VAGUE – GENERAL – FUZZY
The adjective vague qualifies the meaning conveyed by a term, a sentence, or an entire discourse.
Vague is opposed to clear, definite, explicit, specific (MW). The standard orientation of vague is negative, while the orientation of each of its antonyms is positive.
Intension [1]/Extension
The intension of a term corresponds to its meaning, see definition. The extension of a term is the set of things or cases (the zones of the world) to which this term can refer,
Intension and extension vary in opposite directions. As the intension decreases (the definition is generalized), the extension increases, i.e. more cases are covered. There is a loss of precision and a gain of generalization.
Conversely, as the intention narrows (the definition becomes more precise), the extension decreases, i.e. fewer cases are covered. There is a gain in precision and a loss in generalization.
1. General Term – Generic term – Covering term – Collective term
General, generality, generalization
General is in contrast to specific, individual.
General terms have a broader intension/narrower extension than specific terms.
Hypernyms (bird) are less specific/more general than their subordinate terms (sparrow).
Generalization is ambivalent. It is considered a positive step when it shows that a concept, a theory, a method… applies to new cases, different from those originally considered. Its scope is broader than expected; its claims are not ad hoc, that is limited to a few original cases and saying nothing beyond their particulars. The potential for generalization shows that the method is fruitful.
But an extended concept is more susceptible to refutation than a restricted one. Overgeneralization occurs when the extension fails, for two reasons:
— The new cases are clearly outside of the scope of the original claim; the theory has nothing to say about them.
— The new definition says nothing but trivialities about the new entities or new facts that it claims to cover.
A general term is not a collective term. Nouns like set, heap, group, herd, team, collection… are collective terms. In the singular, they refer to a set of objects or individuals taken as a relatively stable whole; in the plural, they refer to several different sets of that kind. They have no upper limit, see sorite.
Generic Terms
Strictly speaking, generic terms function in classifications. They are general words that designate a genus that includes several species, the species being designated by more specific terms, that add specific distinguishing characteristics to their generic characteristics. This « generic + specific » conjunction characterizes the individuals to which the generic term may refer.
Covering Terms, (Umbrella Terms)
Covering (cover) terms, or umbrella terms are general terms whose meaning encompasses the common characteristics of several other terms. The umbrella term may be used in order to focus on the commonalities of the covered terms, as a topical word referring to more specialized concepts. An umbrella term may refer to a list of items etc.
The relationships between generic and specific terms are governed by the strict genus and species organization. The relationship between covering / covered terms, and the links and oppositions terms covered by the same covering term, depends on the area under consideration:
Emotion is a cover term for joy, fear, hate, love, etc.
Cardiovascular disease is an umbrella term for a number of health problems involving the heart and/or blood vessels [2], including myocardial infarction – cerebrovascular accident – atherosclerosis – angina pectoris – heart failure – cardiac arrhythmia – hypertension.
The binary anatomical categorization of male/female genders and sexualities is replaced by the seven self-identified orientations, whose acronym LGBTQIA+ serves as an umbrella term for lesbian, gay, bisexual, transgender, queer, intersex, asexual, and more.
A cover term is not a vague or ambiguous term. The information it conveys applies to a large number of entities or to a variety of cases. For example, the word accident is an umbrella term that refers to a variety of situations: traffic accident, work accident, domestic accident; medical accident, and so on. Nevertheless, “It was an accident” is precise and valuable as the first piece of information available. Precisions will come later, when needed.
As an excluder, “It was an accident” is perfectly precise, because it excludes “It was a crime.
A cover term can only be considered inadequate with respect to the relevance principle organizing the current conversation, for example, if it only says what everyone knows.
2. Vague vs. Precise vs. Relevant
Generalities are said to be vague, irrelevant, when they do not contribute to the specific task at hand. They simply allow the speaker to evade the common task, or to take a noncommittal stance on the issue.
Information can be said to be fuzzy, vague, or on the contrary precise. According to Grice’s Quantity Principle, the precision of information is relative to the conversation it keeps alive. this principle requires that just the right amount of information be provided, no more and no less, see cooperation principle.
Three friends sitting at a sidewalk cafe are looking at a nice car driving by:
S1: How much could such a nice car cost?
S2: More than 100,000 Euros, I think.
S3: 158,225 Euros before tax, plus options.
The answer S2 is neither unclear nor vague but sufficient. It gives an order of magnitude that is perfectly appropriate for a free-flowing conversation, to which it gives it a clear orientation, « You still have to earn some money to have a car like that!« .
S3 is an expert’s answer, absolutely precise, but the degree of precision is not required by the preceding conversation.
The conversation may be about the exact price of this car:
A buyer writing a check to a seller:
S1: So, finally how much?
S2: About 150,000 Euros.
S3: 158,225 Euros.
S2’s answer is now too vague, in the sense of « insufficient », not adapted to the conversation. It does not give the buyer the information he is looking for: the exact amount he will pay. S3 answers S1‘s question in full.
The vagueness/exactness of an intervention depends on the circumstances of the conversation and on the action developed by the participants.
3. Fuzziness as a Zone of Discussion
3.1 The fuzziness of Intercategorical Boundaries
Belonging to a category can be defined in terms of reference to a set of entities that typically belong to the category. One must then distinguish, at the periphery of the clear zone that gathers the prototypical entities of the category, an increasingly blurred zone occupied by borderline objects, that belong less and less to this category, and more and more to another.
Categorization is influenced by context:
A hammock certainly qualifies as a kind of bed; a towel not so much, but less clearly when it is part of the pool equipment, etc.
The arguments a pari,, from the opposite play with the phenomena of continuity / discontinuity of the categories, privileging the attachment of a being to this or that category. This border zone is a zone of discussion.
3.2 Uncertainty as a Subjective-Deliberative Zone
Peirce (1902) defines the word vague in in terms of the variations in the judgments of speakers.
Vague (in logic) [Latin vagus, rambling, indefinite]: Ger. unbestimmt; Fr. vague; Ital. vago. Indeterminate in intention.
A proposition is vague when there are states of things concerning which it is intrinsically uncertain whether, had they been contemplated by the speaker, he would have regarded them as excluded or allowed by the proposition. By intrinsically uncertain we mean not uncertain in consequence of any ignorance of the interpreter, but because the speaker’s habits of language were indeterminate; so that one day he would regard the proposition as excluding, another as admitting, those states of things. Yet this must be understood to have reference to what might be deduced from a perfect knowledge of his state of mind; for it is precisely because these questions never did, or did not frequently, present themselves that his habit remained indeterminate.
Peirce sees vagueness as a problem in individual psychology. The wandering of judgments is related to the fact that situations of vagueness are « infrequent », which is debatable.
Fuzzy logic formalizes the notion of fuzziness as a boundary zone where two categories merge. For example, on the temperature scale, the zone « the weather is nice » overlaps the zones « it is cold » and « it is hot”.
Figure (adapted from Quiroga Aranibar, 1994, p. 9) [3]
| Unanimity of judgment: | 1: cold — 3: nice — 5: hot |
| Discussion: | 2: cold / nice — 4: nice / hot |
Within the zone corresponding to the lexemes cold and hot, the intensifier very defines two argumentative subzones, cold / very cold and hot / very hot to which the same representation applies.
The situation can be described not as a variation in individual judgments but as a variation in interindividual judgments. Even if individual judgments were more stable, fuzzy zones would be created because of different individual sensitivities to cold and hot. Fuzzy zones can be defined as controversial zones. Such variations can lead to discussions, not necessarily pointless ones, about the weather. Fuzzy areas are open to discussion.
[1] Intension, or the conceptual content of a word, should not be confused with intention, which is synonymous with purpose
[2] https://www.pro-activ.com/en-gb/heart-and-cholesterol/heart-health/what-is-cardiovascular-disease
[3] Quiroga Aranibar, Luis Alfonso, 1994. Learning Fuzzy Logic from Examples. Doctoral Thesis, Ohio University.
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