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It is, of course, open to a fictionalist to reject both the basic modal inferences mentioned and the standard interdefinition of possibility and necessity.
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So the basic modal characterization seems flawed.
(According to the basic modal characterization, an essential property is the same as a necessary property).
So, according to the basic modal characterization, being a dog is an accidental property of Emma.
Let's call this the basic modal characterization where a modal characterization of a notion is one that explains the notion in terms of necessity/possibility.
According to the basic modal characterization, any such property, if possessed by a contingently existing object, will be counted as an accidental property of that object.
Or she might assert as little as is needed to preserve the basic modal inferences from actuality: for example, every true P is possibly true, and actually true, but this is the limit of literal modal truth.
Since none of the operators of the Traditional Scheme are taken as primitive, and the basic logic is a modal logic with necessity and possibility as the basic modal operators, this is referred to as "a reduction" (of deontic logic to modal logic) Proofs of SDL-ish wffs are then just K-proofs of the corresponding modal formulae involving "d".
Many would say that each individual human could not fail to be human; if so, then the basic modal characterization counts the property of being human as an essential property of each human.
We introduce mathematical programming and atomic decomposition as the basic modal (T-Box) inference techniques for a large class of modal and description logics.
There are other ways of explaining the distinction between essential and accidental properties of objects in modal terms (see Zalta (2006), for example), but what we have called the basic modal characterization and the existence-conditioned modal characterization are the standard ways.
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