Where does quantity collide?

In antiquity, Aristotle made quantity (Greek poson, 'how much') one of the ten basic categories of being set out in his Categories (ch. 6): a fundamental way a thing can be said to exist, alongside substance, quality, relation, and the rest. He divided it into discrete quantity, such as number and spoken sound, and continuous quantity, such as a line, a surface, a solid, time, and place, and held that quantity alone has no contrary and admits no degree. In this meaning quantity is a mode of being that a thing has, a kind of predicate within a scheme of categories. This is not the length of a vowel in speech, the reach of a logical statement, or the mass of a physical body, but a category under which such amounts fall.[1]

Unit

One instance is an item's quantity as a category, either a discrete number or a continuous magnitude

Recovery means

Not applicable

Measured by

Analysed philosophically by whether the amount is discrete (counted in units) or continuous (divisible without a natural least part)

Also in antiquity, Aristotle distinguished statements by whether they speak of all, of some, or of a single subject, in On Interpretation (ch. 7) and the Prior Analytics. Later logicians named this feature the quantity of a proposition, universal ('all S are P') or particular ('some S are P'), and paired it with quality, which is whether the proposition affirms or denies. In this meaning quantity is a property of a judgment, the extent of the subject term it ranges over, and not a count of things. It has nothing to do with a category of being, the duration of a spoken sound, or the mass of an object, though the same word names all of them.[2]

Unit

One instance is the quantity of a single proposition: universal, particular, or singular

Recovery means

Not applicable

Measured by

Classified by inspecting the proposition's quantifier: all, some, or a named individual

Isaac Newton opened the Principia (1687) by defining the quantity of matter as 'the measure of the same, arising from its density and bulk conjointly', the property now called mass. In this meaning quantity is not a bare amount but a specific measured magnitude of a body: the mass that resists acceleration and fixes the body's weight in a given gravitational field. Newton's definition became the foundation of classical mechanics and of the modern treatment of mass. This referent is a physical property of matter, measured in kilograms, and it is unrelated to a category of being, the reach of a logical statement, or the length of a spoken vowel.[3]

Unit

One instance is the mass of a body, in kilograms

Recovery means

Not applicable

Measured by

Determined by weighing against a reference mass, or from the force needed to produce a known acceleration

Nikolai Trubetzkoy's Grundzüge der Phonologie (1939) treated quantity, the distinctive duration or length of a vowel or consonant, as a phonological property that can tell words apart, building on the long and short syllables that ancient Greek and Latin verse had already counted as quantity. In languages such as Finnish, Latin, and classical Greek, a long vowel and a short vowel with the same articulation form different words, so quantity here is contrastive length in relative time. In this meaning quantity is a durational feature of a speech sound, not an amount of anything countable. It is not Aristotle's category of being, the universal or particular reach of a proposition, or Newton's measure of mass.[4]

Unit

One instance is the phonological length of a segment, short or long, in relative duration

Recovery means

Not applicable

Measured by

Established by minimal pairs that differ only in length, and measured acoustically as segment duration