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"logical necessity" is a correct and usable phrase in written English.
It can be used to describe a situation where a certain outcome is logically required or expected. For example, "Given the evidence presented, it was a logical necessity for the judge to find the defendant guilty."
Exact(53)
(Note: In standard deontic logic, the '□' in PD typically designates logical necessity. Here I take it to indicate physical necessity so that the appropriate connection with premise (3) can be made.
Some arguments that fail to be deductively valid are acceptable on grounds other than formal logic, and their conclusions are supported with less than logical necessity.
Logically necessary existence, it is said, is an incoherent idea, for logical necessity applies to the relations between concepts, not to their instantiation.
In this logic, the language permits the expression of two different notions of necessity: the logical necessity, symbolized by □, and the physical necessity, symbolized by ⊡. meaning that logical necessity is stronger than physical necessity: anything that is logically necessary is physically necessary.
Philosophers, therefore, distinguish the physical (or natural) necessity of laws from logical necessity.
(3) The concepts of (logical) necessity and (logical) possibility can be added.
This is peculiar if one is accustomed to thinking of mathematics as governed by logical necessity.
This could seem dandyishly insolent of him: shrugging off the requirement for logical necessity in big-time avant-garde art.
Moreover, a law of nature has no logical necessity; rather, it rests directly or indirectly upon the evidence of experience.
Similar(2)
First, some philosophers will talk of 'logical' necessity or supervenience as a way of discussing what this entry is calling conceptual necessity or supervenience.
Another source of immanency in conceptualizing the life-cycle theory is logical necessity (Poole and Van de Ven, 1995).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com