Is the following correct:
Dispositions make implicit reference to environmental triggers; habits do not.
I suspect that it is, but the latter clause is not a complete sentence, hence my doubts. I thought about using a comma, but then I would surely need a conjunctive (e.g. "whereas")
Yes, the semicolon is perfectly acceptable in your example sentence, and yields a complete thought (in abbreviated form) that can't easily be misunderstood. The full sense of the example sentence is
Dispositions make implicit reference to environmental triggers; habits do not [make implicit reference to environmental triggers].
One of the nice things that semicolons can do in their role as signaling punctuation is to indicate the primary split in a parallel construction, which then permits the author to omit some components of the parallel construction without loss of coherence. Your example is one such instance: The semicolon helps to indicate that "Dispositions make" is in parallel with "habits do not [make]" and that both branches of the parallel construction carry the phrase "implicit reference to environmental triggers" as the explicit or implicit object of the explicit or implicit verb make.
As another example, you might say
Cleveland won three games this week; Detroit, two.
instead of the longer-winded
Cleveland won three games this week; Detroit won two games this week.
Here, the implicit parallel is between "Cleveland won X games this week" and "Detroit won Y games this week." The semicolon lets us reduce the second half of the parallel to its most barebones details—namely, the ways in which the second parallel idea differs from the first, which are in the name of the city ("Detroit," versus "Cleveland") and in the number of games won ("two" versus "three"). Note that in this case a semicolon makes clear what is going on, whereas (in my opinion) a simple comma before Detroit doesn't do the job nearly as effectively:
Cleveland won three games this week, Detroit, two.
Much commentary on this site is dedicated to vindicating the notion that punctuation issues are not grammatical issues. To me, how you characterize the effects that punctuation can have on the clarity and sense of written language—whether grammatical, syntactical, or merely visual—is far less important than that you acknowledge those effects on coherence, which can be profound.
