The adjective vague qualifies communicated meaning. Vague is opposed to clear, definite, explicit, specific (MW). The default orientation of vague is negative, while the orientation of each of its antonym is positive.
1. Vagueness, Precision and Relevance
1.1 The intention / extension quandary
General is opposed to specific, and individual. General terms have a broader extension / narrower intension than specific terms. The extension of a term is the set of individuals to which this term can refer, the intension of a term corresponds to the meaning of this term, S. Definition (1). Hypernyms and covering terms (1) are more general / less specific general than their subordinate terms.
Extension and intension vary in opposite directions. When intension increases, that is, when the definition is extended, more cases are covered, there is a gain in generalization; correlatively, extension increases and there is a loss in precision.
Vice-versa, when the definition is restricted, less cases are covered, there is a gain in precision; correlatively, extension decreases and there is a loss in generalization.
Generalization is ambivalent. It is considered as positive move when it shows that a concept, a theory, a method… applies to new cases, different from those originally envisioned. Their scope is wider than foreseen; their claims are not ad hoc, that is limited to one original case and saying nothing beyond the individual features of that claim. Having a potential for generalization shows that the method is fertile.
But an extended concept is more exposed to refutation than a restricted one. Overgeneralization occurs when that kind of extension fails, for two reasons:
— The new cases clearly fall 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 beings or new facts that it claims to cover.
1.2 Generality, Ambiguity and Vagueness
A term G is more general than another term S if its extension is broader than that of S, and its intension smaller.
Generic terms are general words designating a genus encompassing several species. Species are designated by more specific terms, which add specific differential features to their generic features. This addition in its definition restrict the number of individuals to which the word can refer.
Cover (covering) terms, or umbrella terms are general words whose meaning encompass the common features of various other terms. The covering term is used in order to focus on the common points of the covered terms, or as a current word referring to specialized words.
The relations between generic and specific terms are regulated by the strict organization in genus and species. The covering / covered terms relations, the links and oppositions between covered terms, depends on the field considered. An umbrella term can refer to a simple enumeration of elements.
Emotion is a covering term for joy, fear, hate, love, etc.
Cardiovascular disease is an umbrella term for a set of health issues that affect the heart and/or blood vessels. [1]
myocardial infarction – cerebrovascular accident – arteriosclerosis – angina pectoris – heart failure – cardiac arrhythmia – high blood pressure.
The binary anatomical categorization of masculine/feminine genders and sexualities is replaced by the seven self-identified orientations, their acronym LGBTQIA+ serving as umbrella term for:
lesbian, gay, bisexual, transgender, queer, intersex, asexual, and more.
A general term is not an ambiguous term. The word dog is not ambiguous between the different names of dog species (bulldog, poodle, hound, etc.).
A general term is not a vague or obscure term. The information it communicates applies to a large number of beings or to a variety of cases. For example, the word accident is a covering term referring to a variety of situation: road accident, accident at work; domestic accident; medical accident, etc. Nonetheless, “It was an accident” is precise and valuable as the first available piece of information. Precisions will come later, if needed. As an excluder, “it was an accident” is perfectly precise, since it excludes “it was a crime”.
It can be considered insufficient only in reference to the relevance principle organizing the current conversation, for example, if it only says what everybody can see.
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 distinct sets of this type. They are characterized by the fact that they have no upper limit.
1.3 Vague vs Precise vs Relevant
Generalities are said vague, irrelevant, when they do not contribute to the specific task under way. They just allow the speaker to dodge the common task, and adopt a non-committed stance towards 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 exactly the right amount of information be provided, no more and no less, S.. Cooperation principle.
Three friends look at a splendid car going by:
L1: How much does a nice car like may cost?
L2: (i) At least 50,000 euros, I think
(ii) Not necessarily more than 25,000 euros
L3: (i) 58225 euros before tax, plus options
(ii) 23112 euros before tax, plus options
The answer L2 (i) is neither unclear nor vague but sufficient. It gives an order of magnitude that is perfectly appropriate to the thread of the conversation, to which it gives it a clear orientation, « you still have to make some money to have a car like that!« .
L2 (ii) would give points to another orientation, “If you really want it, you can afford it« .
L3 is more precise, but the degree of precision is irrelevant to the conversation. Whatever the preceding topic were, it was not about the exact price of that car.
A buyer to a seller:
L1: And this model, how much?
L2: Around 50 000 euros
L3: 58225 euros before tax, plus options.
L2’s answer is now vague, in the sense of « insufficient ». It does not give the exact price, corresponding to the amount of the check the buyer will have to write. L3 fully answers L1’s question.
The vague / precise character of an intervention depends on the circumstances of the conversation and on the action cooperative or antagonistic, developed by the participants.
2. Fuzziness as a zone open to discussion
2.1 Indeterminacy of inter-categorical boundaries
Belonging to a category can be defined with reference to a set of beings typically belonging to the category. One must then distinguish, at the periphery of the clear-cut zone that gathers the prototypical beings of the category, an increasingly blurred zone occupied by borderline objects, belonging less and less to this category, and more and more to another one.
A hammock certainly qualifies as a kind of bed; a beach towel not really; an inflatable mattress certainly, if it is intended for the guest room, but less clearly if it is part of the pool equipment, etc.
The arguments a pari, a contrario, from the opposite play on the phenomena of continuity / discontinuity of the categories, by privileging the attachment of a being to such category or to such other. This border zone is a zone of discussion.
2.2 Fuzziness as a deliberative zone
Peirce (1902) defines the word vague in relation to the variations of judgment of the speakers.
Vague (in logic) [Lat, 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 considers vagueness as an issue in individual psychology, and that 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 border zone where two categories merge. For example, on the temperature scale, the zone “the weather is nice” overlaps the zones “it’s cold” and “it’s hot”. The situation can be described not as a variation in individual judgments but as a variation in inter-individual judgments. Such variations can lead to discussions, not necessarily futile, about the weather. Fuzzy zones correspond to argumentative zones:
Representation (after Quiroga Aranibar, 1994, p. 9):
Unanimity of judgement: 1: cold — 3: nice — 5: hot
Discussion: 2: cold / nice — 4: nice / hot
Within the zone corresponding to the lexemes cold resp. hot, the intensifier very defines two argumentative subzones, cold / very cold and hot / very hot to which the same representation applies.
Vagueness does not necessarily reflect the indeterminacy of individual judgments, but the disagreement between interindividual judgments, possibly each firmly entrenched.
Quiroga Aranibar, Luis Alfonso, 1994. Learning fuzzy logic from examples. PhD, Ohio University.
https://etd.ohiolink.edu/apexprod/rws_etd/send_file/send?accession=ohiou1176495652&disposition=inline
[1] https://www.pro-activ.com/en-gb/heart-and-cholesterol/heart-health/what-is-cardiovascular-disease