In this chapter we review the qualitative difference between explicit knowledge and implicit knowledge (underlying mental representation). The chapter focuses on whether instruction affects the latter. We review the accepted finding that instruction does not affect ordered development. We also review the issue of whether instruction affects rate of development and ultimate attainment. We review important variables in the research on instructed acquisition including type of knowledge measured, the nature of assessments used in the research, and short-term vs. long-term studies, among others.

Yes, the developers of contemporary classical logic had a utopian vision. Instead of trying to rehabilitate the festering logical mess that is natural language, they’d develop a new, logically pure, language – one that was free from all of the defects that make it so hard to track or model right reasoning using natural languages. If they succeeded, they’d have a language that would give them some hope of systematizing logic and clarifying our reasoning (instead of one that constantly bewitched them into philosophical confusions).

This chapter lays the foundation for how the field of second language acquisition arose. We briefly review the pioneering work in the late 1950s and 1960s in first language acquisition (e.g., Berko Gleason, Brown, Klima & Bellugi). We also review the generative revolution in linguistics and how it laid the groundwork for the idea of constrained language acquisition. We then review the seminal articles by S. Pit Corder (1967) and Larry Selinker (1972) that posited the major questions in second language acquisition, and end with the pioneering work that mirrored research in first language acquisition (e.g., Dulay & Burt, Krashen, Wode). We end the chapter with the major question that launched second language acquisition research in the early 1970s: Are L1 and L2 acquisition similar or different?

Descriptions like ‘the man’ and ‘a turkey’ seem so simple and foundational to the way we talk that it’s shocking that one can muster more than a few short paragraphs to elucidate their semantics. The more one thinks about how we use these structures in language, however, the more puzzling and intractable they become. Over a century ago, Bertrand Russell tried to set out a simple, elegant theory of descriptions. That should have been the end of it. But it was just the beginning.

This chapter defines what kind of input contains the data necessary for acquisition (communicatively embedded input) and focuses on its fundamental role in acquisition. Subsequently, we review the claims on the role of output and interaction, focusing on these major issues: Comprehensible output is necessary for acquisition; comprehensible output is beneficial for acquisition; comprehensible output does little to nothing for acquisition. We also discuss the nature of interaction more generally, focusing on whether interaction affects the acquisition of formal features of language.

The move from $\mathcal{P}\mathcal{L}$ to $\mathcal{Q}\mathcal{L}$ can seem like a significant ramping up in terms of the complexity and difficulty of proof-making. In this chapter we’ll pause for a bit and work through some more proofs.

In chapter 10, we saw that contemporary classical logic departs from its Aristotelian roots in its tolerance for empty predicates like ‘– is a unicorn’, ‘– is a leprechaun’, and ‘– is a tasty kale recipe’. From the standpoint of formal semantics, such predicates can simply be assigned the null set as their extensions. This makes for some awkwardness, to be sure. It means that claims like ‘All leprechauns are Canadian’ should be counted as true (albeit vacuously so).

In addition to our stock of generic predicates – ready to be interpreted as one needs for whatever context one is using them – we have also introduced one (and only one) special predicate that has the same interpretation across all $\mathcal{Q}\mathcal{L}$ models: the identity predicate, ‘=’. Given the meaning that we have given to this predicate, it is possible to give Intro and Elim rules for it.

In this chapter we touch on the idea of inter-learner variability in outcome (i.e., how far learners get) as well as rate of acquisition among different learners. We then link these issues to the idea of individual differences as explanatory factors. We focus on the most studied: motivation, aptitude, and working memory.

In its heyday, “classical” Newtonian physics was the simplest and most comprehensive model of basic physical phenomena that had come along in the history of science. It’s still taught today, not because it’s accepted as true by the physics community, but because (i) as models go, it’s pretty darn good at explaining and predicting the behavior of a large number of physical systems with reasonable accuracy, (ii) it’s simple, and (iii) it’s elegant. This makes it the perfect entering wedge for learning physics.

As we began to explore at the end of the previous chapter, in addition to making simple claims about particular individuals in the domain of discourse, we will sometimes want to make more general claims about all individuals in the domain of discourse.