It seems hard to deny that some kind of structure, however fragile or unstable, organizes human experience. And it seems hard to deny that a major aspect—if not the determining characteristic—of the structure of experience is time. Let’s grant all that for the purposes of this week’s discussion. If we take as paradigmatic the structure of a formal system, it turns out that there are two possibilities when it comes to a structure, as the early twentieth century’s greatest mathematical minds taught us: if a structure is consistent, it is incomplete; if a structure is complete, it is inconsistent. More strictly, every structure robust enough to be worthy of the name as it were produces an undecidable element—an element that cannot determinately be said either to belong or not to belong to the structure in question; if it is decided, in the name of achieving systemic completeness, that this element belongs to the structure, inconsistency results; but if it is decided, in the name of maintaining systemic consistency, that this element doesn’t belong to the structure, incompleteness results. Thus, completeness and consistency are mutually exclusive when it comes to structures. (Note that this result is easiest to demonstrate when it comes to formal systems, but it equally holds for non-formal systems, as so much work in the so-called soft sciences has shown in the past century.) Coming up against an undecidable, we have a decision to make. (Note that, paradoxical…
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