vagueness resolved.

i promised i'd try to convince seb that we're not as different as he would like to believe. the following are excerpts from my final paper from philosophy of language last semester. the topic? vagueness, of course.

"Discussions of vagueness frequently begin by introducing sorites problems, and the challenge they pose to classical logic... On first glance, one might argue that logic is unequipped to handle these subtleties, and thus vagueness poses a clear and present threat to attempts to describe language in logic.
In this way the debate over vagueness has been restricted to a defense of logic, and most theorists maintain that vague objects must be precisified before they can enter the arena of logical language. This opposition and subsequent attempts to maintain the use of logic in the face of vagueness leads to new problems..."

"...many... problems in the philosophy of language can be shown to stem from one underlying notion: that the behavior of language can and should be described according to logical principles. Without this assumption, vagueness is a boon rather than a problem. W.V.O. Quine, who frequently questioned the uses made of logic in philosophy of language, writes, “A painter with a limited palette can achieve more precise representations by thinning and combining his colors than a mosaic maker can achieve with his limited variety of tiles.” Vagueness should not be immediately considered the enemy of truth or precision."

"Would the same definition suffice if I chopped the apple, or hollowed out the insides, leaving its appearance almost unchanged, or wrapped it in an orange skin? What constitutes an apple?
In asking this question, we have already made an assumption: that the usage of a word depends on the constitution of an object, and that the two correspond in a way that can be described by logical laws."

"The disquotationalist notion of truth, that ‘P’ is true if and only if P, hinges on this same assumption: that facts about the world can be known outside of language, and that they are somehow accessible to humans for comparison to language."

"Quine’s more interesting claim is that, in most natural language settings, vagueness does not impede our ability to utter or assess true statements. He provides examples of statements... that are clearly true, despite their reliance on a vague term. Precification is called for... only in restricted domains of speech such as law, record books, and logic. Quine writes, “When sentences whose truth values hinge on the penumbra of a vague word do gain importance, they cause pressure for a new verbal convention or changed trend of usage that resolves the vagueness in its relevant portion.”"

"‘The Vagueness Problem’ is a misnomer when applied to natural language. Such language functions passably well, despite requiring clarification many times a day. The difficulty of applying logic to vague language has important implications for the relationship of logic and language. Perhaps a more useful study would proceed by limiting the applications of logic and seeking to understand vagueness as an unavoidable part of language use. Through such an inquiry we might gain a greater understanding of how we come to learn language and understand each other in the face of so much uncertainty."

we're not so different, seb and i. i think our real debate is, once again, not about vagueness, but about the definition of 'language'.


Seb said...

I really like the paragraph about the apple.

But at the same time, this post doesn't resolve vagueness for me, because it doesn't address the underlying problems, which are:

1) Logic is actually pretty awesome, with all sorts of useful applications, so it would be nice if we didn't just have to toss it in the face of vagueness, and
2) Saying that natural language works fine with vagueness doesn't solve the unsettling feeling that knowledge might break down under vagueness (which is I think what epistimicism is saying).

I think some of this ties into what I think is a difference of opinion about the medium of our beliefs about the world, and about the primacy of language. Solving vagueness in natural language--by noticing that it works anyway--doesn't solve the problem of vaguess on the conceptual level--which I think you might still consider a language, or a product of language, or something like that?

I don't want to put words in your mouth.

Here's a distinction that I've picked up from a Artificial Intelligence textbook, of all places, that might be useful. It makes the distinction in artificial languages between a communication language, which does what you'd think it does, and a representational language, which is used to store information about the world.

When philosophers talk about language, I think they are thinking about natural language as if it were a representational language which, as I'm sure you'd agree, it's not.

But we need a representational language, or something equivalent, in our minds if we actually store information about the world and use it in our lives. Unfortunately, we communicate this through a communicative language, thereby creating the ambiguity. But if we cut things back a level to a mental, representational language (which I'm claiming exists), then we have a language which should, in theory, be amenable to logic and in which we should be able to "express" (or really, encode) knowledge about the world.

I'm claiming that vagueness, if it's a problem at all, is a problem on this representational level. I think this is different from what you say in your paper.

Cristi said...

i think you hit the nail on the head as far as the site of our disagreement.

i think concepts and representations (which you would probably contrast with communicative language) are inherently vague. let's leave aside for the moment the question of whether they're language-based or not.

i just don't think the distinction between 'heap' and 'not heap' exists without vague (linguistic?) categorization.

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