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Cases of causal redundancy provide another example.
We find out what causal relations amount to by starting with clear cases of causal explanation.
In Section 3, corresponding existence results are formulated for special cases of causal operators, using the main result of Section 2.
Cases of causal overdetermination are extreme examples of causal networks in which probabilistic relevance is washed out or inverted by the causal contributions of an exogenous variable.
It can happen more subtly in cases of "causal misattribution," which is when you associate something you did earlier with a later outcome without evidence.
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It is worth mentioning that, when m=1, systematic encoding of a linear code is a special case of causal encoding.
As an illustration, consider a standard case of causal pre-emption: Gunman one shoots (s1) victim, causing his death d, while gunman two does not shoot but would have shot (s2) also causing d, if s1 had not occurred.
Although all inferences are subject to the same scrutiny, it is especially important in the case of causal inferences, given that they are more likely to be used as the basis for action or to inform policy.
The conception thus provides the "true bond of Unity by which the phenomena are held together" (1847, II, 46), by providing a property shared by the known members of a class (in the case of causal laws, the colligating property is that of sharing the same cause).
In the case of causal inference, if we have an impression of an effect (smoke), the associative principles give rise not only to the idea of its cause (fire), but they also transmit some of the impression's force and vivacity to the idea of its cause, so that we come to believe that fire is the cause of the smoke.
In the case of causal systems, such analogies may also be expressed and understood through diagrams (Ainsworth, Prain, & Tytler, 2011; Forbus et al., 2011; Goldwater & Gentner, 2015) and they can even be glimpsed albeit in fragmentary fashion in everyday language, as when we refer to "feedback loops" or "domino effects".
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com