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.

  • 1
    I'll replace "might have been" with "possibly" for simplicity and use ( ) for scopes (they are scopes of the description, not of the modal operator in Baumann). On the narrow reading:"possibly, Aristotle, i.e. the teacher of Alexander, (was not the teacher of Alexander)." What goes after "possibly" is inconsistent, hence the sentence false. On the wide reading:"Aristotle, i.e. the teacher of Alexander, (possibly was not the teacher of Alexander)." This is true. The first part only fixes the identity of Aristotle in the actual world and has little bearing on what can happen in possible worlds.
    – Conifold
    Commented Jun 22 at 8:13
  • Have you never thought that perhaps being illiterate in formal logic is the biggest problem? It's just impossible to employ fully rigorous logical reasoning, much less discuss about logical reasoning, without knowing how to perform formal proofs in some deductive system. I strongly suggest you learn what you need to learn first, because the longer you wait the more logic misconceptions you would collect and the harder it is for you to fix them.
    – user21820
    Commented Jun 28 at 6:02

1 Answer 1


Let's use the following abbreviations: WS wide scope, NS narrow scope, PN proper name, DD definite description. Now let's formulate four statements in something approximating English but butchered a little to make the content clearer.

  WS-PN: [Aristotle] [might have been] [not the teacher of Alexander]. 
  NS-PN: [It might have been] [Aristotle] [was not the teacher of Alexander]. 
  WS-DD: [The teacher of Alexander] [might have been] [not the teacher of Alexander]. 
  NS-DD: [It might have been] [the teacher of Alexander] [was not the teacher of Alexander]. 

The terms "narrow scope" and "wide scope" indicate whether the name or definite description sits inside or outside the scope of "might have been".

Kripke's point is that WS-PN and NS-PN are both true. Aristotle might not have taught Alexander, had things worked out somewhat differently from the way they actually did. WS-DD is also true, since it is reasonable to understand it as meaning that the person who actually taught Alexander might not have done so. Some teachers might not have been teachers. But NS-DD cannot be true since it states the possibility of a contradiction.

We may state this in terms of possible worlds, something Kripke was fond of doing since he made important contributions to possible world semantics. There is a possible world in which Aristotle does not teach Alexander. There is a possible world in which the person who taught Alexander in our world does not teach Alexander. But there is no possible world in which the teacher of Alexander (in that world) does not teach Alexander (in that world).

Since names and definite descriptions behave differently in modal contexts (and not just "might have been" contexts) Kripke argues that a name cannot be identical in meaning with any definite description, or combination of definite descriptions. It may be that we learn the referent of a name via a definite description, but it does not follow that the name and the definite description mean the same thing.

Dummett objects that Kripke is confusing the wide scope and narrow scope readings of the statements. Dummett supposes that Kripke is comparing WS-PN with NS-DD and attributing the difference in truth value to the difference between names and definite descriptions, when the difference is just a matter of scope. But this objection misses Kripke's point. The WS-PN and NS-PN readings both come out true, according to Kripke, so the difference in truth value between NS-PN and NS-DD cannot be an issue of scope but concerns the difference between names and definite descriptions.

For Kripke, this difference resides in the fact that when we talk about counterfactual possibilities, we are still talking about Aristotle, not some other person. Kripke describes this by saying that the name 'Aristotle' is a rigid designator. Definite descriptions, by contrast, are not rigid designators. There is a handy introduction to the subject of rigid designators in the Stanford Encyclopedia.

To be fair to Dummett, his objections to Kripke run rather deeper and it is not easy to summarise them in a short answer.

Saul Kripke, Naming and Necessity, 1974, pp. 6-14. 61-63.

Michael Dummett, Frege: Philosophy of Language, 2nd edition, 1981, pp. 110-151.

Michael Dummett, The Interpretation of Frege's Philosophy, 1981, pp. 557-603.

  • SEP has a separate article on transworld identity, which also seems to be relevant here.
    – Kevin
    Commented Jun 23 at 8:51

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