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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.

Conifold
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  • so you are interested specifically in epistemic logics? –  Aug 14 '15 at 18:00
  • I have a forthcoming paper on the Kp -> KKp principle. You can find it here: https://www.academia.edu/8272914/The_Infinitely_Iterated_Labyrinth –  Aug 14 '15 at 18:09

2 Answers2

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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..." https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction#Quine.27s_criticisms – Conifold Aug 14 '15 at 01:15
  • And the end of the quote from wikipedia (!) is "for poor reasons" – virmaior Aug 14 '15 at 09:33
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    @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: https://en.wikipedia.org/wiki/Predicate_abstraction –  Aug 14 '15 at 18:03
  • Essentialism is rejected even by some modal logicians (Armstrong), conventionalists and a long list of epistemologists cited by SEP. Without it or some other metaphysical prop one can't say if water is necessarily H20 or if talking donkeys are possible. So modality in terms of possible worlds is either circular: possible is defined via "maximally consistent sets", but consistency is just another word for "jointly possible", or trivial, anything is possible and nothing is necessary. Predicate closure was well known to Quine, but it does nothing to help with the necessary/possible distinction. – Conifold Aug 15 '15 at 22:26
  • @virmaior I doubt Friedman does it for poor reasons, he is very sympathetic to Carnap, but admits that the distinction is unworkable. Even those claiming it exists make no plausible suggestions as to how it is to be drawn. Kripke declares some properties "essential", but what makes them essential is as murky as what makes Carnap's truths "analytic", and even that is hardly enough to tell which sets of propositions are "consistent" or "maximal". IEP lists other prescriptions for necessary/possible, all of them characterized as circular except Lewis's, which has a host of other problems. – Conifold Aug 16 '15 at 02:11
  • @Conifold all I did was complete the quote from wikipedia, because even though I don't put too much stock in wikipedia, I'd be surprised if it said Quine's objections are widely accepted among philosophers, because that completely disagreed with the attitudes of the logicians I've met (I'm not an expert in modal logic). – virmaior Aug 16 '15 at 13:06
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    @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. –  Aug 16 '15 at 13:20
  • Quine assumed analyticity and necessity coextensional, but it matters little if they aren't, both are introduced by fiat with explanations that run in a circle: necessity, essence and consistency are just like analyticity, synonymy and semantic rules. Water is H20 necessarily because of its essence, and analytically because of synonymy. Necessity of "green is extended" is as obscure as its analyticity, Quine's argument goes for either. Kripke's "necessary aposteriori" examples are predicated on his essentialism, so the new necessity/analyticity distinction doesn't help. – Conifold Aug 19 '15 at 02:15
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    I don't see what you're on about here at all. –  Aug 19 '15 at 13:10
  • This is a response to your claim that Quine's critique begs the question against Kripke due to the difference between analyticity and necessity. But Kripke's assertion of necessary aposteriori does beg the question against a non-essentialist, who should be the target audience if they are to be used as motivation. Without essences Kripke can't motivate necessity/analyticity distinction, and even with them his reasoning is still as circular as Carnap's about synonymy, etc. – Conifold Aug 22 '15 at 22:37
  • @Conifold, I still don't follow. Water is H2O necessarily because (i) `water' is a natural kind term, (ii) natural kind terms are rigid designators, (iii) H2O and (iv) identity is a necessary relation. Clauses (i) and (ii) are empirical questions of linguistics, and I think Kripke's right about them. Clause (iii) is an empirical discovery, so it's not thought experiment intuition mongering. It's an actual scientific discovery. Clause (iv) is the result of a philosophical argument, the one I gave elsewhere. The combination of those two claims does yield a kind of essentialism. –  Aug 23 '15 at 11:43
  • But so what? It's not actually the modal logic that's driving Kripke-style essentialism, it's the combination of claims about the linguistic properties of natural kind terms and the philosophical argument about identity being defined by Leibniz's law. You could think modal logic is peachy keen and reject essentialism entirely by rejecting (i) and (ii), or even rejecting (iv). –  Aug 23 '15 at 11:46
  • None of i-iv is empirical, first two are conventions, and iii-iv have "necessary" in them. Imagine that Mach's view prevails: atoms are useful fictions and water=H20 is a metaphor. Let me try a different tack. First, there is only necessity relative to some X. I see clearly articulated X in Pearl's treatment of counterfactuals for example (structural equations), but not in Kripkean logics. I see no means to track how necessity changes with X there. This is parallel to Quine's request for analyticity relative to L. – Conifold Aug 26 '15 at 02:15
  • Second, if we unwind "disembodied mind is possible, ergo mind and body are separate" argument according to declared semantics, it amounts to "'true' can be assigned to 'disembodied mind exists', ergo mind and body are separate", which is empty. Possible world talk is intuition pumping, and atomistic constructions of "worlds" are therefore grossly misleading. This is a modal version of Quine's criticism of atomic facts. What IEP means by "mistaken in most basic assumptions" is that possible worlds may have to be discarded as a vehicle for expressing modality. – Conifold Aug 26 '15 at 02:37
  • (i) and (ii) are claims about human languages, therefore they are empirical linguistic claims. You can reject essentialism by saying "human language might be characterized by these terms and therefore human language is radically defective." But that's an important theoretical cost. I don't follow your other points. And SE is not intended for long detailed comment threads such as this, so I won't pursue them further. –  Aug 26 '15 at 12:40
  • That natural languages are epistemologically defective is hardly surprising, they reflect pre-Newtonian or at best Newtonian intuitions. So linguists can't tell us if rigid designation etc. is adequate for modal logic. Quine's *epistemological* arguments to the contrary weren't even engaged by Kripke, all he addresses are technicalities. Don't worry about SE, robot or moderators transform comment threads into chats if they are deemed too long. – Conifold Aug 27 '15 at 00:10
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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".

Conifold
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    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.) –  Aug 14 '15 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 Aug 15 '15 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. –  Aug 16 '15 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. –  Aug 16 '15 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 Aug 19 '15 at 01:57
  • Empirical input is not needed to fill out a truth table, nor is empirical input needed to distribute truth values over possible worlds, because in both cases the distribution is a *stipulation*. I don't need empirical data to confirm whether bachelors are unmarried if I stipulate that "bachelor" =df "unmarried man." Likewise, I don't need empirical input to know whether there is a possible world in which it is false that Nixon lost the election. Since possible worlds (as the semantic devices in Kripke semantics) are abstract entities I can stipulate them into being at will. –  Aug 19 '15 at 13:10
  • @shane Of course you can, that's why I included fiction as a possible system of presuppositions. But then we have no idea if "possible worlds" built out of essences and atomic facts are possible in anything but name. Which is fine as long as modal logic is a game of symbols with no relevance to the empirical world. But of course "semantic devices in Kripke semantics" are ultimately used to make claims about that one. And then modal logician has to explain how essences and atomic facts relate to a world which entertains neither, e.g. why independently changed truth values remain compatible. – Conifold Aug 22 '15 at 22:56
  • I don't know why you keep bringing "essences" into the picture and I don't what evidence you have that the actual empirical world *doesn't* contain essences? All of the essentialists I know think of the essences of things as being discovered scientifically. (See Brian Ellis's book `Scientific Essentialism' or the work of Alexander Bird.) –  Aug 23 '15 at 11:40