Kolodruidtale: Arc of ??? (help!)

[Druidpeter]

I plan to draw a series of comics that are set in my own conworld, The Kölldrunn. Each of these comic series are titled according to a standard convention. Kolodruidtale: Arc of <PHRASE>. I have planned the following series (in chronological order, but not the order of publishing):

Kolodruidtale: Arc of Toad
Kolodruidtale: Arc of Ancients
Kolodruidtale: Arc of Conflict
Kolodruidtale: Arc of Agefall
Kolodruidtale: Arc of ""

As you can see, the last one isn't complete. This isn't because I don't know what to put. I know exactly what concept I want to encapsulate, but I can't seem to figure out an english word or phrase that does the trick. The meaning is:

The hypothetical definite logical consequence of a process which nonetheless by definition and acknowledgement has no logical termination point.

Basically, consider the case of an unstoppable force vs an immovable object. There's no logical resolution to that situation, right? But, much like the letter i is nonetheless the defined value of the square root of -1, mathematically speaking, the defined logical resolution can be defined to exist and be named as... what?

I don't even know if such a concept exists in the english lexicon, but I'm wondering if maybe we could bang our heads together to find out? Also, does such a concept have a word or phrase in any other languages, natural of constructed, that you guys know of?

Sorry for the trouble. I didn't know whether this would have been better in conlangery or linguistics subforum, so I just picked conlangery.

[akam chinjir]

Aporia? (Impasse?)

[Salmoneus]

There is no logical resolution to this antinomy, or to any antinomy. You could define one, as you say, but such a definition would be meaningless, and hence it would be an error to label such a term with any meaningfuly word. You may as well call it "blorb". "Blorb" is meaningless, but since blorb never arises in practice anyway, only in faulty reasoning, the uselessness of the word has no negative consequences, as you never need to use it.

You cannot call it an "impasse", for instance, because "impasse" is meaningful, and thus cannot correctly be used to describe something meaningless. In the case of the force and object, for example, "impasse" means a lack of movement, which only applies if the immovable object "wins" - if an force is irresistable, then by definition there can be no impasse.

One term that might be relevant, from the philosophy of antinomies, is "synthesis". An antinomy is said in Kant to consist of a thesis and an antithesis; in Fichte, thesis and antithesis resolve in "synthesis", and this idea becomes central in Marxist analysis of history (it's often said to be the foundation of Hegelian dialectic, but Hegel himself doesn't use those terms). This, however, is misleading, as the opposition of thesis and antithesis in Fichte and Marx is not truly antinomous - the thesis and antithesis aren't truly incompatible, but only appear so.

Another term that might be relevant is "dialetheia". A dialetheia is a proposition that is both true and false at the same time. Hypothesising dialetheias is one way to resolve an antinomy: the force both is and isn't irresistable, and the object both is and isn't moved. In classical logic, the existence of one dialetheia entails trivialism: if one proposition is both true and false, then all possible propositions are true. Hence, a dialetheist who does not want to be a trivialist must reject the principle of 'ex contradictione quodlibet' (i.e. "explosion"), and embrace paraconsistent logics.

However, it should be noted that dialetheias are only one way to resolve antinomies, and hence are in some sense an arbitrary resolution, not a purely logical one.

Along similar lines, ancient Buddhist logicians recognised either four or five truth values: only true, only false, true and false, and neither true nor false; with some adding a fifth state, not true and not false but also not neither true nor false. Some Jain logicians added a sixth, entirely and only true but also both true and false. I don't know the Sanskrit terms for these values, however.

Stepping back, there is of course the word "antinomy" itself. An antinomy is the opposition of two, independently undeniable yet mutually incompatible propositions.

More broadly, an antinomy is one type of paradox, a situation that appears to be impossible to assign truth values to within a specific logic. [some people use the two words as synonymous, but I think it's more helpful to specify antinomies as paradoxes arising from two independent chains of reasoning]

In the later Wittgenstein, antinomies (though he doesn't use the word) can frequently arise in language; their resolution is choice.

[Pedant]

...begging your pardon, but if you’re trying to get a sense of resolution without a resolution actually needed, why not go for the poetic version? Say, Arc of Silence? And then through the story you can show things getting quieter and quieter and eventually fading away completely, a demonstration that the story needs an ending but also really didn’t need a ending. So to speak.

[Druidpeter]

Salmoneus, yes it is a difficult situation. I'm surprised that non binary logical systems existed outside of the normal True/False dichotomy. Having said that, I'm specifically interested in if there is a term that describes the process of finding an explicit resolution of an antimony. Basically the literary analogue to the mathematical term of "Analytical Continuation". Analytical continuation basically operates by extending mathematical processes outside of their owned defined realms to produce valid results.

Granted, this is a stretch. If I can find such a term, I would greatly wish to use that term specifically. I'm not too worried about the actual process of solving antinomies, in particular or in general.

@Pedant, That's actually an interesting idea. If all else fails, I just might go with that, actually. So, the way the story is set up, I actually do have an explicit resolution of a narrative antinomy. If we were to use the unstoppable force/immovable object dichotomy, then the result is that the clash of forces causes a change in the underlying supportive environment, which is responsible in the first place for the immovable/unstoppable properties of the two forces in the first place. The result creates a paradigm shift that *does* actually reach a logical, definite conclusion, lol.

Hmm... so, if there is no english term for the concept I suggest, does that mean I'm allowed to coin one? Right here and now? Hmm...

I think I'll take the the Ukrainian root of the word 'Consume': Spozhyvate, and convert it to a prefix: Sipog, and then tack it onto Antinome:

Sipogantinum.

All right. What do you guys think? Any orthographic suggestions?

[Ares Land]

The hypothetical definite logical consequence of a process which nonetheless by definition and acknowledgement has no logical termination point.

I don't even know if such a concept exists in the english lexicon, but I'm wondering if maybe we could bang our heads together to find out?

Sure, there is. It's called 'Brexit'.

(Sorry, sorry. I'll show myself out).

[Druidpeter]

lol. No worries, Ars Lande. I think I'll be going with "Arc of Silence". Thanks for your help, everyone!