The Specific Problem

I saw this question a couple days ago and started writing an answer, but didn't finish. When I came back to it, I reloaded the page to check if anyone else had answered and found that the question had been put on hold for being unclear. While the question is worded somewhat confusingly, I believe that understand what the OP intended to say.

The OP ostensibly describes a first-order theory of propositional logic with an additional relation "explains," written "$E$," which I would assume they have defined elsewhere. The mention of Platonism and propositions being "objects" are not strictly relevant, and likely have more to do with the context or motivation for the question than the details of the question itself. This does not affect the answer.

My Understanding

The OP presents two issues:

1) how can a particular natural-language expression (marked 2. in the original post) be converted to a symbolic expression in the language of their theory?

2) which statements cannot be converted to such an expression, and are there stronger logics in which such statements could be expressed?

For the first of these, the OP states:

...consider this statement:

  1. For any propositions x and y, if x explains y, then for any proposition z if z is true then x conjoined with z explains y.

It appears,..., we can't translate this into FOL. (sic)

The confusion seems to stem from an assumption that the statement is not expressible in FOL. This is not the case, the statement can be written as follows$^*$:

$$\forall x.\forall y.x E y\implies[\forall z.z\implies (x\land z) Ey]$$

or, using the OP's "is true" predicate:

$$\forall x.\forall y.T(x E y)\implies[\forall z.T(z)\implies T((x\land z) Ey)]$$

For the second point, the OP seems to be asking for a quick explanation of higher-order logics.

I could be wrong about my interpretation of the question, but as far as I can tell, this is what the OP meant. Assuming that my understanding of the question is correct, what should I do about it?

The General Problem

Not every question is going to be worded perfectly. SE users are human, and humans are notoriously error-prone. Maybe I'm mistaken, but it seems that some questions get closed for being unclear when in actuality they're just stated in an unconventional manner. This is especially true when the question mixes vernacular and technical language or the poster mistakingly uses one term in place of another - something which the muggles among us are especially prone to. While I don't understand every question that I come across, there are times [I hope] when I can get the 'gist' of what a user is saying and provide an appropriate response, even if the question isn't ideal.

What should I do when I think that I understand and/or have an answer to an on-hold or closed - and, more specifically, "unclear" - question?

$^*$ the use of the logical conjunction is based on the use of the word "conjoin." "conjunction" is a deverbal noun with the same root as "conjoin." The word "conjoin" corresponds to the verbal form of the root "conjungo" ("conjunctio" $\to$ "conjunction" : "conjungo" + "tio" $\to$ "conjoin" + "tion"). In context, "$x$ conjoined with $z$" most likely means "the conjunction of $x$ and $z$," referring to logical conjunction. Why the OP would use "conjoined with" instead of "and," we may never know.

  • $\begingroup$ FYI, the post you linked to currently has one delete vote. I believe it will only take $3$ votes, but possibly $4$ due to the upvote (I don't recall the exact rules off hand), to delete it. If you wish to try to edit the question to improve it, as suggested in quid's answer (and I agree with the suggestion as well), so it may get reopened & you can then answer it, you should make the edit fairly soon before the post might be deleted. $\endgroup$ – John Omielan Aug 28 at 3:29
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    $\begingroup$ As you've expressed your understanding of the Question, there seem to be two quite broad problems to answer. I'd try to encourage the OP to narrow the Question rather than to try and tackle it in its current form. In particular, is it clear to you that the OP knows about second-order logic as a "conventional" means of quantifying over propositions? $\endgroup$ – hardmath Aug 28 at 15:10
  • $\begingroup$ @hardmath The OP asked about propositions, not predicates, although they might be confusing the two. Quantification over propositions is possible in FOL, since this is the same as quantifying over the set truth values, but quantifying over predicates is not. I do not think that the OP knows about second order logic. $\endgroup$ – R. Burton Aug 28 at 16:54
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    $\begingroup$ Propositions are nullary predicates, so I think that second order logic should at least form a background topic if you want to repost the Question (and I would have sought the stated clarification from the OP before attempting an Answer). $\endgroup$ – hardmath Aug 28 at 17:43
  • $\begingroup$ get it out of a holding pattern ? $\endgroup$ – Roddy MacPhee Aug 30 at 12:56

You ask:

What should I do when I think that I understand and/or have an answer to an on-hold or closed - and, more specifically, "unclear" - question?

You should help to make the question more clear, so that it can be reopened.

To do so you can propose changes and improvements in comments. You can even propose edits directly. For larger changes this is not ideal though, as you might inadvertently change the authors intent. Moreover, as a user that does not yet have the edit-privilege, you might have a hard time to get a major edit through the suggested-edit review.

Once the question is improved, it should be reopened. Edits put the question in a review queue towards reopening. If this does not work out directly, you can post to this thread Requests for Reopen & Undeletion Votes (volume 07/2018 - today)

If the above process fails, for example, the original poster might be unresponsive, you could then resort to posting your own version of the question and self-answer it.

Also see this recent meta-question which is quite similar Wrongly closed question needs a better answer.

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    $\begingroup$ +1 for "posting your own version..." this works and adds value to the website. Even if one doesn't have the answer but can post a newer improved version of the question, that's fine. $\endgroup$ – Paramanand Singh Aug 28 at 1:27

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