Let's call something a rigid designator if in every possible world it designates the same object, a non-rigid or accidental designator if that is not the case. Of course we don't require that the objects exist in all possible worlds.... When we think of a property as essential to an object we usually mean that it is true of that object in any case where it would have existed. A rigid designator of a necessary existent can be called strongly rigid.
Everything necessarily is or is not, and will be or will not be; but one cannot divide and say that one or the other is necessary.I mean, for example: it is necessary for there to be or not to be a sea-battle tomorrow; but it is not necessary for a sea-battle to take place tomorrow, or for one not to take place--though it is necessary for one to take place or not to take place.
Any necessary truth, whether a priori or a posteriori, could not have turned out otherwise.
Certainly the philosopher of 'possible worlds' must take care that his technical apparatus not push him to ask questions whose meaningfulness is not supported by our original intuitions of possibility that gave the apparatus its point.
Logic and metaphysics make use of more tools than all the rest of the sciences put together, and do the least work.
Everything actual must also first have been possible, before having actual existence.
The problems of philosophy and the systems designed to solve them are formulated in terms which tend to refer, not to the realm of actuality, but to the realms of possibility and necessity: to what might be and what must be, rather than to what is.
Proper names are rigid designators.
Nothing is necessitated whose opposite is possible.
For things remain possible, even if God does not choose them. Indeed, even if God does not will something to exist, it is possible for it to exist, since, by its nature, it could exist if God were to will it to exist.
The only roads of enquiry there are to think of: one, that it is and that it is not possible for it not to be, this is the path of persuasion (for truth is its companion); the other, that it is not and that it must not be - this I say to you is a path wholly unknowable.
If pressed to supplement Tweedledee's ostensive definition of logic with a discursive definition of the same subject, I would say that logic is the systematic study of the logical truths. Pressed further, I would say that a sentence is logically true if all sentences with its grammatical structure are true. Pressed further still, I would say to read this book.
