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.

The simplest sentences of natural languages like English, on the other hand, do have internal structure, and the logical properties of those sentences (and the logical relations between them) are, in part, a function of these internal structures. In this chapter, we will begin to explore and model the fine-grained structure of propositions (and the sentences that express them), drawing inspiration from Aristotle’s categorical logic, which is the historical inspiration for classical logic (and the reason we call it classical logic).

This chapter covers three different ideas about nativelikeness in L2 acquisition. The first is that learners can become nativelike in all domains of language and language processing. The opposite idea we will cover is that learners cannot become nativelike in any area of L2 acquisition. The final idea we will treat is that learners can become nativelike in some domains of language but not others. We discuss what “nativelike” means and what kinds of measures are used to assess learner knowledge and ability. We also review key hypotheses and constructs such as the Fundamental Difference Hypothesis, the Shallow Structure Hypothesis, Full Transfer/Full Access, the critical period, and others.

The metatheoretic formal semantics that we gave in Chapter 12 was rife with talk of functions, like the semantic valuation function for assigning extensions to formulae of $\mathcal{Q}\mathcal{L}$. Functions again took center stage in Chapter 19, which discussed intensions as functions from possible worlds onto extensions. Functions, functions, functions.

In the epilogue, we reflect on some of the major themes linked to the questions driving research in second language acquisition and return to the question that started the field in the 1970s: Are L1 and L2 acquisition similar or different?

$\mathcal{P}\mathcal{L}$ can be thought of as the logic of truth functions. The connectives of $\mathcal{P}\mathcal{L}$ are introduced with characteristic truth tables because they all express truth functions – each is used to produce complex sentences the truth values of which are completely determined by the truth values of the component subsentence(s).

As has hopefully become increasingly clear throughout this text, the task of logical theory construction is a difficult one – one that’s full of choices. These choices have ramifications that aren’t always easily foreseen. Frege thought that he was on his way to reducing all of mathematics to classical logic when Russell pointed out that seeds of contradiction had been built into the foundations of Frege’s system.

In this chapter we address the question of whether or not language acquisition is largely implicit in nature. After reviewing key constructs (e.g., explicit and implicit knowledge, explicit and implicit processing/learning, intentional and unintentional learning), we discuss the major positions currently under scrutiny in the field: (1) Explicit learning is necessary; (2) explicit learning is beneficial; (3) explicit learning does little to nothing (i.e., acquisition is largely if not exclusively implicit in nature). A key issue in this chapter is how one defines “language” and how one construes “input processing.” We will review how definitions of these constructs color the researcher’s perspective on the issues.

The prophet to whom Paul was referring was Epimenides of Knossos, a strange sixth- or seventh-century BC Greek philosopher–prophet who was known for his cryptic tattoos and an ability to separate himself from his body (once leaving it sleeping in a cave for 57 years – probably to provide himself with an excuse for missing departmental meetings). He was put to death by those who wanted more favorable prophesies from him. When his body was discovered to be covered in tattoos, his skin was put on display in Sparta. A touching tribute.

The extensions of more complex structures were a systemic function of the extensions of their components. Gottlob Frege, one of the pioneers of this kind of compositional semantics, discerned a tension between the extensionality of the formal theory and the apparent non-extensionality of ordinary natural language. An examination of Frege’s worry will lead us to consider the notion of intension.

In this chapter we review the competing perspectives on the role of language transfer, namely, the role that a first language plays in the acquisition of a second language. Do learners begin with the L1 and transfer all properties and processes into L2 acquisition? Or is transfer partial and selective at the outset? Or do L2 learners not transfer any aspects of the L1 and begin with universal properties of language and universal processes for acquiring language? As such, we review such key hypotheses as Full Access, Full Transfer/Full Access, and important constructs such as minimal trees, input processing, and processability. We also touch on the notion of third and subsequent language acquisition and competing perspectives on what languages get transferred if any (and how).

In Chapter 2, when we were introducing the Boolean connectives, we had occasion to observe that there are some apparent disconnects between the English operators ‘and’, ‘or’, and ‘not’ and their $\mathcal{P}\mathcal{L}$ counterparts. In the present chapter, we’ll take a closer look at a few of these disconnects and see if a pragmatic theory (a theory about how language is used and interpreted in context) can help bring the two back into line with each other.