Page 18 - The Logic of Causation

18 THE LOGIC OF CAUSATION

Table 2.2. Necessary causation

No Element/compound Modus Source/relationship
.
1 C possible implied by (ii)
2 notC possible (iii)
3 E possible implied by (ii)
4 notE possible implied by (i) + (iii)
5 C E possible (ii)
6 C notE open
7 notC E impossible (i)
8 notC notE possible implied by (i) + (iii)

Necessary causation conforms to the paradigm of causation by means of the same main
9
clause (i) ; whereas its clause (ii), note well, concerning what happens in the presence of C,
substitutes for the invariable presence of E (i.e. “then E”), the not-invariable absence of E
(i.e. “not-then notE”). However, remember, contraposition of (i) implies that “If E, then
C”, meaning that in the presence of E we can be sure that C is also present .
10
Clause (ii) means that (C + E) is possible, so we are sure from it that C is possible and E is
possible; also it teaches us that C and E cannot be incompatible. Technically, it would
suffice for us to know that E is possible, for we could then infer clause (ii) from (i); but it is
best to specify clause (ii) to fit the paradigm of causation. As for clause (iii), we need only
specify that C is unnecessary; it follows from this and clause (i) that (notC + notE) is
possible and so that E is also unnecessary.
Note well the nuance that, to establish such causation, the effect has to be found invariably
absent in the absence of the cause, otherwise we would commit the fallacy of post hoc ergo
propter hoc; but the effect need not be invariably present in the presence of the cause: it
suffices for the effect not to be invariably absent.
Note the matrix of necessary causation, i.e. the segment of the above table numbered 5-8
(shaded).

Lastly, notice that complete and necessary causation are ‘mirror images’ of each other. All
their characteristics are identical, except that the polarities of their respective cause and
effect opposite: C is replaced by notC, and E by notE, or vice-versa. The one represents the
positive aspect of strong causation; the other, the negative aspect. Accordingly, their
logical properties correspond, mutatis mutandis (i.e. if we make all the appropriate
changes).

Following the preceding analysis of necessary and complete causation into two distinct
components each of which independently conforms to the paradigm, we can conceive of
complete causation without necessary causation and necessary causation without complete
causation. These two additional determinations of causation are conceivable, note well,
only because they do not infringe logical laws; that is, we already know that the various
propositions that define them are individually and collectively logically compatible.

9
Notice that clause (i), here, in necessary causation, was labeled as clause (ii) in complete
and necessary causation. The numbering is independent.
10
In some but not all cases, E not only implies but causes C, note.