Take from Possible world- an introduction to logic and its philosophy. p-21
Following quote provide us with necessary definition of what "logically necessary" or as far as i think "necessary truth" is.
"In saying that propositions of the several main kinds discussed so far are logically necessary truths we are, it should be noted, using the term "logically necessary" in a fairly broad sense. We are not saying that such propositions are currently recognized as truths within any of the systems of formal logic which so far have been developed. Rather, we are saying that they are true in all logically possible worlds."
Then the author assert -
"the truths of mathematics must also count as another main kind of logically necessary truth." p-21
"Among the most important kinds of necessarily true propositions are those true propositions which ascribe modal properties — necessary truth, necessary falsity, contingency, etc. — to other propositions. Consider, for example, the proposition
(1.15) It is necessarily true that two plus two equals four.
(1.15) asserts of the simpler proposition — viz., that two plus two equals four — that it is necessarily true. Now the proposition that two plus two equals four, since it is a true proposition of mathematics, is necessarily true. Thus in ascribing to this proposition a property which it does have, the proposition (1.15) is true" p-22
But my question is that how do we know for certain that mathematical truths like 2+2=4 are necessary true, that is they are true in all possible world as asserted by author? For e.g., what if the 2,4 etc don't carry their usual meaning in some other possible world supposed? Or is it supposed they carry their usual meaning?
P.S.-Pardon me, I am new to logic. If i may have wrote something erroneous.