Philosophy investigates the basic structure of how things are. In addition, many philosophers have claimed that philosophy must also look at how things must be – that is, at what is necessary. But philosophers do not all agree about the nature of necessity and the related notion of possibility. In fact, these ‘modal’ notions are the focus of a debate which goes back to the earliest Greek philosophers, and many of the questions which the ancients asked about the nature of necessity can still be seen to occupy a central position in present-day philosophical discussion.

Some years ago when we three editors were reflecting together on current views about modality, possible worlds, and related issues, we started asking where philosophers through the ages have thought that necessity originates. What have they said necessity is? What do they say are its roots? We began to explore notions of necessity as they emerged in philosophers’ and logicians’ works over the centuries, and in doing so we were struck by the enormous range of different approaches to these topics, both from the point of view of contemporary metaphysics and from the point of view of the connection between logical inference and argument. We were also struck by the connection between the intuitive notions of necessity and the validity of ‘logical’ arguments in ordinary life. Even while these themes sit at the heart of much in philosophy, it seemed to us that the contemporary debates around them do not often suggest much awareness of the older philosophical discussions. And so we quickly came to feel the need for a more thoroughgoing study, one which is fundamentally historical and which brings together world experts on various philosophers and eras. We approached these experts seeking their guidance in looking back at the notion of necessity throughout its long history, and through close attention to the primary texts.

There are, we think, special advantages in taking the historical approach to a subject such as necessity. Not least among these advantages is the way in which the historical approach affords philosophers room for reflection, which allows us to sit outside the philosophical debates. However partisan one's views about modal reasoning might be, philosophers as a rule adopt a position of agnosticism when studying historical greats such as Aristotle or Abaelard or Locke or Leibniz.

Introduction

C. I. Lewis is sometimes accused of taking a purely syntactic approach to logic. His favourite logics, S2 and S3, are sometimes claimed to be mere collections of axioms without representing any coherent notion of logical necessity, possibility, or deducibility (Anderson and Belnap, 1975, p 117). Lewis did, however, say a great deal about the meaning of the modal operators. In this chapter I examine what Lewis actually says about the modal operators and his philosophy of logic more generally and argue that there is much more to these systems, S2 and S3 in particular, than mere collections of axioms. I claim that certain of the features of these logics that are often criticized are in fact well motivated by his epistemological and semantical views.

I do not claim, however, that Lewis had a well-developed semantics of modality when he first put forward his logic of strict implication in 1911. Most of his remarks on semantical issues occur much later than that. Which, if any, of his later views he had in mind when he originally constructed his modal logic is impossible to tell. He does not make any remarks about this either in his published writings or (as far as I know) in the manuscripts in his Nachlass.

Moreover, his philosophical views changed, in some ways rather radically, over the course of his career. In his PhD thesis and his early philosophical writings, he is a Kantian idealist, but he adopts a form of pragmatism in the 1920s that has important consequences for his views about modality. In his more mature writings – especially in the 1940s and later – the influence of Kant is much less pronounced and his metaphysical views seem more realist. These more realist metaphysical views are reflected in his theory of meaning and his philosophy of logic.

We see Lewis's philosophy of logic develop along with his other philosophical views. In the 1910s, Lewis presented his modal logic largely as a response to classical logic. In the 1920s he provided an epistemological interpretation of modal logic. In the mid-1930s, he attempted to link his logic of strict implication with the notion of a tautology from Wittgenstein's Tractatus. In the 1940s, this connection took a more metaphysical and algebraic cast.

The place of modality in a priori knowledge

The problem of justifying our beliefs about what is possible or necessary has been a recurring theme for us since Chapter 2. One of the central reasons why people have postulated a priori knowledge is in order to deal with modal knowledge. In this chapter we face this problem directly using the resources that we developed in earlier chapters.

Radical empiricism

We have already briefly discussed the radical empiricists' view about modal knowledge in Chapter 6. By and large, they reject modal knowledge. Mill, for example, says:

This is just a simple rejection of necessity. But in Quine the matter is somewhat more subtle than this.

Quine distinguishes between three ways to interpret modal statements. He calls these “three degrees of modal involvement” ([1953] 1976c). First, one might treat necessity as a predicate of sentences. This means we take the word “necessary” to indicate some property of a sentence. Quine thinks that this is legitimate.

Introduction

In this chapter I discuss the epistemology of Immanuel Kant (1724–1804) and of a Kantian, Michael Friedman. Kant is a nativist. He holds that there are certain innate concepts, intuitions and beliefs that we use to organize our understanding of the world. According to Kant, these concepts, intuitions and beliefs are a priori in two senses. First, they are not learned. Second, the possibility of our having experience depends on our having these concepts, beliefs and intuitions. As we shall see, within Kant's system his innate beliefs are not empirically defeasible. Moreover, they provide many of our other beliefs with a priori justification.

Nativism, however, is only one of Kant's doctrines. As we shall see, some modern Kantians abandon nativism. For them, the important aspect of Kant's epistemology is the idea that we construct the world according to principles that we do not extract empirically from the world. They think that we impose these principles on the world. For Kantians, as for Kant, these principles are a priori.

In this chapter I discuss “theoretical philosophy” only in the Kantian sense of this term. Theoretical philosophy includes only metaphysics and epistemology. Kantian ethics, on the other hand, is what he calls “practical philosophy”. I examine Kantian ethics – or, rather, metaethics – in Chapter 9.

Kant on phenomena and noumena

Kant's theoretical philosophy has two central aims. First, he wants to defeat scepticism about the external world.

What is nativism?

Nativism – sometimes called “psychological nativism” – is the doctrine that we have innate capacities, ideas or beliefs. Historically, nativism has been closely related to rationalism. Many rationalists have also been nativists. Plato thinks that our understanding of the forms is, to a large extent, innate; Descartes thinks that we have a great many innate ideas, as do Spinoza and Leibniz. These philosophers all use innateness to help explain how we have a priori knowledge. The sense in which innate ideas or beliefs are independent of experience is quite clear. We do not need to learn them either from experience or from anything else. But, as we shall see, the epistemological status of innate beliefs is rather complicated.

One problem with nativism is that, on some characterizations, every philosopher would seem to be a nativist. Almost every philosopher thinks that we have innate capacities of some kind or other. Hume, who is usually thought to be an enemy of nativism, thinks that we have the innate tendency to form beliefs by the association of ideas. We expect, for example, that a thing will fall if we see its being released because we have formed a habit after seeing this combination many times in the past.

One way of narrowing the class of nativists is to characterize them as holding that we not only have innate general reasoning abilities, such as the disposition to do induction, but we also have domain-specific innate ideas, beliefs or capacities.

Rationalism

“Rationalism” is defined in various ways in the philosophical literature. In the canon of English-speaking philosophy departments, rationalism is associated with three philosophers: Descartes, Spinoza and Leibniz. With these philosophers in mind, Charlie Huenemann (2008: 7–8) characterizes rationalist epistemology in terms of the following four theses:

1. (i) There is a priori knowledge.

2. (ii) We have innate ideas or beliefs.

3. (iii) We have a “privileged cognitive machinery which allows for the distinction between the intellect and imagination”.

4. (iv) Pure reason is more reliable than empirical justification.

Chapter 4 of this book is devoted entirely to discussing innate ideas and beliefs, so we shall not discuss thesis (ii) at any length in this chapter. Thesis (i), of course, is the topic of this entire book, and all the theories that we discuss, except radical empiricism, accept it. In this chapter we shall concentrate on theses (iii) and (iv).

Thesis (iii) is particularly interesting. Empiricist critiques of rationalism often accuse rationalists of confusing the limits of their imaginations with real insight into what is necessarily true. For example, some rationalists claim that we can know that nothing can be both red and green all over at the same time. A radical empiricist, such as Mill, would reply that we cannot imagine such an object, but that may just be a fact about what we can imagine at the moment rather than a fact about things.

Introduction

Aristotelianism holds that we gain some of our knowledge from the abstraction of concepts from our experience and reflection on these concepts. This may sound more like empirical knowledge than a priori knowledge, but the justification involved is remarkably similar to analytic justification. In analytic justification, we learn the meanings of words empirically. Then using these meanings together with only our reasoning abilities we determine if a particular sentence is true. According to Aristotelianism, we first abstract concepts from experience and then reason by reflecting on these concepts. We can characterize Aristotelian justification as the process of reasoning using concepts that are abstracted from experience (rather than, say, concepts that are innate or those that we associate with the meanings of words).

Aristotelian justification is very much like the rationalists' rational insight. Aristotelian justification, unlike rationalists' justification, is restricted to those cases in which the concepts involved are abstracted from experience.

Aristotelianism is an attractive theory of the a priori. It does not involve innate concepts. It allows a priori justification about objects that are independent of our minds. It also fits well with empiricism.

I begin the chapter, as usual, with a history of the theory. Then I defend Aristotelianism against the charges that it is not a form of a priori reasoning and that it is not reliable. The chapter ends with a brief discussion of the relationships between Aristotelianism and coherentism, reliabilism and foundationalism.