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Because is treated as a dialectic of , we can expect any attempt at a formal definition of to be rather vague and indistinct. In fact, The Homeless Mathematician will argue that it is a categorical mistake to attempt any definition of . This is because any definition is an instance of Reasoning by . As such, is beyond the scope of what may be defined in a comprehensive manner.

The key to a deep understanding of is the use of Reasoning by , as presented in The Paradigm of Form and Substance.

Further, the word is rather unusual in that it may be used as either a noun, an intransitive verb, or a transitive verb. This duality of grammatical usage is in conformity to The Canonical Form of Distinction, as detailed in the treatment of Non-Numerical Arithemetic. Specifically, may be treat as specifying either intent or content.

The kind reader is invited to study a dictionary definition of to determine the veracity of these claims by The Homeless Mathematician.

noun

1. a. The shape and structure of an object. b. The body or outward appearance of a person or an animal considered separately from the face or head; figure.
2. a. The essence of something. b. The mode in which a thing exists, acts, or manifests itself; kind: a form of animal life; a form of blackmail.
3. a. Procedure as determined or governed by regulation or custom. b. A fixed order of words or procedures, as for use in a ceremony; a formula.
4. A document with blanks for the insertion of details or information: insurance forms.
5. a. Manners or conduct as governed by etiquette, decorum, or custom. b. Behavior according to a fixed or accepted standard: Tardiness is considered bad form. c. Performance considered with regard to acknowledged criteria: a good jump shooter having an unusual form.
6. a. Proven ability to perform: a musician at the top of her form. b. Fitness, as of an athlete or animal, with regard to health or training. c. The past performance of a racehorse. d. A racing form.
7. a. Method of arrangement or manner of coordinating elements in literary or musical composition or in organized discourse: presented my ideas in outline form; a treatise in the form of a dialogue. b. A particular type or example of such arrangement: The essay is a literary form. c. The design, structure, or pattern of a work of art: symphonic form.
8. a. A mold for the setting of concrete. b. A model of the human figure or part of it used for displaying clothes. c. A proportioned model that may be adjusted for fitting clothes.
9. A grade in a British secondary school or in some American private schools: the sixth form.
10. a. A linguistic form. b. The external aspect of words with regard to their inflections, pronunciation, or spelling: verb forms.
11. a. Chiefly British. A long seat; a bench. b. The resting place of a hare.
12. Botany. A subdivision of a variety usually differing in one trivial characteristic, such as flower color.

verb
formed, form·ing, forms verb, transitive

1. a. To give form to; shape: form clay into figures. b. To develop in the mind; conceive: form an opinion.
2. a. To shape or mold (dough, for example) into a particular form. b. To arrange oneself in: Holding out his arms, the cheerleader formed a T. The acrobats formed a pyramid. c. To organize or arrange: The environmentalists formed their own party. d. To fashion, train, or develop by instruction or precept: form a child's mind.
3. To come to have; develop or acquire: form a habit.
4. To constitute or compose a usually basic element, part, or characteristic of.
5. a. To produce (a tense, for example) by assuming an inflection: form the pluperfect. b. To make (a word) by derivation or composition.
6. To put in order; arrange.

verb, intransitive

1. To become formed or shaped.
2. To come into being by taking form; arise.
3. To assume a specified form, shape, or pattern.

Synonyms: form, figure, shape, configuration, contour, profile.

These nouns refer to the external outline of a thing.

• Form is the outline and structure of a thing as opposed to its substance: stalactites of curious forms; a garden in the form of a lovers' knot.
• Figure refers usually to form as established by bounding or enclosing lines: The cube is a solid geometric figure. "Europe is disclosed as a prone and emaciated figure, the Alps shaping like a backbone, and the branching mountain chains like ribs, the peninsular plateau of Spain forming a head" (Thomas Hardy).
• Shape implies three-dimensional definition that indicates both outline and bulk or mass: "Rowing [at night], he faced her, a hooded and cloaked shape" (Joseph Conrad).
• Configuration stresses the pattern formed by the arrangement of parts within an outline: The map shows the configuration of the North American continent, with its mountains, rivers, and plains.
• Contour refers especially to the outline of a three-dimensional figure: I ran my finger along the soft, curving contour of the child's cheek.
• Profile denotes the outline of something viewed against a background and especially the outline of the human face in side view: We glimpsed the profile of the church steeple against the last glow of the sunset. The profile of the old warrior was characterized by a strong jaw and an aquiline nose.

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Updated 95/11/04