Kripke introduces the target notion as follows:

For brevity I will tend to drop the qualifications ‘subjunctive’ and ‘de dicto’. In the literature, our topic is most often called ‘metaphysical necessity’, and this is in keeping with Kripke’s classification of the notion as metaphysical as opposed to epistemological. I will avoid this loaded label for the time being, but in Chapter 7 I will begin to interrogate it.

A further important point to note is that the target notion is supposed to be the dual of an unrestricted notion of possibility.⁵ Consider: ‘It is true that I stayed home yesterday. This couldn’t have been otherwise, as I had to be there to let the electrician in’. This utterance may be true, but in that case we are dealing with a restricted range of ways things could have been. We are ignoring ways things could have been in which I never made the appointment with the electrician, or the appointment was on a different day, or I stop caring about electricity. This supplement to Kripke’s characterization has become customary. Witness Timothy Williamson in an interview:

This trafficking in examples brings up a methodological point: this approach to factorizing necessity is set up to be able to accommodate necessary a posteriori and contingent a priori statements, and in developing it I have treated what seem to me the most convincing examples as data. When illustrating the approach, I take the orthodox Kripkean line on a few examples. However, I intend the approach to be quite flexible, offering plenty of room for disagreement about them.

Another important point is that the target notion might be vague, in the sense of there being unclear or borderline cases. (It seems pretty clear that ‘Saul Kripke is not a number’ is necessarily true, whereas ‘Saul Kripke is an influential philosopher’ is contingently true. But with some truths, such as ‘Saul Kripke is male’, or ‘Saul Kripke was born in the twentieth century’, things are not so clear.) It is important to allow for this explicitly, since the appearance of unclear or borderline cases may seem to cast doubt on the legitimacy of the notion. Indeed, it might seem like this is the type of notion which can’t really be vague if it is to be legitimate; but this I think stems from attaching dubious epistemic hopes to the notion, as I explain in Chapters 7 and 8.

One final introductory point: while for simplicity’s sake I proceed for now as though there is a single target notion, I do not really mean to rule out the view that there is more than one notion which fits Kripke’s characterization and key examples.¹³ On the contrary, I end up taking this prospect seriously in Chapters 7 and 8.

So much for introducing the target notion. The next part of the necessary groundwork takes the form of ground-clearing; I want to deal in advance with some considerations which might seem to cast doubt upon our project of attempting to rescue the idea that there is something a priori and semantic about necessity.

This challenge must be given its due. One reply to it that I emphatically do not endorse is to object that indicative necessity is merely epistemic, whereas subjunctive modality is objective (‘metaphysical’). Firstly, such an objection may be countered with a ‘So what?’;¹⁴ a notion being epistemic hardly disqualifies it from being philosophically central. Furthermore, if it is epistemic, the notion is epistemic only in a general, idealized way; it is not about what is knowable for some particular person or group, or even humanity in general. If indicative necessity is epistemic, then it just is apriority or something closely related, and a priori truths are those which can in principle be known without recourse to experience. An even bigger problem with the objection is that indicative necessity may not be merely epistemic at all. The indicatively necessarily true statements, it might be argued, are those which are inherently incapable of being false. Given what they mean, the only truth value they can have is true.¹⁵ Knowability without recourse to experience lies downstream from that. Apriority is a consequence of indicative necessity. The fact that a statement is only capable of truth is an objective fact about that statement, not itself having to do with how it may be known.

This viewpoint about indicative necessity and its explaining typical cases of apriority is controversial and hard to maintain given the state of present philosophical thinking about linguistic meaning, but the views I develop in Chapters 4 and 5 fit well with it. I want to remain open to the idea that with modal issues in philosophy, the relevant modality is often indicative or might as well be. It is nonetheless important that we clarify subjunctive modality and its relation to meaning. If a modal issue arising in philosophy can be construed as subjunctive, then it often will be, and so we need to understand the place of a priori reflection, and reflection on meaning in particular, with respect to the issue so framed. One reason that modal issues tend to get framed subjunctively is that indicative necessity—as opposed to the apriority that stems from it—is currently poorly understood, indeed hardly recognized as a distinctive objective modality. There are also powerful imaginative considerations in favour of the subjunctive. The characteristic way in which subjunctive possibility and impossibility judgements depend on empirical input encourages the view that subjunctive modality is as it were better informed than indicative. There are the ways the world could actually be—the ways depicted by the world of coherent representations, so to speak—but then there is the more circumscribed range of ways the world really could have been, and our knowledge of this space must be empirically informed. This fits almost uncannily well with general ideas about how philosophy ought properly ...