I am looking for good/classical references on objections/criticism of modal logic.

I am a bit familiar with the work of Quine but find his objections around the paradoxes of material implication or the debate on extenstionality/intensionality a bit too high level. In fact, I am more interested in objections to the axioms of modal logics, by which I mean objections to, e.g.:

  1. Kp-->p

  2. Kp-->KKp

  3. -Kp-->K-Kp

  4. K(p & q)-->Kp & Kq

where K designs the necessity or knowledge operator.

  • so you are interested specifically in epistemic logics?
    – user5172
    Commented Aug 14, 2015 at 18:00
  • I have a forthcoming paper on the Kp -> KKp principle. You can find it here: academia.edu/8272914/The_Infinitely_Iterated_Labyrinth
    – user5172
    Commented Aug 14, 2015 at 18:09

2 Answers 2


What do you mean by "objections to the axioms"? Are you looking for criticisms of the very idea of there being a modal logic? Quine is going to be the best there is on the front. (Quine's quite wrong, incidentally. All of the problems he produces arise simply because the technical resources of modal logic in the 50s were not adequate. Those problems have been solved since the early 60s.)

On the other hand, you might mean, "what are the objections to various modal systems"? Because different systems of modal logic are distinguished in terms of which of the various axioms they accept. And then the question should be something more precise like: "What arguments can be given that the correct modal logic to represent metaphysical possibility is S4 rather than S5?"

  • Quine's principal objections are not technical, they are against Aristotelian essentialism and the analytic/synthetic distinction, technical issues are raised as reflections of these. Nor were they resolved, "some argue that Quine's rejection of the distinction is still widely accepted among philosophers..." en.wikipedia.org/wiki/…
    – Conifold
    Commented Aug 14, 2015 at 1:15
  • And the end of the quote from wikipedia (!) is "for poor reasons"
    – virmaior
    Commented Aug 14, 2015 at 9:33
  • 2
    @Conifold I've never met a professional philosopher who thinks Quine's reasons to reject modal logic have not been decisively refuted. (Maybe some exist, but I haven't seen them.) The objection to what Quine (erroneously) calls Aristotelian essentialism is a technical problem, and it's resolved by a device called predicate abstraction, which is the modal analogue of the definite description operator. See: en.wikipedia.org/wiki/Predicate_abstraction
    – user5172
    Commented Aug 14, 2015 at 18:03
  • 1
    @Conifold, SE style discourages long arguments in the comments section. I suggest you make a new question: "Why do many contemporary philosophers think Quine's criticisms of modal logic are wrong?" If you make that question, I'll try to answer it later today.
    – user5172
    Commented Aug 16, 2015 at 13:20
  • 1
    I don't see what you're on about here at all.
    – user5172
    Commented Aug 19, 2015 at 13:10

There are multiple systems of axioms for modal logic. Perhaps, the most influential is Kripke's based on his theory of rigid designation, which is a revival of Aristotelian essentialism (some properties of objects are "essential", and pick out the same objects in all possible worlds, others are not). You can find a survey of objections to it, with references, in the Stanford article. Another popular system is Lewis's modal realism, which is criticized by Lycan in Modality and Meaning, and... by Lewis himself in On the Plurality of Worlds. More recent criticisms include van Inwagen's Modal Epistemology, which argues that modal knowledge we can have is largely trivial, and Felt's Impossible Worlds, which questions cogency of possible worlds semantics.

As for Quine, his objections were more philosophical than technical, they were not resolved, and after Marcus and Parsons many logicians misunderstood their nature. A detailed historical account is given by Tuboly in Quine and Quantified Modal Logic. Quine's primary objection expressed in Reference and Modality was that necessity of statements seems to depend on how objects in them are designated ("nine" is necessarily greater than seven, but "number of planets" is not), which creates problems for quantification into modal contexts. Kripke's modal semantics introduced in the late 1950s enables such quantification, and many authors mistakenly thought that it also solves the original epistemological problem. Kripke however realized that an answer requires making sense of "de re" or "metaphysical" modality that applies directly to objects rather than to ways of describing them.

Kripke attempted such construction in Naming and Necessity by affirming intuitions about properties essential and inessential in modal contexts:

"Suppose that someone said, pointing to Nixon, ‘That’s the guy who might have lost’. Someone else says ‘Oh no, if you describe him as “Nixon”, then he might have lost; but of course, describing him as the winner, then it is not true that he might have lost’. Now which one is being the philosopher, here, the unintuitive man? It seems to me obviously to be the second... If someone thinks that the notion of a necessary or contingent property... is a philosopher’s notion with no intuitive content, he is wrong. Of course, some philosophers think that something’s having intuitive content is very inconclusive evidence in favor of it. I think it is very heavy evidence in favor of anything, myself."

However, experimental studies since showed that these modal/essentialist intuitions are culturally dependent and context sensitive, i.e. answers depend on how a question is asked, see Beebe-Undercoffer's Cross-cultural Differences in Semantic Intuitions. This brings back Quinean doubts about cogency of modal statements, especially in the context of science, which was his primary concern. Reliance on intuition also raises the issues of ambiguity and illicit metaphysical committments, see Cummins's Reflections on Reflective Equilibrium. This was also anticipated by Quine in Two Dogmas of Empiricism, see summary of objections and rebuttals in the IEP article:

"whether Quine or the conventionalist is right, the primary lesson of this section stands, namely, that metaphysical accounts of possible worlds might be mistaken not just in detail, but in their most basic assumptions".

  • 2
    It is perfectly simple what kripkean possible worlds are--they are distributions of truth values over the entire set of atomic propositions. A "world" in possible worlds semantics is just like a really big truth-table and the existence of these is no more problematic than the existence of numbers or sets or other abstract objects. The "possible worlds" of David Lewis are quite different. Lewis tried to argue that there must be real concrete entities that corresponded to the distributions of truth values, but most metaphysicians don't buy that (Kripke, Plantinga, et al.)
    – user5172
    Commented Aug 14, 2015 at 18:06
  • @shane Truth values are interdependent, reducing everything to "atomic propositions" was Carnap's lifelong project, and it is as hopeless today as it was at the time of Two Dogmas. "Truth tables" don't decide the possibility of perpetuum mobile or flying horses, pet metaphysics of possible worlds does. And how problematic it can be is seen from Kripke's modal "argument" for mind-body dualism, or Plantinga's "transworld depravity" defense of God's benevolence and possible worlds defense of the ontological "argument" of God's existence. Lewis is not alone in his modally metaphysical exuberance.
    – Conifold
    Commented Aug 15, 2015 at 22:37
  • I'm not sure why you keep putting "argument" in quotation marks. Also, note from the IEP article you quote: "Yet Quine’s investigation bears on modal terms as well, since he presumes that a statement would be analytic if and only if it is necessary." That is simply to say that Quine's argument in "Two Dogmas" is question begging against Kripke who explicitly thinks there are plenty of cases of necessary truths that are not analytic: "Water is H2O" is an example.
    – user5172
    Commented Aug 16, 2015 at 13:25
  • @cornifold, I find it strange that you think of the truth value of the atomic sentences as interconnected, given your (empiricist?) rejection of modality. If the truth values of the atomic sentences are interconnected (in any strong sense), then I ought to be able to infer the truth value of some atomic sentence from another, without needing to observe anything. That would have sounded like just the kind of dogmatism Hume thought he was getting rid of in rejecting modality.
    – user5172
    Commented Aug 16, 2015 at 13:30
  • @shane Atomic sentences can't be assigned truth values individually, only as a "corporate body", and empirical input is needed to do it. Empirically equivalent theories may assign opposite values to the same sentence or even leave it meaningless. Alas, empirical input is lacking for the possible, but modality has to play by the same rules if at all. Specify a system of presuppositions, be it theism, physicalism or fiction, that regulate assignment of the truth values wholesale. Possible world jargon is only obscuring metaphysical commitments with essences, atomic "facts" and truth tables.
    – Conifold
    Commented Aug 19, 2015 at 1:57

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