Let every imperative I have a counterpart why-form, i.e., "Do X," has, "Why do X?" Let "ask why" be some I. Then there should be, "Why ask why?" for this.

But if you then fold this question into itself, you get, "Why ask 'why ask why?'" Question: is it possible for there to be a meaningful infinite folding of this question into itself, i.e. is the question, "Why ask 'why ask 'why ask...''?" a meaningful question?

Bonus subquestion: let the cardinality of an infinite why-structure vary over arbitrarily many possible cardinalities. Supposing any are meaningful, is there a limit to which are? For example, countably many why's might be meaningful, but uncountably many might not.

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    "Meaningful" how? You can define an infinitary language that allows this sort of thing, countable or not, but what's the point? – Conifold Feb 28 at 0:24
  • I'm not sure how it would be meaningful outside of itself, so to say, as if the only action that could be justified by answers to such an erotetic structure would be the very act of constructing this structure in the first place? EDIT: or how would an answer to such a question exist? – Kristian Berry Feb 28 at 1:06
  • Seems like it just alludes to humans forming thoughts in a recursive process. – TheLoneDeranger Feb 28 at 2:04
  • My deeper curiosity regards the possibility of deontic cardinals, if they're a legitimate concept of large cardinals. Let D be the smallest of these, then iterate why-ask-why D-many times. Let us say the Dth iterate of a deontic structure is "transperfect." Does the I action corresponding to the D-long WAW-structure amount to, "Be transperfect," or something like that? Maybe, "Make X transperfect," where X is... Idk...? So "Why ask why be transperfect?" But then is transperfection itself the reason why? (Is this some weird analytic truth?) – Kristian Berry Feb 28 at 22:57

In order to answer questions like this, it becomes necessary to get at the essence of "why". To do this we need to look at what role these questions play in the mind. We consider the mind as an agent seeking to achieve certain goals.

When the agent asks "why should I do X?" he is asking for a justification - this would be a persuasive argument of some kind - that shows how X helps to achieve the agent's implicit goals. If the agent hears this argument and is persuaded, the agent will then agree to do X. For example, if the agent wants food as an implicit goal, and then hears an argument about how there are noodles in the fridge, the agent will be persuaded to open the fridge. Why open the fridge? To obtain food.

So what does it mean when the agent wonders, "Why ask why?" In this case he is asking for a justification - a persuasive argument of some kind - that shows how asking "why do X?" helps to achieve the agent's implicit goals. The answer is that asking "why do X?" is the first step to working out a justification for X. And a justification of X helps the agent to decide whether X is useful to achieve the agent's implicit goals. To recap, the agent asks why, in order to obtain justifications, which are useful for deciding on better actions to achieve the agent's goals.

What does it mean when the agent asks, "why ask 'why ask why'?" In this case the agent is uncertain about the benefit of asking "why ask why," and seeks a justification for that action. The justification would be, asking "why ask why?" helps the agent to understand the value of asking "why," so that the agent will do so more often in the future. As above, that in turn will help the agent to obtain justifications for actions, which help the agent to decide on better actions to achieve the agent's implicit goals.

Next we may consider the agent's question, "why ask 'why ask "why ask why"'?" Well, as before:

  • To find a justification for "why ask 'why ask why'?" because this justification helps the agent to decide whether to ask "why ask 'why ask why'?"
  • Specifically, the justification for "why ask 'why ask why'?" is the one in the previous paragraph.

We can keep iterating as long as we wish. However, what we would find is that as the iterations increase, the question "Why ask 'Why ask "Why ask ... "'" becomes less and less useful to the agent's implicit goals. So the answers start to become more in the line of "don't bother" than in any rational justification, because there is no valid justification, because these recursive questions are not useful to the agent's goals.

  • This is a good answer, though sadly it seems to imply that an infinite WAW-structure would be infinitely useless? I'm too obsessed with infinity to give up that easily 🤣 although this is nothing against your argument! – Kristian Berry Feb 28 at 23:01

We discussed Why does Man ask Why questions?

Following that, I 'why?' has this feature moving 'up' or 'out' of the layer of explanation. And that from an anti-foundationalist stance, we find these explanations eventually looping, or at least leaning on each other - like say Deutsche's 4 methodoligies in The Fabric Of Reality. Hofstadter finds specifically tangled hierarchies of knowledge, with looping and self-reference, to be characteristic of minds or subjectivities.

So, I would say the recursions are useful up to a point. Everyone asks why. Philosophers ask why we ask why. Meta-philosophy and meta-mathematics go more abstract still.

We can also invert the procedure:

"The whole problem of justifying nature, of trying to make life mean something in terms of its future, disappears utterly. Obviously, it all exists for this moment. It is a dance, and when you are dancing you are not intent on getting somewhere… The meaning and purpose of dancing is the dance." - Alan Watts

But in considering infinite steps, I would look at another recursion: Who watches the watchmen? We have a structure of scrutiny, within structures, and between them. We have circles of accountability, like say division of powers. And we can go inward, impulse control, superego. But the conceptual 'watches' starts to fray, and transform, as the domain alters. Does your superego 'watch' you? Do judges 'watch', their power is more a backstop, a failsafe. And isn't it, the people, and the social contract, that is the real 'watcher' of the executive?

I'd say around where we ask, why we ask why we ask why we ask why, you have a complex enough hierarchy to start tangling it, creating structures of internal consistency, and the 'weave' of different modes working together, where we judge 'how well things hang together', rather than say foundations and steps. Because the loops can recur infinitely without going anywhere - more than on the horns of Munchausen's trident, instead in our own strange-loop satisfaction with understanding our place in our cosmos.

Edited to add:

I was just reading: In physics, the fourth, fifth and sixth derivatives of position are defined as derivatives of the position vector with respect to time – with the first, second, and third derivatives being velocity, acceleration, and jerk. Although rarely used, the next differentials are snap, crackle, and pop. Spacestations set limits on jerk and snap. I feel there is an analogy to be drawn to the linguistic effect of applying why to why, with kind of taking a derivative.

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