difference between first order and second order logic
Second-order logic First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, also quantifies over relations. For example, the second-order sentence   ∀ P ∀ x ( x ∈ P ∨ x ∉ P )  {\displaystyle \forall P\,\forall x(x\in P\lor x\notin P)}  says that for every unary relation (or set) P of individuals, and every individual x, either x is in P or it is not (this is the principle of bivalence). Second-order logic also includes quantification over sets, functions, and other variables as explained in the section Syntax and fragments. Both first-order and second-order logic use the idea of a domain of discourse (often called simply the "domain" or the "universe"). The domain is a set over which individual elements may be quantified.
Two-level utilitarianism Two-level utilitarianism is virtually a synthesis of the opposing doctrines of act utilitarianism and rule utilitarianism. Act utilitarianism states that in all cases the morally right action is the one which produces the most pleasure, whereas rule utilitarianism states that the morally right action is the one that is in accordance with a moral rule whose general observance would create the most happiness. In terms of two-level utilitarianism, act utilitarianism can be likened to the 'critical' level of moral thinking, and rule utilitarianism to the 'intuitive' level.[4]