Hume's 2 (or is it 3?) Definitions of Cause:

a. "an object, followed by another, and where all the objects similar to the first are followed by objects similar to the second"
 

a*. "an object followed by another where, if the first object had not been, the second never had existed"
 

b. "an object followed by another, and whose appearance always conveys the thought to that other"
 
 
 

Theses in Moral Philosophy and Metaphysics:

1. OUGHT implies CAN but not IS.
 

2. OUGHT is not implied by IS. (Hume)

(No OUGHT statement can be deduced from propositions that express matters of fact and/or relations of ideas.)
 

2*. No NECESSARY proposition can be deduced from ASSERTORIC premisses.