Meaning, Logic, and Paradox

Prolegomena to Any Future Analyticity: The Kantian Revolution Defended

Semantic Logicism

The Fundamental Question of Philosophy of Language

Seven Points of Logical Semanticism

The Reformation of Philosophic Logic

Protected: The Complete Intensional Semantic Axiomatic Set Theory in PDF

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Phenomenology Re-Considered

Modality and Probability Calculus: The Belcher and Turner Project

New Semantics for Modal Logic

It has previously been mentioned that there are numerous problems with the Kripkean semantics for the modal alethic operators (necessity and possibility), namely the metaphysical baggage.  It has been suggested that instead of "all possible worlds" as the definition of necessity, we instead develop semantic necessity of which does not appeal to possible worlds at all.  But before we develop the precise definition of semantic necessity, let us first given some examples.  Take the following propositions: "Dasha is the wife of Scott"; "Dasha signifies (is) the 'gift of God'"; "The gift of God is the wife of Scott."  The basic problem in this transitive relation is that the first proposition and the second proposition are two very different types of identity relations but logically they are quantified in the same procedure.  In other words, the difference is lost in quantification which creates the problem of the subsitutivity of identicals.  The first proposition "Dasha is the wife of Scott" involves the reference of the female Dasha to the description, but the second proposition "Dasha is the 'gift of God' does not necessitate reference at all, for the relation entails the etymological meaning of the term Dasha with that of its description.  Thus, if the third proposition is not disambiguated from these two very different identity relations, the problem of the substitutivity of identicals is created.  So far this operates simply on the level of predicate logic but as Quine as repeatedly shown, the problem extends to modal logic (if it is not corrected).  Here is the difference between what I am proposing and what Kripke and others are espousing.  In my understanding of modality, the second proposition, "Dasha is the gift of God" becomes semantically necessary, it is the relation of two abstract general terms to one another without appeal to a referent.  In the Kripkean system, all these propositions would be quantified as possibilities.  But by quantifying the second proposition as merely possible, there is no way of overcoming the problem of the substitutivity of identicals.  It may be that in other possible worlds the etymological meaning of Dasha is not what it is, but that does not concern us, for the naming becomes necessary in this semantic-logical system.  In general, the necessity operator that applies to a definite singular term is always signifying some semantic quality as in the above example of the second proposition.  If N signifies necessity and P signifies possiblity, then NDg is the modal and predicate logic for: "it is semantically necessary that Dasha is/means the gift of god.  Instead of "all possible worlds" perhaps we could say that semantic necessity is what Lewis calls "truths in virtue of their meaning", or semantic analyticity.  This extends to intensions that are not associated with a definite singular term.  This also would apply to the absolute general terms "parrot", "chair", and other examples previously worked out on this site.  So what becomes of possibility?  Quite simply, possibility takes the role of any term/meaning that can be conjoined with the necessary meanings of a term without contradiction.  From an epistemological standpoint, we could say that possibility takes on the role of empirical generalizations.  For instance, if a parrot is necessarily defined as winged, beaked, zygodactyl…etc, etc., and we discover a red parrot, then one could say that P(Pr)…or, "it is possible that a parrot is red."  This takes on the metaphysical mystery out of modality and makes the field epistemologically and scientifically useful.  Similarly it makes modal logic able to combine with probability calculus, if probabilities are taken epistemologically.  The aRb can be associated with its probabilities and these probabilities can be expressed as modal possibilities.  This can be done completely without appeal to possible worlds.