There are some propositions such as 1+1=2 that seem to be true in all possible worlds. That is, there is no possible world in which 1+1=2 is not true. Propositions like this that seem to be true in all possible worlds are said to be true necessarily.

There are two ways to interpret the claim that 1+1=2 is true necessarily, as epistemic modality and as metaphysical modality ("modality" is a general term to refer to necessity, possibility, and related concepts).

In the following, I'm going to abbreviate "necessarily true" as "necessary".

Epistemic modality is fairly unproblematic. Before I explain it, let me define another term: a proposition is said to be a priori if its truth can be determined without looking at any empirical evidence--that is, without looking at the actual world to see how things are. If you can determine the truth of a proposition without looking at the actual world, then that proposition must be true in all possible worlds--that is, necessary. Contrariwise, if you can determine that a proposition is necessary--true in all possible worlds--then it must be that you can determine the truth of that proposition without looking at the actual world, so that proposition must be a priori. Therefore, the epistemic approach to modality is that the necessary propositions are just the a priori propositions.

However, there are examples of propositions that are not a priori but are necessary. Consider the sentence,

In all possible worlds in which Jane Fonda exists, Jane Fonda is the daughter of Henry Fonda.

Note that I'm not saying that in all possible worlds having a woman named Jane Fonda, that woman has a father named Henry Fonda; there are possible worlds in which both names are different, but in order for the names to be different, the people have to be the same. That is, in any possible world in which Jane Fonda exists, regardless of her name in that possible world, she is the same person as Jane Fonda in this world. I'm using the name in the actual world to pick out two people in the actual world and saying that in any possible world, if those two people exist, then they have that relationship. Jane wouldn't be the same person as the Jane in this world if her father were not the same person as the Henry in this world.

Therefore, it is necessary that Jane Fonda is the daughter of Henry Fonda. She wouldn't be Jane Fonda if she had a different father. But it is not a priori that Jane Fonda is the daughter of Henry Fonda; that is not something that you could determine without looking at the actual world. So that proposition is necessary but not a priori, violating the claim of epistemic modality.

It seems then that there is another kind of modality, metaphysical modality, that is not dependent on knowledge, but dependent on the nature of things. This would seem to cause problems for two different groups of philosophers: empiricists and materialists.

It seems to cause problems for empiricists because it means that we can know things about possible worlds as a metaphysical reality. Where would this knowledge come from? It can't come from empirical experience because we can only experience the actual world and there doesn't seem to be any way that the actual world can give us knowledge about non-actual worlds.

It seems to cause problems for materialists because possible worlds are not material. Since only the material exists, how can you have true propositions about possible worlds?

Is this correct? Do empiricists and materialists have to reject metaphysical modality?

  • Quine famously rejected Kripke's modal metaphysics, but the more common strategy is not to reject but to deflate it. Why are Samuel Clemens and Mark Twain necessarily the same? Because "intuitions", it is not like we can check. Kripke simply postulates such essentialism and constructs his "metaphysical" possible worlds accordingly, see Zvolenzky. Empiricists deflate that to linguistic constructs/fictions that spell out folk semantics, not metaphysics, see IEP.
    – Conifold
    Commented Aug 12, 2022 at 13:48
  • 2
    Possible worlds may be real according to Lewis's modal realism, in a PW where contingent materials and physical laws are different than ours horses may indeed be able to fly, thus metaphysical modality is orthogonal to materialism. As for Kripke's Necessary a Priori, there's a recent post discussing this for your ref... As for empiricists they just accept our impure knowledge comes from experience but cannot logically derive there's no such PW ontologically or really... Commented Aug 13, 2022 at 3:31

5 Answers 5


Interesting question!

What you are talking about seems to be addressed by the Stanford Encyclopedia of Philosophy. According the Epistemology of Modality (SEP):

Kant famously argued that what is a priori coincides with what is necessary, thereby ruling out the category of a posteriori necessities. However, Kripke (1971) pointed out that there are necessary truths that can only be known a posteriori. (emphasis mine)

That puts the shoe on the other foot. If some truths are necessarily empirically, how can a rationalist defend the claim that experience isn't necessary for necessity? That implies that most consistent and reasonable positions require to accept that there are both rational and empirical necessities. Then the article goes on:

In general, modal rationalists prioritize a priori methods for acquiring knowledge of metaphysical modality... By contrast, modal empiricists pursue a posteriori accounts of knowledge of metaphysical modality. Often they still acknowledge that a priori methods might contribute to modal knowledge. (See Fischer & Leon 2017) (Emphasis mine)

So, according to the article, there are those who emphasize the a prioriticity and those who emphasize the a posteriori. The fact that the article invokes the term "modal empiricists" suggests that empiricism isn't necessarily incompatible with possible worlds. One solution, for instance, is to consider possible worlds as a mathematical object. For instance, in Poole and Mackworth's Artificial Intelligence possible worlds are used (pages 125, 346, 438, and 719) to denote model-theoretic models. A possible world therefore is nothing more than a set of truth-conditional claims subject to the coherence definition of truth.

Lastly, the article goes on to state that some philosophers downgrade or reject the distinction between a prioriticity and a posteriority:

Some philosophers have challenged the philosophical significance of the a priori/a posteriori distinction.

Philosophers such as these challenge a claim like '1+1=2 is true a priori'. A mathematical empiricist, for instance, rejects that this is an a priori truth. Some philosophers reject mathematics is a priori. From WP:

Mathematical empiricism is a form of realism that denies that mathematics can be known a priori at all. It says that we discover mathematical facts by empirical research, just like facts in any of the other sciences.

The article treats the entire notion of modality thoroughly talking about nesting of domains, the relationship between intuition and modal claims of truth, and so on, revealing there is a lot of metaphysical presumption that goes into deciding what is necessary and what is not, a priori or otherwise.


I've lately been trying to defend nominalism, of all things (at least as an exercise in pluralism), so I'll try to adapt a line of reasoning from my defense of that, to this case.

Let's suppose that knowledge and understanding come in amounts and degrees. Intuitively, there "might" be a connection between amounts and degrees of existence, and the epistemic categories. So let us suppose that knowledge of mere possibilities (more on that "mere" qualifier in a moment) is knowledge of objects with a very low, maybe vanishingly small/infinitesimal, such degree. Contrariwise, knowledge of actuality is more "robust" and requires a more robust faculty/substrate than the ether of mere thought. Ditto, except a fortiori, for knowledge of necessity.

So rather than all-out empiricism, we say something like, "Almost all knowledge and understanding of substantive, objective facts, is empirical; there is some slight a priori knowledge, but it is not as vivid or even impressive, all things considered (usually), as empirical knowledge."

A pseudo-Kantian response. Another option is to hold that knowledge of mere possibility is inferrable from knowledge of actuality; the rule licensing the inference might be construed as "innate" or a priori or whatever, but it can take only concrete empirical inputs and can yield only abstract metaphysical outputs. Kant goes so far as to ask, however, whether we can infer general possibilities from particular possibilities, or only particulars from particulars (and then uselessly). The modal generalist sees a red dove and thinks, "It is possible for doves to be red," while the particularist, here, sees the same thing, but concludes only with, "It is possible for that dove to be red (whenever it is seen to be red); whether it is possible for it to be red any other time, or all the time, I've no way of knowing, and nevermind all the other doves there are or could be!"

Similarly, knowledge of a posteriori necessity is sometimes read off a partly empirical, partly rational, argument scheme: we empirically know the relevant premises (e.g. that the same man went by two names), and we know a priori that this name-sharing, coupled with a sufficient variant of the law of identity, manufactures the item of modal knowledge, AKA the modalized variant of the empirical sentence in question. It would be the difference between, "I know that Stephen King is Richard Bachman," and, "I know that necessarily, Stephen King is Richard Bachman."

A quick interjection: Stephen King isn't Stephen King, one might counterargue. "Stephen King" is a name, and, "One man goes by two names," is only contingently true; "Stephen King is Richard Bachman," can be translated into, "A man named 'Stephen King' also goes by the name 'Richard Bachman.'" Though the giving of names can be interpreted as an a priori (because epistemically proactive) affair, name-giving also has a clear empirical side (e.g. when we learn the names we've been given), so it is not apparent that the a posteriori knowledge we have about men with multiple aliases is knowledge of an a priori necessity to boot).

Actualism vs. possibilism. Yet another option is to reconfigure the imagery of possible worlds as possible closed sets of sentences/propositions covering any entire world. Since even if they were concrete alternative realities (or whatever), other possible worlds would correspond to such sets, so we lose nothing, so far, by focusing just on these sets. The upshot is that there would be no "modal aliens", i.e. objects whose whole substance was never before actual; but only reconfigurations of actual objects would occur, here. At any rate, "1 + 1 = 2 in all possible worlds," then becomes, "In all possible reports of every fact at once in the actual world, 1 + 1 = 2 is a subfact," perhaps.

Infinite empirical intuition? The hardest part about knowledge of pure possibilities and attendant necessities is how indefinitely large it can seem to be. By trying to cover endless cases of addition with a single thought, we seem to try to anticipate eternity. But I have often thought that Kant was looking in the right direction by identifying space and time as "formal intuitions" grounding mathematical knowledge, because many who doubt, "1 + 1 = 2," are wondering not about individual moments of computation, but whether we have a "right" to assume that our computation will always go the same, wherever we are: so modulo space and time overall, or even in general, then. But for Kant, the infinity encoded into space and time was still a priori (because proactive/"spontaneous," in the activity of the imagination to a great extent and degree, no less); but so I wonder whether it would be possible(!) to believe in infinite-scope passive, hence empirical, intuition. Perhaps as far as robust objects go, we only see everything at and within a certain distance; but when we concentrate on pure spacetime concepts and perception, maybe we see the whole of spacetime as such, and we can see that in every part, "1 + 1 = 2," is true.

That will depend, then, on the viability of the a priori/empirical distinction itself. I've been referring to passive vs. proactive epistemic states (which allow for interactive such states, too), but action-based theories of perception exist, and do not quite seem reducible to a Kant-style harmony between passive sensation and proactive discursion. And that might be a sort of "last word" on the question of the OP: depending on how we define experience/perception/sensation/aposteriority on the one hand, and possibility/necessity on the other, then whether an empiricist could know about mere possibilities or rigid necessities is just a matter of otherwise arbitrary uses of the entangled terms, and so someone who says, "Empirical knowledge is the only knowledge, so if modal knowledge cannot be had empirically, then there is no modal knowledge," ends up saying something meaningless. (Or worse: something that cannot possibly mean anything, because it involves rejecting the concept of possibility itself. I will issue a severe equivocation warning with respect to this semantic argument, however.)

P.S. I don't know enough about materialism to offer any sources for analysis on this score, except to say that I myself believe in the following, "Either physicalism is true, or the distinction between physicalism and non-physicalism is meaningless; and I am not one to know which disjunct is true." I do suspect that talk of "virtual particles" in physics carries a trace of "mere possibilia"-talk; but I also would expect that there could be a priori materialists generically, who advert to "reconfiguration" versions of possible-worlds talk; and so for all that, these would be materialists with modal knowledge that was not too difficult to come by.


For what this may be worth, Kripke's "success" for modal logic follows in the wake of Carnap's failure.

In "Meaning and Semantics," Carnap subsumes both Wittgenstienian states of affairs and Leibnizian possible worlds into a single notion. Leibnizian possible worlds are motivated by partiality (of information). This need not be true of at least one application of Wittgensteinian states of affairs.

When Wittgenstein deflates the role of negation, he does so on the basis that a language user understands both a proposition and its denial. That is, a language user can "imagine" states of affairs under which each obtains.

This is not a semantic conception of truth. It falls under a pragmatic conception of truth in so far as it it involves the meaning of statements to language users.

Along similar lines, Carnap had pursued an analytic conception of truth. The necessary truth of reflexive equality statements obfuscates the difference between a metaphysical "law of identity" and the enforcement of uniform interpretation of terms needed for an analytic conception of truth.

Analytic conceptions of truth hold that truth arises from the meanings of the words. Consequently, the role of "meaning postulates" arise in Carnap's work and still find application in the study of intensional logics.

Importantly, the necessary truth of reflexive equality statements does not follow from a semantic conception of truth alone. Tyler Burge's paper on truth and singular terms probably has the best explanation of this fact. And, this accounts for why the algebraization of first-order logic demands a change to the typical inference rules for quantification.

Essentially, then, the first-order paradigm presupposes an analytic conception of truth to which a semantic conception of truth is applied. It is this methodology with which Kripke's semantics is compatible.

Within this paradigm, one has Beth's definability theorem. In so far as a term given using a definite description may be compared with a rigid designator, the explicit definition is correlated with a class of models which serve as an implicit definition.

Arguably, then, the issue arises because use of the word "truth" is not specific enough.


Can empiricists and materialists accept metaphysical modality?

I wouldn't know but if we judge the metaphysical modality from what you say, then it doesn't look good.


For example, it is true in all possible worlds that Samuel Clemens and Mark Twain are the same man. (...) That is true because those names both pick out the same man in the actual world (...) Let's call this man Mr. X. Now, in all possible worlds, it is the case that Mr. X is Mr. X. It is simply an application of the law of identity.

This is transparently fallacious.

There is no doubt that it is an application of the law of identity that Mr. X is Mr. X, but it is just as certain that the law of identity does not imply that Samuel Clemens and Mark Twain are the same man.

You could articulate your argument to make it good, so the question is why didn't you?

  • 3
    this is a comment, not an answer. The response to your comment is that I took that argument directly from SEP which took it from Kripke, one of the most respected logicians of all time. Many professional philosophers have taken the argument seriously either in favor or to refute it. As it happens, I myself agree with one of the refutations, but I'm not so arrogant as to call it "transparently fallacious". Commented Aug 12, 2022 at 18:44
  • @DavidGudeman It questions the premises of the question, which is legitimate frame challenging. And the rest of your comment seems to be argument from authority. It does appear to be transparently fallacious, and I don't see how it's arrogant to express the evaluation. Commented Aug 13, 2022 at 4:18
  • @Acccumulation, it is a strong argument from authority, not a fallacious one. And I didn't say he shouldn't have challenged my premise, I said that it was a comment, not an answer. Commented Aug 13, 2022 at 7:39
  • @DavidGudeman "this is a comment, not an answer." This is an opinion, not a fact. - 2. "SEP" + "Kripke" SEP is really good but it has nonetheless many dubious contents. Kripke didn't seem to have arrived at any correct formal model of human logic. Maybe he was and still is respected by logicians, but like Sextus Empiricus in his time, I observe that logicians today still disagree among themselves and pretty much about everything. 3. "arrogant" Is it arrogant to tell the truth? Commented Aug 13, 2022 at 17:56
  • @Speakpigeon, it is arrogant for a nobody to call an argument respected by many famous logicians and philosophers "transparently fallacious". It implies that you have some superior logical sensibility that lets you easily detect fallacies that have escaped the combined attention of lots of talented people, part of whose job is to detect fallacies. Commented Aug 13, 2022 at 19:17

You state in a comment to Speakpigeon's answer that you based your question on SEP, which based their article on Kripke, which makes your question a third-hand version of this argument. I did a little bit of googling and found that Kripke claims that "Samuel Clemens" is a "rigid designator", and more googling was required to find that this term means "a term that identifies the same object or individual in every possible world." You didn't have any discussion of this term, or Kripke's claim that "Samuel Clemens" qualifies, or an argument in support of that claim. The term "rigid designator" seems like a rather incoherent concept. No two worlds have exactly the same objects. If two objects are in different worlds, then they are different objects.

And then on top of that, you write "That is true because those names both pick out the same man in the actual world". So you seem to be making a different claim than Kripke: Kripke claims that in all worlds in which "Samuel Clemens" and "Mark Twain" exist, they are the same person, but you are claiming that in this world, Samuel Clemens and Mark Twain are the same person, and the claim "In X, Samuel Clemens and Mark Twain are the same person" is true in all worlds, where X is some designation that identifies the world that we live in.

This raises quite a few questions. For instance, what could X possibly be? What method of designating worlds is there? If X is simply a comprehensive description of our world, then Samuel Clemens and Mark Twain being the same person would be part of that description, so the claim boils down to "In the world in which Samuel Clemens and Mark Twain are the same person, and [a bunch of other stuff], Samuel Clemens and Mark Twain are the same person", which is rather clearly a priori. So you have failed to present a clear explanation of how you think there are necessary statements that are not a priori.

  • I didn't say I based my question on SEP. I've read this material in numerous places. I didn't define rigid designators because I thought I could make my point without that sidetrack. I wasn't trying to prove Kripke's argument (in part because I don't believe it myself) only alerting people to the existence of the controversy. As to your misunderstanding of the argument, I'll update the question to try to clarify. Commented Aug 13, 2022 at 7:08

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