Are [ə] and [ʌ] different phonemes in American English?

[Хahar 🤔]

As I understand it, [ə] only exists in unstressed syllables while [ʌ] only exists in stressed syllables, which would mean that there are no minimal pairs. In my own speech, I can't distinguish between the two.

[homelycooking]

I don't think so. Is there a difference in other languages?

[ilikeverin]

I don't think so. Is there a difference in other languages?

It's a difference in other varieties of English, actually.  One of my phonetics/phonology profs in undergrad was a native speaker of Indian English, and he had some minimal pairs (or near-minimal pairs).  He tried to convince me that they were phonetically distinguishable, but I couldn't hear the difference at all.  Not just the way I can't hear the difference between [ɑ] and [ɔ], where I feel like I can hear a phonetic difference but it's completely uninformative to my grammar, but, like, I just couldn't hear anything.  I think it's still maintained in other Englishes, too.

So, sorry, Xahar, you just have to memorize that [ʌ] happens in stressed syllables and [ə] in unstressed ones!  At least your prof isn't penalizing you for not distinguishing /ɑ/ and /ɔ/

[Хahar 🤔]

What were these minimal pairs? Also, is /ʌ/ as rare as Wikipedia says it is? I certainly can't think offhand of many languages in which it exists.

[Linus Van Pelt]

If [ʌ] does not appear unstressed, what is the second syllable of "backup"? Do you not distinguish this from the second syllable of "ketchup"?

[muon2]

If [ʌ] does not appear unstressed, what is the second syllable of "backup"? Do you not distinguish this from the second syllable of "ketchup"?

My dictionary lists "backup" as having a secondary stress on the second syllable, which it does not for "ketchup".

[Хahar 🤔]

I assume secondary stress is assigned to the second syllable precisely because [ʌ] appears in that position.

[Oakvale]

It's so weird that this forum has a sizeable contingent of linguistics enthusiasts as well as the predictable map nerds.

[ilikeverin]

It's so weird that this forum has a sizeable contingent of linguistics enthusiasts as well as the predictable map nerds.

I think we're just particularly talkative.  I wonder why linguists like talking

[Хahar 🤔]

If secondary stress is determined by the presence of [ʌ], then I suppose it would be tautological to say that it only appears in stressed syllables.

[minionofmidas]

It's so weird that this forum has a sizeable contingent of linguistics enthusiasts as well as the predictable map nerds.

I think there is a certain degree of crossover appeal.

My dictionary lists "backup" as having a secondary stress on the second syllable, which it does not for "ketchup".

Yes, that's immediately obvious to my ear. (Though German speakers would put a similar secondary stress on the second syllable of ketchup.) What's less obvious is that that makes the sound in "ketchup" not an [ʌ].

(deeks around)
Ah, indeed wiktionary offers [ʌ] and [ə] as both valid for ketchup. [ə] basically is just what a lot of vowel sounds collapse to when they're utterly devoid of stress.