Where does form collide?

In Plato's dialogues (around 375 BCE), a Form is an eternal, non-material archetype that exists independently of the changing things that resemble it: a drawn circle is always imperfect, but the Form of the circle is perfect and unchanging, and to know something is to grasp its Form rather than its copies (see the Republic and Phaedo). Aristotle's Metaphysics later recast form as the organising principle that, together with matter, makes a particular thing what it is, so that a bronze statue is bronze (its matter) shaped into a figure (its form). Here the referent is a metaphysical essence or universal, and it has nothing to do with a polynomial in algebra, an abstract pattern of social interaction, or the outward shape of a spoken word.[1][2]

Unit

One Form: a single universal that many particular things share

Recovery means

Not applicable

Measured by

Not measured empirically; identified through philosophical argument and the analysis of definitions

In mathematics a form is a homogeneous polynomial, one in which every term has the same total degree, and the theory was set on a systematic footing by Gauss's 1801 Disquisitiones Arithmeticae, which classified binary quadratic forms such as a times x squared plus b times x y plus c times y squared. The term and its reduction theory reach back to Lagrange's arithmetic work of the 1770s, and the idea later extended to differential forms and bilinear forms across geometry and algebra. The referent is an algebraic object graded by degree, studied for its symmetries and invariants under a change of variables, not an eternal essence, a pattern of social life, or the shape of a linguistic unit.[3]

Unit

One form: a homogeneous polynomial of fixed degree in several variables

Recovery means

Not applicable

Measured by

Characterised by its degree, rank, signature, discriminant, and invariants under a change of variables

Georg Simmel's 1908 Soziologie made form the central object of sociology: he separated the content of an interaction (its purpose, such as love, gain, or defence) from its form (the pattern of relating, such as conflict, exchange, subordination, or sociability), and argued that the same form recurs across very different contents. Later readers, working from Kurt Wolff's 1950 English edition, treated these recurring patterns of association as the discipline's proper subject. The referent is an abstracted pattern of human interaction, identified across many cases, and it is distinct from a metaphysical archetype, an algebraic polynomial, or the shape of a word.[4][5]

Unit

One social form: a pattern of relating abstracted from its content

Recovery means

Not applicable

Measured by

Identified through comparative and interpretive analysis of interactions across different settings

Ferdinand de Saussure's posthumous 1916 Cours de linguistique générale drew the founding distinction between form and substance, holding that a language is a system of formal relations, so a sign's form is its place in that system rather than its physical material. Bloomfield's 1926 postulates then defined a linguistic form precisely, as a recurrent phonetic shape that carries a constant meaning, giving the term a working definition for structural analysis. The referent is the observable shape or arrangement of an expression, held apart from what it means, and it is not a Platonic essence, an algebraic polynomial, or a pattern of social interaction.[6][7]

Unit

One linguistic form: a recurrent phonetic shape with a constant meaning

Recovery means

Not applicable

Measured by

Delimited by distributional analysis and minimal-pair tests over a body of recorded utterances