Page 147 - Courting the Media Contemporary Perspectives on Media and Law

138 Geoffrey Sykes

purpose. ―No application ... of a general formula, such as (x+y)z = x z + y z,
could be made of such an abstract statement without translating it into a
sensible image.‖ [Peirce, 3.364]

THE HYPOTHETICAL AND THE ACTUAL –
DIAGRAMMATIC FORMS

As well as representing cases indexically, as shorthand for innumerable
verbal utterances, the algorithm expresses them in a very hypothetical,
intuitive form of reasoning that Peirce called abduction, in which possible as
well as actual values and situations can be entertained. Peirce‘s explanation of
such abstract logic was in terms of behaviour and perception, as well as
cognitive ―intuition‖, occurring in diagrammatically recursive and elaborative
forms. The production of new values explores association, not equivalences.
The above algorithm encodes explicit complex inferences that are best
expressed visually, in non-linear, complex and changing diagrammatic forms.
―In such manipulation, we are guided by previous discoveries which are
embodied in general formula. These are patterns, which we have the right to
imitate in our procedure, and are the icons par excellence of algebra. The
letters of applied algebra are usually tokens, but the x, y, z, etc., of a general
formula, such as

(x+y)z = x z + y z,

are blanks to be filled up with tokens, they are indices of tokens. Such a
formula might, it is true, be replaced by an abstractly stated rule (say that
multiplication is distributive); but no application could be made of such an
abstract statement without translating it into a sensible image.‖[Peirce, 3.364]
It is the latter that is translated into the complex form of an image, for the
purposes, Peirce notes well, of ―application‖ and ―manipulation‖. This sense
of manipulation and action rather than representation or cognition, is central
both to Peirce‘s first presentation, in 1885 and quoted above, of iconic
Firstness, and to his whole pragmatic and ethnographic account of
mathematics and language.
The analysis of potential image or diagrammatic form of verbal
―translation‖ from qualitative to quantitative language is between divergent
and seemingly incommensurate sign types, between ―sensible image‖ and an