Chapter 4 sketches how the contribution of ordinary language philosophers like Ryle, Kenny and Vendler to linguistic semantics has added to persistent terminological confusion. Their delivery of the Aristotelian legacy to linguistics consists of a sort of naive physical ontology at the cost of the principle of compositionality. The misleading translation of Greek verb forms occurring in the crucial passus of Metaphysics 1048b into the English Progressive Form will be argued to have been decisive for what natural (language) philosophy handed to linguists: an outdated vision on motion. The chapter also sketches the heavy work of a verb in taking all sorts of different arguments and argues that features are insufficient for the semantics of tense and aspect: they should be used as abbreviatory and for convenience only.

Chapter 8 focusses on the nature of the second binary opposition, the one between SYN and POST. In view of the fact that POST can be argued to be modal, the leading idea is that the opposition can be understood in terms of a strict opposition between realis (indicative) and different forms of irrealis (subjunctive, conjunctive, etc). The chapter culminates in reaching S’ at the end of the journey from the tenseless bottom of phrase structure to the tensed top S’ including all the distinctions made on the way between the different factors summarized at the end of Chapter 5. This makes it possible to see binary tense structure as expressing tense, mood and aspect in a systematic compositional way.

Chapter 7 presents a theory of the Progressive Form in which the PROG-operator is broken up into BE and -ING. This makes it impossible to maintain the central position attributed to the Progressive in the analysis of imperfectivity. The situation turns out to be more complex but can be accounted for compositionally by giving -ing its own semantic value. The chapter also shows how the binary approach to compositionality bridges the gap between the analysis of Slavic and non-Slavic aspect. It formalizes an aspectual theory which accounts for a wide variety of Slavic languages. It continues by focussing on the position of the aorist in rich tense systems where it has to survive marginally or where it has obtained an important position. A comparison is made with aoristic tense forms in systems that are (re-)organized binarily such as French. That opens the way for a deeper insight in the semantics of tense forms in languages where the aorist does not or no longer appears.

Chapter 2 corrects the tendency to let any serious theory of tense start in 1947 with the publication of Reichenbach (1947). It is absolutely necessary to connect the current theory of tense with classical grammar in order to take into account the aorist or its current descendants. This leads to a discussion of different ternarily organized tense systems as part of a closer inspection of notions like point, interval, fleeting ??, landmark, etc. This prepares the way for showing which sort of role they have in a binary approach. The chapter also gives a sketch of the so-called present perfect puzzle preparing for a solution in Chapter 6.

Chapter 3 presents an updated version of the tense system of Verkuyl (2008) organized on the basis of the three binary oppositions. The update is needed in view of a number of improvements – substantively and notationally – due to later work. The main ingredient of this chapter is the strict distinction between the notion of present domain and the notion of the fleeting point ??, which has a counterpart in the distinction between past domain and then-fleeting point ??’. The parallelism in a binary tense system is argued to be a dominant force in its organization.

Chapter 1 identifies three lines of research that stand in the way of compositionality and sketches the Babylonian confusion of terms that are in use for dealing with tense and aspect. In this way, it prepares for a central theme: how to deal with the persistent unclarity about the opposition between perfect(-ive) vs imperfect(-ive). A strict compositional approach aims at unravelling this tangle.

Chapter 6 aims at accounting for modification by temporal adverbials. The binary approach allows them to operate on different levels of tense structure above S_0. Crucial is the new insight that the relation between modifier A and modified B is not to be expressed as location of A in B but rather as the intersection of A and B. This insight and the flexibility of (deictic) adverbial modification offers the possibility of presenting a structural solution to the Present Perfect puzzle. It also sheds light on the nature of the in/for-test: it explains why terminative sentences with a for-adverbial introduced at a higher level may be regarded as well-formed as opposed to those which require a token interpretation.

Chapter 5 describes how all verbs are anchored in the system of positive real numbers R+ by focussing on the meaning of a verb without taking into account its arguments. This makes it possible to distinguish stative from non-stative verbs by assigning to each of them a (mathematical) function determining the value of the eventuality argument ?? of the verb. The next step is then to separate non-stative verbs expressing continuity in R+ from verbs expressing discreteness in N by assigning to the latter a discretizing function mapping from R+ to N. A formal account of aspectual composition from the tenseless bottom to the tensed top S’makes it possible to distinguish the (ten) factors that are in play on different levels of phrase structure.