While Lewis's account avoids some of the familiar objections to simple regularity accounts (e.g., problems with substitutivity
, furnishing genuine explanations, etc.), there are still serious objections.
An argument like the following can be given against the possibility of contingent identity statements: First, the law of the substitutivity
of identity says that, for any objects x and y, if x is identical to y, then if x has a certain property F, so does y:
It explains this disparity between indicative and counterfactual conditionals by clarifying important logical differences between them: (a) substitutivity
of identity holds for indicatives but fails for counterfactuals, and Co) counterfactuals preserve possibility while indicatives preserve only truth.--Correspondence to email@example.com
An intensional logics is exactly one in which substitutivity
salva veritate fails for some of the sentences of the logic.
Boshernitzan and Caroll  have found a sufficient condition for substitutivity
of an infinite word coding an exchange of r intervals.
(2010) Component Simulation-based Substitutivity
Managing QoS Aspects.
and dialog initiative concerns user interactions aspects of the system.
(4) The Substitutivity
Principle: If two expressions have the same meaning, then substitution of one for the other in a third expression does not change the meaning of the third expression.
(It would seem that Kripke draws back from Millianism, since --for instance-- he is worried about the substitutivity
of proper names in propositional attitude contexts.
Requirement: a definiens must be substitutable salva veritate for its definiendum.
In this way, Dancy reveals Socrates' commitment to the following three assumptions about adequate definitions: 1) the substitutivity
requirement that the definition of F-ness specify necessary and sufficient conditions for something's being F (81-2); 2) the paradigm requirement that the definition provide a model by which the applicability of 'F' can be determined (115), and 3) the explanatory requirement that the definition explain why F things count as F (135).