There are some necessary conditions on causal relations that seem to be so trivial that they do not merit further inquiry. Many philosophers assume that the requirement that there could be no temporal gaps between causes and their effects is such a condition. Bertrand Russell disagrees. In this paper, an in-depth discussion of Russell’s argument against this necessary condition is the centerpiece of an analysis of what is at stake when one accepts or denies that there can be temporal gaps between causes and effects. It is argued that whether one accepts or denies this condition, one is implicated in taking on substantial and wide-ranging philosophical positions. Therefore, it is not a trivial necessary condition of causal relations and it merits further inquiry.
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I would like to thank Sara Bernstein, Anjan Chakravartty, Xavi Lanao, Samuel Newlands, Caleb Ontiveros, Mark Puestohl, Sebastian Murgueitio Ramirez, Norman Sieroka, and Jeremy Steeger for discussion, guidance, and helpful comments on earlier drafts.
Appendix: Russell’s Overall Argument
Appendix: Russell’s Overall Argument
~~NTG. [assumption for reductio proof]
Either both causes and effects are instantaneous, or not. [disjunction introduction]
Both causes and effects are instantaneous. [assumption for conditional proof]
If both causes and effects are instantaneous, then there is a duration between them.
If there is a duration between causes and effects, then ~NTG.
~NTG. [P3, P4, P5, modus ponens]
If both causes and effects are instantaneous, then ~NTG. [P3, P6, conditional proof]
It is not the case that both causes and effects are instantaneous. [P1, P7, modus tollens]
Causes are not instantaneous. [P8, Baldwin’s definition]
Either causes are processes that undergo change over time, or causes are static through time and do not change. [P9]
Causes are processes that undergo change over time. [assumption for reductio proof]
If causes are processes that undergo change over time, then they have temporal parts.
Causality is universal.
If causes have temporal parts, causality is universal, and NTG, then each temporal part of a cause could only be caused by the temporal part prior to it and could only cause the temporal part posterior to it.
If each temporal part of a cause could only be caused by the temporal part prior to it and could only cause the temporal part posterior to it, then only the last temporal part of the cause could be the cause of the first temporal part of the effect.
There could not be a last temporal part of a cause.
Only the last temporal part of a cause could be the cause of the first temporal part of its effect, and there could not be a last temporal part of a cause. [P11, P12, P13, P14, P15, modus ponens, P16, conjunction introduction]
There are no causes that are processes that undergo change over time. [P17]
There are causes that are processes that undergo change over time.
It is not the case that causes are processes that undergo change over time. [P11, P18, P19, reductio proof]
Causes are static and do not change over time. [P10, P20, disjunctive syllogism]
If causes are static and do not change over time, then there are no causes in nature and there are no explanations of why effects occur when they do.
It is not the case that there are no causes in nature and there are no explanations of why effects occur when they do.
It is not the case that causes are static and do not change over time. [P22, P23, modus tollens]
~NTG [P1, P21, P24, reductio proof]
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Clay, G. Russell and the Temporal Contiguity of Causes and Effects. Erkenn 83, 1245–1264 (2018). https://doi.org/10.1007/s10670-017-9939-6