In this dissertation, I provide a syntax and a semantics for the unbound additives myös and myöskään as well as the bound additives –kin and –kAAn in Finnish. While both types of additives may be used to express plain vanilla additivity, the bound type also allows for a number of distinct uses that are not available for the unbound type. I argue that this difference in distribution is rooted in the involvement of three operators with distinct semantic properties: ADD (unbound forms), BADD (bound forms), and CADD (bound forms). Specifically, the division between unbound and bound additives is partly explained by if we assume that BADD is type-flexible in terms of arguments, source-flexible in terms of antecedents, and does not encode a distinctness requirement, and partly by assuming that CADD corresponds to a quantificational closure operator with (mostly) a truth-conditional effect on the semantics of its prejacent. In contrast, the second major division – between –kin and myös on the one hand, and –kAAn and myöskään on the other – is proposed to be syntactic in nature. Instead of relying on sentence polarity, I argue for an analysis in terms of a topicality feature. This analysis makes better predictions for scope not only for –kAAn and myöskään (which are traditionally argued to be polarity-sensitive), but also for –kin, when the whole distribution is taken into account. The meaning contributed by the four Finnish additives is analysed as a speaker presupposition in this dissertation. I propose that the relevant presupposition is a metaproposition about the context: it states that there is – in some part of the context – an antecedent, and the form of that antecedent is determined the focus semantic value of the prejacent, as in Alternative Semantics. I argue that this analysis represents the right kind of compromise between existential an anaphoric approaches to additivity, and that it accounts for the presuppositional part of the distribution of Finnish additives in a natural way.