Modality and identity

Kripke semantics will be discussed in some detail along with a fairly common modification which will be central to the arguments of this paper. In order to explicate this modification a discussion of several semantic issues will be helpful. These will include the difference between representational semantics and interpretational semantics, how interpretational semantics can be seen as a type of counterpart semantics, and how the modified Kripke semantics can be viewed as a representational-interpretational hybrid semantics.

Several types of modality will be discussed. The paper will be primarily concerned with alethic modality as opposed to deontic, temporal or other general categories of modality although epistemic modality will be discussed briefly. The types of modality which will be discussed include narrow and broad logical modalities, intermediaries between these two types of logical modalities which include mathematical modality and what will be termed semantic modality, and natural modality. Relations between these modalities will be investigated with particular attention to the semantic theories which will be presented and several common misconceptions about modal logic will be dispelled.