Abstract
This chapter motivates my general strategy of approaching interpretive issues in Spinoza’s epistemology, especially the natures of the three kinds of knowledge, via an interrogation of the ontology of mathematical entities. I provide relevant background regarding the “mathematization of nature” in the seventeenth century, contrasting different forms of mathematical realism and antirealism, and canvassing the respective views of Descartes, Galileo, Gassendi, and Hobbes as representative of the intellectual landscape. I outline my argument for attributing a geometrical realist position to Spinoza and overview the chapters of the book.
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Notes
- 1.
Cognitio presents a difficult choice for the translator. While “knowledge” is the more common translation (and the one used by Curley), a number of commentators opt for “cognition.” The latter tend to cite the fact that the first kind of cognitio is a cause of falsity (E2p41), whereas nothing worthy of the name “knowledge” should cause falsity. Since “cognition” is more epistemically neutral than “knowledge,” it better encompasses the first as well as the second and third kinds of cognitio (both of which contain only true ideas). However, if we consider that the first kind of cognitio , for Spinoza, can be understood as a part or fragment of a true idea in God’s intellect, then it makes sense, in my mind, to consider it as a kind of knowledge, albeit a partial or fragmentary kind of knowledge. This line of reasoning is reinforced when we consider such passages as E5p38dem: “The Mind’s essence consists in cognitione (by E2p11); therefore, the more the Mind cogniscit things by the second and third kind of cognitionis, the greater the part of it that remains […].” As I see it, to translate cognitio and cognoscere here with the neutral “cognition” and “cognize” obscures the fact that the epistemic situation is not neutral. It is in our nature to know, and to the extent that we do not know, it is only because we are parts of God’s infinite intellect, and thus lack knowledge. Whether our cognitio is inadequate (and thus a cause of falsity) or adequate (and thus true), then, it is a question of epistemically non-neutral knowledge, rather than neutral cognition. There is, however, another argument for translating cognitio as “cognition,” namely, it offers an easy solution for respecting the difference between cognitio and scientia. If cognitio is rendered as “cognition,” this leaves “knowledge” for scientia. I do not think this outweighs the disadvantages of the sterility of “cognition,” however, so I will use “knowledge” for both cognitio and scientia, despite the problem with this procedure. Some have used “science” for scientia to solve this problem. While this might work in certain contexts, rendering scientia intuitiva (Spinoza’s third kind of cognitio ) as “intuitive science” sounds tortured to my ear. See Curley 2:637–38 for further discussion.
- 2.
See KV 2.4.9/G 1:61; KV 2.26.6/G 1:109; E5p28/G 2:297. The notion of reason as a step** stone, which receives strong emphasis in the Short Treatise, is much less apparent in the Ethics, signaling, as I will suggest later, an elevation in the status of reason from the early works to the Ethics. Nevertheless, Spinoza consistently stresses the superiority of the third kind of knowledge, and its status as the pinnacle of human knowing throughout his works.
- 3.
AT VI: 62.
- 4.
The only one of which I am aware, at least in English, is Parkinson 1954. A. Garrett 2003, which is more recent, should also be mentioned. Although it is devoted to Spinoza’s method, there is significant overlap between methodology and epistemology in Spinoza, and Garrett’s erudite study offers valuable insights into the latter. None of this is to say, of course, that there have not been many fine papers devoted to aspects of Spinoza’s epistemology. I will have occasion to reference many of these over the course of this book.
- 5.
I have in mind, in particular, Bennett’s A Study of Spinoza’s Ethics (1984) and Della Rocca’s Spinoza (2008). While addressing Spinoza’s distinction between inadequate and adequate ideas, Della Rocca (2008) ignores the three kinds of knowledge altogether. Bennett, for his part, has some brief things to say about reason and imagination, but only condescends “reluctantly” to touch on intuitive knowledge in order to document its contribution to the “unmitigated and seemingly unmotivated disaster” that is, in Bennett’s estimation, the second half of Ethics Part 5 (1984, 357).
- 6.
My article, “Geometrical Figures in Spinoza’s Book of Nature” (Homan 2018b), is a forerunner of some of the interpretive ideas developed in greater detail here.
- 7.
Gueroult 1974, 471, my translation.
- 8.
Viljanen 2011, 21.
- 9.
Viljanen 2011, 2.
- 10.
Viljanen stresses formal causation in his interpretation of Spinoza’s ontology. When I speak of formal in this context, I do not refer to formal causation, but the form-content distinction.
- 11.
E3pref/G 2:138. Curley renders “de lineis, planis, aut de corporibus” as “lines, planes, and bodies” (my emphasis). I have opted for the more literal translation of “aut” here.
- 12.
One of the questions to be taken up in this study (especially in Chap. 3) is whether Spinoza conceives bodies in geometrical terms or in some non-geometrical fashion. Spinoza’s phrase, “lines, planes, or bodies,” provides prima facie evidence for the geometrical interpretation that I will defend, since the association with “lines” and “planes” suggests that by “bodies” he means geometrical solids.
- 13.
CSM 1:247.
- 14.
Galileo 2008, 183.
- 15.
For a discussion of Descartes’ project of mathematization, see Gaukroger 1980. See, especially, Gaukroger 1980, 123–35, for a useful comparative analysis of the respective Cartesian and Galilean projects of mathematization. Cf. Ariew 2016. Ariew argues against associating this passage with the mathematization thesis on the grounds that Descartes’ physics is not founded on mathematics per se, but on the metaphysics of clear and distinct ideas; it is simply a coincidence, according to Ariew, that “mathematicians rely on some of the same clear and distinct ideas as natural philosophers do” (2016, 121). It is not clear to me, however, why it should matter to the validity of the mathematization thesis whether the overlap between physics and mathematics is coincidental or not. Even if it is due ultimately to a shared metaphysics of clarity and distinctness, the principles of physics end up being mathematical either way.
- 16.
Koyré 1978, 2–3.
- 17.
Gorham et al. 2016, 5.
- 18.
The charge of oversimplification is the guiding thesis of the recent volume of essays, The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the Seventeenth Century (2016), edited by Gorham et al. The authors of the volume’s introduction point out how the notion of mathematization glosses over important differences between types of mathematization. Intuitive geometrical models contrasted with less intuitive algebraic methods, for instance, and seventeenth-century figures debated the respective merits of both. While the idea of mathematization had a great deal of power in the seventeenth-century imagination, this was not always matched with the success of mathematization efforts in practice. A number of fields resisted mathematization while even in physics, many philosophers, such as Descartes, failed to articulate basic laws of nature in mathematical terms. Many prominent early moderns, moreover, such as Gassendi and Locke, who did much to advance “modern” thought, showed relatively little interest in mathematics. For further discussion of the oversimplification charge, see Gorham, Hill, and Slowik 2016, 1–28.
- 19.
For discussion of Platonism in contemporary philosophy of mathematics, see Balaguer 2009.
- 20.
Some philosophers of mathematics associate this form of non-Platonist realism with Aristotle. (See Franklin 2009.) Since Aristotle’s philosophy of mathematics is a matter of scholarly dispute and since Aristotelianism is freighted with myriad connotations in the context of discussing early modern philosophy, I avoid this terminology here. I will touch upon Aristotle’s philosophy of mathematics as background for considering Descartes’ and Spinoza’s in Chap. 3. “Psychologism” is considered by some philosophers of mathematics to be another form of non-Platonist realism. (See Balaguer 2009, 38.) Since psychologism is the view that mathematical entities exist as mental entities, this realist categorization is potentially misleading, since in this study the view that figures exist only as mental entities is categorized as a form of antirealism. My categorization hews more closely to the terminological landscape in the philosophical discussion of the problem of universals (which overlaps with, but is distinct from, the discussion of the ontology of mathematical entities in philosophy of mathematics).
- 21.
- 22.
I touch on the question of Descartes’ Platonism in Chap. 3.
- 23.
In dubbing Hobbes an anti-rationalist, I mean to highlight primarily his hostility to innate ideas, as exhibited in his objections to Descartes’ Meditations. (The same goes for Gassendi, too.)
- 24.
This is not to say, of course, that there are no differences between Gassendi and Hobbes, too. See n. 27.
- 25.
CSM 2:135.
- 26.
CSM 2: 223.
- 27.
A difference between Gassendi and Hobbes is that whereas Gassendi appears to recognize the existence of general concepts, Hobbes generally appears not to do so. Gassendi’s talk of a common nature formed in the intellect in the passage quoted in the previous paragraph exhibits this recognition. The view that universals exist only as concepts in the mind is often called “conceptualism.” In this case, “nominalism” would represent the stronger view that universals do not even exist as concepts. This terminological division can be seen in, for instance, Di Bella and Schmaltz 2017, 4–7. According to this terminology, then, Gassendi, along with many other early modern philosophers (including, arguably, Descartes), is a conceptualist while Hobbes is a nominalist. Usage of these terms is quite inconsistent, however. LoLordo (2017) depicts Gassendi as recognizing universal concepts, but characterizes him as a nominalist. Leibniz (1989, 128), notably, characterizes the mainstream early modern view as “nominalist,” reserving the term “super-nominalist” for Hobbes. I am following Leibniz and LoLordo in using “nominalist” here in the broad sense that encompasses “conceptualism.”
- 28.
Sepkoski’s monograph Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy (2007) is notable for its association of the term “constructivism” with the nominalism (and antirealism) of such figures as Gassendi, Hobbes, and Berkeley. Sepkoski defines constructivism in explicitly antirealist terms as “the belief that mathematical objects are not mind-independent entities or abstractions from physical reality, but rather are artificial ‘constructions’ produced by the mind that serve as tools in mathematical demonstration” (2007, 129). For usage of the term “constructivism” in relation to Spinoza, see Hübner 2016, 59. Gorham et al., by contrast, deploy the term “instrumentalism” in contrast with “realism” in discussing attitudes toward mathematization (2016, 3).
- 29.
See Hobbes 2005, 6.
- 30.
Francis Bacon is perhaps an exception here, though even in his case, recent scholars have found him friendlier to mathematics and quantification than traditionally thought. See Jalobeanu 2016.
- 31.
Bennett 1984, 21. See also Curley 1988, 33; Allison 1987, 25; Lecrivain 1986, 15–24; and Lachterman 1978, 75–80. In defending an alignment of Spinoza with the modern mechanistic philosophy of Descartes and Hobbes, Lachterman (1978, 76–7) takes himself to be departing from the previous, romantic, and idealist interpretations of Spinoza, which downplayed or ignored the scientific dimensions of his thought. In this light, I certainly do not suggest that the interpretation of Spinoza as a realist about mathematics was always standard.
- 32.
- 33.
- 34.
I assume that Spinoza has a physical ontology, and, thus, that Spinoza is not an idealist. I recognize that some commentators have read Spinoza as an idealist, and thus my assumption that he is not might be deemed question-begging. To this charge I would say the following. First, although I accept that there are viable grounds for an idealist reading of Spinoza (notably, Spinoza’s definition of attribute in E1d4), it is nevertheless the case that the vast majority of textual evidence tends in the opposite direction. I have in mind Spinoza’s affirmation of a seemingly self-sufficient attribute of extension and his ubiquitous talk of extended bodies and their motions. Second, although I will not engage directly with the arguments for the idealist reading (i.e., I will not discuss the controversy surrounding E1d4 at any length), I will present arguments on behalf of geometrical figures as the determinations of finite bodies in Chap. 3. Inasmuch as these arguments help make the case for the realist reading of physical nature in Spinoza, my interpretation does not beg the question. Admittedly, Spinoza’s affirmation of finite bodies is not without well-known problems, even if mind-independent physical reality is assumed. I touch on some of these issues in Chap. 3. For an overview of idealist readings of Spinoza, see Newlands 2011. For a recent defense of a realist reading of the attributes, see Melamed 2018, 90–5. See also, my paper, Homan 2016, in which I argue for the parity of thought and extension qua attributes, thereby countering a major motivation for the idealist reading.
- 35.
It is perhaps futile to attempt to list the epistemological issues I will not take up, since there are indefinitely many that could be identified, but I want to mention three notable omissions. (1) One interesting question outside the scope of this study pertains to Spinoza’s theory of error as privation: what happens to an imaginative, inadequate conception of X when we come to achieve an intellectual, adequate understanding of X? Is the former radically transformed (perhaps eliminated) or do we go on experiencing the world as we did prior to gaining adequate understanding, albeit with the addition of adequate ideas? For a thought-provoking discussion of this question, see Cook 1998. (2) Another issue is the question of whether Spinoza’s theory of epistemic justification is foundationalist or coherentist. Since God is the epistemic foundation in Spinoza’s system, and since God is, in a sense, everything, it would not be wrong to say that to know anything one must know everything. Nevertheless, in my view, it is God as foundation that is doing the epistemic work, not God as everything. While I do not argue for this point explicitly, what I say in Chap. 2 should help to motivate, and partially justify, my view, if only indirectly. For discussion of this issue and defense of a coherentist reading, see Steinberg 1998. (3) Finally, I do not explicitly take up the question of Spinoza’s commitment to the principle of sufficient reason. The PSR is emphasized in Michael Della Rocca’s highly influential interpretation of Spinoza (especially in Della Rocca, 2008) and, as a result, has recently been much discussed by Spinoza scholars. (For critical discussions of Della Rocca’s PSR-focused reading of Spinoza, see Laerke 2011, Garber 2015, and Lin 2019, 164–81.) There is no doubt that the PSR is relevant to Spinoza’s epistemology. As I will emphasize and discuss in more detail below, to know X, for Spinoza, is to know the cause of X. Inasmuch as this suggests a commitment to the PSR, the PSR looms large over any study of Spinoza’s epistemology. For Della Rocca, however, the PSR is an Ur-principle that governs all aspects of Spinoza’s system, thus transcending epistemological matters (at least as narrowly conceived). Indeed, perhaps somewhat ironically, one of the few areas of Spinoza’s philosophy that Della Rocca has relatively little to say about are the three kinds of knowledge themselves (especially the second and third kinds). To take up the PSR as understood by Della Rocca in any systematic manner, then, calls for a very different kind of study than what is proposed here.
- 36.
Curley 1: 5.
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Homan, M. (2021). Introduction. In: Spinoza’s Epistemology through a Geometrical Lens. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-76739-6_1
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