Ideas from 'Mathematical Methods in Philosophy' by Horsten,L/Pettigrew,R [2014], by Theme Structure
[found in 'Bloomsbury Companion to Philosophical Logic' (ed/tr Horsten,L/Pettigrew,R) [Bloomsbury 2014,978-1-4725-2303-0]].
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5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
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18739
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Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-)
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5. Theory of Logic / E. Structures of Logic / 1. Logical Form
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18741
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Logical formalization makes concepts precise, and also shows their interrelation
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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18744
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Models are sets with functions and relations, and truth built up from the components
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7. Existence / A. Nature of Existence / 1. Nature of Existence
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18740
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If 'exist' doesn't express a property, we can hardly ask for its essence
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10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
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18745
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A Tarskian model can be seen as a possible state of affairs
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18747
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The 'spheres model' was added to possible worlds, to cope with counterfactuals
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10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
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18748
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Epistemic logic introduced impossible worlds
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10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
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18746
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Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment
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18750
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Using possible worlds for knowledge and morality may be a step too far
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