Page 16 - The Logic of Causation

AVI SION : THE LOGIC OF CAUSATION
16

Chapter 2. THE GENERIC DETERMINATIONS

1. Strong Determinations.

The strongest determination of causation, which we identified as the paradigm of
causation, may be called complete and necessary causation. We shall now repeat the three
constituent propositions of this form and their implications, all of which must be true to
qualify:

(i) If C, then E;
(ii) if notC, then notE;
(iii) where: C is contingent and E is contingent.

As we saw, these propositions together imply the following:

The conjunction (C + E) is possible;
the conjunction (notC + notE) is possible.

Clauses (i) and (iii) signify complete causation. With reference to this positive component,
we may call C a complete cause of E and E a necessary effect of C. Where there is
complete causation, the cause is said to make necessary (or necessitate) the effect . This
5
signifies that the presence of C is sufficient (or enough) for the presence E.
Clause (ii) and (iii) signify necessary causation. With reference to this negative component,
we may call C a necessary cause of E and E a dependent effect of C. Where there is
necessary causation, the cause is said to make possible (or be necessitated by) the effect.
This signifies that the presence of C is requisite (or indispensable) for the presence E .
6
Clause (iii) is commonly left tacit, though as we saw it is essential to ensure that the first
two clauses do not lead to paradox. Strictly speaking, it would suffice, given (i), to
stipulate that C is possible (in which case so is E) and E is unnecessary (in which case so is
C). Or equally well, given (ii), that C is unnecessary (in which case so is E) and E is
possible (in which case so is C). The possibilities of the conjunctions (C + E) and (notC +
notE), logically follow, and so need not be included in the definition.

Looking at the paradigm, we can identify two distinct lesser determinations of causation,
which as it were split the paradigm in two components, each of which by itself conforms to
the paradigm through an ingenuous nuance, as shown below.
Also below, I list the various clauses of each definition, renumbering them for purposes of
reference. Then a table is built up, including all the causal and effectual items involved
7
(positive and negative) and all their conceivable combinations . The modus of each item or

5 The expression “X makes Y impossible” means that X makes notY necessary, incidentally.
6
We commonly say, in such case, that C is a sine qua non (Latin for 'without which not') or
proviso of E.
7
I use the word 'item' to refer to a cause or effect (or the negation of a cause or effect),
indifferently. An item is, thus, for the logician, primarily a thesis (in the largest sense), i.e. a
categorical or other form of proposition. But an item may also signify a term, since theses are
ultimately predications. An item, then, is a thesis, or term within a thesis, involved in a causal
proposition.