Vagueness: A Crash Course
Greenough (Patrick)
Source: St. Andrew's Website
Paper - Abstract

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Author’s General Overview

  1. 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).
  2. 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.
  3. 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?
  4. 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.

  1. What is Vagueness and Why is it a Problem?
  2. Fuzzy Logic and Degrees of Truth: the Cool Wind of Sanity Fanning our Brow?
  3. Closing the Curtains on Incompleteness: is Super-Truth Really so Super?
  4. Dreaming of a Precise Meta-language: the Problem of Higher-order Vagueness.
  5. How to be an Epistemicist: Must the Truth about Vagueness be so Strange?


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