International Encyclopedia of Systems and Cybernetics

1) "A representation in a selected code, not directly reproducing the features of its model" (J.Z. YOUNG, 1978, p.289)

2) The search for regular patterns through noise.

As to the first definition, the "selected code" is of course a condition for the coherent search for patterns.

For G. KLIR, abstraction is: "The isomorphic transformation from an interpreted system into the corresponding general system" (1991 , p.17). The interpreted system is already a somehow homomorphic model of some concrete system. Such model can then be generalized (p.73).

R. LILIENFELD quotes the Spanish philosopher J. MARIAS: "Abstract truths do not refer to reality, but to diagrammatic rendering of reality "… while " … thinking about the concrete … presents much greater difficulties" and "… disciplines like logic and the theory of knowledge would assume a very different appearance if they were to state their problems in all their radicality and amplitude, so that the present forms of these disciplines would be reduced to mere chapters corresponding to particular cases" (MARIAS.1975, p.126-7, quoted in 1979, p.5).

Fuzzy sets and deterministic chaos, for example, now justifies MARIAS' views (which may have implied a critique of premature oversimplifications in social sciences) In the same vein A.G. BARTO observes: "The disposition to reify abstractions is particularly strong when abstractions have been very successful in ac-counting for observations, i.e when models based on such abstractions have successfully undergone extensive validation testing and have displayed great predictive power" (1978, p.167).

As pattern-forming is the progressive recognition of regularities, abstraction is an emergent phenomenon.

(See BERTALANFFY's comments on categories formation-(1962, p.71-84).

In G. KAMPIS words: "…abstraction narrows down interest from the entirety of a natural system to a phenomenal domain. During abstraction, usually some units of investigation are named and a set of observables is assigned to the natural system" (1989, p.90).

Abstraction cuts through complexity by selecting only some limitedly characterized aspects of the concrete system under study, specifically by reducing in the model its degrees of freedom. Keplerian and Newtonian mechanics, as compared with POINCARÉ's three bodies problem, are good examples.

G. BATESON explains thus our need for abstraction: "Habit can deal successfully only with propositions which have general or repetitive truth, and these are commonly of a relatively high order of abstraction" (1967, p.254).

The basic condition for abstraction is thus the repeated recognition of some identified signal in multiple circumstances (See KORZYBSKI's structural differential) (1950).

Abstraction can however become a conceptual quagmire: We should never forget WHITEHEAD'S caveat about the risks conveyed by misplaced reification of abstract models.

Finally a mathematically inspired view on abstraction could also be useful: the replacement of a set by another with a diminished level of cardinality, this leads us again to KORZYBSKI's structural differential (see fig. under the corresponding article)