Semantics of Modality

Definitions of Definition

 

Intension is the relation of a set of attributes stipulated as intrinsically true of a sign; judged by the degree of mereological equivalence of the relation.

 

Extension is the function of a set of objects denoted as true by implication of the intension of a set; judged by the correspondence of object to its function.     

 

Modality of Extension

 

Epistemic necessity is the modal quantification of any extensional relation, whereby some class of objects or states of affairs is probabilistically judged as always true of some denoted term in a particular doxastic system Đ. 

 

Epistemic possibility is the modal quantification of any extensional relation, whereby some class of objects or states of affairs is probabilistically judged as sometimes true of some denoted term in a particular doxastic system Đ. 

 

Epistemic impossibility is the modal quantification of any extensional relation, whereby some class of objects or states of affairs is probabilistically judged as never true of some denoted term in a particular doxastic system Đ. 

 

Metaphysical necessity is the modal quantification of any extensional relation, whereby some class of objects or states of affairs is true in all possible worlds.

 

Metaphysical possibility is the modal quantification of any extensional relation, whereby some class of objects or states of affairs is actualizable; and therefore true in some possible worlds.

 

Metaphysical impossibility is the modal quantification of any extensional relation, whereby some class of objects or states of affairs is non-actualizable or logically contradictory; and therefore true in no possible worlds. 

 

Modality of Intension

 

Semantic necessity is the modal quantification of any intensional relation, whereby some class of definiens ϕn(xn) is stipulated as always true of some definiendum ϕ in a particular intensional system Ł. 

 

Semantic possibility is the modal quantification of any intensional relation, whereby some class of definiens ϕn(xn) is stipulated as sometimes true of some definiendum ϕif and only if there is no contradiction with the class of definiens ϕn(xn) that are stipulated as always true of the definiendum ϕin a particular intensional system Ł.

 

Semantic impossibility is the modal quantification of any intensional relation, whereby some class of definiens ϕn(xn) is stipulated as never true of some definiendum ϕin a particular intensional system Ł.

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~ by Scott Pellegrino on October 26, 2008.

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