Definition

Early modern interest in definitions began inauspiciously with the rejection of the scholastic model of science. For the scholastics — medieval thinkers heavily influenced by the work of Aristotle — science was the name given to knowledge acquired by being logically deduced from certain axioms (i.e., from statements whose truth is assumed and considered not in need of independent proof). These axioms were what they called ‘real definitions’. On this picture, a real definition tell us what properties are essential to the thing defined (e.g., “Kitty is a cat” counts as a real definition of Kitty insofar as it is essential to Kitty that she is a cat), and is to be contrasted with a nominal definition which merely stipulates an association between a word and a thing (e.g., between Kitty and the name “Kitty”). Most notably, this scholastic view of science came under fire in 1620 from Francis Bacon, who sought to defend an alternative, inductive model of science driven by observation and experimentation. Bacon argued that real definitions were unfit to serve as axioms and that ‘proof by syllogism’ (i.e., by means of strict logical proof) was ill-suited to the study of nature (Jardine and Silverthorne, 16). Thomas Hobbes also challenged this scholastic orthodoxy in Leviathan (1651) by arguing that definitions are simply stipulations of arbitrary and conventional associations between words, making them — and indeed the axioms of scholastic science — subject to radical change from one linguistic community to another (see Ch.4 of Leviathan).

‘Porphyriana Arbor’ from László Spaics, Tractatus in Aristotelis logicam sub A: R: patre Alexandro Brunczwik per mi Georgium Spaich. 1748. Graphic by Martin Prokes. © Hungarian National Digital Archive. (CC BY 4.0).

Porphyrian trees were frequently used in contemporary logic textbooks to represent the process of defining things according to species and differentiae (distinguishing characteristics).

Many of Bacon’s influential objections were subsequently echoed by René Descartes in a variety of philosophical works published between 1628 and 1644. Unlike Bacon, however, Descartes sought to replace the scholastic model of science with his own axiomatic conception. For Descartes, the role of scientific axioms is played not by real definitions, but by ‘intuitions’, i.e., by self-evident and incontrovertible judgements. Perhaps the most important difference between Cartesian intuitions and real definitions is that the former are mental states characterised by being ‘very simply and self-evident’ (AT IX 8 / CSM I 195-6), whilst the latter are propositions which state metaphysical claims about essences of things. For Descartes, only intuitions are fit to serve as axioms for science insofar as they cannot be doubted. Definitions, on the other hand, lack this property, so granting them axiomatic status inevitably leads to ‘some of the most serious errors in the sciences’ (AT X 524 / CSM II 417).

Ironically, in spite of Descartes’ low opinion of definitions, it was the influence of a Cartesian work that ensured their prominence in later early modern conceptions of science. The enormously influential Port-Royal Logic (1662) of Antoine Arnauld and Pierre Nicole attempts to harmonise Cartesian and scholastic views. The authors cleave to Cartesian orthodoxy in asserting that axioms must be intuitions, which they describe as ‘propositions which are clear and evident in themselves’ (Buroker, 246). However, they go beyond Descartes in claiming that intuitions are also a species of real definition. In order to effect this synthesis, the authors recast real definitions as claims not about the essences of things, but about relations of containment between ideas. Thus, to judge that Kitty is a cat is to define her — in the real sense — in virtue of the fact that idea KITTY contains the idea CAT. Intuitions are, in this formulation, a special class of real definitions in which, to know whether or not what one is judging is true or false, one ‘only need to consider the idea’ (Buroker, 247-8). E.g., it is self-evident that all bodies are extended given that whenever one examines the idea BODY, one finds that it contains the idea EXTENSION. Nominal definitions are also recast in a psychological mould as stipulative associations between a word and an idea (e.g., between the word “Kitty” and the idea KITTY).

Jean Massard, after Jean Baptiste de Champaigne. Antoine Arnauld Docteur de la Maison et Société de Sorbonne. 1755-1822. Etching and engraving. © The Trustees of the British Museum.

The Port-Royal conception of a real definition appears a stark divergence from the scholastic notion. For scholastics, such as Francisco Suárez, ‘the basis for a [real] definition […] is the essence of a thing’ (Doyle, 131). But for Arnauld and Nicole, it is a relation between mental representations. In actual fact, the two are more natural bedfellows than one might expect. In spite of its psychological formulation, the Port-Royal account is supposed to result in definitions which ‘explain the real nature of things’ (Buroker, 62). Arnauld and Nicole achieve this reconciliation by stipulating that what an idea contains is not a matter of arbitrary convention; rather, it is unchanging over time and the same for all thinkers. Consequently, containment relations between mental representations come to represent immutable and public semantic facts. Insights into these relations is thus seen as providing a secure guarantee of facts about what is metaphysically essential.

Sympathetic rationalist thinkers developed these ideas in ambitious new directions. Most notably, throughout the period of 1666-1716, Gottfried Wilhelm Leibniz envisioned as an ideal of scientific knowledge an encyclopedia written in a formal language which mirrors exactly the system of ideas, and which is undergirded by a ‘calculus of containing and being contained’ (Couturat, 256). The response from empiricist philosophers, however, was decidedly less favourable. John Locke argued in his Essay Concerning the Human Understanding (1689) that one must distinguish ‘the very being of any thing, whereby it is, what it is’, which we calls the real essence of a thing, from the collection of ‘abstract Ideas […] which the General, or Sortal […] Name stands for’, which he calls its nominal essence (Nidditch, 417). E.g, the real essence of Kitty would be the metaphysical ground which explains why she is what she is. The nominal essence of Kitty will be, instead, those general properties (e.g. being a cat) which we know that she embodies by determining what our idea of her contains. As Locke points out, it is only nominal essences which are the concern of Port-Royal-style real definitions, but it is the real essence they are assumed to be identifying. Furthermore, for Locke, it is only what he calls ‘complex ideas’ which contain other ideas. But he makes clear that ‘all Complex Ideas are made’ (i.e., put together by a given thinker from simple ideas based on regularities they observe between them) (Nidditch, 163). Hence, for Locke, both complex ideas and the containment relations in which they stand to one another crucially lack the fixed and public semantic properties attributed to them by thinkers like Arnauld and Nicole. Crucially, this means that ‘no Definitions, […] are of force enought to destroy constant Experience’, and, consequently, could never function as the axioms of a science (Nidditch, 116).

In these ways, the early modern period saw what had been a scholastic device for metaphysical explanation reconstructed as a means of describing relations between mental representations. Consequently, the question of the nature and value of definition, far from receding from view, came to stand at the heart of several important modern debates in epistemology, semantics, and, indeed, metaphysics.

Nicholas Currie is a PhD Candidate in the Department of Philosophy at UCL.

AT = Adam and Tannery (1964-74) / CSM = Cottingham et al. (1985)

Selected Bibliography

Adam, C. and P. Tannery (Eds.). Oeuvres de Descartes, vol. I-XI (Paris, 1964-74).

Baumgold, D. (ed.). Three-Text Edition of Thomas Hobbes’s Political Theory: The Elements of Law, De Cive and Leviathan (Cambridge, 2017).

Buroker, J. V. (ed.). Arnauld and Nicole: Logic, or the Art of Thinking (Cambridge, 1996 [1683]).

Cottingham, J., R. Stoothoff, and D. Murdoch (Eds.). The Philosophical Writings of Descartes, vol. I-III (Cambridge, 1985).

Couturat, L. (ed.). Opuscules et fragments inédits de Leibniz (Paris, 1903).

Doyle, J. P. (ed.) Suârex: A Commentary on Aristotle’s Metaphysics (Milwaukee, WI., 2004 [1597]).

Jardine, L. and M. Silverthorne (Eds.). Bacon: The New Organon (Cambridge, 2000 [1620]).

Nidditch, P. (ed.). Locke: An Essay Concerning Human Understanding (Oxford, 1975 [1689]).

29 April 2021.