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Wednesday, 23 September 2015

Impossible logics or logic beyond the linguistic turn? A debate with myself

In opposition to what I wrote in the last post, I now think that maybe all constellations correspond to a logic, no matter if they are formulated at all. See my post in philpercs

Are some logics universally impossible?

Leibniz and Whitehead as ontologists of agents and on metaphysicians of perspective agree that when we consider the whole process (or the whole class of monads) there are no contradictions. Yet, finite beings can only coordinate what they perceive within perspectives and are guided by finite lab-like simplifications of the whole. These simplifications cannot be taken apart from the whole, and yet they provide some sort of mathesis localis. Maybe we can think of different logical systems in this way: they capture something but only by failing to be fully coordinated with all the rest.

In our investigation of galaxies (classes of possible worlds associated to each logic), we are now wondering whether there are classes of possible world (that we call constellations) that cannot be galaxies. That is, there is no signature F of formulae that could formulate a logic that would make possible exactly the worlds in these constellation. Take a constellations formed by two or more worlds with nothing in common (intersection of the classes of truth in all worlds of the constellation is empty). We conjecture (and provided a proof for simple cases) that there could be a galaxy in any F. In no F there could be a formulation of a logic for such constellation. It would follow that there are constellations that are not galaxies in any F and therefore that some collections of possible worlds could never be such that there is an underlying logic to them. At least not one that can be formulated.

To be sure, we are assume a classical meta-logic for most of our operations and therefore there is some relativity to these results. Further, one could think of logics as something that require no language - and assume every constellation provide a logic even if it is not something that could be expressed otherwise. However, it seems like there are limits to what is possible when we feel the pressure of something beyond the mathesis localis.

Tuesday, 22 September 2015

Conversation and animation

I've been thinking about what is at stake in conversations. Conversations are frictions of perspectives - they could involve many or just two parts, but not one. They are very different from simple apprehensions of information - something like a mirror image of what is being conveyed. In fact, conversations are not really about conveying anything, monologues get a message through, conversations have a different geometry. Grice's implicatures show that in a conversation interaction there are expectations built both from the conversation history and from the very structure of what a relevant, cooperative, well-mannered, qualitative and quantitative contributive dialogue is supposed to be. What is said in a conversation wouldn't mean the same or even make sense outside the frame of that conversation - contexts are part of the message. It seems further that there is no message without context (and no capture without coordination) for often the only way to find out is to go and have a chat.

As part of the project of a linguistic turn of 360 degree, I was thinking of replacing the model of access (to the external world, to things, to the great outdoors) with one of conversation. Granted, conversations are types of relations (and correlations). Yet they have different features. In a conversation (like in alliances or negotiations), both parts are expecting, assuming, coordinating - they are both experimenting. Conversation is an image of animation - and not one of extracting data from a corpse (from what Whitehead calls "nature" in Modes of Thought - what is devoid of impulse). If we consider bits of a conversation, we can consider them in the age of the correlate and therefore either hostages to one part's spontaneity or escaping from it imagining a correlation that is absolute. But if we somehow exorcise this temptation to isolate parts of the ongoing conversation with the world, we can stop thinking knowledge and aboutness in terms of access and start thinking in terms of conversations. We could exorcise the temptation to isolate bits of the conversation because that would be a perverse way to fall prey of the Whiiteheadian myth of the finite facts according to which a fact could be just a fact. Facts appear only in conversations. Our partner in a conversation can be somehow absolute, but only as much as we are absolute in our engagement in the talking. To know (or to think through) something would be then something closer to talking than to viewing (or contemplating).

Now, if this model could be worked out, it would be a model not only of our knowledge and thinking about the world, but maybe also an image of how things end up being the way they are. If each thing has a perspective on all the rest, each one is arguably in engaged in conversation with the rest where renegotiation is always taking place. They are all in a multifaceted, ongoing, perhaps an entretien infini.

Monday, 14 September 2015

Slow activism

Last week I went to "Desfazendo Gênero", a queer event in Bahia bringing together activists and people reflecting on undoing gender. It was a tense event. Internal disputes framed by a hostile external environment in a reactionary country made it explosive. Keynote was given by Judith Butler who wise enough to sense the atmosphere and defend the rhythm of theory in a very elegant way. Theory building is slow and piecemeal thinking of alternatives and production of different tonalities. Theory construction is slower than usual activism because it can be read as slowed down territory where we can afford some attitudes otherwise difficult and rare. It can afford, above all, gestures of hospitality.

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.