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Borderline cases of vague predicates form a special category. When asked, non-philosophers tend to hesitate from making categorical claims. 



Disagreements about borderline cases of vague predicates form a special category. On the one hand, they might be subject to the normative variation due to their subject matter, as ordinary disagreements do. On the other hand, because of the peculiar nature of the phenomenon of vagueness, there might be other factors that interfere with truth’s normative function and which explain the sense of hesitation, hedging, and uncertainty that disputants typically have in the presence of the disagreement.

This research cluster explores intuitions about vagueness among native English speakers. Ulatowski, Robert Barnard (Mississippi), and Jonathan Weinberg (Arizona) have designed a questionnaire that explores intuitions about borderline cases of vague predicates. People who recognise that they disagree about such borderline cases often display a sense of hesitation, hedging, or uncertainty. Because of the peculiar nature of the phenomenon of vagueness, this behaviour could be explained by any number of factors.


The literature on vagueness has paid little attention to this phenomenon of hesitancy related to borderline cases. Prominent theories of vagueness, such as supervaluationism, postulate a form of semantic indeterminacy—e.g. truth-value gaps—that mandates acceptance of borderline proposition as incorrect. Moreover, the empirical data discussed in literature give rise to controversial assessments of borderline cases. Some present data suggesting that subjects presented with borderline cases behave as if they were standard cases of ignorance, whereas others present data suggesting that subjects tend to accept contradictory-looking sentences—e.g. “The man is both bald and not bald”. Moreover, some discuss data suggesting that borderline cases cause a peculiar instability of judgements. Not much more empirical analysis has been produced in relation to vagueness as the recent companion on experimental philosophy (Sytsma 2016) shows. Barnard, Ulatowski and Weinberg hypothesise that the phenomenon of hesitation, hedging, and uncertainty appears to give rise to a different normative profile for borderline cases. The hypothesis to be tested is thus that borderline cases are situations where, for all we know, none of the attitudes of acceptance, rejection or suspension of judgement are inconsistent with conceptual competence involved in such cases, hence nothing mandates any of these attitudes. The presence of vague concepts leaves open what to think when borderline cases are concerned. I take this intuition to be one of central features of the manifestation of vagueness.

Relevant Background

Philosophical concern over vagueness has been with us since at least antiquity. The so-called Sorites paradox, or heap paradox, suggests that in the case of some concepts the application of ordinary inferential practices to ordinary categorization judgments can result in paradox. The paradox can be constructed using a variety of familiar examples: heaps, balding heads, or whole numbers. And, as this characterisation suggests there are two places where philosophical analyses of vagueness have tended to begin: the concepts we use and our inferential practices. Both are frequent targets of empirically informed analysis.

The construction of a Sorites paradox usually depends upon the identification of a sorites series, an observed or constructed set of cases ordered according to some concept. Thus, the distribution of height among people in the room can be used to order those people in a series from shortest to tallest, or a series of sand piles can be ordered from least number of grains to most. Sometimes the series are understood to continue beyond observation or to continue to a limit e.g., a pile of sand with 0 grains.

Here is a traditional Sorites series:

Consider a pile of sand with n grains of sand in it. Assume that this pile can properly be categorized as a HEAP. Now ask, is there a pile of sand such that it would not count as a heap? Certainly a 0 grained pile is a non-heap. Here we can proceed in a couple of ways. We might ask: Given that a pile of 0-grains is not a heap and a pile N-grains is a heap, then there must be some transition point T such that T grains of sand in a pile is not a heap, but T+1 grains IS a heap. This is prima facie intuitive. There is a series from 0 to N, 0 and N are characterized differently. There is a way to move stepwise through the series, one grain at a time. So we should certainly be able to find T.

Since Russell’s famous article in the inaugural issue of the Australasian Journal of Philosophy (1923), a defining feature of vagueness cases has been the problem of borderline cases. If a given person is neither determinately tall nor determinately short, but falls in between, such a person may be a borderline case of tall.  From a logical point of view the claim asserting that the borderline person is tall, may be true, false, or qua borderline, both true and false, or neither true nor yet false.

In recent years a number of studies have tried to assess how the folk respond to borderline cases. The clear consensus among these studies seems to be that sentences such as:


A man x is both tall and not tall

A man x is neither tall nor not tall

are understood to be neither true nor false, hence “gappy” since there the truth value of such a statement is missing. Bonini et al (1999) found that that gaps emerged in truth assignments using predicates such as ‘is tall’, ‘is a mountain’, and ‘is old’ as well as a number of other similar cases. Bonini et al offered a series of free response prompts of the following form:

Age: ‘When is it true/false to say that a man is ‘old’? [in terms of age].

Height: It is true/false to say that a man is ‘tall’ if his height is greater than or equal to ___ cm.


They found that there was a statistically significant difference between the mean truth judgement and the mean false judgment. They inferred that this result was incompatible with attributing truth gluts to vague terms in borderline cases, but it was in favour of truth gaps, a sharp but unknown boundary.

Alxatib and Pelletier (2011), Ripley (2011), and Egre and Zehr (2018) all reported broadly similar findings. The clear consensus among recent empirical studies seems to be that non-philosophers judge sentences like “A man x is tall and not tall”or “A man x is neither tall nor not tall” to be “neither true nor false,” hence “gappy” since the truth value of such a statement is missing. Bonini, et al. (1999) found that gaps emerged in truth assignments using predicates such as ‘is tall’, ‘is a mountain’, and ‘is old’ as well as a number of other similar cases, which they use to support the hypothesis that vagueness is a kind of ignorance.  Alxatib and Pelletier (2011) try to explain the finding using a semantic-pragmatic distinction. Ripley (2011) uses his findings to advance the general project of supporting  dialetheism.  Finally, Egre and Zehr (2018) seek to use the results to ground a distinction between strict and tolerant meanings of vague terms that vary pragmatically with context.

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