Modality

• A concept having necessity means that it has been selected, or specified as "this concept".  
• Of course it may have some "global" context in ADEPT LION, but that will come from its third consideration, and the instance of occasions in which it resides.  Its "local" context is "built out" as it participates in logical statements.  
• Its opposite in pattern (involution) is itself.  
• If an occasion of necessity takes an approximate value, it represents one piece of all that is necessary: the collection of all occasions in that instance having the pattern type of the necessary (SEH*-).

• A concept having contingency means that it is a self-contradiction.  It is "not itself" or a "non-concept".  
• And what we take that to mean in pattern logic is that it is counter-factual, or an alternative conception.  
• And however counter-intuitive this may seem, it also stands alone: it is not dependent on any other occasion for its existence.  But just like necessity, it may have a local context that is built out such as in the copula occasion of a logical implication.  In such a case it is a counterfactual conditional.  
• Its opposite is itself. 
• If an occasion of contingency takes an approximate value, it represents one piece of all that is contingent: the collection of all occasions in that instance having the pattern type of the contingent  (SEH-*).

• A concept having possibility is unspecified: it just is, in the most general sense.  
• Possibility has no transformational connection to necessity or contingency in pattern.
• It is the opposite (involution) of impossibility.  Yet as a monadic occasion, it is not reliant on its opposite to exist.  
• If an occasion of possibility takes an approximate value, it represents one piece of all that is possible: the collection of all occasions in that instance having the pattern type of the possible (SEH**).

• A concept having impossibility is a representation of precisely nothing.  
• If contingency is a non-concept, impossibility is an un-concept.  
• It is the opposite of possibility, yet may exists without reliance upon possibility.  
• If an occasion of impossibility takes an approximate value, it represents one piece of all that is impossible: the collection of all occasions in that instance having the pattern type of the impossible (SEH--).

• Terms,
• Variables,
• Predicates,
• Counterfactuals,
• Premises,
• Conclusions,
• Connectives,
• Determinations,
• Judgements...

...these are all modal concepts in Pattern Logic.

It is very tempting to omit modality as a needlessly complicating factor in logical systems.  They are complex enough as they are, so why include modality?

There are certainly cases where it is safe to ignore modality without any consequences.  The fact that the opposite of a necessary or contingent occasion is itself is one reason why modality can sometimes be safely ignored.  Take for example, an apodictic syllogistic system which only deals in necessary premises and conclusions.  

But for similar reasons, we cannot treat possibility in the same manner as necessity because it does have an opposite (involution) in the impossible.

Thus modality lurks in the logical shadows waiting to trouble us if its presence is not acknowledged.  

Fortunately, Pattern Logic helps us better understand and track the effects of modality in any logical system it expresses.