke: (1981): 'Are Vague Predicates Incoherent?', Synthese 46, pp. 121-41.
- Zadeh, L (1975): 'Fuzzy Logic and Approximate Reasoning', Synthese 30, pp. 407-28. (This an accessible paper by the founder of the theory of fuzzy sets.)
- Goguen, J. A. (1969): 'The logic of inexact concepts', Synthese 19, pp. 325-73.
SEMINAR 3: CLOSING THE CURTAINS ON INCOMPLETENESS: IS SUPER-TRUTH REALLY SO SUPER?
Fine, K. (1975): ‘Vagueness, truth, and logic’, Synthese, 30, pp. 265–300, reprinted in the set text. (This is THE account and defence of the supervaluational conception of vagueness. It closely resembles the conception touted (but then rejected) by Dummett (1975). What is striking about this paper is that Fine seems to think vagueness is simply the phenomenon of borderline cases but hardly seems to recognise that vagueness is also a species of tolerance. This is a detailed and at times very difficult paper. Refer to some of the reading below if you get stuck.)
- Sainsbury, R. M. (1995): Paradoxes, Chapter Two.
- Hyde, D. (1997): ‘From heaps of gaps to heaps of gluts’, Mind, 106, pp. 641–60. (This a very clear paper which contrasts a standard supervaluational conception with its 'dual' paraconsistent conception, namely a subvaluational conception in which vague statements are taken to be both true and false, but where the law of non-contradiction is nonetheless preserved. Hyde argues for the modest thesis that subvaluation is just as plausible as its more popular cousin, supervaluation.)
- Williamson, T. (1994): Vagueness, chapter 5. (This is the most complete criticism of supervaluation to date. Roughly: supervaluation lacks a proper truth-theory, proof-theory, and cannot do justice to higher-order vagueness. Enjoyable stuff.)
- Keefe, R. (2000): Theories of Vagueness, Chapter 7 and 8. (Keefe's main aim in these chapters is to defend supervaluation from the criticisms given by Williamson. Her key idea with respect to the problem of higher-order vagueness (see seminar six) is to adopt a hierarchy of distinct meta-languages--much as Tarski proposes such a hierarchy in order to combat the liar paradox.)
- McGee, V. and McLaughlin, B. (1995): ‘Distinctions without a difference’, Southern Journal of Philosophy 33, (supplement), pp. 203–51. (These authors defend a non-standard 'modal' version of supervaluation in which classical logic is not restricted but rather augmented by the addition of a 'definitely' operator.)
- Williamson, T. (1995): ‘Definiteness and knowability’, Southern Journal of Philosophy, 33, (supplement), pp. 171–91. (This paper picks up on a claim made in Williamson (1994, ch.5 section 7, ch.6, p.195) that those such as McGee and McLaughlin who hope to preserve classical logic via a modal version of supervaluation fail to provide a convincing case that the operator 'definitely' does not bear an epistemic reading. Effectively, Williamson's overall aim in this paper is to suggest that any theory which validates classical logic and classical semantics entails an epistemic conception of vagueness.)
- Field, H. (1994b): ‘Disquotational truth and factually defective discourse’, Philosophical Review, 103, pp. 405–452, reprinted with emendations in his collection Truth and the Absence of Fact, New York: Oxford University Press, 2001. (Field effectively defends a view similar to that of McGee and McLaughlin. Here Field is only primarily interested in distinguishing the vague from the non-vague and not in giving a particularly detailed account of the source of linguistic vagueness.)
- Akiba, K. (1999): ‘On super- and subvaluationism: a classicist’s reply to Hyde’, Mind, 108, pp. 727–32. (Akiba attempts a rapprochment between supervaluation and subvaluation via developing these logics as modal extensions of classical logic. The advantage of this view is that classical patterns of inference can be preserved. One also represents super-truth as structurally similar to necessary truth and sub-truth as structurally similar to possible truth. Hyde replies to this paper in the same volume of Mind.)
- Mills, A. (1995): ‘Unsettled problems with vague truth’, Canadian Journal of Philosophy, 25, pp. 103–117. (A useful attempt to get to grips with the various possible interpretations one might give to a 'definitely' operator.)
- Koons, R. (1994): ‘A new solution to the sorites problem’, Mind 103, pp. 439–449. (This paper is much neglected. Koons defends a 'hybrid' conception of vagueness which accommodates the intuition that language is to indeterminate to the extent that there simply cannot be a fact of the matter in borderline cases, but that the limits of this borderline area are sharp but unknown Hence, Koons is not required to give a (semantic) model of higher-order vagueness--though he is still beholden it seems to give an epistemic model of higher-order vagueness.)
SEMINAR 4: DREAMING OF A PRECISE META-LANGUAGE: THE PROBLEM OF HIGHER-ORDER VAGUENESS
Sainsbury, M. (1990): ‘Concepts without boundaries’, inaugural lecture, published by King’s College London, Dept. of Philosophy, and reprinted in the set text. (This a highly readable article which endeavours to lay the foundation for a genuinely indeterminist conception of vagueness--one which does not get embroiled in the problem of higher-order vagueness via the adoption of a sharp meta-language. Sainsbury rejects any form of set-theoretical model of language, including many-valued or supervaluational conceptions, in favour of an ontology of vague sets. The trouble with such an intriguing proposal is how one might best express this proposal within some logical framework. Sainsbury suggests adopting Tye's three-valued semantics (Tye 1990), but such a logic mishandles some of our basic intuitions (see Sainsbury and Williamson 1997).
- Sainsbury, M. (1991): ‘Is there higher-order vagueness?’, Philosophical Quarterly, 41, pp.167–82. (This is a companion piece to his 1990 article. Well worth reading. It's here that Sainsbury develops his 'polar' model of concepts. However, Sainsbury now seems to have abandoned the view espoused in this paper and his 1990 paper. In Greenough (2003) I argue that it is possible to resurrect what Sainsbury calls in this paper 'the characteristic sentence approach' to defining vagueness.)
- Williamson, T. Vagueness, ch.5 section 6. (See particularly pp. 160-161.)
- Keefe, R. (2000): Theories of Vagueness, last chapter. (It's here that Keefe recognises that supervaluation is in deep trouble because of the arguments given by Sainsbury, and, in turn, Williamson with respect to higher-order vagueness. She hopes to rescue the view by proposing that supervaluational semantics requires a infinite hierarchy of distinct meta-languages in order to express what the truth-conditions of object-language sentences are. Vertiginous stuff.)
- Hyde, D. (1994): ‘Why higher-order vagueness is a pseudo-problem’, Mind, 103, pp. 35–41. (Intriguing attempt to defend the thesis that the notion of 'borderline case' is ambiguous between the type of borderline cases which can arise from terms which are merely semantically incomplete and the type of borderline cases, i.e. genuine cases of vagueness, in which a notion of higher-order vagueness is built in from the very start. Hyde alleges that this solves the problem of what he calls the 'iterative conception of higher-order vagueness. Worth looking at, though the issues are pretty tough, so be warned.)
- Wright, C. (1992b): ‘Is higher-order vagueness coherent?’, Analysis, 52, pp. 129–39. (This paper tackles higher-order vagueness from a different perspective, and relates back to material first given in his 1987 paper and discussed by Sainsbury in 1991. Wright offers the following challenge: first-order vagueness can receive an unproblematic definition, while an attempt to define higher-order vagueness issues in paradox.)
- Edgington, D. (1993): ‘Wright and Sainsbury on higher-order vagueness’, Analysis, 53, pp. 193–200. (Edgington resolves Wright's paradox in one of two ways: either reject his rule DEF on principled grounds or reject the inference of reductio ad absurdum. The latter is the best option in my view--should you want to sponsor a indeterminist conception of vagueness.)
- Heck, R. (1993): ‘A note on the logic of (higher-order) vagueness’, Analysis, 53, pp. 201–8. (Heck resolves Wright;'s paradox of higher-order vagueness differently from Edgington, though the effect is similar. Effectively Heck argues that Wright's rule DEF is not valid under the scope of indirect proofs such as reductio or conditional proof. One consequence of this is that the deduction theorem fails since while D(a) is a logical consequence of A, it is not provable that if D(A) then A. In my view, any logic which lack the deduction theorem is no logic at all--so Edgington's second response is better.)
- Burgess, J. (1990): ‘The sorites paradox and higher-order vagueness’, Synthese 85, pp. 417–74. (In this article and the next, Burgess defends the view that the orders of higher-order vagueness terminate at some (unknowable) point. For some relevant, but difficult, discussion, see Williamson 1999. In Greenough(2003) I argue that this an untenable view.)
- Burgess, J. (1998): ‘In defence of an indeterminist theory of vagueness’, Monist, 81, pp. 233–52.
- Williamson, T. (1999): ‘On the structure of higher-order vagueness’, Mind, 108, pp. 127–43. (Not for the faint-hearted. This article develops the formal appendix of Williamson (1994) and endeavours to give a precise formulation of higher-order vagueness within a standard modal system.)
- Sorenson, R. A. (1985): ‘An argument for the vagueness of "vague"’, Analysis, 45, pp. 134–7. (This argument is exploited by Hyde, but arguably it is based on a mistake belief that just because a sentence is vague does entails that the predicate of the sentence is vague. See Deas (1989).)
- Deas, R. (1989): 'Sorenson's sorites', Analysis. (This article shows, amongst other things, why 'true' is not a vague predicate. Worth looking at)
- Varzi, A, (2003): 'Higher-order Vagueness and the Vagueness of "Vague"', Mind 112.
- Hyde, D. (2003): 'Higher-Order Vagueness Reinstated', Mind 112.
- Graff, D. (in draft): 'Infinitely Higher-order Vagueness (and other problems for Supervaluation)', (Link).
- Greenough, P. (2003): Vagueness: A Minimal Theory, Mind 112. (In the last section, I argue that higher-order vagueness is a fact of life for everyone.)
SEMINAR 5: HOW TO BE AN EPISTEMICIST: MUST THE TRUTH ABOUT VAGUENESS BE SO STRANGE?
Williamson, T. (1992): ‘Vagueness and ignorance’, Proceedings of the Aristotelian Society, Supplementary volume, 66, pp. 145–62, and reprinted in the set text
Additional Reading on Standard Epistemicism:
- Simons, P. (1992): ‘Vagueness and ignorance’, Aristotelian Society, suppl. 66, pp. 163–77. (Simons seems to have been the first to entertain what I call an optimistic conception of vagueness whereby the truth-values of borderline statements, and indeed the cut-offs drawn by vague terms are in principle discoverable.)
- Keefe, R. (2000): Theories of Vagueness, Cambridge: Cambridge University Press, ch. 3. (This chapter contains a useful evaluation of Williamson's brand of epistemicism, particularly his employment of margin for error principles to explain why we are ignorant in borderline cases. There is also a useful discussion of Williamson's thesis that 'meaning supervenes on use in unsurveyably chaotic ways'. Recommended reading.)
- Wright, C. (1995): 'On the epistemic conception of vagueness' Southern Journal of Philosophy, supplementary volume.
- Sainsbury, M. (1995a): ‘Vagueness, ignorance, and margins for error’, British Journal for the Philosophy of Science, 46, pp. 589–601. (This excellent review of Williamson's 1994 book is mostly an attempt to make sense of the particular epistemology Williamson employs in developing his epistemic conception of vagueness. Highly recommended.)
- Cargile, J. (1969): (This is one of the first defences of the epistemic view of vagueness since the stoic logicians. Cargile is an extreme realist and an eminently clear writer to boot.)
- Campbell, R. (1974): (Campbell is not quite the standard epistemicist as he seems to locate the source of ignorance in borderline cases in 'semantic uncertainty'. This suggests that, unlike Williamson, he takes speakers of the language to fail to know exactly what vague statements mean--they only have partial understanding of the meaning (or truth-conditions) of vague statements. )
- Sorenson, R. A. (1988): Blindspots, Oxford: Oxford University Press.
- Horwich, P. (1997): ‘The nature of vagueness’, Philosophical and Phenomenological Research, 57, pp. 929–35. (Horwich is an epistemicist of the pessimist variety. In many ways, Horwich defends the strongest form of pessimism in the literature--not only does he think that it is metaphysically impossible to know the cut-offs drawn by vague terms (or the truth-values of vague statements) he takes it to be conceptually impossible to do so. Williamson thinks (or at leas leaves it open) that it is at least metaphysically possible to know the cut-offs drawn by vague terms. )
- Williamson, T. (1992a): ‘Inexact knowledge’, Mind, 101, pp. 217–42. (Williamson employs so-called margin for error principles to explain why the KK principle must fail and why we lack knowledge in borderline cases. This model of knowledge does not entail his version of epistemicism, nor vice versa, however it does provide added support for the epistemic view in that it discharges an explanatory obligation placed upon the view--namely to explain why we are ignorant in borderline cases.)
- Williamson, T. (1994): Vagueness, ch. 7 and ch.8.
- Williamson (1996b): ‘Wright on the epistemic conception of vagueness’, Analysis, pp. 39–45.
- Williamson, T. (1996d): ‘What makes it a heap?’, Erkenntnis, 44, pp. 327–339.
- Williamson, T. (1997a): ‘Imagination, stipulation, and vagueness’, in E. Villanueva (ed.), Truth: Philosophical Issues, vol. 8, Atascadero, CA: Ridgeview. (Amongst other things, Williamson endeavours to defend his version of epistemicism against the charge that one can stipulate a meaningful to term to give rise to borderline cases. Such a term will fail to validate bivalence. Williamson responds to this problem with a view that such a stipulation is, in a way, unfinished and still answerable to future stipulations which may complete the meaning of the term. Given that one can in any case adopt non-bivalent forms of epistemicism (e.g. Koons 1994), Williamson's efforts seem unnecessary in any case.)
- Graff, D. (2002): 'An Anti-Epistemicist Consequence of Margin for Error Semantic for Knowledge', Philosophical and Phenomenological Research, 64, (Link).
- Gómez-Torrente, M. (1997): Two Problems for an Epistemicist View of Vagueness, in E. Villanueva (ed.), Philosophical Issues VIII: Truth, Ridgeview, Atascadero (California).
- Gómez-Torrente, M. (2002): 'Vagueness and Margin for Error Principles', Philosophical and Phenomenological Research 64.
- Dorr, C (in draft): 'Vagueness Without Ignorance', (Link).
- Sorenson, R. (2001): Vagueness and Contradiction, OUP. (I'm writing a review on this which will appear in Phil Quarterly soonish.)
Additional Reading on Non-Standard Epistemicism (e.g. Quandarism)
- Wright, C. (2000): 'On Being in a Quandary', Mind 110. (This is a long and demanding paper, so you should only read this at the end of the course. It's an intriguing defense of intuitionistic logic as the correct logic for vagueness (cf. Putnam 1983). What's novel about this position is that Wright seeks to portray his intuitionistic solution as a form of the epistemic conception of vagueness. The slogan for this view is: 'epistemicism without bivalence'--vagueness is a special species of ignorance that generates what Wright calls quandary in borderline cases--but this does not mean that vague statements are either true or false (nor that they are unknowable). This paper is hard in parts but very rewarding--if this view cannot be stabilised then the standard epistemicism of Williamson is favourably placed.)
- Wright, C. (in draft): 'Vagueness: A Fifth Column Approach'.
- Rosenkranz, S. (forthcoming): 'Wright on Vagueness', Mind.
- Wright, C. (forthcoming): 'Reply to Rosenkranz', Mind.
© Patrick Greenough, April 2003.