prof,
Still, I hope you just used this as an example and that your hearing at 14 000 Hz is as sharp as a knife.
"...I can not reliably detect tones above, say, 14 kHz. This suggests my claim to be able to hear up to 20 kHz is false."I am not sure if this is the case, or it is an example you made for the discussion. In any case, you could have a dip at around 14 000 Hz and then hear 16 000, for example. It is a relatively well-known occurence but the name escapes me now. Not being able to hear 14 000 Hz at your age may suggest, but does not come even close to confirming, that you will not hear something above it.
Still, I hope you just used this as an example and that your hearing at 14 000 Hz is as sharp as a knife.