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Galaxies and universal metaphysics Hilan Bensusan

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The nature of contingency Thinking about the accidental vs thinking about the substantial. What does it mean to say that something is open to change? The contingent: impermanent, non-universal, non-immune, non- necessary and non-impossible. The nabla: what is not impossible and not necessary. (Or, the possible that is non-necessary) Contingency and possible worlds: p is contingent if it is true in some possible worlds and false in others. Contingency thought in terms of possible worlds. The issues concerning logical and metaphysical necessity.

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Worlds and logics Much metaphysical reasoning appeals to the notion of possible world. Metaphysical theses are supposed to be true in all possible world (or in all possible worlds visible from the actual one). “A paradise for philosophers”: Lewis stays clear from impossible worlds. Possible worlds are logically possible worlds – they have an underlying logic. Worlds that don’t satisfy the underlying logic are deemed impossible. Where is the dividing line between logics and metaphysics? Why use classical logic? Because it is more entrenched. What if we consider more than one logic? The endeavor of universal logic: comparing logics, fusing them, combining them, dividing them. Different logics will lead to different classes of possible (and impossible) worlds. Look at those several classes instead of looking at a single one: a universal topology of possible worlds.

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A logic and its galaxy From an abstract point of view, a logic can be defined as where F is a set of formulas and C a consequence relation. We can now define a galaxy as a class of possible worlds associated to a consequence relation It is easy to see that for each consequence relation there is one and only one galaxy (G). If a logic is sound and complete, it has one and only one galaxy. Roughly speaking, a logic is connected to a galaxy. To present a logic is to present a galaxy. To combine, fusion, compare or divide logics are therefore operations in classes of possible world.

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Some diversity of logics In order to study the galaxies of a logic, we define an antilogic and a counterlogic for each logic. A logic L is sound and complete if and only if its corresponding antilogic is sound and complete. A logic L is sound and complete if and only if its corresponding counterlogic is sound and complete. If a logic is well-behaved (if it entails something it doesn’t entail its negation), then the the counterlogic of L is a sublogic of the antilogic of L. Square of oppositions between a logic, its antilogic, its counterlogic and its anti-counterlogic (which is also its counter- antilogic).

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Galaxy theory and a topology of possible worlds There are worlds that are common to the galaxies of a logic and of its antilogic. How do we know in which galaxy is our world? Metaphysical theses are themselves galaxy-relative. Is this pointing towards a universal metaphysics that considers more than one galaxy at once? In particular, contingency are galaxy-relative. What is logically contingent, for example, is not antilogically contingent. It could seem that, once we introduce the distinction between possible and impossible worlds (that is, once we reason within a logic), nothing is (galaxy- independently) contingent. But then, what is the ontological status of a possible world? If we are concretists, about which possible worlds are we realist? About which galaxy? Can we be realist about all?

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Kit Fine on reality and perspectives Plurality of galaxies are similar to plurality in (say, tense) perspectives. It shows that reality cannot be neutral, absolute and coherent. Kit Fine’s approach: to compare standard realism (the thesis that reality is absolute and coherent but not neutral) with non-standard versions (that reality is neutral, even though it is not absolute or not coherent). Nonstandard realism: either perspectivism – which gives up absoluteness and makes reality indexed – or fragmentalism – that gives up coherence and ushers in an über-reality that aggregates what is in each perspective. Fine favors the latter. Fragmentalism and incoherence: in each perspective, there are no inconsistencies. It is only when we aggregate them that incoherence comes up.

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Fragmentalism and the reality of logics Standard realism about galaxies: just pick one logic (one galaxy), maybe classical predicate calculus, as a parameter for reality. Just one galaxy is real. Fragmentalist about galaxies: the assemblage of all galaxies form an ( über-) reality which is not coherent. Dialetheas? That maybe entails that there ought to be inconsistencies in reality if we consider all galaxies. Contingency: in a galactical über-reality, there can be no contingencies (those are galaxy-relative).

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