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This question is based on the discussion arising from ["Unsolvable
Problem"](https://japanese.stackexchange.com/questions/2303/unsolvable-
problem)

* * *

Start of Excerpt

* * *

Relevant discourse extracted from "Unsolvable Problem":

> Quoted from Derek Schaab's reply to "Unsolvable Problem":
>
> ○ （私は）この問題{もんだい}が解{と}けない。 [I] can't solve this problem.
>
> × この問題は解けられない。 This problem can't solve itself.
>

>> The second sentence might sound fine at first (from a grammatical
standpoint), but when you think about it, **assigning an ability to an
inanimate subject doesn't work here.** (Even in English, the better way to
express the idea behind sentence #2 is, "This problem **will not** solve
itself.")

>
> Because of this, only 解{と}けない問題 is correct.

* * *

Also from Derek Schaab's reply to "Unsolvable Problem":

> istrasci also mentioned the `～にくい` suffix. I was about to agree with this,
> but then I saw sawa's edit which reminded me that `解く` can be read as both
> **`と`**`く` and **`ほど`**`く`, and `解ける` can be read as both **`と`**`ける` and
> **`ほど`**`ける`. (The meanings differ between readings.) `～にくい` can be attached
> to both `ほどく` and `ほどける`, such as in this way:
>

>> ほどきにくいくつひも a shoelace that is difficult to untie

>>

>> ほどけにくいくつひも a shoelace that won't come undone easily

>
> …and to `とく`, but not to `とける`:
>

>> ○ ときにくい問題 a problem that's difficult to solve

>>

>> × とけにくい問題

* * *

End of Excerpt

* * *

**(Question 1)** Why is `ほどけにくい` acceptable while `とけにくい` unacceptable?
Following the logic of "I cannot assign ability to an inanimate subject", it
should cause both to be unacceptable since both are intransitive and by
extension force the existence of the "inanimate subject"

**(Question 2)** If it is true that there are cases for which
`Intransitive+にくい` are acceptable, does it imply that there are cases for
which `Intransitive+られる` (Potential form) are acceptable?

**(EXTRA Question 2.1)** If there are cases for which `Intransitive+られる`
(Potential form) are acceptable, how do we decide if we can assign
ability/potential to an inanimate subject?

* * *

**Appendix:** Other points taken from the comments in ["Unsolvable
Problem"](https://japanese.stackexchange.com/questions/2303/unsolvable-
problem) for your consideration

> From Derek Schaab:
>

>> Could it be related to whether the verb expresses a continuous or discrete
change? `～にくい`, when it means `なかなか～しない`, seems to imply that the verb may
happen only gradually over a period of time, but never quickly and easily.
Because of the gradual transition, a continuous-change verb (such as `ほどける` or
`燃{も}える`) is required. But `解{と}ける` expresses a discrete change: a problem is
either solved or it isn't, and the change from unsolved to solved takes place
instantly. Perhaps this is why `解{と}けにくい` sounds odd, but other combinations,
such as `溶{と}けにくい`, work.

>
> From Matt:
>

>> But you can say `割{わ}れにくい`, and that is instantaneous. Perhaps `〜eにくい` has
some sort of restriction relating to concrete vs abstract subjects?
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grammar conjugations potential-form morphology
Transitive/Intransitive + にくい (and +られる)
**1** When you're walking and your shoelaces come undone, they appear to do
that on their own. 靴ひもがほどける does not mean that someone unties them, but that
they "untie themselves". The meaning is closer to an intransitive active than
to a passive; therefore にくい is appropriate. On the other hand, 問題が解ける means
that the problem is solved by someone, not that it solves itself somehow; and
the way to say that it is hard for someone to solve it is 解き難い. Compare to
English: "this problem is difficult to be solved" is unnatural, and you would
say instead "this problem is difficult to solve".

**EDIT** : as Matt and Derek pointed out, examples like 割れ難い suggest that the
problem is not agency. Matt suggests, in the other thread, that the
distinction may have to do with concrete vs abstract subjects, but I think
this is unlikely, considering things like 言い難い (although maybe the reasoning
could be restricted to intransitive verbs).

I think agency still comes into play, but in a more subtle way, involving
purpose. Consider 割り難い and 割れ難い: it seems to me that the former is used when
you want to break something, eg この木が割り難いから大きい斧を使う, while the latter is more
likely to be used when you're concerned about the possibility of something
breaking, eg この皿が割れ難いから心配しないで (compare with この皿が割れやすいから気をつけて; please excuse
the silly examples).

Similarly, when we want to untie the shoelaces, but we have trouble with it,
we use ほどき難い; when we want them to stay tied, we use ほどけ難い. For problems, we
use 解き難い when we want to solve them; 解け難い is not used because it would be
strange to wish for a problem to stay unsolved (otherwise it wouldn't be
considered a problem in the first place).

Is this more convincing?

**2** Sure. For example, いられない, the potential form of the verb 居る, is quite
common.
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I will go in conjecture mode here, as I do not have the knowledge of the
validity in question.

> (Question 1) Why is ほどけにくい acceptable while とけにくい unacceptable?

I guess that it's related to the subject. A shoelace, in English too, gets
loose and unties itself. The shoelace can do the action of untying itself,
with ease or not, hence the (claimed) validity of ほどけにくい. However, the problem
cannot solve itself, it needs an external intervention, an external agent for
whom it will be hard. So, you couldn't say とけにくい since there is no notion of
ease for the problem itself which cannot do anything.

> Following the logic of "I cannot assign ability to an inanimate subject", it
> should cause both to be unacceptable since both are intransitive and by
> extension force the existence of the "inanimate subject"

I think that the shoelace is active as I tried to explain, and that it then
does not fit the "inanimate" constraint.

> (Question 2) If it is true that there are cases for which Intransitive+にくい
> are acceptable, does it imply that there are cases for which
> Intransitive+られる (Potential form) are acceptable?

I think that

  * as I just said, some intransitive+にくい are possible, and
  * sentences like ドアが開かれない are perfectly valid in contexts like "once locked, the door can't open itself."

> (EXTRA Question 2.1) If there are cases for which Intransitive+られる
> (Potential form) are acceptable, how do we decide if we can assign
> ability/potential to an inanimate subject?

Well, I think I gave a constructive proof of intransitive+rareru potential
form. I reckon you have to simply think about the meaning of the verb,
who/what does the action (or even wonder "is it an action?") and then, it
should be obvious if I'm right.
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