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FUTURE LOGIC
©
Avi Sion, 1990 (Rev. ed. 1996) All rights reserved.
CHAPTER 56.
APPLIED FACTOR SELECTION.
1.
Closed Systems Results.
2.
Some Overall Comments.
3.
Rules of Generalization.
4.
Review of Valid Moods.
5.
Open System Results.
1.
Closed Systems Results.
We will, to begin with, deal with the closed system of natural modality,
first listing the results of factor selection, then analyzing and justifying our
proposals. As usual, all the results obtained can by analogy be replicated for
the closed system of temporal modality. The corresponding results for the more
bulky open system of mixed modality will be presented later.
The following table shows the proposed preferred (natural) factors for
natural gross formulas, selected on the basis of the uniformity principle.
Deductive cases, those with a single factor on formal grounds, are included for
completeness.
The information in the elementary or compound premise is always assumed
to be all available data on the subject to predicate relation concerned. If more
data makes its appearance, then we are faced with another premise, and the
conclusion may accordingly be different.
The column 'NF' indicates the original number of factors, the next column lists
them in sequence, and the column 'SF'
shows the selected factor among them, which is our proposed conclusion..
Table
56.1 Factor Selection in Natural Modality.
|
Premises |
NF |
Factors |
SF |
Conclusion |
|
Group F1 |
|
An |
1 |
F1 |
F1 |
(An) |
|
AIn |
2 |
F1, F6 |
F1 |
(An) |
|
A |
3 |
F1, F3, F6 |
F1 |
(An) |
|
ApIn |
4 |
F1, F6, F8, F13 |
F1 |
(An) |
|
ApI |
6 |
F1, F3, F6, F8, F10, F13 |
F1 |
(An) |
|
Ap |
7 |
F1, F3, F4, F6, F8, F10, F13 |
F1 |
(An) |
|
In |
8 |
F1, F5-F6, F8, F11-F13, F15 |
F1 |
(An) |
|
I |
12 |
F1, F3, F5-F6, F8-F15 |
F1 |
(An) |
|
Ip |
14 |
F1, F3-F15 |
F1 |
(An) |
|
Group F2 |
|
En |
1 |
F2 |
F2 |
(En) |
|
EOn |
2 |
F2, F7 |
F2 |
(En) |
|
E |
3 |
F2, F4, F7 |
F2 |
(En) |
|
EpOn |
4 |
F2, F7, F9, F14 |
F2 |
(En) |
|
EpO |
6 |
F2, F4, F7, F9-F10, F14 |
F2 |
(En) |
|
Ep |
7 |
F2-F4, F7, F9-F10, F14 |
F2 |
(En) |
|
On |
8 |
F2, F5, F7, F9, F11-F12, F14, F15 |
F2 |
(En) |
|
O |
12 |
F2, F4-F5, F7-F15 |
F2 |
(En) |
|
Op |
14 |
F2-F15 |
F2 |
(En) |
|
Group F3 |
|
AEp |
1 |
F3 |
F3 |
(AEp) |
|
ApIEp |
2 |
F3, F10 |
F3 |
(AEp) |
|
AOp |
2 |
F3, F6 |
F3 |
(AEp) |
|
IEp |
4 |
F3, F9-F10, F14 |
F3 |
(AEp) |
|
ApIOp |
5 |
F3, F6, F8, F10, F13 |
F3 |
(AEp) |
|
(IOp) |
8 |
F3, F6, F9-F11, F13-F15 |
F3 |
(AEp) |
|
IOp |
11 |
F3, F5-F6, F8-F15 |
F3 |
(AEp) |
|
Premises |
NF |
Factors |
SF |
Conclusion |
|
Group F4 |
|
ApE |
1 |
F4 |
F4 |
(ApE) |
|
ApEpO |
2 |
F4, F10 |
F4 |
(ApE) |
|
IpE |
2 |
F4, F7 |
F4 |
(ApE) |
|
ApO |
4 |
F4, F8, F10, F13 |
F4 |
(ApE) |
|
IpEpO |
5 |
F4, F7, F9-F10, F14 |
F4 |
(ApE) |
|
(IpO) |
8 |
F4, F7-F8, F10, F12-F15 |
F4 |
(ApE) |
|
IpO |
11 |
F4-F5, F7-F15 |
F4 |
(ApE) |
|
Group F3-4 |
|
ApEp |
3 |
F3-F4, F10 |
F3-4 |
(AEp) or (ApE) |
|
ApOp |
6 |
F3-F4, F6, F8, F10, F13 |
F3-4 |
(AEp) or (ApE) |
|
IpEp |
6 |
F3-F4, F7, F9-F10, F14 |
F3-4 |
(AEp) or (ApE) |
|
IpOp |
13 |
F3-F15 |
F3-4 |
(AEp) or (ApE) |
|
Group F5 |
|
InOn |
4 |
F5, F11-F12, F15 |
F5 |
(In)(On) |
|
InO |
6 |
F5, F8, F11-F13, F15 |
F5 |
(In)(On) |
|
IOn |
6 |
F5, F9, F11-F12, F14-F15 |
F5 |
(In)(On) |
|
InOp |
7 |
F5-F6, F8, F11-F13, F15 |
F5 |
(In)(On) |
|
IpOn |
7 |
F5, F7, F9, F11-F12, F14-F15 |
F5 |
(In)(On) |
|
IO |
9 |
F5, F8-F15 |
F5 |
(In)(On) |
|
Group F6 |
|
AInOp |
1 |
F6 |
F6 |
(In)(IOp) |
|
ApInOp |
3 |
F6, F8, F13 |
F6 |
(In)(IOp) |
|
Group F7 |
|
IpEOn |
1 |
F7 |
| |
