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Pragmatic Holism - Bruce Edmonds

4 The number - complexity analogy

Rosen introduces an analogy between what he calls complexity (i.e. things that aren't mechanisms) and infinity; the reductionist/syntactic approaches to modelling correspond to finite steps. He claims that many systems (including all living organisms) are unameanable to such steps and qualitatively different - they correspond to infinity. Thus he postulates that to model these "complex" systems require some transcendental device, like taking limits or some form of self-reference.

I wish to alter this analogy and hopefully deepen it. I wish to take an analogy between numbers and complexity. This size corresponds to the difficulty of modelling a system in a descriptive top-down fashion given a language of representation and almost complete information (model) from the bottom-up perspective of it components*1. Thus infinite size would correspond to infinite such difficulty - i.e. impossibility of such modelling (which roughly corresponds to Rosen's "complexity"). The abstract debate would then correspond to the question "Are there systems with infinite complexity?".

Here we need to examine what we mean by the existence of such systems. The problems of showing that such systems exist are remarkably close to those involved in showing that infinity exists. You can not exhibit any real manifestation of infinity, since the process of exhibiting is essentially finite. Even if we lived in a universe that was infinite in some respect, you could not show a complete aspect that was infinite, only either that an aspect appeared unbounded or that a reasonable projected abstraction of some aspect was infinite.

Note that I am not saying that infinity is meaningless, merely that it is always an abstraction of reality and not a direct exhibitable property of any thing. That infinity is a very useful abstraction is undeniable - it may be possible to formulate much of usable mathematics without it, but this would surely make such symbolic systems much more cumbersome. So when we say something is infinite, we are talking about an abstract projected property of our model of the item, even if the thing is, in fact, infinite. It is just that exhibiting is essentially a finite process.

I suspect that the same is true of the irreducibly complex. A language of irreducible "wholes" is useful in the same sense that infinity is useful, but only as an abstraction of our model, irrespective of whether these "wholes" exist. If they do not exist, the language of the holist is still useful as an abstract shorthand for systems whose complexity is potentially unbounded. If they do exist the language of "wholes" would still be necessarily abstract, i.e. not referring to direct properties of real things, even if the systems referred to were irreducible. It is just that exhibiting such systems (especially formally) is essentially a reductive process.

Pragmatic Holism - Bruce Edmonds - 22 FEB 96
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