At face value for me these don't mean the same thing but I'm struggling to find if they are separate concepts. Are there examples where they differ? Are they or aren't they separate ideas? I can't fully articulate why (maybe coffee hasn't kicked in) "not possible without" and "necessary for" seem different, just that they feel different for metaphysical reasons.

What inspired me to ask for more clarification was user Philip Klöcking's

Kantian a priori basically is "if that was not the case, the empirical knowledge we have would not be possible". It is not a positively determined belief or proposition everybody shares. As I wrote elsewhere, propositions a priori can be quite counter-intuitive. The a priori, ie. before all experience does bear a logical meaning in Kant. It means it is something that is logically prior to, a necessary condition of, experience. Using your header, then, we can answer clearly: As soon as non-humans become cognisant of the necessary conditions of their experience, they can gain a priori knowledge. That is not the same as hard-wired, dogmatic beliefs, though.[1]

Is everything which has something which makes it possible also following necessarily from that something? If I do equate them, am I buying into some metaphysics? Can we settle this without metaphysics?


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    It's an instance of the elementary interdefinability of the necessity and possibility operators in modal logic: "The operator ◊ (for ‘possibly’) can be defined from □ by letting ◊A=∼□∼A. In K, the operators □ and ◊ behave very much like the quantifiers ∀ (all) and ∃ (some). For example, the definition of ◊ from □ mirrors the equivalence of ∀xA with ∼∃x∼A in predicate logic." Dec 19, 2022 at 17:26
  • @KristianBerry I suspect I have some idiosyncratic or incomplete notion of possible and necessary as a confounding issue. Is it necessary we exist? Well no, there could have been no humans if Earth never formed. But since we have the experiences we do, we necessarily exist, like a Cartesian argument I think therefore I am. We do necessarily exist then...Possible is just as concerning. Most of these modal situations seem to concern existence which is one of the most troubling concepts too. I probably need a good book on Modal logic to make any progress there. Thanks for the help
    – J Kusin
    Dec 19, 2022 at 18:26
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    @AgentSmith, I'm not sure what your note about inconsistency is referring to. At any rate, I would think Kant would've had to have something like only(◇X) → only(K), i.e. knowability (of experience) only if possibly X (for X = the conditions of possible experience). Or probably not quite that formatting, but something to that effect. Dec 20, 2022 at 2:43
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    @AgentSmith, unfortunately, this particular SE does not support LaTeX. Perhaps the originators didn't anticipate that symbolic logic would be used much here, or perhaps they deferred to Unicode copy/paste options (that's how I have to insert arrows) and the <sub>/<sup> function to cover that base. Dec 20, 2022 at 10:08
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    This equality is called duality. Possibility and necessity are not dual in intuitionistic modal logic, for example, but most non-dual logics are used under alternative interpretations, like obligations and permissions in deontic logic. See also SEP, Varieties of Modality and Medieval Theories of Modality for various conceptions of modality.
    – Conifold
    Dec 20, 2022 at 19:51

1 Answer 1


Kant's modal semantics are rather novel, or he tried to make them out to be so, at any rate (he seems mostly successful, in my opinion; not that his position is confirmed beyond all doubt, but at least he was offering a relatively new idea). In the first Critique, he says at one point:

Possibility, existence, and necessity nobody has ever yet been able to explain without being guilty of manifest tautology, when the definition has been drawn entirely from the pure understanding. For the substitution of the logical possibility of the conception—the condition of which is that it be not self-contradictory, for the transcendental possibility of things—the condition of which is that there be an object corresponding to the conception, is a trick which can only deceive the inexperienced.27

27 In one word, to none of these conceptions belongs a corresponding object, and consequently their real possibility cannot be demonstrated, if we take away sensuous intuition—the only intuition which we possess—and there then remains nothing but the logical possibility, that is, the fact that the conception or thought is possible—which, however, is not the question; what we want to know being, whether it relates to an object and thus possesses any meaning.

For Kant, even necessity "is not a predicate." Ditto for possibility, for he says elsewhere that a hundred possible dollars (thalers) are not qualitatively different from a hundred real dollars.

So when Kant says that his category-based principles are necessary, he is not speaking of the kind of free-floating necessity that theologians attached to God:

Finally, as regards the third postulate, it applies to material necessity in existence, and not to merely formal and logical necessity in the connection of conceptions. Now as we cannot cognize completely a priori the existence of any object of sense, though we can do so comparatively a priori, that is, relatively to some other previously given existence—a cognition, however, which can only be of such an existence as must be contained in the complex of experience, of which the previously given perception is a part—the necessity of existence can never be cognized from conceptions, but always, on the contrary, from its connection with that which is an object of perception. But the only existence cognized, under the condition of other given phenomena, as necessary, is the existence of effects from given causes in conformity with the laws of causality. It is consequently not the necessity of the existence of things (as substances), but the necessity of the state of things that we cognize, and that not immediately, but by means of the existence of other states given in perception, according to empirical laws of causality.

Further reading: "Transcendental Arguments (Stanford Encyclopedia of Philosophy)".

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    I think this confirms "Necessary = not-possible-without" then in Kant's philosophy. I guess I need to look in more exotic places if I want to hold them as more separate, distinct, and unequal concepts. Thanks for the souces
    – J Kusin
    Dec 20, 2022 at 18:38

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