Purely Negative Concepts

• Possibility
• Potential
• Infinity (nondenumerable)
• Randomness
• Unpredictability
• Chance
• Irrational numbers
• Incomputable numbers
• Nondeterminism
• Incompressibility
• a priori
• Consistency
  Caution: Consistency is negative.
  Inconsistency: there's a proof of contradiction.
  Consistency: it is not inconsistent.

co- as in Recursively enumerable vs co-Recursively enumerable. 

Randomness and Chance#

See Landsman's paper. " Combining these ideas, I submit that randomness is not just any old Wittgensteinian family resemblance, but a special one that is always defined negatively".

Specifically, randomness is usually that which arises in the absence of an intellect:

Chance, in atheistical writings or discourse, is a sound utterly insignificant: It imports no determination to any mode of Existence; nor in deed to Existence itself, more than to non existence; it can neither be defined nor understood; nor can any Proposition concerning it be either affirmed or denied, excepting this one, “That it is a mere word.” (De Moivre, 1718)

An intelligence which could comprehend all the forces that set nature in motion, and all positions of all items of which nature is composed–an intelligence sufficiently vast to submit these data to analysis–it would embrace in the same formula the movements of the greatest bodies in the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as well as the
past, would be present to its eyes. (Laplace, 1814)

This we call the ignorance interpretation of randomness and chance. Probabilities with chance interpreted with its origin in ignorance are often called objective probabilities and were in e.g. statistical mechanics. 

Loewer (2001, 2004) claims that the probabilities in statistical mechanics are as objective as those in quantum mechanics (and hence are objective).