Why Leibniz should have agreed with Berkeley about abstract ideas

ABSTRACT

Leibniz claims that Berkeley “wrongly or at least pointlessly rejects abstract ideas”. What he fails to realize, however, is that some of his own core views commit him to essentially the same stance. His belief that this is the best (and thus most harmonious) possible world, which itself stems from his Principle of Sufficient Reason, leads him to infer that mind and body must perfectly represent or ‘express’ one another. In the case of abstract thoughts he admits that this can happen only in virtue of thinking of some image that, being essentially a mental copy of a brain state, expresses (and is expressed by) that state. But here he faces a problem. In order for a thought to be genuinely abstract, its representational content must differ from that of any mental image, since the latter can represent only something particular. In that case, however, an exact correspondence between the accompanying mental image and the brain state would not suffice to establish a perfect harmony between mind and body. Even on Leibniz’s own principles, then, it appears that Berkeley was right to dismiss abstract ideas.

KEYWORDS:

• Gottfried Wilhelm Leibniz
• George Berkeley
• abstraction
• imagination
• mind–body parallelism

Acknowledgements

My thanks to two anonymous referees for this journal, whose comments on a previous draft led to many improvements.

Notes

1 This copy resides today in the Gottfried Wilhelm Leibniz Bibliothek in Hannover and may be accessed online at http://digitale-sammlungen.gwlb.de/resolve?PPN=797331344.

2 Translations of parts of this note are my own, from the Latin at Robinet, “Leibniz: Lecture du ‘Treatise’”, 218; cf. AG 307.

3 This second kind of abstraction is sometimes called ‘generalizing abstraction’; see, e.g. Reid, Essays, Essay 5, Chapter 3; Winkler, Berkeley: An Interpretation, 28–30; Rickless, Berkeley’s Argument for Idealism, 104–6. Bolton (“Berkeley’s Objection”, 64) and Rickless (Berkeley’s Argument for Idealism, 104–5) refer to the first kind of abstraction as ‘singling abstraction’, though this invites confusion, because Berkeley also conceives the generalizing kind of abstraction as involving a ‘singling out’, namely, of what many things have in common (see Atherton, “Berkeley’s Anti-Abstractionism”, 48–9). As he writes of the example of extension in his discussion of generalizing abstraction in §8, the mind “considers apart or singles out by itself that which is common, making thereof a most abstract idea of extension, which is neither line, surface, nor solid, nor has any figure or magnitude, but is an idea entirely prescinded from all these” (my emphasis). The same point applies to Grayling’s description of the first kind of abstraction as “abstraction by separation” (Berkeley: The Central Arguments, 29). For a more fine-grained taxonomy of abstract ideas in Berkeley, see Pappas, Berkeley’s Thought, 40–4.

4 Here I follow Leibniz in taking Berkeley’s view to be that all ideas are images, a stance which Berkeley himself seems to endorse in §33 of the Principles: “The ideas imprinted on the senses by the Author of Nature are called real things: and those excited in the imagination being less regular, vivid and constant, are more properly termed ideas, or images of things, which they copy and represent” (PHK §33). For a careful defense of this stance, see Winkler, Berkeley: An Interpretation, 10–14. Some commentators have maintained that Berkeley’s critique of abstract ideas should not, or at least need not, be understood to be predicated on the view that ideas are images: see, e.g. Pitcher, Berkeley, 62–90; Flage, “Berkeley on Abstraction”, 500–1; Winkler, Berkeley: An Interpretation, 22–48. Whether that is the case is a question I will not pursue here.

5 This passage was added to the second edition of the Principles (1734) and thus would not have appeared in Leibniz’s copy.

6 For a helpful discussion of Berkeley’s account of how general words acquire meaning, see Pearce, Language, 31–6.

7 For further discussion of Berkeley’s theory of generality, see, e.g. Mackie, Problems from Locke, 118–21; Dancy, Berkeley: An Introduction, 29–37; Jesseph, Berkeley’s Philosophy of Mathematics, 33–8; Dunlop, “Berkeley’s Account of Generality”.

8 See NE 109 for the description of an idea as an “immediate internal object” of thought (and as “an expression of the nature or qualities of things”). For similar characterizations, see DM 26; Leibniz to Thomas Burnett, 11 June 1695, GP 3:162; GP 3:240–1; “Sample of Reflections on the First Book of the Essay of [Human] Understanding”, 1698, A 6.4:11–12/GP 5:21. Leibniz also construes ideas as dispositions to think: see “What Is an Idea?”, ca. 1677, A 6.4:1370–1/L 207-8; NE 52, 106; see also NE 86–7. For helpful discussion of this latter conception, see Jolley, Light of the Soul, 132–9. In my view Leibniz intends these accounts of ideas to be compatible: the enduring internal object of a thought, he thinks, just is what disposes us to think that thought when the occasion presents itself.

9 This parallelism obtains not only between perceptions or thoughts in the soul and material traces in the brain, but also between the tendencies to these respective states, that is, appetitions in the soul and physical forces in the brain. It also extends to their respective laws, which in the soul are laws of final causes and in the brain laws of efficient causes (see, e.g. M 78–9). Our concern here, however, will be only with the first of these, i.e. the harmony between thoughts, and in particular abstract thoughts, and the corresponding traces in the brain.

10 For Descartes’ view, see, e.g. Meditations on First Philosophy, Sixth Meditation (AT VII, 72–3); Descartes to Guillaume Gibieuf, 19 January 1642 (AT III, 479). An especially clear statement of the Cartesian view can be found in Malebranche, The Search after Truth, Book I, Chapter 4.

11 For a helpful introduction to the PSR in Leibniz, and a good entry wedge into the expansive literature on this topic, see Melamed and Lin, “Principle of Sufficient Reason”.

12 Leibniz refers to this principle (i.e. that God must have created the best of all possible worlds) variously as the Principle of Perfection (A 6.4:1445/AG 19; A 6.4:1448/AG 22; GP 7:272/L 478) or the Principle of the Best (GP 6:44, 386; M 48; GP 7:390).

13 For a similar reflection in the context of Leibniz’s rejection of empty space, see the appendix to his fourth letter to Samuel Clarke (GP 7:378), where he argues that there is no sufficient reason for choosing any ratio of matter to vacuum other than 1:0. For discussion of this passage, see Puryear, “Evil as Privation”, 481–3, 486–9.

14 See also Essay Concerning Human Understanding, II, viii, 13; IV, iii, 6. For helpful discussion of Locke’s view, see Langton, “Locke’s Relations”.

15 The sense of ‘cause’ here is of course what Leibniz calls ‘ideal causation’. On this kind of causation, and the related notion of ‘ideal action’, see Puryear, “Monadic Interaction”; Jorati, Leibniz on Causation, 47–52; Jorati, “Embodied Cognition”, 255–6. On the intelligible connection between our confused perceptions of sensible qualities and their causes, see Phemister, “Mind-Body Relations”; Puryear, “Metaphysics of Color”, 332–6; Ott, “Leibniz on Sensation”.

16 See also GP 4:575/WF 141: “Someone will perhaps say that the sensation of heat does not resemble the motion: yes, without doubt, it does not resemble a sensible motion, such as that of a carriage wheel; but it does resemble the assemblage of small motions in the fire and in the organs, which are its cause; or rather it is only their representation”.

17 On Leibniz’s view, our sensations of such qualities, despite appearing simple, are in fact composed of many smaller perceptions, which are the perceptions of the individual mechanical qualities which together cause the sensation. The sensation thus has a hidden complexity or structure in virtue of which it corresponds to the structure of its cause. On this, see Simmons, “Changing the Cartesian Mind”, 61–70; Puryear, “Metaphysics of Color”, 332–6; Ott, “Leibniz on Sensation”, 140–5; Pearce, “Veridicality of Body Perceptions”, 2–5.

18 In the essay “What is an Idea?” (ca. 1677), Leibniz defines expression as a certain “correspondence” or “analogy” between the relations (habitudines) of the expression and those of the thing expressed, one which allows us to “pass from a consideration of the relations in the expression to a knowledge of the corresponding properties of the thing expressed” (A 6.4:1370/L 207). See also Leibniz to Arnauld, 9 October 1687, A 2.2:240/LA 240–1: “One thing expresses another (in my language) when there is a constant and ordered relation between what can be said of the one and of the other”. For helpful discussion of Leibniz’s theory of expression, see Kulstad, “Leibniz’s Conception of Expression”; Swoyer, “Leibnizian Expression”.

19 This is not to deny that there can in a sense be arbitrary connections in the world. As we will see in Section 4, Leibniz himself characterizes the connection between an abstract thought and its associated symbols as an arbitrary one. It should be noted, however, that from his perspective these arbitrary connections could only be established by imperfectly rational beings, not by a perfectly rational one, and must be arbitrary not absolutely, or from the point of view of God, but only relative to the knowledge of finite minds.

20 An anonymous referee points out that numbers might be an exception here: they are abstract, yet can seemingly be expressed by mental images, e.g. the number seven by seven tally marks. This may be so, though the fact remains that many if not most abstract contents would be like man or being in not being expressible by any image.

21 See also “Letter Touching on What Is Independent of the Senses and of Matter”, 1702, A 1.21:340/AG 188.

22 See also “On Forms, or the Attributes of God”, 1676, A 6.3:514/L 160.

23 For other texts in which Leibniz affirms that abstract thoughts require some act of imagination, see GP 3:466/WF 177; GP 4:541/WF 100; GP 4:559/WF 112; GP 4:563/WF 117; GP 4:574/WF 140; GP 6:626/AG 226; see also A 1.21:344/AG 191. For helpful further discussion of the role of imagination in Leibniz’s account of abstract cognition, see Jorati, “Embodied Cognition”, 259–67. See also Sepper, “Rationalist Reconceptions of Imagination”, 329–34, for further background on Leibniz’s conception of imagination.

24 Compare Jorati’s suggestion that, for Leibniz, abstract thoughts have both an abstract content and a sensible vehicle (“Embodied Cognition”, 263–4).

25 For a fuller development of this reading, see Leduc, “Epistemological Functions”, 58–67, and especially Leduc, “Imagination and Reason”.

26 If such a world were not possible, then Leibniz’s situation would be even more dire, as his views would seem to commit him to the absurd result that there are neither abstract nor general ideas.

27 One implication would concern his philosophy of mathematics. Clearly he could no longer suppose that our ideas of mathematical objects such as numbers and geometrical figures are abstract, i.e. are ideas of abstract objects. Perhaps he would instead need to say that our ideas of these mathematical objects, being ideas of relations, are in fact particular ideas that we make to stand for other particular ideas (or things). I will not develop that thought any further here, or speculate on what changes it might require with respect to Leibniz’s first-order mathematical views, but the reader may find it helpful to consider how Berkeley himself develops his non-abstractionist philosophy of mathematics (on which see Jesseph, Berkeley’s Philosophy of Mathematics).

28 For a fuller account of this, see Puryear, “Leibniz über Begriffe”; see also Broad, Leibniz: An Introduction, 138–40.