2. How can we speak of what does not exist?

Statements that purportedly refer to something that does not exist, whether fictional or not, have been especially problematic in the history of philosophy. ‘How can we speak of what does not exist?’ suggests that in order to understand existential statements, we need to recall Frege’s claim that number statements are assertions about concepts. Existential statements are really just a type of number statement. When we make an existential claim, we are not attributing a first-level concept to an object, but a second-level concept to a first-level concept. The work of Bertrand Russell (1872–1970) is also discussed along with the Russell Paradox and his Theory of Descriptions.

1. How many things are there?

‘How many things are there?’ introduces Gottlob Frege (1848–1925), one of the main founders of analytic philosophy whose central concern was with the nature of mathematics, and arithmetic in particular. It considers the question ‘How many things are there?’, concluding a simple answer is not permitted without specifying the relevant concept(s) by means of which to think of the things. If how to answer a given question is not immediately obvious, then we need to identify its possible meanings. Perhaps we will find the intended or relevant meaning by understanding the context; if not, then we may need to imagine possible contexts in which the question has an answer.

4. Are there limits to what we can say or think?

‘Are there limits to what we can say and think?’ considers the possible limits of our language and whether we can have thoughts that outstrip our ability to say what they are. It introduces Ludwig Wittgenstein (1889–1951), arguably the greatest philosopher of the 20th century, and his publication, Tractatus Logico-Philosophicus (1921), which describes his philosophical ideas. The paradox of inference is discussed along with how Wittgenstein distinguishes between senselessness and nonsense. It concludes that there are indeed limits to what we can say or think, and while there may be difficulties in saying what they are, they can certainly be shown by carefully elucidating the complex workings of language.

6. So what is analytic philosophy?

There are various similarities and differences between the respective approaches to analytic philosophy of Frege, Russell, Moore, Wittgenstein, and Stebbing. But is there anything in common that could be taken to characterize analytic philosophy as a whole? ‘So what is analytic philosophy?’ explains that analytic philosophy is ‘analytic’ in an extra special sense because it made use of modern logic together with all the new techniques that emerged in its wake and the greater understanding of the relationship between logic and language that this generated. It looks at later analytic philosophy—ordinary language philosophy, ideal language philosophy, and scientific philosophy—before considering what is wrong and good about analytic philosophy.

5. How can we think more clearly?

Analytic philosophy places great emphasis on clarity. But what does ‘clarity’ mean and how can we think more clearly? How does clarity connect with other virtues of analytic philosophy? ‘How can we think more clearly?’ introduces L. Susan Stebbing (1885–1943) who published the first textbook of analytic philosophy in 1930, doing more than anyone to promote the development of analytic philosophy in Britain. Stebbing’s work outlines different types of thinking—purposive, logical, and critical—discussing a range of ways we can be misled, from logical fallacies and potted thinking to analogies and ambiguity. In drawing our attention to them, Stebbing shows how we can think more clearly by avoiding them.

Introduction

One claim often made about analytic philosophy is that it places great emphasis on clarity of thinking, precision of expression, and rigour of argumentation. But other intellectual virtues that might be considered are creativity, fruitfulness, and systematicity. The Introduction aims to give some sense of the conceptual creativity of analytic philosophy and the bigger picture in which its fruitfulness and systematic ambitions can be appreciated. Analytic philosophy is called ‘analytic’ because of the emphasis placed on analysis. But this just raises the question of what is meant by ‘analysis’, and what forms of analysis are employed in analytic philosophy. This is best answered by considering a range of philosophical questions.

3. Do you know what I mean?

From the very origins of philosophy, philosophers have been especially conscious of the inadequacies and limitations of language. But they have disagreed on whether this reflects a corresponding deficiency in thought, on what its explanation and implications are, and on how we should respond—in short, on what this itself means. ‘Do you know what I mean?’ explains that in actual cases of analysis, three different dimensions—interpretive, decompositional, and regressive—are typically involved. It also introduces G. E. Moore (1873–1958) who, alongside Russell, inaugurated analytic philosophy in Britain. Moore’s main interests lay with epistemology (the theory of knowledge) and ethics. The paradox of analysis is also discussed.