I wish to indicate something about my purposes in setting up the modeling for quantified modal logic, and some philosophical views about the matter. After discussion of some alternative views, it will be argued that the main question is not "what is a possible world?" but what is the relation to other worlds in the structure. Sometimes one cannot identify a world in and of itself, but only in relation to the structure. Some of the conceptual problems in conceiving such a structure, however, will be indicated as reservations.

Puzzles about sentences containing expressions of certain sorts, such as predicates of personal taste, epistemic modals, and ‘know’, have spawned families of views that go by the names of Contextualism and Relativism. In the case of predicates of personal taste, which I will be focusing on, contextualist views say that the contents of sentences like “Uni is delicious” and “The Aristocrats is hilarious” vary somehow with the context of utterance. Such a sentence semantically expresses different propositions in different contexts, depending on what standard or perspective (or whose standard or perspective) is implicitly adverted to. According to relativist views, the propositional content of such a sentence is fixed, but what it takes for that proposition to be true varies somehow with the context, depending on the relevant standard or perspective. I will argue that such views are neither well supported by the data nor well motivated by the puzzles themselves. Even so, there is an element of truth in each.

I will sketch an alternative view, dubbed Radical Invariantism, according to which the appearance of context sensitivity is illusory. Rather than impute either kind of context sensitivity to these sentences or to their contents, Radical Invariantism says that these sentences are distinguished by what they don’t do. Because they are not explicitly relativized, they leave a certain semantic slack. They fall short of fully expressing a proposition, instead expressing merely a “propositional radical.” We can explain away the appearance of semantic context sensitivity pragmatically, by taking into account facts about how, and under what conditions, speakers who use or encounter these sentences manage to pick up the slack. This can occur in either of two ways. Speakers either take a certain standard or perspective as understood, or else they treat the sentence as if expresses a standard- or perspective-independent proposition even though it does not.

What is right about Contextualism is that the problematic sentences do not have context-independent propositional contents. What is right about Relativism is that these sentences do not have context-dependent propositional contents. What is wrong about both is their implicit assumption that these sentences have propositional contents at all. Radical Invariantism denies that they do. To appreciate how and why this can be, we will compare explicitly relativized sentences (“Uni is delicious to sushi lovers”) with their puzzling unrelativized counterparts (“Uni is delicious”), and compare both with analogous sentences containing straightforwardly relative terms like ‘neighbor’, ‘obvious’, ‘tall’, ‘rich’, ‘legal’, ‘poisonous’, and ‘scary’. The basic argument will be that the explicitly relativized sentences do express propositions, that they do so only because they are explicitly relativized, hence that their unrelativized counterparts fall short of doing so. This argument will be complemented by a pragmatic account of what speakers mean, and of how they manage to be understood, when they utter unrelativized sentences containing relative terms. I will argue that there is no need to posit special semantic parameters (standards, perspectives, judges) for predicates of personal taste. Despite having some distinctive pragmatic properties, predicates of personal taste can be treated semantically in the same way as relative predicates of other sorts. It is enough to explain under what conditions a speaker can, and under what conditions he cannot, reasonably expect to convey what he means without making the intended standard (perspective, judge) explicit.

The technological "singularity", or I.J. Good's "intelligence explosion", is the rapid transition from greater-than-human artificial intelligence to superintelligence. I will give set out and analyze the argument for an "intelligence explosion", and will consider the forms that such explosion might take. Focusing on the likelihood that it will take place within a simulated world, I will consider resulting practical and philosophical issues. How, if it all, can we control the impact of superintelligence in a simulated world on our world? Will systems in a post-singularity world be conscious? Can we be among them?