What case can be made for considering whether [ə] and [ʌ] are different phonemes or not in American English? Please note the focus is on standard American English. EDIT: i.e.: on General American.
Many dictionaries use /ʌ/ in stressed position and /ə/ in unstressed positions. So we get transcriptions such as:
However, if these truly constitute two different phonemes, then we should be able to come up with minimal pairs to illustrate the contrast between both sounds.
I cannot think of a single minimal pair to contrast /ə/ and /ʌ/.
It's interesting to look at CMU Dictionary, the pronouncing dictionary of American English.
CMU Dictionary uses
AH for both sounds. So we get:
D AH1 S T
L AH1 V
B AE1 K AH2 P
K EH1 CH AH0 P
K AH1 S T AH0 M
(0 = unstressed, 1 = primary stress, 2 = secondary stress)
My understanding is that, provided the stressed syllables are pronounced longer and with more energy, saying BACKUP, KETCHUP and CUSTOM as
[ˈkəs·təm] would not hinder comprehension in the least.
As I see it, there's only one phoneme here, which happens to be realized [ʌ] in stressed position and as a schwa [ə] in unstressed positions.
This leaves us with two problems:
Problem 1 : if /ə/ and /ʌ/ are different phonemes, what are some examples of minimal pairs between the two?
Problem 2 : if they are allophones, which notation should be used for the phoneme? I assume /ə/.
The reason I'm asking is because I'm teaching American English with a lot of phonemic transcriptions – why teach two phonemes when there's only one.
Finally, where would professional linguists locate those sounds on the following chart (again, from an American point of view)?
EDIT (DEC 2018): FYI, I was asking the question in the context of designing an IPA chart for American English (General American), to teach phonetics and ESL, which implies deciding just which phones to teach -- and why.