This past evening, your host received a call from Oh Brother SC, requesting that he settle a dispute between OBSC and a friend. The question was whether "diminished" contained three syllables, or four.
Now, the cheap and easy answer would be "go check a dictionary" (you can do so here). But it wasn't clear that a dictionary was close at hand, and so SC was forced to try to explain how we count syllables to two people who both have bachelor's degrees from upper-tier American universities. Shades of Mark Liberman's concern that linguistic education for nonlinguists is woeful.
It was probably, on reflection, a mistake to try to explain syllable weight, or the notion of moras. Ditto for onsets, nuclei and codas (if you want definitions of these, or any other linguistic terminology, this is an excellent, albeit slightly dated, resource). Fortunately, your host was able to communicate the essential idea that there were three vowels about which the rest of the phonological material syllabified, and that there weren't any syllabic consonants to mess things up.
Or so he thought. Immediately after going through all that, OBSC's friend piped up, "But there are four vowels in the word!". It turns out that it's rather difficult to convince people -- at least on short notice -- that there isn't necessarily a 1:1 correspondence between sound and spelling, even though they may recognize in the abstract that English spelling isn't phonetic. Although the discussion ended with a consensus that there were in fact only three syllables in "diminished", the reasoning was more of a deferral to authority -- "you've got the master's" (or, from another perspective, "I have the power!") -- than an intellectual breakthrough.