This book is about Spinoza's philosophy of ratio. The Latin term ratio can mean reason, relation, and proportion, as well as mathematical ratio. It is all these senses of ratio, and the relations between them, that we address in this book. The book argues that Spinoza's philosophy is a philosophy of ratio: not a ‘rationalist’ philosophy, but a philosophy based on the interactions of reason, relation, and proportion. In this short introduction I introduce these concepts, direct the reader to the chapters that discuss them, and consider how Spinoza's philosophy of ratio is reflected in architecture, one of the book's key themes.

Ratio is a significant term in Spinoza's philosophy. Spinoza is typically (if not entirely accurately) characterised as a rationalist, for whom reasoning has central importance. In the Ethics, reason is Spinoza's ‘second kind’ of knowledge (E IIP40S2), sitting between empirical awareness or imagination (knowledge of the first kind) and intuitive intellection (knowledge of the third kind). In reasoning, we understand things adequately: we start from axioms, definitions, and basic properties and analytically or deductively build up true understanding of the causes of – or reasons for – things being as they are. Reasons are what reason understands; as Michael LeBuffe discusses in Chapter 2, those reasons may be ideal or corporeal. Developing one's reasoning is the primary goal of the human mind, and is key to our flourishing: the ethical arguments of Spinoza's Ethics rest on the principle that our wellbeing, virtue, and freedom develop in tandem with our reasoning. The freest and ethically ‘best’ person – that is, the person who has the most autonomous control of her or his own actions and reactions – is also the most rational.

But reason is only the most obvious sense of ratio in Spinoza's philosophy. Spinoza says that every physical body is governed by a characteristic ‘ratio of motion and rest’ (E IIL5). This may be understood as a mathematical ratio (of degrees of motion to degrees of rest) but Heidi M. Ravven, in Chapter 3, argues that it may be better understood as the body's unique equilibrium. This characteristic ratio determines and provides the reason for the body's individual form: as LeBuffe argues, bodies contain their own reasons. In striving to understand these ratios/reasons, the mind strives to maintain its own equilibrium which, according to Ravven, Spinoza conceives as ‘biologised’.