Phonemes and the biuniqueness

[ˈd̪ʲɛ.gɔ kɾuˑl̪]

I understand labelling /t/ and /d/ when they're flapped as a one archiphoneme and thus creating a while bunch of new phonemic vowels.
I also understand labelling all three English nasals as |N| when it's clear which one comes in certain positions. (Both of these are on the Wikipedia, Phoneme, Neutralization and archiphonemes.) But, as always, I had to start thinking and I realised this article didn't explain things like a chain shift in certain positions, my example will be Danish:
In the simplest cases, when orthography strictly corresponds to the pronunciation, word-initial /t/ and /d/ give [ts] and [t], whereas word-finally they give [t] and [ð], respectively.
In this case, what should we do? Keep the biuniqueness and assign two different graphemes to one phoneme? If so, should we assign the two left sounds to two different phonemes or to just one and be amazed how /t/ and /d/ alternate with each other? Or maybe should we distribute one phone ([t]) between two phonemes and stick to the orthography and tradition?
What do you think? I've kinda given up with this, I can't choose. Also, if it looks rude or like an emotional outburst (I have a feeling it can), it ought not to. So, let the discussion begin .

[zompist]

That's a neat example. What happens to these phonemes intervocalically?

I think phonemes are abstractions and the symbol we choose is arbitrary. That is, there's no fact of the matter whether your /t/ "is really" a /t/. I think the choice often comes down to matters of taste and convenience. Ideally, I think, you'd choose the simplest symbol which suggests the widest range of allophones. So /x/ or /&/ would be bad choices.

If I remember Lass, some phonologists would be bothered by [t] showing up as the realization of two different phonemes. I don't get why that would be a problem. But it's fine if it makes us ask questions. E.g., is there any reason we can't assign [#t] and [#t] to one phoneme, [ts] and [ð#] to another, contrary to the orthography? (I wouldn't be surprised if there is, if you play around with the morphology.)

[Travis B.]

I disagree with the notion that two different phones cannot belong to the same phoneme. Take, for instance, the English here - what are conventionally considered as /t d/ realize as [ɾ] or are elided intervocalically, but are distinguished by preceding vowel length there. So does the dialect here have phonemic vowel length? You can say sure, but this gets problematic when one considers that final /t d/ also realize as [ɾ] or are elided, distinguished by preceding vowel length, when followed by a word beginning with a vowel! But if /t d/ cannot be realized as the same phone, how does one handle this case? Posit that every word ending in /t/ or /d/ have a separate allomorph for when the next word begins with a vowel? But the problem is that this is completely regular, and allomorphy is rarely regular (because if it were, it would not be allomorphy). Also, this has the problem that one must introduce a complete new factor to the entire phonology, phonemic vowel length, to handle a small set of corner cases (namely intervocalic /t d n nt nd v ð b/ where they may be neutralized or elided), where the rest of the phonology does not behave like vowel length is phonemic (specifically because vowel length is clearly allophonic in final syllables of words and morphemes which do not contain an obstruent in their codas - chalking this up to allomorphy requires systematic, and suspiciously regular, allomorphy).

[ˈd̪ʲɛ.gɔ kɾuˑl̪]

@Travis Well, for this regular allomorphy we have a term sandhi which you should know, I think.
The very abstract version of what question I asked is:
In position 1 we have sounds [a] and , in 2 (being derived from 1) we have and [c], all [a], and [c] are similar phonetically (to prevent situations like with [h] and [ŋ] which could be analysed as one phoneme), [a] is more similar to than to [c] and [c] is more similar to . In this situation should we analyse it as chain mutation /a/>/b/>/c/, mutual mutation /a~c/ <>/b/ or break the biuniqueness and why (@zompist)?

[Travis B.]

I really see no reason why phonemes should not be able to have overlapping realizations myself, and the idea that they cannot seems to be some silly idea that some phonologists have come up with that may very well result in more complex analyses than otherwise (e.g., as mentioned, forcing turning things that would normally be allophony into allomorphy).

[Travis B.]

@Travis Well, for this regular allomorphy we have a term sandhi which you should know, I think.

Normally sandhi is allophony, not allomorphy, and the thing about allomorphy is that it normally is not regular at all, but rather is lexicalized.

[Chuma]

That's a neat example. What happens to these phonemes intervocalically?

The realisations are for syllable onset and coda, keeping their pronunciations in compounds and derivations. As for -VCV- in roots, in the examples I can think of, they seem to stick with the most stressed vowel.

is there any reason we can't assign [#t] and [#t] to one phoneme, [ts] and [ð#] to another, contrary to the orthography? (I wouldn't be surprised if there is, if you play around with the morphology.)

I'd be quite surprised if there isn't.