I just cannot wrap my head around this concept, if anyone can make it clear for me I'd be greatly appreciate it. I've tried reading the literature, but the papers I read invariably start putting the modal statements into formal logic -- which I have no idea how to parse. I'm illiterate in the symbols of formal logic.
For context, I am writing a paper on Kripke's argument against descriptivism in his 1970 lectures Naming and Necessity. Baumann in Kripke’s Critique of Descriptivism Revisited illustrates the argument with a sentence like "Aristotle might not have been the teacher of Alexander":
Premise 1: If “Aristotle” means “the teacher of Alexander” then “Aristotle might not have been the teacher of Alexander” would be false (it would be equivalent to "Aristotle might not have been Aristotle", which is contradictory).
Premise 2: But, “Aristotle might not have been the teacher of Alexander” is true. (Had circumstances been different (i.e. in some other possible world) someone else, e.g. Speusippus, could have taught Alexander.)
Conclusion: “Aristotle” does not mean “the teacher of Alexander.”
This is intended to show that descriptivism must be false (more precisely, that a definite description cannot be semantically equivalent to a proper name, because doing so generates propositions with disparate truth-values.
This all makes sense. But now I'm trying to understand Dummett's objection to Kripke in his 1973 book 'Frege: Philosophy of Language'. He argues, I think, that Kripke's argument is little more than a kind of equivocation. Baumann writes:
"On the narrow reading, the definite description appears after the modal operator... On this reading, the sentence expresses a falsehood; the sentence is self-contradictory. On the wide scope reading, the definite description appears before the modal operator... The sentence could express a true proposition on the wide scope reading, since someone other than the person who taught Alexander (Aristotle, in the actual world) could have been his teacher instead, e.g. Speusippus. Dummett’s objection is that in Premise 1 the description is being interpreted narrowly but in Premise 2 widely. Thus the modal argument is a sort of equivocation; it is invalid as it stands."
So Dummett is essentially arguing, I think, that names -- like definite descriptions -- also admit of distinct wide and narrow readings. And that the disparate truth-values of the statements in premise 1 and 2 above is a consequence of arbitrarily changing the scope (narrow or wide) with which Kripke interprets the statements, rather than a legitimate semantic difference. Kripke's argument only works because he arbitrarily interprets the statement in Premise 1 with a narrow (I think??) scope, and the proposition in premise 2 with a wide (I think??) scope. But he doesn't demonstrate that definite descriptions cannot be semantically equivalent to proper names.
So Dummett might say that a sentence like (1) "Aristotle might not have been the teacher of Alexander" can be interpreted narrowly or widely with respect to the modal operator (might), which then changes its truth value. But, this does not disprove that "Aristotle" is still semantically equivalent to "the teacher of Alexander" (the descriptivist claim).
My problem is, I have no idea what a "wide" or "narrow" reading of a modal operator actually means. Can someone please put the difference into simple English for me? And then maybe use the above example ("Aristotle might not have been the teacher of Alexander") to demonstrate the difference by illustration.
Thanks and all the best.
-- Joseph.