: fractionally factual (Alt.
, fractionally actual.)
A generalisation of the notion of a half-truth, to cover the whole set of values between zero and one, a fractual is a proposition taking a truth-value which is fractional - obviously this is different from fuzzy logic, where a proposition takes an expectation rather than a truth-value. Whether this value is rational or real is as yet an open question.
For example, the sentence 'this sentence is false',
problematic in the normal predicate calculus, is
simply a fractual taking a truth-value of 0.5.
Exercise: what is the truth-value of the fractual: 'the truth-value of this fractual is 0.1'?
Fractuals with values approximating one are said to be
'as good as true' (or, more colloquially, 'as near as
damnit') while the other end of the scale is occupied
by the so-called marginal truths, with near-zero truth-values.
The ortho-fractual is a further extension of fractuals onto the complex plane. The imaginary component, rather than the obvious interpretation (which is simply the trivial sum: 1 minus the value of the original fractual, ie. the lie-value) is the measure, or (normalised) degree with which a putative proposition fits Wolfgang Pauli's condemnation: not even wrong.
Chomsky's 'colorless green ideas sleep furiously' is a nice ortho-fractual with a marginal truth-value and a fairly large 'imaginary' component (or, as I prefer to call it, daft-value.)
The terms arise from my own little known work in the field of conversational logic. It is allowed that they are somewhat self referential - indeed, it is hypothesised that all writeups are in fact the product of (ortho-)fractual noding.
(Also, a common mis-spelling of fractal.)
It has been pointed out to me by an eminent E2 mathematician that my model does not adequately map to the complex plane, as it admits neither negative 'real' nor negative 'imaginary' values. I propose to correct this by an extension, introducing the following classificatory schema for the four quadrants:
(2) | (1)
(-,+) | (+,+)
lies | bullshit
(3) | (4)
(-,-) | (+,-)
damned | statistics
In this proposed model, mathematical truths occupy the
open interval (-1,1) on the real line, normal human
discourse takes place above this (in quadrants 1 and 2) and quadrants 3 and 4 are occupied by politics and science, respectively. Philosophical truths tend to cluster around the origin, at a mean distance of 1/inf., but may appear in any quadrant.
D I S C L A I M E R : I have not earned this bullshit. Think on.