The τὰ in τὰ μὲν...

… ἤλεγχον τὴν κύκλῳ πᾶσαν χώραν τίς ἑκάστη εἴη. οἱ δὲ ἔλεγον ὅτι τὰ μὲν πρὸς μεσημβρίαν … ἡ δὲ πρὸς ἕω … (Xenophon Anabasis 3.5.14-15; μέν does not appear in some editions)

Translations I have seen include: “the region to the south” (Brownson), “the parts toward the south” (Anthon), and “the areas to the south” (Huitink and Rood). Is τά the article for an omitted neuter plural noun such as χωρία (which Boise [an old commentary] says should be supplied, and which Liddell and Scott say could mean “places” or “a district”)? Or is it a more indefinite demonstrative pronoun meaning “those non-person things” for which the reader would be expected to understand, based on the question that was asked in the preceding bit of text, that some notion of “region/parts/areas” is indicated even if there is no corresponding neuter plural noun that could be supplied for it. But if it is the latter, why is ἡ used (and all the commentaries say ὁδὸς is to be supplied) instead of τό in the δέ part of this μέν … δέ construction? Wouldn’t τό be enough to indicate “road” in the same way that τά is enough to indicate “region/parts/areas”?

Or how about this one:

ἐπειδὴ δὲ καὶ τοῦτο συμφαῖεν, οὐκοῦν ἐν ταῖς πρὸς μεσημβρίαν βλεπούσαις οἰκίαις τοῦ μὲν χειμῶνος ὁ ἥλιος εἰς τὰς παστάδας ὑπολάμπει, τοῦ δὲ θέρους ὑπὲρ ἡμῶν αὐτῶν καὶ τῶν στεγῶν πορευόμενος σκιὰν παρέχει. οὐκοῦν, εἴ γε καλῶς ἔχει ταῦτα οὕτω γίγνεσθαι, οἰκοδομεῖν δεῖ ὑψηλότερα μὲν τὰ πρὸς μεσημβρίαν … (Xenophon Memorabilia 3.8.9)

I have seen “wall”, “side”, and “parts” supplied in translations. Does τά indicate a particular neuter plural noun, or just the indefinite “those non-person things” for which we understand that some notion of the wall/side/part of the house is indicated even if there is no neuter plural noun that can be supplied for it?

In the Anabasis passage, τὰ μὲν πρὸς μεσημβρίαν …, ἡ δέ, the τά doesn’t indicate any particular neuter plural noun, though here the reader would automatically assume something like χωρια. τά is often used in this general sort of way, with an adjective or an adverbial phrase as here. With ἡ δέ we naturally understand οδος,

Similarly in the Memorabilia passage, τὰ πρὸς μεσημβρίαν. (The μέν doesn’t come into it.)