Is the set of universally valid formulas identical to the set of necessary truths? For example, "Necessarily, nothing is both red and blue all over." Would that be a logically valid?
No. Logical validity is formal. "It is not the case that there exists an x such that x is F and x is not-F" is a logical necessity, because the predicate 'is F' and the predicate 'is not-F' are *logically* contradictory. But "it is not the case that there exists an x such that x is B-all-over and x is R-all-over" is not a *logical* necessity, because the predicate 'B-all-over' and the predicate 'R-all-over' are not *logically* contradictory. That something cannot be blue-all-over and red-all-over is a *metaphysical* impossibility, but not a logical impossibility. To make the metaphysical impossibility into a logical impossibility, you would need a meaning postulate to the effect that "B-all-over" and "R-all-over" are incompatible.
No. That all bachelors are males is not valid/logically true, as there are some interpretations of the predicates ...is a bachelor and ...is a male in which some value of a variable, say x, is both an element of the set of bachelors but is *not* in the set of males. Ergo, there are some sentences that are necessarily true but not logically true. However, in my opinion, the converse holds.
Is the set of universally valid formulas identical to the set of necessary truths? For example, "Necessarily, nothing is both red and blue all over." Would that be a logically valid?
No
No. Logical validity is formal. "It is not the case that there exists an x such that x is F and x is not-F" is a logical necessity, because the predicate 'is F' and the predicate 'is not-F' are *logically* contradictory. But "it is not the case that there exists an x such that x is B-all-over and x is R-all-over" is not a *logical* necessity, because the predicate 'B-all-over' and the predicate 'R-all-over' are not *logically* contradictory. That something cannot be blue-all-over and red-all-over is a *metaphysical* impossibility, but not a logical impossibility. To make the metaphysical impossibility into a logical impossibility, you would need a meaning postulate to the effect that "B-all-over" and "R-all-over" are incompatible.
No. That all bachelors are males is not valid/logically true, as there are some interpretations of the predicates ...is a bachelor and ...is a male in which some value of a variable, say x, is both an element of the set of bachelors but is *not* in the set of males. Ergo, there are some sentences that are necessarily true but not logically true. However, in my opinion, the converse holds.