I recently learned the the flap [ɾ] letter is part of both the /t/ and /d/ phonemes. A common example is writer /ˈraɪtər/ and rider /ˈraɪdər/. If they're both pronounced [raɪɾər], then shouldn't the two phonemic transcriptions be the same?
What is the language you transcribe? Assuming Standard (American or British) English, writer /ˈraɪtər/ and rider /ˈraɪdər/ are different and the transcription is correct.
When you do a phonetic transcription of some dialect (or even a phonemic one after determining the phonemes of that dialect) you'll use the flap [ɾ] letter.
Yes, the phonemic transcriptions should be the same. But they're not the same, so this is a problem for phonemic analysis. It has been much discussed. Generative phonologists give up phonemics entirely, other linguists have attempted to weaken the principles of phonemics somehow, to accommodate such difficult cases.
Update: So I asked my teacher, and he explained it well enough that I think I finally understand it (though correct me if I'm wrong :/).
Basically, he said that phonemes not only capture phonetics, but they also take into account root words and meaning. So while "writer" and "rider" both have the same phonetic transcription, this is only because the "-er" suffix and the flap rule cause neutralization. However, with the "-es" suffix we get "writes" [raɪts] and "rides" [raɪdz], which now have different transcriptions. This distinction comes from the difference in phoneme bases, "write" /raɪt/ and "ride" /raɪd/.
So I guess the idea is that phonemic transcription doesn't just look at phonetics, but also factors in similar words and root words (in both meaning and phonetics) to determine the phonemic breakdown.
In standard US English intervocalic /t/ merges with intervocalic /d/. "Writer" is thus pronounced identically with "rider". From a strictly US-English point of view there is no justification in distinguishing between the two at a phonological level. The OED writes: "Brit. /ˈrʌɪtə/, U.S. /ˈraɪdər/". Please note the slashes: this is phonology not phonetics.