Modality

• A concept having possibility means that it has been selected, or specified as "any of this concept".  
• Its opposite in pattern (involution) is itself.  
• If an occasion of possible 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 possibility (SEH*-).

• A concept having contingency means that it is a self-negation.  It is "not itself" or a "non-concept".  
• And what we take that to mean in pattern logic is that it is counter-identity.  
• And however counter-intuitive this may seem, it also stands alone: it is not dependent on any other occasion for its existence.  
• 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 necessity is unspecified: it just is, in the most general sense.  
• Necessity has no transformational connection to possibility 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 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 impossibility is a representation of precisely nothing.  
• If contingency is a non-concept, impossibility is an un-concept.  
• It is the opposite of necessity, yet may exists without reliance upon necessity.  
• 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,
• Premises,
• Propositions,
• 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.