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Thirteenth post in the ongoing series on important innovations in logic theory to be found in my works. The present post continues and ends my brief account of causative logic started three or four posts ago.
My newly completed and published book, The Logic of Causation, is the proudest of my contributions to logic theory. Although I rank my work on factorial induction in Future Logic (briefly described in an earlier post) equally high in significance, the logic of causation was a more difficult achievement. The Logic of Causation had four major tasks: to define causation and its conceivable varieties; to describe how it is induced; to find ways to determine all the deductive properties of its forms, singly and in diverse combinations, and finally (only after having thus studied the matter in detail) to pass judgment on past ideas concerning causation.
The task of definition was relatively easy. It was largely fulfilled by proposing four generic forms (determinations) of causation (complete, necessary, partial and contingent). We found that only four specific combinations of these are logically possible (complete-necessary, complete-contingent, necessary-partial, and partial-contingent). Later, we distinguished ‘absolute’ partial and/or contingent causation, which make no mention of the complements involved in the causation, and ‘relative’ partial and/or contingent causation, which do specify the complements involved. Causation as a whole, then, could be defined as the applicability of any of its conceivable forms. At a much later stage, we were able to define causation as such in a more radical manner.
With regard to the induction of causation, the task was also relatively easy to fulfill. Having in our definitions of the forms of causation identified the conjunctive and conditional propositions jointly underlying each form, we could simply say that the induction of each causative proposition relied on the induction of its several logical constituents. Another way causative propositions could be induced was of course by adduction – that is, by hypothesizing such a proposition to be true and checking the evidence on behalf of it and counterevidence going against it.
But the most daunting task was the study of the deductive properties of causation. This seemed at first easy, in view of the reducibility of causative forms to sets of conjunctive and conditional propositions. And indeed, such reduction made readily possible certain immediate inferences (oppositions and eductions). However, to solve syllogistic problems involving causative propositions, we had to resort to matricial analysis. I had already used matrices in Future Logic to analyze disjunctions – but the job here was much more complex. Still, we succeeded by this means in evaluating (validating or invalidating) a large number of moods of the syllogism in the three main figures (Phase I).
However, this initial method of ‘macroanalysis’, as we later called it, was inadequate on three counts: it was very manual and time-consuming, it was not sure to be infallible or thorough, and it could not resolve all issues - in particular, it could not evaluate syllogisms with some negative premise(s) and/or conclusion. A more detailed sort of matricial analysis, which we called ‘microanalysis’, was seen to be sorely needed and gradually developed. The forms of causation were to begin with analyzed piecemeal, and thereafter more systematically (Phase II). This development allowed us to solve most problems relating to three-item syllogism, with considerably more certainty than previously.
However, this improved method too was open to criticism, again with reference to its dependence on human effort and especially because it could not deal with four-item syllogisms. To overcome these inadequacies, an enlarged perspective and a more mechanical approach were used (Phase III). The results of this last phase of the research were very satisfying. For the first time in history, we now have a means for resolving all three-item and four-item causative syllogisms, whether positive or negative, with whatever polarity of items, with utter conviction and thoroughness. This required the production of massive tables (with logical calculations from matrixes), some of which were 72,000 pages long.
Have a long look for instance at Table 24.3, which is posted online in pdf format at the following address: http://www.thelogician.net/4_logic_of_causation/4_phase3_pdf/4_table_24.3.pdf. The following is an example of its content:
Mood 122 (b) - premises: mq/mq (abs / rel S)
Q is a complete and contingent cause of R
P is a complete and (complemented by S) contingent cause of Q
Positive conclusion(s): mq abs
P is a complete and contingent cause of R
Negative conclusion(s): causative: not-q rel to notS; preventive: none
P (complemented by notS) is not a contingent cause of R
This summary table lists all valid and invalid positive causative syllogisms (144 moods in each of three figures). If we look at the statistics, 19% of the moods were found invalid, i.e. to yield no valid positive or negative causative or even preventive conclusion; the remaining moods yielded some sort of conclusion (of course, all conclusions not listed as valid are invalid). Some of these results are intuitively obvious; but many are clearly not (in particular, note the negative conclusions obtained in some cases). Yet we can now boast for them the precision and certainty of mathematical theorems.
Such lists and statistics go to show the importance of the whole enterprise. Without matricial analysis, we would not know how to reason correctly with causative propositions. And after all, what are we talking about, here? Causation! One of the supreme categories of rational thought! This is not about some obscure form of discourse hardly ever encountered in human reasoning, but concerns one of our main tools for understanding the world around us! Think about it, and you will hopefully be motivated to study the matter closely. Certainly, anyone claiming to be or wishing to be a logician should study it. But so should laypeople who care about fallacy-free reasoning.
To conclude, as I do in the book itself: This is the first time anyone has worked out and published these syllogisms, which are crucial to both ordinary and scientific thinking processes.
For more details on THE LOGIC OF CAUSATION, see: http://www.thelogician.net/4_logic_of_causation/4_lc_frame.htm
For the latest results and conclusions – Phase III – see: http://www.thelogician.net/4_logic_of_causation/4_lc_phase_three.htm
To purchase the book, go to: http://stores.lulu.com/thelogicianbooks
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