It was assumed that God's existence must be validly inferred from generally acceptable premises.
It cannot be validly inferred from the idea of an eternal and independent being that there actually is such a being.
In this sense, (2) can be validly inferred from (1) because all of the scenarios in which it is true that someone envies everybody are also scenarios in which it is true that everybody is envied by at least one person.
A proposition G, for example, can be validly inferred from another proposition F when all of the scenarios represented by F the scenarios in which F is true are also scenarios represented by G the scenarios in which G is true.
This is usually thought to mean something much more general: that no ethical or indeed evaluative conclusion whatsoever may be validly inferred from any set of purely factual premises.
But then no definition of "good" in purely natural terms can succeed, since it cannot capture the term's action-guiding force; nor can an evaluative conclusion be validly inferred from premises none of which have such force.
For example: if George W. Bush is the eldest son of the vice-president under Ronald Reagan, and George W. Bush is the current U.S. President, then it can be validly inferred that the eldest son of Reagan's vice-president is the current U.S. President.
For example, knowledge that \(Y\) can be validly inferred from \(X\) does not license one to believe \(Y\) if one believes \(X\); it may be more rational to abandon one's belief in \(X\), or to take up a sceptical position towards both \(X\) and \(Y\) (see Harman 1984).
Collectively, these reliability measures and item-total correlations confirm that such concepts as learning climate, learning opportunities, skills improvement and attitude enhancement do exist and can be validly inferred from the response patterns of pharmacy students and their preceptors.
"If a person is validly registered to vote, the signature should count".
So for example if there is a theorem universally quantifying nominal variables, such as '∀a⌈any a is an a⌉', we can validly infer 'any Λ is a Λ' even though the name is empty.
