more on this theme
|
more from this thinker
Single Idea 9729
[filed under theme 4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
]
Full Idea
Modal Square of Opposition 2: 'It is not necessary that not P' and 'It is possible that P' are the subcontraries (not both false) of 'It is not necessary that P' and 'It is possible that not P'.
Gist of Idea
Modal Square 2: ¬□¬P and ◊P are 'subcontraries' of ¬□P and ◊¬P
Source
report of Aristotle (On Interpretation [c.330 BCE], Ch.12b) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4
Book Ref
Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.7
The
19 ideas
from 'On Interpretation'
|
22272
|
Aristotle's later logic had to treat 'Socrates' as 'everything that is Socrates'
[Potter on Aristotle]
|
|
2337
|
For Aristotle meaning and reference are linked to concepts
[Aristotle, by Putnam]
|
|
13763
|
Spoken sounds vary between people, but are signs of affections of soul, which are the same for all
[Aristotle]
|
|
1701
|
A prayer is a sentence which is neither true nor false
[Aristotle]
|
|
1702
|
Things may be necessary once they occur, but not be unconditionally necessary
[Aristotle]
|
|
1703
|
It is necessary that either a sea-fight occurs tomorrow or it doesn't, though neither option is in itself necessary
[Aristotle]
|
|
21593
|
In talking of future sea-fights, Aristotle rejects bivalence
[Aristotle, by Williamson]
|
|
1704
|
Statements are true according to how things actually are
[Aristotle]
|
|
1705
|
It doesn't have to be the case that in opposed views one is true and the other false
[Aristotle]
|
|
1706
|
Non-existent things aren't made to exist by thought, because their non-existence is part of the thought
[Aristotle]
|
|
1707
|
Maybe necessity and non-necessity are the first principles of ontology
[Aristotle]
|
|
1708
|
In "Callias is just/not just/unjust", which of these are contraries?
[Aristotle]
|
|
9405
|
Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values
[Aristotle]
|
|
9728
|
Modal Square 1: □P and ¬◊¬P are 'contraries' of □¬P and ¬◊P
[Aristotle, by Fitting/Mendelsohn]
|
|
9729
|
Modal Square 2: ¬□¬P and ◊P are 'subcontraries' of ¬□P and ◊¬P
[Aristotle, by Fitting/Mendelsohn]
|
|
9730
|
Modal Square 3: □P and ¬◊¬P are 'contradictories' of ¬□P and ◊¬P
[Aristotle, by Fitting/Mendelsohn]
|
|
9731
|
Modal Square 4: □¬P and ¬◊P are 'contradictories' of ¬□¬P and ◊P
[Aristotle, by Fitting/Mendelsohn]
|
|
9732
|
Modal Square 5: □P and ¬◊¬P are 'subalternatives' of ¬□¬P and ◊P
[Aristotle, by Fitting/Mendelsohn]
|
|
9733
|
Modal Square 6: □¬P and ¬◊P are 'subalternatives' of ¬□P and ◊¬P
[Aristotle, by Fitting/Mendelsohn]
|