There is currently no general definition of logical constanthood with which all philosophers of logic agree. In this paper, we address this issue by putting forward a proposal regarding the distinctive feature of logical constants. Our background position is that by focusing too much on structural features, we have forgotten central aspects of the original motivation that gave rise to the modern study of logic along Fregean/Peircian lines. On the basis of this realization, we argue that a logical constant has to be seen as encoding some kind of dynamic meaning, which marks the presence of an inferential transition among propositional contents. Following a pragmatist rationale, according to which some notion can be identified as a logical constant by considering the way in which it is used in our everyday reasoning practices, we put forth a characterization of logical constants that takes into account their syntactic, semantic and pragmatic roles. What follows from our proposal is that logical constanthood can be best understood as a functional property that is satisfied only by certain uses of the natural-language counterparts of the conditional, negation, disjunction and the compound of conditional-plus-quantifiers. After briefly discussing these cases, we turn to conjunction in order to show why it needs to be excluded from our set of genuine logical constants.