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FUTURE LOGIC©
Avi Sion, 1990 (Rev. ed. 1996) All rights reserved.
APPENDIX: On Factorial Analysis - Open
Systems Analysis.
The table in the following pages is an appendix to Chapter 53 (in
particular, Section 5).
It shows the factorial analysis of all 195
gross formulas (listed in the column labeled FORMULAS),
in terms of the 63 factors (columns F1-F63)
in the 'open system' of mixed (natural and temporal) modality. Due to the size of the table, it is split into three web-page segments.
Thus, to see
the factors allowed for by any gross formula, it is necessary to look along the
row corresponding to it in all three segments.
The factors of any gross formula are signaled by a '1'
in the cell concerned (where row and column cross); if a cell is blank, it means
that the factor heading the column is not a possible outcome of the gross
formula heading the row.
The gross formulas are first sorted into elements and compounds. Then the
20 elementary (plural) propositions and the remaining compound formulas
(consisting of two or more elements) are, respectively, sorted according to the number
of factors they each have (indicated in the column labeled NF).
The factors of the 20 elements are already known (see ch. 52). The
factors of the remaining 175 gross formulas (compounds), follow automatically
from them. We need only do the following: 1.
Split the compound into its component elements
(which number two, three or four, as the case may be). 2.
Look and see which, if any, of these elements
have the factor concerned. 3.
If all have
it, the compound in question also has it; otherwise, not.
(For example, the compound AcInOp
has factor F8, because its three component elements Ac, In and Op,
have only this one factor F8 in
common.)
The value of this table is, as we have seen (ch. 54-59), to guide us in
generalization and particularization, by indicating successive inductive
preferences. In some cases (the eleven cases with a single factor, to be
specific), it even indicates deductive inferences.
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