Page 5 - The Logic of Causation
P. 5

and their negations (grand matrices). Each such possible combination is called a ‘modus’
and is assigned a permanent number within the framework concerned (for 2, 3, or more
items). This allows us to identify each distinct (causative or other, positive or negative)
propositional form with a number of alternative moduses.

This technique greatly facilitates all work with causative and related forms, allowing us to
systematically consider their eductions, oppositions, and syllogistic combinations. In fact,
it constitutes a most radical approach not only to causative propositions and their
derivatives, but perhaps more importantly to their constituent conditional propositions.
Moreover, it is not limited to logical conditioning and causation, but is equally applicable
to other modes of modality, including extensional, natural, temporal and spatial
conditioning and causation. From the results obtained, we are able to settle with formal
certainty most of the historically controversial issues relating to causation.
Phase III: Software Assisted Analysis. The approach in the second phase was very
‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work
involved by means of spreadsheets (to begin with). This increases reliability of calculations
(though no errors were found, in fact) – and also allows for a wider scope. Indeed, we are
now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of
causative and other forms needed to investigate 4-item syllogism. As well, now each
modus can be interpreted with greater precision and causation can be more precisely
defined and treated.

In this latest phase, the research is brought to a successful finish! Its main ambition, to
obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being
truly fulfilled. This was made technically feasible, in spite of limitations in computer
software and hardware, by cutting up problems into smaller pieces. For every mood of the
syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets),
testing all forms of causative and preventive conclusions. Until now, this job could only be
done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000
pages of spreadsheets to generate the sought for conclusions.
This is a historic breakthrough for causal logic and logic in general. Of course, not all
conceivable issues are resolved. There is still some work that needs doing, notably with
regard to 5-item causative syllogism. But what has been achieved solves the core problem.
The method for the resolution of all outstanding issues has definitely now been found and
proven. The only obstacle to solving most of them is the amount of labor needed to
produce the remaining (less important) tables. As for 5-item syllogism, bigger computer
resources are also needed.

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