-ibility

(Latin: a suffix that means "able to [be]"; a variation of -ability)

incognoscibility (s) (noun), incognoscibilities (pl)
The quality or condition of being beyond comprehension or knowing: No matter how hard Jacob tried, his incognoscibility regarding how to use the new computer program was more and more frustrating for him and so he had to call a specialist to unravel his incognoscibilities.
incompatibility (s) (noun), incompatibilities (pl)
1. Uncongeniality; incapability of existing together in harmony: Meg asked for a divorce because of the incompatibility in her marriage with Sam.
2. Contrariness in character; discordancy: Susan wanted to avoid an incompatibility of colors in her living room.
3. That which cannot coexist or be conjoined: Tom was aware of the incompatibility of long hours at work and his family life.
4. The quality of biological substances that interfere with one another physiologically: Dr. Smart said that, because of the incompatibility of the two types of blood, it wasn't possible to use the donors blood in the transfusion for Mrs. Long.
5. In pharmacology the incongruity of drugs in which they interfere with one another chemically or physiologically: Because of the incompatibility of the two medicines, Dr. Thompson said that they could not be mixed or prescribed together.

A little incompatibility is the spice of life, particularly if he has income and she is pattable.

—Ogden Nash
incomprehensibility (s) (noun), incomprehensibilities (pl)
Something which is impossible to understand because of being unintelligible: Little six-year old Jimmy's speech was full of incomprehensibilities because his words were meaningless, jumbled and incoherent.
incompressibility
incorrigibility
1. Incapable of being corrected or amended.
2. Unable to be corrected or changed.
incorruptibility (adjective)
incredibility
The quality or fact of being incredibile; a thing that cannot be believed; an incredible notion or circumstance.
indigestibility
indivisibility (s) (noun), indivisibilities (p)
The nature of something that cannot be divided or portioned into different parts or pieces: The philosopher claims that he believes in the indivisibility of the soul and the mind.
ineligibility
The quality, or state, of not being legally entitled or qualified to do, to be, or to get something.
infallibility (s) (noun), infallibilities (pl)
1. The quality of never making an error or a mistake: The presumption of infallibility by the supervisor, Mr. Williams, resulted in severe criticism by his workers.
2. Being certain that something will function as it should: Successfully piloting an airplane depends on the infallibility of the engine and the service personnel.
insensibility (s) (noun), insensibilities (pl)
1. The lack of physical sensations or consciousness: Cara fell to the ground, hit her head, and consequently was lying in a state of insensibility.
2. Unawareness of or unresponsiveness to something: Trevor experienced amnesia and a state of insensibility to the voices of his wife and daughter.
intangibility (s) (noun), intangibilities (pl)
invincibility
A condition in which it is difficult or impossible to be defeated or subdued.
invisibility
1. That which is incapable by nature of being seen or inaccessible to view; hidden.
2. Imperceptible, inconspicuous; not appearing in published financial statements or not reflected in statistics.