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2.4 Irrelevances to the debate

2.4.5 Particular formal languages (2-valued logic)

One particular bugbear of holists, is classical two-valued logic. This is criticised as not being expressive enough to capture all the meaning orreasoning necessary to model some systems. Sometimes it is Zermelo-Frankel set-theory that is the target. For example Rosen [14] suggests a approach to modelling in terms of category theory as a possible way forward in modelling complex biological systems.

Often it seems that the importance of whether a formal system is applicable is based on a shallow reading of the formal system's immediate properties and passes-over what further expressive features can be formalised within it.

In fact the choice of formal system is not critical in absolute terms, as long as the system is expressive enough. For example category theory and set theory can both be used to formalise the other [12], similarly Classical first order logic can be used to formalise almost any other logic [6]. So there is no fundamental absolute grounds for preferring one such formal system to an other*1.

Pragmatic Holism - Bruce Edmonds - 22 FEB 96
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