3 Kinds of Vaguess

Posted on March 24, 2008
Filed Under Philosophy | 2 Comments

I want to deal with broader philosophical questions than just the religious ones. However I am thinking through a lot of issues in preparation for this weekend’s SMPT. One thing I’ve been thinking through is the issue of vagueness.

There are, I believe, three somewhat related senses of vagueness.

Vagueness as Fuzzy Boundaries This is vagueness due to border issues. The best example are the Sorites Paradoxes. The example Timothy Williamson gives is a man who keeps losing hairs from his head. When is he bald? There are two ways to take this.

The most popular view is to effectively deny a logic with the law of excluded middle. One example of this is fuzzy logic. There we have what one might call partial truths.

The second view is one Timothy Williamson takes. Williamson sees tons of problems with fuzzy logic. He thinks that there is a truth of the matter of when someone is bald but we simply don’t know it. So there is a point at which a man becomes bald.

I’m pretty dubious about this, although perhaps that’s because I am an anti-realist towards predicates like phenomenal redness, baldness and so forth. If I’m an anti-realist about these and see a social community establishing meaning then it may well be there is a range of possible answers. Talking about truth in such a setting becomes problematic though.

Vagueness as Epistemic Limits This is the form C. S. Peirce uses. In this sense something is vague with respect to a predicate if there is a truth condition to the predicated subject but we are not free to determine it. This is opposed to generality where we can set it. The example Peirce uses is “Man is mortal.” We are free to think of any particular mortal man. However, “a man who I could mention is vain” does not allow us to pick which man we are talking about. There is a truth about the matter but there is missing information.

Williamson, as I understand him, sees both kinds of vagueness as really the same thing. I think he is in a minority in this though.

Vagueness as Equivocation This is ambiguity due to a term having multiple meanings. I don’t think this is vagueness in the usual sense except in the sense that it is an epistemic vagueness about the meaning being used. So the word “bank” can refer to the financial institution or the dry side of a river.

This ends up being a rather uninteresting use of vagueness except to the degree that we think we are maintaining stable differences of meaning when we really aren’t. This can happen when we are referring to signs or ideas that are not our own.

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Comments

2 Responses to “3 Kinds of Vaguess”

I think you are correct to point to a social community which establishes its own notions of truth (and therefore what constitutes vagueness). Wittgenstein: “the meaning of a word is its use in the language.” Defining vagueness here would be a specific use of an imprecise predicate in a particular context. Wittgenstein famously discourses in his “Remarks on Colour” that when we reflect on the nature of color (“is that bicycle white or light gray?”) we conclude that our conceptualizations of “color” are integrated into the indeterminateness of our concept of the sameness of color. We generate a paradox or an imprecision ourselves when we insist that color should be determinate (determinative of their extensions in all possible cases).

The Peircean way to address this problem which he feels avoids the traditional idealist/realist dichotomy is to posit an ideal community of inquirers who, in the future, will have consensus. There are some problems about this (primarily related to the indecision’s about #1) but it really is quite useful. It’s realist since truth doesn’t depend upon what you, I or any finite group of people believe. It’s idealist since it is still related to mind.

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