Abstract
Conditional constructions – constructs of the form If A, then B – have for over a century been subject to intense study in a wide variety of philosophical areas, as well as outside of philosophy. One important reason is that such constructs allow one to encode connections and dependencies, be they causal, epistemic, conceptual, or metaphysical. This chapter briefly outlines some of the main formal models that have been employed to analyze such constructs, as well as their philosophical motivation.
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Notes
- 1.
The field is far too wide to enable an exhaustive survey in these few pages and so the present overview largely reflects the author’s own interests and prejudices. Many important issues are ignored or treated only in passing and countless important contributions will not be credited. References given reflect (but by no means exhaust) works of seminal importance, works that give a more thorough overview of the issues, as well as work that may point towards interesting new developments.
- 2.
Arló-Costa [3] presents a thorough overview of the logic of conditionals and how they relate to structural conditions.
- 3.
Reflexivity: v ≤u v. Transitivity: If v ≤u w and w ≤u z, then v ≤u z. Completeness: Either v ≤u w or w ≤u v.
- 4.
The limit assumption is not, strictly speaking, necessary, but if one omits this constraint the semantic clause becomes more complex.
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- 7.
Some have argued that counterfactual conditionals can be given an epistemic interpretation, but this is a matter of considerable controversy.
- 8.
A probability measure is, as is standard, here taken to be a real-valued function P that take sentences as their arguments and satisfies (a) 0 ≤P(A) ≤ 1, (b) P(¬A) = 1 −P(A), and (c) P(A ∨ B) = P(A) + P(B) −P(A ∧ B).
- 9.
Conditionalisation only covers the case when P(A) > 0; to deal with the case when P(A) = 0 one can use Popper-measures or let P ∗ A be a non-standard measure that assigns probability 1 (or 0) to all sentences.
- 10.
* Indicates recommended reading.
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Cantwell, J. (2018). Conditionals. In: Hansson, S., Hendricks, V. (eds) Introduction to Formal Philosophy. Springer Undergraduate Texts in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-77434-3_6
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