Editing Causality (section)

=== Counterfactual theories ===
{{Main|Counterfactual conditional}}

Counterfactual theories define causation in terms of a counterfactual relation, and can often be seen as "floating" their account of causality on top of an account of the logic of [[counterfactual conditionals]]. Counterfactual theories reduce facts about causation to facts about what would have been true under counterfactual circumstances.<ref>{{Cite book |last=Ney |first=Alyssa|author-link=Alyssa Ney |url=https://www.taylorfrancis.com/books/9781351141208 |title=Metaphysics: An Introduction |date=2023-02-23 |publisher=Routledge |isbn=978-1-351-14120-8 |edition=2 |location=London |language=en |doi=10.4324/9781351141208}}</ref> The idea is that causal relations can be framed in the form of "Had C not occurred, E would not have occurred." This approach can be traced back to [[David Hume]]'s definition of the causal relation as that "where, if the first object had not been, the second never had existed."<ref>{{cite book|last1=Hume|first1=David|title=An Enquiry concerning Human Understanding|date=1748|location=Sec. VII}}</ref> More full-fledged analysis of causation in terms of counterfactual conditionals only came in the 20th century after development of the [[possible world semantics]] for the evaluation of counterfactual conditionals. In his 1973 paper "Causation," [[David Lewis (philosopher)|David Lewis]] proposed the following definition of the notion of ''causal dependence'':<ref>{{cite journal|last1=Lewis|first1=David|title=Causation|journal=The Journal of Philosophy|date=1973|volume=70|issue=17|pages=556–567|doi=10.2307/2025310|jstor=2025310}}</ref>

:An event E ''causally depends'' on C if, and only if, (i) if C had occurred, then E would have occurred, and (ii) if C had not occurred, then E would not have occurred.

Causation is then analyzed in terms of counterfactual dependence. That is, C causes E if and only if there exists a sequence of events C, D<sub>1</sub>, D<sub>2</sub>, ... D<sub>k</sub>, E such that each event in the sequence counterfactually depends on the previous. This chain of causal dependence may be called a ''mechanism''.

Note that the analysis does not purport to explain how we make causal judgements or how we reason about causation, but rather to give a metaphysical account of what it is for there to be a causal relation between some pair of events. If correct, the analysis has the power to explain certain features of causation. Knowing that causation is a matter of counterfactual dependence, we may reflect on the nature of counterfactual dependence to account for the nature of causation. For example, in his paper "Counterfactual Dependence and Time's Arrow," Lewis sought to account for the time-directedness of counterfactual dependence in terms of the semantics of the counterfactual conditional.<ref>{{cite journal|last1=Lewis|first1=David|title=Counterfactual Dependence and Time's Arrow|journal=Noûs|date=1979|volume=13|issue=4|pages=455–476|doi=10.2307/2215339|jstor=2215339}}</ref> If correct, this theory can serve to explain a fundamental part of our experience, which is that we can causally affect the future but not the past.

One challenge for the counterfactual account is [[overdetermination]], whereby an effect has multiple causes. For instance, suppose Alice and Bob both throw bricks at a window and it breaks. If Alice hadn't thrown the brick, then it still would have broken, suggesting that Alice wasn't a cause; however, intuitively, Alice did cause the window to break. The Halpern-Pearl definitions of causality take account of examples like these.<ref>{{cite book |last1=Halpern |first1=Joseph Y. |title=Actual Causality |date=2016 |publisher=The MIT Press |url=https://www.cs.cornell.edu/home/halpern/papers/causalitybook-ch1-3.html}}</ref> The first and third Halpern-Pearl conditions are easiest to understand: AC1 requires that Alice threw the brick and the window broke in the actual work. AC3 requires that Alice throwing the brick is a minimal cause (cf. blowing a kiss and throwing a brick). Taking the "updated" version of AC2(a), the basic idea is that we have to find a set of variables and settings thereof such that preventing Alice from throwing a brick also stops the window from breaking. One way to do this is to stop Bob from throwing the brick. Finally, for AC2(b), we have to hold things as per AC2(a) and show that Alice throwing the brick breaks the window. (The full definition is a little more involved, involving checking all subsets of variables.)