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Monday, 14 September 2015

The plurality of formalities

In my work on logical compatibilities and classes of possible worlds (together with Alexandre, Rodrigo and Edelcio) we were led to tackle with the ambiguities in the current use of the notion of a possible world. Sometimes the expression is used to mean whatever is compatible with a given logic - and therefore given, say, classical propositional logic, a single possible world would be so that the snow is white or not. I'm inclined to refer to these uses of "possible world" with the alternative name of "world scheme". A world scheme reveals what is compatible with a given logic but a class of possible world in the sense that different world are compatible with the same logic is what we call a galaxy of a logic and it is can be seen as its ontological counterpart in the space of world. The study of galaxies opens some interesting horizons, one of them - which we haven't explored thoroughly yet - is the very issue of real contradictions, that is of the ontological status of inconsistencies. Or, to put it with Graham Priest, whether a realism about dialetheas is granted.

Whitehead, in his beautiful lecture of understanding in Modes of Thought, opens interesting avenues to think inconsistencies through. He starts out with the very Leibnizian intuition that avoiding contradictions one restricts oneself to a finite realm. Leibniz held that demonstrative reason works within finitude because it is guided by contradiction avoidance. However, Whitehead proceeds, if we consider the infinite agents in process of the universe, there are no contradictions for "process is the way by which the universe escapes from the exclusions of inconsistency" (Free Press Paperback, 54). The idea is interesting: if we consider all processes within the universe, it is possible to show how any apparent contradiction fades away - unless we confine ourselves in an abstraction. So, in the real world (concreteness, or rather the processes of concrescence) there are no contradictions. There is, in fact, no sense in which a contradiction could be found. However, this doesn't settle the case against dialethea realism. This is because abstractions act like a lure for feelings - they increase understanding by making things self-evident. For Whitehead, the importance of abstractions (and finitude) is constitutive of how things are because perceptual experience is widespread. So, in order to make some things visible - and others not - we have different formalities. Galaxies act as guidance to deal with worlds within the universe. Real contradictions are not a human construction out of a world with no contradictions but rather they are ways of seeing aspects of a universe where no single formality prevails.

Note: Whitehead's choice of the word "formality" is inspired. Formalities are what enable finite predictions both through formal systems and through regular behavior within an association (of people, animals, molecules or whatever). Tarde would have that there are some associations that are more social than others - they have more formalities. This is what emerges from a comparison between a Western and an Japanese human society (I think this is Tarde's example, if I remember right) or between human societies and the societies of molecules where formalities are far more ubiquitous.


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