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SEP and others have transcendental arguments as claims “namely that X is a necessary condition for the possibility of Y—where then, given that Y is the case, it logically follows that X must be the case too.”

I have heard Anselm, Descartes, and Kant among others used such arguments.

  1. Even if we have Y we can not know or wish to remain agnostic as to if Y is possible right?(As Jo Wehler seems to be saying this wish to remain agnostic seems to already be a minority view in modal logic?)

  2. I guess I want a logic where Y does not imply Y is possible or necessary. Just Y. What would this philosophical position be called, where Y does not imply Y is possible? This seems very “natural” to me. To have Y and then claim either Y is possible or necessary seems like an extra assumption. I just want Y. Is this a minority position?

To clarify: If I have Y (a cat in front of me, or experience of the cat in front of me), I do not know if Y (the cat in front) was due to natural law/necessity, brute fact, a possible outcome/world, God, etc. I just have the undeniable simple experience of the cat first. Then I begin layering assumptions. Saying Y->"Y is poss" is an assumption no?

  1. What weaknesses are to “Y” doesn't imply “Y is possible"? Like, do I have to operate in a minority logical structure outside mainstream? Do I have to redefine probabilities in any sense, get rid of free will or counterfactual thinking?

Thanks

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6 Answers 6

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I don't see any need to be 'sceptical' of transcendental arguments. It's rather like being sceptical of deduction whether done classically or modally. And in fact, a transcendental argument relies on classical modal logic.

What one can be sceptical of is whether that specific transcendental argument holds.

Simply because someone can make an error in logic does not mean that logic has been brought into disrepute, but that the reputation for that person for sound reasoning has; especially when they double down on their mistake after it has been pointed out, after all, anyone can make mistakes.

If you want a logic that is 'sceptical' or 'agnostic' of transcendental arguments, then first order classical logic is enough as modality is not expressible in that logic and transcendental arguments relies on modality. But this is an impoverished view of logic as modality does obtain in our world.

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  • Thanks that helps a lot. I guess I’m just super avoidant of the use of necessary outside of logic and syntax that these arguments give me pause. (And relatedly for possible one meaning might be “not necessary”)
    – J Kusin
    Mar 1, 2022 at 17:45
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The argument form that you quote is straightforwardly valid in standard logic. It might be symbolised as

1. ◇Y → X
2. Y
3. Y → ◇Y
therefore, 
4. X 

You give 1 and 2 as premises, and 3 is the T axiom of modal logic. The conclusion follows by two applications of modus ponens.

Although you say you want a logic where Y does not imply that Y is possible, this is highly unusual. Since 'not possible' is a synonym for 'impossible', it amounts to saying that you wish to allow that Y might be both true and impossible. There are modal systems that lack the T axiom, but they are not typically concerned with necessity and possibility, but with some other modality.

It may be that you have in mind the idea that nothing can be merely possible without being actual. When speaking of the existence of things, this position is called actualism. It amounts to holding that everything that exists is actual and that nothing only possibly exists. This is plausible, though it faces the problem of explaining how we make sense of common notions like I might have had a younger sibling, though in fact I don't.

Or possibly you have something much stronger in mind, a kind of necessitarian position under which everything that is true could not have been otherwise. This is much less common, since it purports to exclude modality entirely.

As to transcendental arguments in general, there is no reason to object to them on principle. Each one must be evaluated on its merits.

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  • Does Y not implying anything about the necessity or possibility of Y really mean [Y and not Y]? When I said I want a logic where Y doesn’t imply Y is possible, I think I mean something a little narrower. Y is possible to me means Y is not necessary. Therefore to go from just Y to Y is not necessary seems epistemically and logically premature.
    – J Kusin
    Mar 2, 2022 at 23:12
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    I think you may be confusing possibility with contingency. Necessity and possibility are dual to each other, which means that 'not necessarily' is equivalent to 'possibly not'. To say something is not necessarily true implies that it is either impossible, i.e. necessarily false, or contingent, i.e. neither necessarily true nor necessarily false. If you were to say instead that "Y does not imply that Y is contingent", then this is unproblematic, since it merely allows that some propositions are necessary truths.
    – Bumble
    Mar 3, 2022 at 2:09
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Keeping a fairly narrow scope to Modal Logic here, I think a key concept that might help you out here is Access in modal frames. Kripke's frame semantics introduce not just the idea of possible worlds, but also a relation of Accessibility between them.

According to this view of modal logic, for something to be possible at a world W is for it to be true at a world that is accessible to W, and for something to be necessary at W is for it to be true at all worlds that are accessible to W

What you're suggesting seems to be that epistemic access need not be Reflexive. Just because something is in fact true doesn't mean that it's epistemically accessible - the actual world is not guaranteed to be one of the worlds that the modality of epistemic possibility considers.

This is a tenable position in the metatheory of modal logic, if not necessarily a common one. Many standard studied modal logic systems use a reflexive frame condition, but not all of them - Kripke's basic modal logic K does introduce a very weak notion of necessity without introducing the reflexive axiom T.

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    Thanks for the conceptual lead!
    – J D
    Mar 1, 2022 at 18:50
  • Was there a motivation for such a logic or just someone exploring the space of possible modal logics? It's hard for me to imagine a problem that such a logic would solve. Mar 1, 2022 at 20:50
  • @DavidGudeman Boolos' logic of provability within a formal system does not use T, because to do so would build in the assumption that the formal system is sound, which we don't want to do. Also, deontic logic does not use T, since the counterpart of 'possible' in the logic of obligation is 'permissible', and things that are not permissible may nevertheless actually happen.
    – Bumble
    Mar 1, 2022 at 21:22
  • I wasn't asking about modal (in the general sense) logics that don't use T; my question was about modal (in the strict sense) logics, logics of possibility and necessity, that don't use T. Mar 1, 2022 at 22:51
  • @DavidGudeman: I believe those are formally known as alethic logics or alethic modalities. Kripke's system K was not really designed to be used by itself, certainly not as an alethic logic, anyway. Rather, Kripke was trying to formalize the semantics of modal logics in general, including but not limited to alethic logic. Personally, I find it hard to believe that anyone is seriously doing alethic logic without axiom T, but maybe they're out there somewhere.
    – Kevin
    Mar 2, 2022 at 6:07
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I guess I want a logic where Y does not imply Y is possible or necessary. Just Y. What would this philosophical position be called, where Y does not imply Y is possible? This seems very “natural” to me. To have Y and then claim either Y is possible or necessary seems like an extra assumption. I just want Y. Is this a minority position?

This is a position that inherently contradicts itself.

You want a logic where the following two statements can both be true:

  • Y is true.
  • "Y is possible" is not true.

If "Y is possible" is not true, then by definition that implies Y is not true. This combination of truths therefore contains both "Y is true" and "Y is not true", making a contradiction.

On seeing your comment, I think your point of confusion is that you have misunderstood what "possible" means. Specifically, you are using "possible" to mean what I would say as "only possible", or more clearly as "possible and not necessary".

The definition of "Y is possible" is, solely and entirely, that "Y is true" does not contradict any other known facts. It does not indicate anything about whether "Y is not true" would contradict anything or not. If the world can't have been any other way, then everything is both necessary and possible. The terms are not mutually exclusive, and in fact all things that are necessary are also possible.

What you apparently mean by "possible", I would call "uncertain", or "undetermined", or some similar term.

What most people mean by "possible", I think would match your previous understanding of "either possible or necessary".

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  • Maybe the world can’t have been any other way. Then nothing is possible, rather everything just is, or is necessary.
    – J Kusin
    Mar 2, 2022 at 22:54
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    @JKusin I think I see what your issue is. You're not using the same definition of "possible" as everyone else. See my edit which addresses this.
    – Douglas
    Mar 2, 2022 at 23:22
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    @JKusin Edited again. Take your current understanding of the word "possible" and assign it to the word "uncertain" instead, or something.
    – Douglas
    Mar 3, 2022 at 1:07
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    This is the root issue here. Great job on identifying the different interpretation used by OP on the meaning of the word "possible" compared to general use of "possible".
    – justhalf
    Mar 3, 2022 at 8:05
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    @JKusin Because regardless of whether Y is necessary or uncertain, the same argument is valid, and using "possible" expresses it more concisely.
    – Douglas
    Mar 3, 2022 at 17:53
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The term "possible" has no transcendental or otherwise "weird" meaning. It simply means that Y being true does not lead to contradictions.

So saying you want just the pure truthfulness of Y without saying anything about requiring possibility of Y is equivalent to proposing that Y is true and not caring whether it leads to a contradiction.

There is nothing special about you wanting to do that - you can simply do it. There is no inherent meaning (within whatever system of logic you are using) to what you're doing. If you then follow up to base any further conclusions on your argument, you may end up with a building of statement which just collapses if indeed Y leads to contradiction.

The (to me) relatively weird formulation in the quote you are asking about,

namely that X is a necessary condition for the possibility of Y

in the strictest interpretations, just means that deriving or postulating Y will lead to inconsistencies further down the line unless X is also true. Or, equivalently, this is the statement that "Y and not(X)" necessarily leads to inconsistencies. Again, this is just a sentence without any special, "transcedental" meaning, and it should be quite easy to find simple examples to show what that means:

  • Y = "the sun is shining brightly in Central Europe in March 2022"
  • X = "the time of day is between 4am and 22pm"
  • Axiom: "the sun is bright between roughly 8am and 17pm in Central Europe in March"

Clearly, X is a necessary condition for the possibility of Y. X is not enough for Y (there may be clouds), but not(X) is clearly far outside the window of bright sun. Nothing keeps you from just picking Y and not bothering about any other statement to consider its possibility. Y can be true even if you do not look at your watch (i.e. if there are no axioms or derived statements which tell you about the current time). And clearly, finally, "Y and not(X)" is false, or a contradiction. The sun is never shining brightly in the deep of the night, no matter which other statements you have in your system, due to the Axiom.

As you mention the word "God" once - if that entity exists (or if you want it to be so for the sake of argument), then you can simply model it as an axiom in your system of logic, and add a large amount of statements based on that axiom; this would probably tremendously change the truth value of many statements in your system, but would not by necessity break you out of "Logic" as a concept.

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  • But your example doesn’t use “possible” anywhere in your X,Y, and Z. You need some postulate that says “___ is possible” in there too right? To me that additional “possible” postulate may be destabilizing, if you later learn [not ___ is possible], (maybe ___ is necessary instead).
    – J Kusin
    Mar 3, 2022 at 15:07
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"Possible" here basically means it's a thing that can be true. So to say "Y doesn't imply Y is possible" would to be say there can exist a statement which cannot be true (it's not possible for it to be true) while being true. So I could say there are no circumstances under which you have an apple (i.e. "You have an apple" is not possible), while you're holding an apple (i.e. "You have an apple" is true). That is absurd.

If you accept that Y is true, you cannot logically remain agnostic as to whether Y is possible (nor can you reject the possibility of Y).


"Necessary" basically just means there are no circumstances under which something can be false (given the premises we're accepting). It has to be true, i.e. it's necessary for it to be true. Necessity is the negation of possibility: Y is necessary if and only if not Y is not possible. For example, if it's necessary that you have an apple, it's impossible for you to not have an apple.

Saying "X is a necessary condition for the possibility of Y" doesn't mean Y is necessary. It's a statement about the necessity of X.

Whether you believe things being true implies they're necessary seems largely irrelevant. You just need to believe things being necessary implies they're true (as in the other way around). Beyond that, if you believe that Y is true, you should believe that anything that's a necessary condition of Y (or the possibility of Y) is also true. Because that's what a "necessary condition" means.

As for whether truth implies necessity, it seems logical to say that it does. If you already know something is true, then there are no circumstances under which it can be false; therefore it's necessary. Why truth implies necessity is similar to why truth implies possibility. Well, we can't truly know whether anything is true, but it is sufficient for the above if we simply accept that it's true. If you accept that it's true, then you should accept that it's necessary (to the same degree of confidence).

Note: this is not saying that some observed result of an experiment will be the same if we go back in time and do it again. It's saying that we can't go back in time, so the fact that we got some result in an experiment is necessary if we already know that we got that result. That sounds a bit like a tautology, but that's not quite what it is: it's "(X is true) implies (X is necessary)".

How can you be skeptical of transcendental arguments?

By being skeptical of whether X is really a necessary condition for (the possibility of) Y.

By being skeptical of whether Y is really true.

The argument is valid (the conclusions follow from the premises), so question whether it's sound (are the premises true?).

You can also be skeptical of whether any given argument someone presents is in the proper form. A small change could make the argument invalid and it could still sound compelling if you assume it's in a proper form.

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