Sentence examples for logically true from inspiring English sources
The logicist program sought to show that mathematics is reducible to logic, in other words that mathematical proofs can be shown to consist of logical deductions from logically true premises.
A logic formulated in a given language L* is said to be sound with respect to a semantics for L* if and only if every formula of L* that is a theorem of the logic is valid (logically true) relative to that semantics (i.e., is true in every interpretation or model of the semantics).
Logically true sentences and logical inferences convey the same empirical information, but their analytic information may differ.
That, however, would turn every purely logical proposition either into a logical truth or into a logical falsity according to our definition, in contrast to the fact that the proposition [There is something], i.e. [[something] has non-emptiness], is not logically analytic; it is a truth of logic, but nevertheless not logically true (WL II, 375).
Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the "logical constants" of a language from its nonlogical expressions.
These are conditionals that turn out to be logically true in classical and modal logic, just because the antecedent is a (necessary) falsity, and without any real connection between antecedent and consequent.
The logically analytic true propositions are instances of logical laws.
Malcolm supported that definition of God and suggested that it makes the proposition of God's existence a logically necessarily true statement (in the same way that "a square has four sides" is logically necessarily true).
More generally, one can validly argue from p to q if and only if the implication "If p, then q" is logically true i.e., true in virtue of the meanings of words occurring in p and q, independently of any matter of fact.
For example, if two responses cannot logically both be true, it is unclear which of the two is true.
We can all understand that to be true logically.
