On Vagueness: Evaluating the Linguistic, Metaphysical, and Epistemic Theories

Achille Varzi. Photo owned by Columbia University.

Achille Varzi. Photo by Columbia University.

Alright philosophers, another serious philosophical post tonight. It’s not that I don’t have more gut-wrenching things to talk about – I most certainly do – but I have been trying to use some of what I learned in my study of Buddhism and Taoism to improve my mental and emotional states. It isn’t working yet, but I haven’t been practicing for long. The first steps are to be aware of the negative and painful thoughts (as if I could not be aware), and to try to consider them rationally. The negativity is supposed to wither away and leave only a matter of fact set of propositions. Again, its not working yet, but I’m desperate for anything to make me feel better about life, myself, and this great loss.

So, here’s a discussion on vagueness. I hope you all enjoy. As always, shoot me a question, comment, or correction if you are so inclined.

Yours in Contemplation,



Vagueness inheres in all human endeavors. Its effects are felt in all of our attempts to think, and communicate about objects and phenomena in the world. But where is the vagueness? Does our language simply not have the development it needs to speak precisely about qualia? Or could it be the case that objects themselves are vague, having no precise boundaries between themselves and other things? Yet another possibility is that there are those definite boundaries, but that we could never know them. These are several theories of where vagueness comes from, and are known as the linguistic theory of vagueness (LTV), the metaphysical theory of vagueness (MTV), and the epistemic theory of vagueness (ETV), respectively. We will discuss each of these theories in turn, and evaluate the strength of the arguments for each. I will conclude that the ETV is the most plausible account for the source of vagueness.

The LTV argues that vagueness does not exist in the world, but vagueness arises from imprecise language. So objects are precise, and with definite boundaries, but we simply cannot communicate about them. The problem arises because there are numerous objects in the world that can be picked out when referring to some thing using a specific word, or term. Achille Varzi takes up this very position, he says, “There is no such thing as a vague mountain. Rather, there are many things where we conceive the mountain to be, each with its precise boundary, and when we say ‘Everest’ we are just being vague as to which thing we are referring to.”[1] This means that there are numerous “candidates” that can satisfy our meaning of the term that we’re using to refer, and therefore, the statement is vague. For example, if we claim, “Sam is on Mount Everest at point X,” it is neither true nor false. This is not because “Everest” itself is vague; rather it is that “Everest” is vague in reference. We would have to be very clear on what we were talking about in order to avoid the vagueness. The solution to this problem is a “tweak” to the truth-values that we assign to such to statements; that tweak is called supervaluationism. By assigning super-truth, or super-falsity to sentences with vague terms, vagueness, it is hoped, can be eliminated. The supervaluation assignments are made by precise specifications as to what will always be true, and what will always be false; no matter what interpretation one comes up with, those supervaluations will always hold. So if Sam is on the peak of Mount Everest, then the claim super-true. This is because the peak of Everest will be included in any description of it. The converse of this is also true. if Sam is 15 miles away from the base of the mountain, then the claim is super-false because no one includes the spot 15 miles away as being part of Everest. But if terms are left unspecified, then claims can be sometimes true, and sometimes false. Varzi addresses this; “It is only when the statement comes out true under some precisifications and false under others that there is trouble. In such cases, the statement suffers a truth value gap.”[2] The solution is simply to have very precise specifications (or “precisifications”, as Varzi says). But even then, it may still be the case that there are sentences which are sometimes true, and sometimes false, and is likely to happen the moment one enters the middle-ground between super-true, and super false conditions. The Sorites paradox seems tailor made for just such a middle ground, and as such, LTV has no real way of avoiding the paradox. Additionally, truth-value gaps undermine its strength. For these reasons, LTV and its supervaluationism provide little in the way of plausibly solving the problem of vagueness.

Next is the MTV, which states that objects in the world are vague, and predicates have vague extensions. This means that objects have “fuzzy” boundaries that make it impossible, even for God, to know where exactly one thing begins, and another ends. Varzi says, “Vague terms refer to vague objects, objects which lack precise spatial or temporal boundaries.”[3] This means that it is impossible to know the precise moment when Sam steps off of Mount Everest. This is because the boundaries of Everest are genuinely, metaphysically vague. In order to justify propositions containing vagueness, then, we employ various degrees of truth.[4] For example, the highest degree of truth would be assigned to the claim, “Sam is on Mount Everest,” if she is standing on the peak. The truth of claim degrades gradually as she descends the peak, and upon crossing some unknown point, becomes gradually more false as she moves away from it. The problem here is that the borderline case still exists, and thus, so does the problem of the Sorites. For the question remains unanswerable, “At what exact point does the claim become false that ‘Sam is on Mount Everest?’” Varzi echoes this concern when he points out that; “… a point exists where one goes from full truth to partial truth, and from partial truth to falsehood.”[5] This lack of resolution, and playing directly into the Sorites paradox makes this argument implausible as a solution to the problem of vagueness.

Finally, we come to the ETV. According to the ETV, vagueness comes from our ignorance about the satisfaction of conditions for the object, not any metaphysical/ontological vagueness. There is some property expressed by the predicate, and an object either satisfies it, or it doesn’t. So there is no real vagueness in the world, but our ignorance about the satisfaction of the properties causes us to think there is. There are, then, many conditions in which the term could be correctly applied, and many of them we can know, but we don’t know all of them. This means that we can use vague terms, but understand the intended meaning via context, but we will never know the full range of applications for the term. Timothy Williamson addresses this issue; “To know what a word means is to be completely inducted into a practice that does in fact determine a complete intention.”[6] In other words, a person (including the speaker) adopts the convention of applying a certain set of commonly used meanings to a particular term, and so in this way, the person understands the term, albeit, not every single circumstance to which the term applies. This is what Williamson means by being “inducted.” This means that people can generally know what others mean by the term “Everest,” although they do not know the specific point at which Everest stops being Everest. On the other hand, someone who is omniscient, perhaps God, would know where that exact boundary is. Since people cannot be omniscient, we have to be satisfied with generalizations about the truth and falsity of claims; they can be either true or false. The chances of our claims issuing in bivalence are determined by whether we are talking about borderline cases, or cases where there is very little vagueness. (If Sam is standing on the peak of Everest, then her chances are 100%; if shes standing somewhere at the bottom, it could be 50%, or otherwise.) Despite our ignorance of the full set of conditions that a term can be used in, we can still make true or false statements about a term if we know the general meaning of the term, and how the term is generally used. (The meaning of terms is determined by their conventional use.) This allows us to say that terms are either true or false, as opposed to neither true nor false, as in LTV, and MTV. ETV avoids the middle ground where bivalence is denied by excluding the middle altogether on grounds that there is a definite boundary. The Sorites is overcome by this approach. For example, it may be true at n steps, Sam is on Mount Everest, but at n+1 steps she crosses that boundary, and is no longer on Mount Everest. Therefore it cannot possibly be true that Sam is both on Mount Everest, and not on Mount Everest (a denial of bivalence). This is consistent with rules of logic, namely, the principle of non-contradiction because it does not deny bivalence. Williamson elaborates; “The denial of bivalence amounts to a rejection of [using vague sentences]. One is rejecting the practice while continuing to engage in it.”[7] This position of denying bivalence is obviously inconsistent, and is represented on p.520 in logical form: ~P ∧ ~~P.

Because the ETV avoids the Sorites problem, and adheres to the rules of classical logic by not denying bivalence (as MTV, and LTV both do), it emerges as the most plausible explanation of vagueness.

[1] Arguing About Language, Varzi. P. 513.

[2] Arguing About Language, Varzi. P.514.

[3] Arguing About Language, Varzi. P. 511.

[4] Arguing About Language, Varzi. P. 512.

[5] Arguing About Language, Varzi. P. 513.

[6] Arguing About Language, Williamson. P. 527.

[7] Arguing About Language, Williamson. P.522.


About facedownphilosophy

Proud recipient of the "Award for Outstanding Excellence in the Field of Unrivaled Superiority"
This entry was posted in Language, Metaphysics, Philosophy, Writing and tagged , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

1 Response to On Vagueness: Evaluating the Linguistic, Metaphysical, and Epistemic Theories

  1. whitefrozen says:

    I wonder if its of any signifigance that the theories propounding vagueness are extremely precise.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s