Kit Fine (born
March 26, 1946) is Silver Professorof Philosophyat New York University. He previously taught for several years at UCLA. The author of several books and dozens of articles in international academic journals, he has made notable contributions to the fields of philosophical logic, metaphysics, and the philosophy of languageand also has written on ancient philosophy, in particular on Aristotle's account of logic and modality.
Fine received his Ph.D. from the
University of Warwickin 1969, under the supervision of A. N. Prior. He is a former editor of the " Journal of Symbolic Logic" and a corresponding Fellow of the British Academy. He is the ex-husband of the author Anne Fine.
Vagueness, Truth and Logic (1975)
In his paper, Vagueness, Truth and Logic [From Synthese, 30, (1975) 265-300; D. Reidel Publishing Company, Dordrecht-Holland] , Kit Fine defends an interpretation of a
non-classical logicin order to explicate vaguenessin some referring sentences. The view put forth makes the central claim that a vague sentence is one which can be made true or false by precisification, but which is neither before it is made precise. Such a sentence thus holds an intermediary position between true and false. This paper stands in a recent tradition of denying Aristotle's Law of the Excluded Middle(arguably not to be confused with the Law of Bivalence), which states that any given sentence is either true or it is false.
He begins the paper by presenting traditional non-classical logics with multiple truth-values, such as those developed by
Jan Łukasiewiczand Lotfi Zadeh, and then criticizes their short-comings with respect to truth-functionality. Here he introduces the notion of penumbral connections, which are logical relations between sentences which are indeterminate--relations which logics have not respected.
He then defines specification space as the set of ways of assigning indeterminate truth values to logical operators and predicates (with emphasis on the predicates), such that they respect classicality where truth-values are classical. There may be many spaces. One selects an appropriate specification space intuitively, under the conditions of fidelity, stability, and completablility. Fidelity is simply the classicality guarantee. Stability guarantees that no improved specification loses determinate truth-values. (Thus, as you specify, no sentence goes from either true or false to indeterminate; the hope is that indeterminate sentences become true or false.) Completability is the condition that, on the domain of specifications, ∀(t)∃(u)(u ≤ t) where 'x ≤ y' means that every classical truth-value assignment in x is the same assignment in y. A statement is true-simpliciter if and only if it is true at the appropriate specification.
To give an example, take the predicate 'the x is red' and 'the x is pink' and there is some borderline case of a pinkish-reddy 'c'. Under traditional many-valued logics, where Pc and Rc are indeterminate, (Pc & Rc) is indeterminate. However, the conjunction of the statements in natural English is obviously a false one, no matter how you parse the predicates. The claim is that we are operating under a common specification, the appropriate one, but that we might extend this specification to one which assigns Pc and Rc classical values, thus giving their conjunction a classical value. There are many such extensions. More importantly, though, (Pc & Rc) is false-simpliciter because the only specifications under which the conjunction is true are specifications which violate the appropriate one. Likewise, for any statement of the form Px & ~Px, even where Pa is vague or indeterminate, the conjunction is false.
Here an expression is precisified by precisifying its terms.
The project is to then formalize an understanding of language which accomodates increased pressure on the terms. As language faces new situations, it must adopt new distinctions.
The problem Kit now addresses in his paper is the interpretation of specification: Either (i) we can consider expressions as ordered pairs of a statement A and precisification t, in the notation (A,t); or (ii) we can take each expression to be associated with one precisification, and each precisification has a unique set of expressions. The former best models the behavior of our language, because according to this account each point of extension corresponds to a real-language specification. Supposedly, this is necessary if no extension of 'red' is to ever overlap with 'pink'. (ii), however, has the advantage that extension relations are already in the extensions themselves. The analogue to real language is that, by grasping the meaning of a term you already understand the ways in which you might make it precise. Where the "actual" meaning is what helps determine its instances and counter-instances, its "potential" meaning is the possibilities for precisification, and it's meaning-simpliciter is a function of both.
In essence, the difference is that the first interpretation takes precisification to be a response to new penumbral connections (new problems). One can exclude subsequent specification and still extend the language. Not so on the latter account. Assume that there are no penumbral connections between 'red' and 'scarlet'. To require that all scarlet objects are red, then, faces no new penumbral connection--there is no issue of vagueness or separation between the two--and so on the former acount this is not an extension of the language. On the latter account, it is a precisification because it informs the language of future possibilities of precisification.
The paper then presents a series of technical discursions on completability, higher-order vagueness, and more. These topics are merely demonstrations of ways to adapt the theory to other formalizations. The essential and highly original contribution of the work is to treat vagueness like the contingency operator in
modal logic. Rather than treating vaguess as just another truth-value, he considers vagueness a field of possible interpretations of a language, formal or natural.
* "Semantic Relationism". Blackwell, 2007. ISBN 978140-510844-7
* "Modality and Tense: Philosophical Papers". Oxford University Press, 2005. ISBN 0-19-927871-7
* "The Limits of Abstraction". Oxford University Press, 2002. ISBN 0-19-924618-1
* "Reasoning With Arbitrary Objects". Blackwell, 1986. ISBN 0-631-13844-7
* "Worlds, Times, and Selves" (with A. N. Prior). University of Massachusetts Press, 1977. ISBN 0-87023-227-4
* [http://philosophy.fas.nyu.edu/object/kitfine Fine's web page] at
New York University.
* [http://www.formalontology.it/finek.htm Annotated bibliography of Fine's writings.]
* [http://www.pyke-eye.com/view/phil_II_11.html Photo of Kit Fine] by Steve Pyke.
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