Abstract
This introduction has two aims. The first is to describe synthetically, for each author belonging to the tradition of classical empiricism, the main characteristics of his approach, the notion of space that results from it, and the place it occupies within his philosophy. The second is to show that, despite the individual particularities of each theory, there are some common features concerning both the content of the notion of space and the method adopted for its determination. This will lead us to an examination of the differences between varying conceptions of the contents of spatial experience, as well as of the diverse ways in which these are analysed by classical empiricists. We will provide a general framework in which to situate the more specific and in-depth discussions that will be developed in the following chapters, of which we will give a brief overview at the end of this introduction.
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Notes
- 1.
- 2.
Locke 1975, hereafter referred as Essay, followed by book, chapter and paragraph number.
- 3.
For instance, Hume’s analysis of space into a mode of disposition of unextended sensible points has been said to be circular because the concept of disposition includes the notion of space that it is supposed to reduce (or to analyse). See below note 38.
- 4.
Hume 1978, 27 (Book I, Part ii, Section i) cited hereafter as T. followed by book, part, section and page numbers.
- 5.
Studies of space in the seventeenth and eighteenth century focus on the transformation of the concept of space in physics and cosmology and little or no attention is generally given to the authors we are studying in this introduction (for instance, Jammer 1993; Grant 1981; Koyré 1957; Casey 1997: Miller 2014). E. Slowik (2016) devotes a section to “The Rise of the Empiricist Approach to Space”, but the section is only a few pages long. There are however monographs on the notion of space of eighteenth-century empiricists, but they concern exclusively Berkeley’s and Hume’s theories of space; see for instance, Frasca-Spada 1998; Jacquette 2001; Jesseph 1993. Less focused on “scientific revolution” is the 1930’s book of J.T. Baker, entitled An Historical and Critical Examination of English Space and Time Theories from Henry More to Bishop Berkeley (Baker 1930).
- 6.
Respectively in: 1) Essay, II. v., II. xiii. 1–6 and II. xv. 1–2; 2) Essay, II. xiii. 13–14 and II. xv. 9–10; 3) II. iv. 3; II. iv. 5 and II. xiii. 11–26.
- 7.
In the secondary literature on Locke’s Essay, the chapters on space (Essay, II. xiii and II. xv, Of simple Modes; and first, of the simple Modes of Space, and Of Duration and Expansion, considered together) are rarely discussed and even less the sections on the parts of space on which we will focus our presentation. For general presentations on Locke’s theory of space see Yolton (1983, 65–71); Ayers (1991, vol. 1, 223–236); Hamou 2012. On the question of Locke and the notion of absolute space see Gorham and Slowik 2014.
- 8.
Descartes 1996, vol. VII, 63–65 (Meditationes de prima philosophia, Meditatio quinta).
- 9.
Essay, II. xiii. 4. See also Essay, II. xiii. 1, II. xiii. 5 (on figures) et II. xvii. 3 and 22.
- 10.
Something of this kind may be associated, for instance, with Suarez’ notion of spatium imaginarium (Suarez 2001, sec. 4, §7; see also Disputatio LI). Hobbes’ notion of spatium imaginarium and its relation to abstraction is discussed in Pécharman in this volume.
- 11.
Essay, II. xvii. 4; Locke pursues some arguments in favour of the claim that “Space in it self is actually boundless, […]” restating, for the essential, the physical and theological arguments in favour of the infinity of space already developed in the chapter on the simple modes of space. See also II. xiii. 21 where the existence of a boundless space is linked to the possibility of movement at the limits of the universe. However, Locke’s position concerning “space in itself” and its infinity is controversial: Gorham and Slowik (2014, 119–137) maintain that Locke defends an absolutist notion of space in the Essay, at least in part linked to Newton; a similar opinion is held by M. Ayers (Ayers 1991, vol. 1, 234–236). G. A. Rogers claims the mutual independence and the conceptual difference between Locke’s concept of space “in itself” and Newton concept of absolute space (Rogers 1978). We agree with G. A. Rogers concerning both the existence of a realistic concept of space in Locke, and its independence from Newton’s notion of absolute space. Indeed, Locke always defends very clearly a relational notion of place (Essay, II. xiii. 7–10). See also Thomas 2018.
- 12.
To distinguish the two domains of his discourse, Locke uses opposite qualifications, such as “actual” versus “mental” (Essay, II. xiii. 13), “in thought” versus “in reality” (Essay, II. xiii. 13), “real existence” versus “idea” (Essay, II. xiii. 23).
- 13.
See Essay, II. v. 9. and II. xiii. 13.
- 14.
Essay, II. xiii. 13 and 14. At Essay, II. xiii. 13, for instance, Locke writes that “The Parts of pure Space are inseparable one from the other; so that the Continuity cannot be separated, neither really, nor mentally”. In a parallel way, in Essay, II. iv. 5, Locke describes the extension of space as “the continuity of unsolid, inseparable, and immovable Parts” whereas the extension of bodies is said to be “the cohesion or continuity of solid, separable, and movable Parts”. Space therefore is a continuum with parts that are inseparable and unmovable. On the infinite divisibility of the idea of space, see also Essay, II. xvii. 12. On the tradition leading to Locke’s position on the parts of space, see Grant 1981, 232–240.
- 15.
On this point, see, however, the next section.
- 16.
On Pierre Coste and his translation of the Essay, see Hamou 2009.
- 17.
The distinction between two domains of discourse is even more explicit in the French version of the note, that is: “Car l’affaire de M. Locke n’est pas de discourir en cet endroit de la réalité des choses mais des idées de l’esprit.”
- 18.
- 19.
- 20.
See, for instance, Essay, II. xiii, 2, 5 and 10. I do not agree with the mainstream interpretation of Locke’s discussion of Molyneux’s question in Essay, II, ix, viii et ix. The theme of the heterogeneity between spatial ideas perceived by sight and by touch is never actually discussed by Locke. On this subject see Berchielli 2002.
- 21.
- 22.
All references to Berkeley are from Berkeley 1979. The following abbreviations are employed: “PC” for Philosophical Commentaries (Berkeley 1979a) followed by entry number; “NTV” for An Essay toward a New Theory of Vision (Berkeley 1979b) followed by section number; “PHK” for A Treatise Concerning the Principles of Human Knowledge, (Berkeley 1979c) followed by section number; “3D” for Three Dialogues between Hylas and Philonous (Berkeley 1979d) followed by page number.
- 23.
In Samuel Johnson’s Dictionary of the English Language of 1785, the term protrusion is defined as “the act of thrusting forward; thrust; push”.
- 24.
NTV 54 and 79–83; 3D, 188 (First Dialogue).
- 25.
PHK, Introduction, 126.
- 26.
See also PHK I, 128: “From what hath been said the reason is plain why, to the end any theorem may become universal in its use, it is necessary we speak of the lines described on paper, as though they contained Parts which really they do not. […] And that when we say a line is infinitely divisible, we must mean a line which is infinitely great […]”. See also PHK Introduction, 15–16 and I, 124–132.
- 27.
S. Storrie (2012) defends in a convincing way the thesis, that I endorse here, according to which Berkeley, when writing NTV, was engaged in two distinct geometrical projects: the first, to develop ex nihilo a non-Euclidean geometry of minima; the second, to account for the validity and universality of Euclidean geometry. See also PHK 131.
- 28.
PC 18, 21, 330, 373, 466.
- 29.
- 30.
For more, see R. Schwartz’ paper and mine, in this volume.
- 31.
- 32.
- 33.
In an interesting way, T. Holden (in Holden 2002) underlines the importance of the metaphysical dimension of Hume’s argument against infinite divisibility and its a priori nature. According to Holden, the “purely mathematical reading” is responsible for the dismissive attitude towards Hume’s theory of space.
- 34.
See T. Introduction, xvi.
- 35.
For the copy principle, see T. I. i. i, 4 “That all our simple ideas in their first appearance are deriv’d from simple impressions, which are correspondent to them, and which they exactly represent; for the separability principle, see T 1.1.7, 18 “whatever objects are different are distinguishable, and whatever objects are distinguishable are separable by the thought and imagination”.
- 36.
T. I. iv. ii, 187–218, see more particularly 205, 208, 209.
- 37.
T. I. II. iii, 33–34.
- 38.
A. Rosenberg denounces such circularity: “[…] the manner of appearance of these coloured points has them either to the left or, to the right of, above, or below one another. But where do these ideas come from? They presuppose space. If so, […], the “manner of appearance” of extended minima must be spatial itself, […]” (Rosenberg 1993, 83).
- 39.
Many authors consider the notion of “manner of disposition” as a problematic one introducing a tension into the distinction between a simple and complex idea, the distinction between impression and ideas, and the copy principle. For an insightful description of the questions relative to the status of the notion of “manner of disposition” in Hume philosophy, see Falkenstein 1997.
- 40.
T. I. II. v, 57–58. In the Appendix, Hume confesses that he discovered an error where he claims that “the distance betwixt two bodies is known, among other things, by the angles, which the rays of light flowing from the bodies make with each other.” In fact he says “‘Tis certain that these angles are not known to the mind, and consequently can never discover the distance” (T Appendix, 636). This sentence is very similar in form and content to sections 12 and 13 of Berkeley’s NTV. It is possible to explain Hume’s “more mature reflexion” on the perception of distance through angles supposing that he actually read the Essay toward a New Theory of Vision, only after the publication of the first and second book of the Treatise.
- 41.
T. I. II. v, 56: “When I hold up my hand before me, and spread my fingers, they are separated as perfectly by the blue colour of the firmament, as they cou’d be by any visible object, which I cou’d place betwixt them.”
- 42.
Fogelin (1988, 56–57) claims that Hume, in the Treatise, defends a sensible notion of equality and therefore a kind of sensible, approximative, geometry. D. Jacquette, on the contrary, maintains that “Hume wisely maintains that his indivisibles confer the idea of equality only for purposes of reasoning, and do not provide a practical basis for determinations of geometrical equality and proportion.” (Jacquette 2001, 178; see also 168–180 for a general discussion of this point). Whether Hume’s position on the status of geometry as an empirical or as a deductive science in the Treatise and in the First Enquiry are essentially the same or if they radically diverge is another claim which is a subject of debate in secondary literature (see Newman 1981, 57–58; Fogelin 1988, 57–58). In an interesting way, W. Waxmann (in Waxmann 1994, 115–127 and especially 123–125) connects the question of the (impossible) exactness of the standard of equality to the use of language.
- 43.
Hume’s criticism of empty, insensible space is a criticism of Newton’s insensible, absolute space. Nevertheless, Hume thinks that this key concept of Newtonian physics can be “rightly understood”, that is, it can be rendered compatible with a correct (empiricist) conceptual analysis of space. See T. Appendix, A note to Book I, line 19, p. 64, 639: “If the Newtonian philosophy be rightly understood, it will be found to mean no more. A vacuum is asserted: That is, bodies are said to be plac’d after such a manner, as to receive bodies betwixt them, without impulsion or penetration. The real nature of this position of bodies is unknown. ...”
- 44.
T. I. II. v., 59.
- 45.
T. I. II. v., 60.
- 46.
T. I. II. iii., 34 and 38; several times in relation to empty spaces at T. I. II. v., 56–59. It is possible that Hume takes care on the symmetry between sight and touch on this point because he dreads the heavy theological consequences that Berkeley collects from his heterogeneity thesis that is taken as an essential part of the thesis of vision as the language that God speaks to men. However, it is also possible that when writing the first book of his Treatise, Hume was not yet familiar with Berkeley’s NTV (see above note 40). For a different point of view on Hume’s conception of the heterogeneity of visual and spatial ideas of space, see Waxman 2008.
- 47.
References to Condillac 1947a (Essai sur l’origine des connaissances humaines) are indicated as Essai, followed by part, section, chapter, paragraph and page number. The reference of the English translation (Condillac 2001) is indicated as E transl., followed by the page number. References to Condillac 1947b (Traités des sensations) are indicated as Traité, followed by part, chapter and page number. The reference of the English translation (Condillac 1982) is indicated as T transl followed by the page number. On this point: Essai, Introduction, 4–5; E transl. 5; and in relation to the discussion of the senses: Traité, Dessein de cet ouvrage, 221–223, T transl. 155–158.
- 48.
See Essai, Introduction, 3–5; E transl. 5–8.
- 49.
Essai, Part I, Sect. I, ch. I, §1, 6a, E transl. 11; and more precisely concerning extension Traité, Part IV, ch. v, §1, 306a note, T transl. 323 38n.
- 50.
See also Essai, Part II, sect. II, ch. iii, §36, 11a); E transl. 212. On Condillac’s notion of “analysis”, see Charrak 2003, 124–128.
- 51.
This is explicit in the title of the first part of the Logique (Condillac 1947–1951, II: 372) that is: Comment la nature même nous enseigne l’analyse; et comment d’après cette méthode, on explique l’origine et la génération, soit des idées, soit des facultés de l’âme. Logique, ou les premiers développemens de l’art de penser.
- 52.
However, Condillac has always underlined the difficulties proper to the thesis of the infinite divisibility of space (for instance, Cours d’études: Art de penser (1775) Cours d’études V. De l’Art de Penser, chap. Xii. Condillac 1947–1951. I:754).
- 53.
The primacy of three-dimensional extension explains why Condillac is neither interested in determining the smallest part of extension perceptible by the senses, nor in suggesting that there are some simple constitutive parts of extension, similar to the sensible points or minimum, as Locke, Berkeley and especially Hume did.
- 54.
This idea that a point should be defined in terms of volume will find a new expression with the development of point-free geometry, initiated by Whitehead. On this, see Whitehead 1919.
- 55.
See Traité, Part I, ch. vii, §1–4, 239a–b, T transl. 202–203.
- 56.
- 57.
See Traité, Part I, ch. ii, §4, 225a, T transl. 178.
- 58.
See Traité, Part I, ch. i–vii, viii, x, xi; Part II chap. i–xii.
- 59.
See Traité, Part I, ch. ix, x, xii; Part III, chap. i–ix.
- 60.
See Traité, Part II, ch. vi–viii, xii.
- 61.
Traité, Part II, ch v, §3, 256a, T transl. 234: “[…] it will experience a continuity of self at its fingertips, so to speak; and this same hand that has brought together the formerly separated parts into a single continuum will thereby render extension more perceptible”.
- 62.
The importance of the movement of proper body will be recognized by the idéologues and some of them will even propose to account movement among the senses which would not anymore be five, but six. For more, see Elisabeth Schwartz in this volume.
- 63.
At NTV 146, Berkeley writes: “The prejudice [about the visual perception of spatial ideas by sight …] sticks so fast ·in our minds· that it’s impossible without obstinate striving and mental labour to get entirely clear of it. […]”, my italics. Therefore, when the perceptual contents are considered with the required “obstinate striving and mental labour,” the visual ideas and their tactile meanings may be distinguished and considered separately.
- 64.
- 65.
- 66.
As far as I know, there is no specific literature on the relationship between space and divine presence for empiricist authors. However, the question is treated in relation to Locke (Grant 1981, 238–240, Thomas 2013), and in a scattered way for Berkeley (see Slowik 2016; and the chapter of L. Peterschmitt in this volume tackles the issue). That Condillac does not mention this issue could be significant. For a general approach to the question of divine presence in space before the eighteenth century, see Funkenstein 1986; Grant 1981. On this issue see also Brooke 1991 and Gorham 2011.
- 67.
On Locke see the Ph. Hamou’s chapter in this volume and Hamou 2018. Berkeley and Hume have an articulated position on this issue (see respectively Berkeley 1979d, 231 (Third Dialogue); and Hume, Treatise 1.4.5.); of course, their positions depend on their ways of conceiving ideas, minds and their relationship. Literature on this point is rather extensive, see for instance Garrett 2018; Pappas 1980; Frasca-Spada 1998; Falkenstein 2006. On Condillac’s position concerning the spatial features of mind and ideas there are divergent interpretations: see Ricken 1999; Coski 2003.
- 68.
See Slowik 2016.
- 69.
Most commentators maintain however that Locke, after having criticized Newton’s notion of absolute space, ended up defending a kind of ‘absolutism” (see, inter alia, Ayers 1991; Gorham and Slowik 2014; Grant 1981). However, the absolute space to which Locke refers in Essay II. xiii. 10 does not allow to identify any kind of absolute movement and thus is far from the metaphysical frame required by Newtonian physics. For a ‘non absolutist” interpretation of Locke’s position on space see Thomas 2018. For a more global reflection on the disunion between science and philosophy in the eighteenth century, see Gaukroger 2016.
- 70.
- 71.
- 72.
For an overview of the relationships between the thoughts of space and diagrammatic devices from the twelfth to the seventeenth century, see Vermeir, K. and Regier, J., eds. 2016.
- 73.
- 74.
- 75.
- 76.
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Berchielli, L. (2020). Introduction: Ideas of Space and Their Relation to Experience in Early Modern Philosophy. In: Berchielli, L. (eds) Empiricist Theories of Space. Studies in History and Philosophy of Science, vol 54. Springer, Cham. https://doi.org/10.1007/978-3-030-57620-2_1
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