Semantic dispositionalism is roughly the view that meaning a certain thing by a word, or possessing a certain concept, consists in being disposed to do something, e.g., infer a certain way. Its main problem is that it seems to have so many and disparate exceptions. People may fail to infer as required due to a lack of logical acumen, inattention, intoxication, confusion, deviant philosophical theories or logics, neural malfunctioning, and so on. I present a theory which states possession conditions of concepts that are counterfactuals, rather than disposition attributions, but which is otherwise similar to inferentialist versions of dispositionalism. I argue that it can handle all the exceptions discussed in the literature without recourse to ceteris paribus clauses. Psychological exceptions are handled by qualifying the possess condition in accordance with counterfactuals roughly of the form, “If x would consider making the inference and has no reason against doing so, x would make the inference”, and by requiring suitably undemanding requirements (unlike that of giving the sum of any two numbers). The non-psychological exceptions, i.e., cases of neural malfunctioning, are handled by requiring that the counterfactuals be true sufficiently often during a relevant interval. I clarify this condition and argue that it accommodates some important intuitions about concept possession. Particularly, it captures a dimension along which concept possession is intuitively vague.