By Brian Skyrms
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Additional resources for Causal Necessity: A Pragmatic Investigation of the Necessity of Laws
While, with a bit of imagination, we can see what an adequate further story about the moon and Roquefort might be like, we presently have no idea of what a further story might be like for a statement negating some law of logic, so nor of what such statements might be used to describe as so. It is not that a claim that some statement and its negation are both true is preposterous. Such a claim does not get so far as being preposterous. For as things stand, there is no answer to the question just what way it is preposterous to suppose things are.
A logical calculus consists of some stock of representations of logical forms (forms for a thought, or, more generally, a bit of the conceptual), to take (on a decomposition), and some rules for calculating on these forms—for moving from given such forms to given others. If it earns the title logical calculus, then these rules capture (represent) some of what some laws of logic say. For a usual calculus, the moves from form to form pass along truth-preserving paths from form to form; some or all of the truth-preserving paths there are, given the relevant laws.
She saw the incidence of petals in the vicinity of the rose’s centre on the decrease. She saw the centre of mass of a collection of rose petals shifting groundwards. And so on. No one such description exhibits the structure of what Pia saw in a way in which the others do not. In that sense, the world is structured in no one way; no one order is its. One might think that representing the world to oneself as thus and so just is structuring it in some one particular way; if one has done the former then, ipso facto, for some particular structure, one has structured things in that way.