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The Logician © Avi Sion All rights reserved |
THE LOGIC OF CAUSATION © Avi Sion, 1999, 2003. All rights reserved.
Phase One: Macroanalysis Chapter
9 - Squeezing
Out More Information 1.
The Interactions of Determinations.
1.
The Interactions of Determinations. Before considering the possibility of
other inferences from causative propositions, let us summarize and extend the
results obtained thus far, and especially try and understand them in a global
perspective. We have in the preceding chapters identified, in the three figures,
66 valid positive conclusions obtainable from positive premises, out of 192
(3*8*8) possible combinations of generic and joint premises. We thus found a validity
rate of 34.4% - meaning that reasoning with causative propositions cannot be
left to chance, since we would likely be wrong two times out of three! The table
shows the distribution of valid and invalid moods in the three figures:
Moreover, not all of the valid moods have equal significance. As the table below shows, some moods (20, shaded) are conceptually basic, while others (46) are mere derivatives of these, in the sense of compounds (16) or subalterns (30) of them. We shall call the former ‘primary’ moods, and the latter ‘secondary’ moods. Note that these terms are not intended as references to validation processes, but to comparisons of results. By which I mean that some of the moods here classed as ‘primary’ (such as #217, to cite one case) were validated by reduction to others; whereas some of the moods here classed as ‘secondary’ (such as #117, for example) were among those that had to be validated by matricial analysis. A primary mood teaches us a lesson in reasoning. For instance, mood 1/m/m/m (#155) teaches us that in Figure 1, the premises m and m yield the conclusion m. A secondary (subaltern or compound) mood has premises that teach us nothing new (compared to the corresponding primary), except to tell us that no additional information is implied. For instances, 1/m/mq/m (#152) is equivalent (subaltern) to 1/m/m/m; and 1/mn/mn/mn (#111) is equivalent to (a compound of) 1/m/m/m plus 1/n/n/n. Such equivalencies are due to the fact that the premises of the secondary mood imply those of the primary mood(s), while the conclusion(s) of the latter imply that of the former. We can thus ‘reconstruct’ the derivative mood from its conceptual source(s). Effectively, primary moods represent general truths, of which secondary moods are specific expressions. This ordering of the valid moods signifies that we do not have to memorize them all, but only 20 out of 66. In the following table, the valid positive moods of causative syllogism are listed for each figure in order of the strength of their conclusions (joint determinations before generics). Within each group of moods yielding a given conclusion, moods are ordered in the reverse order with reference to their premises (the weakest premises capable of yielding a certain conclusion being listed first, so far as possible - some are of course incomparable). Explanations will be given further on. Primary moods (shaded) are distinguished
from compounds and subalterns, and the primary sources of the secondaries are
specified. Notice that all moods with a joint determination as conclusion are
compounds.
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