Unauthored, unpredictable, indifferent to human notions of propriety and consequence.
On the other hand, extensional agreement does not make for the same notion of consequence, and the cases in which such agreement can be achieved comes at expressive costs.
Risk involves notions of failure and consequences of failure.
If one sees the conditional (as the Stoics did) as a notion of consequence in disguise and one does not think that conditionals have truth values, or that the interpretation of conditionals is fixed across a set of believers in an objective manner, the Original Adams Hypothesis makes a great deal of sense.
The Kantian tradition, in contrast, eschews the notion of consequences and urges instead that an action is right only if it is universalizable i.e., only if the moral rule it embodies could become a universal law applicable to all moral agents.
His approach relies upon generalized notions of consequence and compactness.
A fourth solution proposed by Rott (1991) and Cross (1990) consists in making the underlying notion of consequence non-monotonic.
In Gentzen's proof theory for classical logic, a notion of consequence is defined to hold between multiple premises and multiple conclusions.
Of course, this delivers particularly anarchic worlds, not closed under any notion of logical consequence, and not structured as the interpretations of any (however weak) logic.
Jago allows epistemic states to access worlds not closed under any non-trivial notion of consequence.
But as it turns out, following the thread provided by the two key notions (TP) and (ST) as formulated above provides a suitable vantage point to investigate the development of the notion of consequence in the Latin Middle Ages.
