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This book concerns mental states such as thinking that Obama is tall, imagining that there will be a climate change catastrophe, knowing that one is not a brain in a vat, or believing that Martina Navratilova is the greatest tennis player ever. Such states are usually understood as having intentionality, that is, as being about things or situations to which the mind is directed. The contents of such states are often taken to be propositions. The book presents a new framework for the logic of thought, so understood—an answer to the question: Given that one thinks (believes, knows, etc.) something, what else must one think (ditto) as a matter of logic? This should depend on the propositions which make for the contents of the relevant thoughts. And the book defends the idea that propositions should be individuated hyperintensionally, i.e. not just by the sets of worlds at which they are true (as in standard ‘intensional’ possible worlds semantics), but also by what they are about: their topic or subject matter. Thus, the logic of thought should be ‘topic-sensitive’. After the philosophical foundations have been presented in Chapters 1−2, Chapter 3 develops a theory of Topic-Sensitive Intentional Modals (TSIMs): modal operators representing attitude ascriptions, which embed a topicality or subject matter constraint. Subsequent chapters explore applications ranging from mainstream epistemology (dogmatism, scepticism, fallibilism: Chapter 4), to the nature of suppositional thinking and imagination (Chapter 5), conditional belief and belief revision (Chapter 6), framing effects (Chapter 7), probabilities and indicative conditionals (Chapter 8).

Ch. 6: One sense of imagination that matters in epistemology has the word mean reality-oriented mental simulation (ROMS): we suppose that something is the case, develop the supposition by importing background knowledge and beliefs, and check what is true in the imagined scenario. What is the logic of ROMS? Imagination has a reputation for being logically anarchic. In particular, it s hyperintensional: we can imagine A without imagining a necessarily equivalent B. This work considers a Principle of Equivalence in Imagination which, if accepted, will limit the anarchy: when A and B are equivalent in imagination, one will imagine the same things after supposing either in ROMS. What is equivalence in imagination? It is suggested that it s cognitive equivalence. A and B are cognitively equivalent for one when they play the same role in one s cognitive life: whatever one understands, concludes, etc., given either, one does, given the other. ROMS is logically modelled via variably strict modals. Two formal semantics are proposed for them: one uses possible worlds plus an algebra of topics; the other resorts to impossible worlds. The two deal with equivalence in imagination in subtly different ways.

The latter half of the 20th Century witnessed an ‘intensional revolution’: a great collective effort to analyse notions which are absolutely fundamental to our understanding of the world and of ourselves – from meaning and information to knowledge, belief, causation, essence, supervenience, conditionality, as well as nomological, metaphysical, and logical necessity – in terms of a single concept. This was the concept of a possible world: a way things could have been. Possible worlds found applications in logic, metaphysics, semantics, game theory, information theory, artificial intelligence, and the philosophy of mind and cognition. However, possible worlds analyses have been facing numerous problems. This book traces them all back to hyperintensionality: the need for distinctions more fine-grained than the possible worlds apparatus can easily represent. It then introduces impossible worlds – ways things could not have been – as a general tool for modelling hyperintensional phenomena. The book discusses the metaphysics of impossible worlds and applies them to a range of central topics and open issues in logic, semantics, and philosophy: from the problem of logical omniscience in epistemic logic, to the semantics of non-classical logics, the modeling of imagination and mental simulation, the analysis of information and informative inference, truth in fiction, and counterpossible reasoning. The latter half of the 20th Century witnessed an ‘intensional revolution’: a great collective effort to analyse notions which are absolutely fundamental to our understanding of the world and of ourselves – from meaning and information to knowledge, belief, causation, essence, supervenience, conditionality, as well as nomological, metaphysical, and logical necessity – in terms of a single concept. This was the concept of a possible world: a way things could have been. Possible worlds found applications in logic, metaphysics, semantics, game theory, information theory, artificial intelligence, and the philosophy of mind and cognition. However, possible worlds analyses have been facing numerous problems. This book traces them all back to hyperintensionality: the need for distinctions more fine-grained than the possible worlds apparatus can easily represent. It then introduces impossible worlds – ways things could not have been – as a general tool for modelling hyperintensional phenomena. The book discusses the metaphysics of impossible worlds and applies them to a range of central topics and open issues in logic, semantics, and philosophy: from the problem of logical omniscience in epistemic logic, to the semantics of non-classical logics, the modeling of imagination and mental simulation, the analysis of information and informative inference, truth in fiction, and counterpossible reasoning.