Unconscious Conceiving and Leibniz’s Argument for Primitive Concepts, (with Stephen Puryear) more

Unconscious Conceiving and Leibniz’s Argument for Primitive Concepts Paul Lodge (Oxford) Stephen Puryear (Stanford) In a recent paper, Dennis Plaisted examines an important argument that Leibniz gives for the existence of primitive concepts. 1 Plaisted concentrates on a version of the argument found in a piece from the late 1670s called Of an Organum or Ars Magna of Thinking. 2 However, truncated versions of essentially the same argument can be found in several other writings from the period. 3 Plaisted begins his treatment by sketching a natural reading of Leibniz’s argument. He points out that, on this reading, the argument implies something clearly inconsistent with Leibniz’s other views. To save Leibniz from contradiction, Plaisted offers a revision. However, his account faces a number of serious difficulties and therefore does not successfully eliminate the inconsistency. In what follows we explain these difficulties and propose a more plausible alternative. Whilst our paper is constructed around a critique of Plaisted’s article, it has a broader scope. For in responding to the interesting problem that he identifies, we discuss in detail the neglected topic of Leibniz’s views on the nature of conceiving and, in the process, we bring to light his commitment to the somewhat surprising thesis that one can conceive something through a concept even if one has no conscious grasp of that concept. Dennis Plaisted, “Leibniz’s Argument for Primitive Concepts,” Journal of the History of Philosophy 41:3 (2003): 329-41. 2 See A VI iv 156-60/MP 1-4. The editors of A VI iv speculate that this piece may have been written in March or April 1679. In citing the works of Leibniz the following abbreviations are used: A: G. W. Leibniz. Sämtliche Schriften und Briefe (Berlin: Akademie Verlag, 1923- ); AG: Philosophical Essays, R. Ariew and D. Garber, trans. and eds. (Indianapolis, IN: Hackett, 1989); GP: Die philosophischen Schriften von G. W. Leibniz, 7 vols., C. I. Gerhardt, ed. (Berlin: Weidman, 1875-90; repr. Hildesheim: Georg Olms, 1966); LH: Die Leibniz-Handschriften de Königlichen Öffentlichen Bibliothek zu Hannover. E. Bodemann, ed. (Hannover: Hahn, 1889; repr. Hildesheim: George Olms 1966); MP: Leibniz: Philosophical Writing, M. Morris and G. H. R. Parkinson, trans., G. H. R. Parkinson, ed. (London: J. M. Dent, 1973); NE: New Essays on Human Understanding, P. Remnant and J. Bennett, trans. and eds. (Cambridge: Cambridge University Press, 1996). The text of NE appears in A VI vi and the pagination is the same. WF: Leibniz’s ‘New System’ and Associated Contemporary Texts, R.S. Woolhouse and R. Francks, trans. and eds. (Oxford: Clarendon Press, 1997). 3 Although these texts all predate the emergence of Leibniz’s mature philosophy, he never relinquished his belief in primitive concepts and there is no obvious reason to think he ever gave up this argument. For a late affirmation of the existence of primitive concepts, see Monadology §§ 33-35 (GP VI 612/AG 217). 1 1 1. Leibniz’s argument and its attendant problem In the Ars Magna, Leibniz writes: [1] Whatever is thought by us is either conceived through itself, or involves the concept of another. [2] Whatever is involved in the concept of another is again either conceived through itself or involves the concept of another and so on. So [3] one must either proceed to infinity, or all thoughts are resolved into those which are conceived through themselves. [6] If nothing is conceived through itself, nothing will be conceived at all. For [4] what is conceived only through others will be conceived insofar as those others are conceived, and so on; so that [5] we may only be said to conceive something in actuality when we arrive at those things which are conceived through themselves. 4 Leibniz’s reasoning can be expressed more clearly as follows: (1) Every concept is either primitive or complex, i.e., composed of other concepts. (assumption) (2) Every concept that composes a complex concept is itself either primitive or complex. (from (1)) (3) Complex concepts are either composed of other concepts to infinity, or ultimately composed of primitives. (from (2)) (4) Complex concepts are conceived only insofar as their constituents are conceived. (assumption) 5 (5) A complex concept is conceived only if it is ultimately composed of primitives. (from (4) (6) If a complex concept is composed of other concepts to infinity, then it will not be conceived. (from (5)) Clearly this establishes only the conditional conclusion (6) and not the existence of primitive concepts. But Leibniz elsewhere sketches the same basic line of thought and extends it in the following way: 6 (7) Some complex concepts are conceived. (unstated assumption) 7 (8) Some complex concepts are not composed of other concepts to infinity. (from (6), (7)) A VI iv 157/MP 1-2. The bracketed numbers have been inserted to make clearer how the subsequent reconstruction maps onto Leibniz’s own statement of the argument. 5 We follow Plaisted in using locutions such as “conceiving (of) a concept”, which we take to be shorthand for something like “conceiving a thing through a concept”. 6 See LH IV vii Bl., 2, 57r, quoted in B. Mates, The Philosophy of Leibniz: Metaphysics and Language (Oxford: Oxford University Press, 1988), 59; and Plaisted’s discussion at “Leibniz’s Argument,” 333. 7 Though Leibniz never explicitly affirms this, Plaisted convincingly argues that Leibniz commits himself to (7) in many ways and implicitly relies upon it in his argument for primitive concepts. See “Leibniz’s Argument,” 332-33. 2 4 (9) Some concepts are ultimately composed of primitives. (from (3), (8)) (10) There are primitive concepts. (from (9)) (1)-(10) thus constitute Leibniz’s argument for primitive concepts. 8 As Plaisted points out in his discussion, this argument, together with a certain assumption, commits Leibniz to something he clearly denies: that we can actually analyse many complex concepts into their primitive constituents. The assumption is simply that conceiving a concept requires “some conscious awareness of the concept,” 9 and the commitment arises in the following way: (11) A complex concept is actually conceived only if its primitive constituents are conceived. (from (4)) (12) The primitive constituents of some complex concepts are conceived. (from (7), (11)) (13) Conceiving of a concept requires some awareness of the concept. (unstated assumption) (14) If the primitive constituents of a concept are conceived, then that concept can be analysed by us into primitives. (from (13)) (15) Some complex concepts can be analysed by us into primitives. (from (12), (14)) 10 We are now in a position to grasp the difficulty facing Leibniz. If the preceding analysis is correct, his argument for primitive concepts commits him to (15), the thesis that we can analyse our complex concepts into their primitive ingredients. Yet as Plaisted correctly observes, Leibniz rejects precisely this thesis in many places. For example, in the slightly later piece An Introduction to a Secret Encyclopaedia, he writes: An analysis of concepts by which we are enabled to arrive at primitive notions, i.e., at those which are conceived through themselves, does not seem to be within the power of man. 11 Although Plaisted does not lay it out expressly in numbered premise-conclusion form as we have, our reconstruction coheres nicely with his natural reading of the argument. Cf. “Leibniz’s Argument,” 332. Note that Plaisted does number some key claims: our (4) and (7) correspond respectively to his (1) and (3). 9 Op. cit., 338. 10 This account of how Leibniz’s argument for primitive concepts engenders commitment to (15) does differ from that of Plaisted, who sees (15) as following from (7) together with this “obvious corollary” of the argument: (16) “We can conceive of a complex concept only if we can analyse it into the primitive concepts out of which it is composed” (Op. cit., 334). Actually (16) is not strictly a corollary of Leibniz’s argument, but of that argument together with the assumption (13). One way to see this is to note that whereas (4) entails (11), (13) entails (14), and (11) and (14) jointly entail (16), there is no way to derive (16) from (1)-(10) without assuming something like (13). Still, Plaisted is quite right that (7) and (16) collectively entail (15). We nevertheless prefer to think of Leibniz’s apparent commitment to (15) as arising by way of (11)-(14) rather than (16), since doing so renders the logic of the situation more explicit. 8 3 Even in the Ars Magna he expresses scepticism about our ability to analyse concepts into primitives. Having suggested that there may be just two concepts, those of God and nothing, he remarks that “it is not in our power to demonstrate the possibility of things in a perfectly a priori way, that is, to analyse them into God and nothing.” 12 In committing him to (15), then, Leibniz’s argument for primitive concepts leads him into a fairly obvious contradiction. 2. Plaisted’s revision Plaisted proposes to deal with this problem by making an adjustment to Leibniz’s argument. 13 More precisely, he suggests replacing (4) with a slightly different premise that would, according to him, allow the argument for primitive concepts to go through without giving rise to the problematic (15). In order to understand the rationale for this revision, we need to introduce some distinctions drawn in Leibniz’s 1684 publication Meditations on Knowledge, Truth, and Ideas (MKTI). 14 The first that concerns us is this: A notion which is not sufficient for recognizing the thing represented is obscure …. [K]nowledge [cognitio] is clear when I have the means for recognizing the thing represented 15 Obscure notions or concepts are of no interest to us here. 16 What is important is that having a clear concept of something entails being able to recognize that thing. Leibniz continues: A VI iv 530/MP 8. The editors of A VI iv suggest a date for this piece between the summer of 1683 and beginning of 1685. 12 A VI iv 158/MP 3. 13 In fact Plaisted considers another way in which the problem might be avoided, namely by assuming that Leibniz may have come to regard the task of analysis into simple concepts as within our reach. Some texts do suggest this, but as Plaisted points out, they are limited in force and scope. Even if they show that Leibniz thinks that some of our complex concepts (e.g., those of numbers) can be analysed into primitives, they also reinforce the thought that most such concepts cannot be fully analysed. Thus, since Leibniz’s argument seems to require that all complex concepts that we actually conceive be analysable into primitives, these texts do not furnish an adequate solution. They also fail to explain why even in the Ars Magna Leibniz denied that we can analyse derivative concepts into their simple constituents. See “Leibniz’s argument,” 336. 14 Similar accounts can be found at A VI iv 528/MP 6 and A VI iv 1567-68/AG 56. It is notable that as late as 1704 in the New Essays, Leibniz refers readers to the discussion of MKTI as representative of his views. (See NE 254 and 296 for explicit references. But also see NE 127, 219, and 266, where aspects of the discussion are invoked). 15 A VI iv 586/AG 24. 16 Although Leibniz uses the term ‘notion’ [notio] here, it is clear from the rest of his discussion that he is using ‘notion’ and ‘concept’ [conceptus] interchangeably. 4 11 Clear knowledge, again, is either confused or distinct. It is confused when I cannot enumerate one by one marks sufficient for differentiating a thing from others, even though the thing does indeed have such marks and requisites into which its notion can be resolved. 17 Although they are not the only ones, phenomenological concepts are of this kind for Leibniz, as he makes clear later in the same paragraph. A concept such as the concept of red, he explains, must be composite and resolvable into simpler concepts, since red has a cause. But a person can have a concept of red without being able to analyse it into any of those constituents. In that case, she conceives red clearly but confusedly. In contrast: [A] distinct notion is like the notion an assayer has of gold, that is, a notion connected with marks and tests sufficient to distinguish a thing from all other similar bodies. 18 These distinguishing marks of gold are just those given by the concepts that enter into the concept of gold. For example, solubility in aqua fortis (a nitric acid solution) is a mark of gold, which means that the concept of gold includes that of solubility in aqua fortis. One conceives a thing distinctly, then, when one can not only recognize the thing but analyse its concept, at least to some degree. One final component of Leibniz’s discussion is also important if we are to understand Plaisted’s solution. Leibniz adds: But in composite notions, since, again, the individual marks composing them are sometimes understood clearly but confusedly, like heaviness, colour, solubility in aqua fortis, and others, which are among the marks of gold, such knowledge of gold may be distinct, yet inadequate. When everything that enters into a distinct notion is, again, distinctly known, or when analysis has been carried to completion, then knowledge is adequate. 19 The assayer’s distinct concept of gold is thus resolvable into various constituents, which give the distinguishing marks of gold. Some of these constituents may in turn be resolvable into other, simpler concepts, though others, such as the concept of yellow, will not: they will be clear but confused. However, if every concept that enters into some complex concept C is distinct, or in other words if the analysis of C can be completed, then C is said to be not only distinct but adequate. With these considerations in mind, Plaisted contends that Leibniz obviously thinks that “we can have a concept without having it adequately.” 20 The phenomenological concept of red, the colour scientist’s concept of red, and the assayer’s concept of gold, all seem to be of this 17 A VI iv 586/AG 24. Note that Leibniz appears to consider having clear knowledge [cognitio] equivalent to having a clear notion or concept. 18 Ibid. 19 Ibid. 20 “Leibniz’s Argument,” 337. 5 kind. In other words, it seems we can safely assume that Leibniz would not have accepted both (11) and (14), since they jointly entail (16), which is equivalent to the denial of precisely this claim. But (14) follows from the natural assumption that conceiving requires awareness (i.e., (13)), and (11) follows from (4). Hence, given that Leibniz accepted (13), we have reason to suspect that he did not really mean to endorse (4). But then how should we understand the argument from primitive concepts? To answer this question Plaisted looks again to the texts just discussed, which he takes to establish that, on Leibniz’s view, conceiving admits of degrees. Plaisted writes: The maximal degree of conception is adequate conception. Somewhere below that degree lies the clear and distinct degree of conception. Undoubtedly, there are degrees between the clear and distinct level and the adequate level, degrees that correspond, roughly, to how far one can carry the analysis of the marks involved in clear and distinct conception. Then, lying below the clear and distinct degree (again, with degrees between it and the clear and distinct degree) is the clear but confused level. 21 Plaisted is now in a position to offer a revision of (4) that allows us to understand why Leibniz would reject (11) but which still grounds the argument for primitive concepts. He first claims that for Leibniz “the degree to which we can conceive of a complex concept crucially and clearly depends on the degree to which we conceive of its components” 22 and, in light of this, he suggests that (4) should be understood in the following way: (4′) Complex concepts are conceived only if [some of] their component concepts are conceived, and the degree to which a complex concept is conceived is directly proportional to the degree to which we conceive of its component concepts. 23 The advantage of (4′), according to Plaisted, is that it entails (5) but not (11). Recall that (5) is this: (5) A complex concept is conceived only if it is ultimately composed of primitives. As Plaisted has it, (5) follows from (4′) for the following reason. Let C be a complex concept not ultimately composed of primitives. According to (4′), we conceive C to the extent that we conceive its constituent concepts. If all C’s constituents are conceived, then C is fully conceived, and if none, then not at all. Now since C has no primitive components, it must be composed of an infinity of complex concepts. But in that case, Plaisted reasons, we will not be able to conceive C at all: If there were no simple concepts, then every complex concept would be such that one would have to conceive of an infinite number of concepts to conceive of it fully. And, in that case, the degree to which we could conceive of the concepts through which the 21 22 23 Op. cit., 338. Op. cit., 339. Op. cit., 340. Note that our (4′) corresponds to Plaisted’s (1**). 6 complex one is conceived is, for all intents and purposes, zero. Regardless of how far we carry the analysis of the concept, we are no closer to conceiving the component concepts than if we had never even begun the analysis. Thus, it can still be said that if there are no simple concepts, then we will not be able to conceive of anything. 24 Hence, if C is to be conceived at all, it must ultimately be composed of concepts that are not themselves composed of others. In this way, (5) follows from (4′). However, (4′) does not, we are told, entail (11), that is: (11) A complex concept is conceived only if its primitive constituents are conceived. (from (4)) For so long as C ultimately resolves into primitives, it will be possible to conceive C just by conceiving some of its ingredients. We need not conceive all of them, because we can be said to conceive C even if we do not conceive it fully. So (11) does not follow from (4′): a complex concept can be conceived even if its primitive components are not. But if that is so, then Leibniz’s argument for primitive concepts no longer commits him to (15). Plaisted’s revision therefore appears to rescue Leibniz from difficulty. 3. Difficulties with Plaisted’s proposal Despite its initial promise, a closer look at Plaisted’s proposal reveals serious problems. The first stems from Leibniz’s belief that some concepts are so confused we cannot even begin to analyse them. The concept of blue provides an example: “one cannot give marks for recognizing blue if one has not seen it. Hence, blue is its own mark, and in order for someone to know what blue is, we must necessarily show it to him.” 25 Recall that to know a mark of some quality or thing is to grasp an ingredient concept of the concept of that quality or thing, so if we cannot give a mark for blue, save blue itself, that means we cannot discern any of the components of our concept of blue. And what is true of blue is true of sensible qualities in general: [T]he ideas of sensible qualities, proper to organs, like those of colour and heat … are clear, because we recognize them and discern easily the ones from the others, but they are not at all distinct, because we cannot distinguish that which they contain. Thus we cannot give the definition. We can only make them known Ibid. “On What Is Independent of Sense and Matter,” GP VI 500/AG 187. Leibniz sometimes seems to affirm that it is within our power to define or give marks for some colours (see, e.g., GP III 247/AG 287; NE 389-90). But his point in such texts is not that at the time he wrote people were able to define these qualities; his point is that given enough time and scientific progress we would be able to define these qualities. Contrary to appearances, then, Leibniz’s belief that “one cannot give marks for recognizing blue if one has not seen it,” understood as a claim about what could be done in Leibniz’s day, does not conflict with his apparent belief that we will (one day) be able to give such marks for blue. 25 24 7 through examples, and beyond that we must say that they are a je ne sais quoi, until we can decipher their structure [contexture]. 26 Leibniz therefore thinks we have concepts of various sensible qualities even though we cannot (consciously) conceive any of the components of these concepts, something Plaisted himself essentially acknowledges when he writes: “Leibniz also speaks as though we have the concepts of various colors, which are complex concepts, although we really have no idea of how even to begin to analyze such concepts.” 27 But notice that if Leibniz accepted Plaisted’s (4′), he would have to deny that we conceive of such sensible qualities at all. For (4′) includes the claim that “We can conceive of a complex concept only if we can conceive of the component concepts through which it is conceived.” Further, (4′) says that “the degree to which a complex concept is conceived is directly proportional to the degree to which we conceive of its component concepts.” If Leibniz accepted this, then he would have to say that we conceive sensible qualities to degree zero, that is, not at all. Yet he clearly does not think this, and so he evidently would not agree to (4′). Contra Plaisted’s reading, Leibniz thinks we can conceive a concept even if we (consciously) conceive none of its component concepts. In fairness to Plaisted, we observe that he acknowledges this difficulty and addresses it in a footnote, offering the following response: I am not sure how Leibniz would meet this difficulty. Perhaps he would respond that if we do, in fact, possess a clear grasp of a complex concept, then we must have at least some obscure grasp of its components, even if we cannot say what those components are, let alone analyze them. As discussed earlier, Leibniz believes that all ideas already reside in our souls, but there are many of them of which we have no conscious awareness. And so maybe the point here would be that having a clear hold of a complex concept will carry with it a conscious awareness, albeit an obscure, low-level one, of that concept’s components. 28 Plaisted here adds a new wrinkle to his account, suggesting that perhaps awareness, like conception, admits of degrees. This allows him to say that with confused concepts of sensible qualities, we may have a kind of low-grade awareness of the concept’s ingredients—a level of NE 255; see also NE 120, 403; Leibniz to Burnett, 20/30 January 1699, GP III 247/AG 287; IV 550/WF 105; “On What Is Independent of Sense and Matter,” VI 499-500/AG 187. One might object to our use of the text at NE 255 on the grounds that, since Leibniz sometimes accommodates his language to Locke’s and the latter sometimes uses ‘ideas’ to refer to perceptions, Leibniz may really be making a point about perceptions rather than ideas of sensible qualities. It should be noted, however, that the passage at issue appears in the midst of a discussion in which Leibniz (Theophilus), alluding to MKTI, criticizes Locke’s definition of ‘distinct idea’ and clarifies how he (Leibniz) understands the difference between distinct and confused ideas. Given the context and Leibniz’s practice of taking care to distinguish ideas from perceptions or thoughts, it seems unlikely that this is a case in which he is thinking of perceptions but calling them ideas. 27 Op. cit., 337. 28 Op. cit., 339. 8 26 awareness that makes it plausible to say that we conceive those ingredients—but not enough to allow us to analyse the concept or to recognize those ingredients within it. Let us say that to have ordinary, high-grade awareness of something is to be aware1, whereas to have the sort of obscure, low-grade awareness of something envisioned by Plaisted is to be merely aware2. Plaisted’s idea would then be that analysis requires us to be aware1 of the ingredients of a concept, whereas conceiving requires only that we be at least aware2 of a concept. So Leibniz could say that when we conceive a sensible quality clearly but confusedly, we are aware1 of the concept but only aware2 of (some of) its ingredients. Accordingly, we could conceive at least some of the ingredients of the concept, being aware2 of them, and therefore conceive the concept itself to some degree, without being able to analyse it at all, because we are not aware1 of any of those ingredients. We consider this response highly unsatisfactory. In the first place, Leibniz’s writings provide no clear evidence that he ever accepted or even entertained this sort of distinction between two levels of awareness. If anything they suggest the opposite, for he goes out of his way to emphasize that our confused ideas of sensible qualities, though complex, appear simple, and do so because “we are at least not aware of any divisions within them [au moins nôtre apperception ne les divise pas].” 29 In saying this, he seems to deny that we have any awareness of the constituents of these concepts, since awareness of the constituents would require awareness of divisions within the concepts themselves. It follows that if conceiving a concept requires some awareness of that concept (per (13)), then Leibniz would admit that we can conceive many concepts even though we cannot conceive any of their ingredients. And this is precisely what causes trouble for Plaisted’s (4′). Further, we find it hard to see how one could genuinely be aware of the components of a confused concept without at least being able to analyse that concept into those components, especially when those components are themselves clear concepts. Consider Leibniz’s example of the concept of green, which according to him includes those of yellow and blue. 30 On Plaisted’s proposal, conceiving green would require us to conceive yellow and blue with at least some degree of awareness (i.e., awareness2). A person who conceives green would thereby (consciously) conceive yellow and blue. But in that case, it would seem that nothing prevents this person from being able to analyse green into yellow and blue. Imagine a pre-scientific person who has seen all these colours and therefore has clear but confused concepts of them, but who knows nothing more about them than what they look like. If Plaisted’s suggestion were correct, then when this person conceived of green clearly but confusedly, she would also conceive of yellow and blue and would have some low-level awareness of these components in her concept of green. But if this person truly had some awareness of these components, even a low-level one, then analysing green into yellow and blue ought to come rather easily to her. Merely by attending to these concepts of which she had some (low-level) awareness, she ought to be able to see that her concept of green contains the familiar concepts of yellow and blue. Yet this is far from how Leibniz views the matter. On his view, discovering the true analysis of a colour requires more than just attention to what we conceive when we conceive the colour; it 29 30 NE 120; see also NE 170, 299. See NE 120, 297, 403; “Praefatio ad Libellum Elementorum Physicae,” A VI iv 2005-6/L 287. 9 requires a considerable amount of reasoning and experimentation. 31 Thus, Leibniz would evidently want to deny that when we have a maximally confused concept of a colour like green, we have any awareness of the constituents of this concept. In view of these points, we conclude that Plaisted has not adequately addressed this objection. Returning now to Plaisted’s strategy for blocking commitment to (15), a second difficulty is that (4′), his replacement for (4), actually rules out the very thing it was supposed to accommodate: the possibility of conceiving a concept without conceiving all its components. To see why, suppose we have some complex concept C only some of the constituents of which we conceive. Of the constituents we actually conceive, consider those that are the simplest, that is, those which we would arrive at if we carried the analysis of C as far as we can. By hypothesis we conceive these concepts; yet (4′) says: (4′) Complex concepts are conceived only if [some of] their component concepts are conceived, and the degree to which a complex concept is conceived is directly proportional to the degree to which we conceive of its component concepts. According to (4′), then, we would have to say that we conceive these concepts—the simplest ingredients we actually conceive—to degree zero, that is, not at all; for we do not conceive any of their component concepts. This, however, contradicts the hypothesis. So once we accept (4′), we cannot coherently allow partial conception. Either we conceive all the way down to the primitives entering into C—conceive C fully—or we do not conceive C at all: there is no middle ground. 32 A third problem: even on Plaisted’s revised reading the argument for primitive concepts still commits Leibniz to the problematic (15). It does so because, like its predecessor, (4′) entails (11) A complex concept is conceived only if its primitive constituents are conceived. Again, consider our concept C. Since by hypothesis C is a complex concept that we do not fully conceive, it must have some component concepts that, whilst complex, are the simplest ones that we conceive. As we argued above, though, (4′) entails that these relatively simple concepts will not be conceived at all, since by hypothesis none of their components are conceived. But then for the same reason, (4′) entails that we do not conceive the concepts that these simpler concepts compose either, and in this way our failure to conceive the simpler concepts percolates up to the more complex ones, with the effect that not even C itself is conceived. Hence, if C is conceived at all, it must be conceived fully, at least in the sense that all its component concepts are See NE 120; G IV 575/WF 141. The same conclusion follows from Leibniz’s claim, in another presentation of his argument for primitive concepts, that “if we do not conceive of anything per se, we do not conceive of anything at all” (LH IV vii Bl., 2, 57r, quoted in Mates, op. cit., 59). According to this claim, conceiving requires not only that there be per se concepts, but that we actually conceive them. 32 31 10 conceived. For this reason, (11) follows from (4′); but then (15) is still a consequence of Leibniz’s argument. So Plaisted has failed to save Leibniz from inconsistency. 33 Notice that these second and third objections could be removed by Plaisted were he to understand (4) as the claim that (4′′) Complex concepts are conceived by us only to the degree that we can analyse them. In that case he would have to admit that our analysis of C terminates in concepts that we do not actually conceive, since we would be completely unable to analyse these simplest accessible concepts. But so long as he was willing to bite that bullet, he could consistently maintain that complex concepts are only partially conceived. These simplest accessible concepts would not be the simplest concepts that we actually conceive; rather the latter concepts would resolve into the former. So the simplest components that we actually conceive would truly be conceived, at least to some degree. Further, since these components would actually be conceived, the more complex concepts that they compose would also be conceived at least to some degree: there would be no percolation problem. Hence, (4′′) would neither rule out the idea of partial conception nor entail (11). But Plaisted could argue that it nonetheless entails (5) for the same basic reason (4′) does: namely because, in the absence of primitives, there would for all intents and purposes be no analysis at all. Hence, Leibniz’s argument for primitive concepts would still go through, but without committing him to (15). We find this proposal unacceptable for two reasons. First, it still requires Plaisted to say that concepts of sensible qualities, and more generally the simplest accessible components of our complex concepts, are not conceived at all. For since we cannot even begin to analyse these complex components, (4′′) would entail that we cannot even begin to conceive them. Yet Leibniz maintains that sensible qualities can be conceived even if we cannot begin to analyse our concepts of them. Second, we reject (4′′) as a reading of (4) because it distorts Leibniz’s intended meaning. When he remarks that “what is conceived only through others will be conceived insofar as those others are conceived”, he leaves little room for reading this as a claim about analysis. One reason we might think otherwise is that Leibniz’s claim leads him to infer that we actually conceive something only when we “arrive at” [incidemus] its primitive components. This talk of arriving at primitives could be interpreted plausibly enough as referring to analysis, but then (4) would need to be understood along the lines of (4′′) in order for (5) to follow. However, we believe Leibniz’s talk of arriving at primitives is unclear and that the more perspicuous and straightforward (4) should be allowed to clarify what he means by this expression, not the other way around. We consider it best, therefore, to take (4) at face value and The fundamental problem with (4′) is that it is logically equivalent to (4). If complex concepts are conceived only insofar as their components are conceived, it will follow that (a) such concepts are conceived only if their components are conceived and (b) such concepts are conceived to a degree directly proportional to the degree to which we conceive their components. That is, (4) entails (4′). Further, if (a) and (b) are true, then complex concepts will be conceived only insofar as their components are conceived. So (4′) entails (4). Given the equivalence of (4) and (4′), it is unclear what advantage is supposed to be gained by replacing the former with the latter. 11 33 interpret the claim that conception requires that we “arrive at” primitives as meaning nothing other than that we must conceive those primitives. For these reasons we reject the replacement of (4) with (4′′) as a solution to the problem. Now for our final objection: we think Plaisted’s reading of the argument for primitive concepts misconceives the thought behind the move from (4)/(4′) to (5). As we saw above, he explains this inference as follows. Since a complex concept not ultimately composed of primitives will have an infinity of components, no matter how many of these we may conceive we will always be infinitely far from conceiving them all. For all intents and purposes, then, we will conceive none of them. But then by (4)/(4′), we will not conceive the complex concept at all. So (4)/(4′) entails: (5) A complex concept is conceived only if it is ultimately composed of primitives. Whilst this may be one way to understand the inference from (4)/(4′) to (5), we think Leibniz had something else in mind, and we speculate that Plaisted’s failure to see this explains why he fails to grasp the full logical import of (4′). The key to understanding Leibniz’s thought is what he says just after sketching his argument for primitive concepts (i.e., (1)-(6)) in the Ars Magna: I will illustrate this by a simile. I give you a hundred crowns, to be received from Titus; Titus will send you to Caius, Caius to Maevius; but if you are perpetually sent on in this way you will never be said to receive anything. 34 Leibniz tells us here that unless someone pays rather than deferring to others, nothing will be received at all; that is, nothing will have been received from Leibniz unless one of the people to whom we are sent himself delivers the goods. The implication is that in much the same way a complex concept will not be conceived at all unless it has ultimate constituents that are conceived through themselves rather than through others. But if that is what the simile shows, then it is hard to see how to reconcile it with Plaisted’s understanding of the argument. If that understanding were correct, we would expect the simile to go rather like this: You collect a hundred crowns each from Titus, then Caius, then Maevius, and so on. But if there are an infinity of people from whom to collect, then no matter how many crowns you collect, you will still be infinitely far away from receiving the full number. And so for all intents and purposes you will have received nothing. But the example Leibniz actually gives involves a situation in which no crowns are received at all, not one in which though some crowns will be received, these will essentially amount to nothing. A VI iv 157/MP 2; Leibniz gives essentially the same simile in another of his presentations of the argument for primitive concepts. See LH IV vii Bl. 2 57r, quoted in Mates, op. cit., 59. 12 34 The inference from (4)/(4′) to (5) can be understood more plausibly by supposing that implicit in (or perhaps lying behind) his claim that “what is conceived only through others will be conceived insofar as those others are conceived” (i.e., (4)) is the thought that complex concepts inherit their content from the concepts that compose them. (Leibniz appears to voice this thought when he remarks in another context that “there is nothing except alien elements in the concept of that which is conceived through something else.” 35 ) One attractive feature of this supposition is that it would explain why Leibniz accepts (4). If complex concepts must (continually) borrow their content from the constituents, then it would stand to reason that we cannot conceive a complex concept without in the process conceiving its constituents. For in grasping the (borrowed) content of a complex concept, we would in effect be grasping the content of its components. Furthermore, if we suppose that this inheritance thesis lies behind (4), then Leibniz’s simile fits nicely with the argument he takes it to illustrate. Just as no crowns will be received at all unless one of the people to whom we are sent actually pays, the payment in effect being “inherited” from those others, so also nothing will be conceived at all unless the complex concept ultimately resolves into concepts that do not inherit their content from others, since conceiving requires that there be a content to conceive. In both cases the fundamental idea is the same: in order for anything to be received or inherited at all, there must be something that gives of itself rather than receiving or inheriting from another. Viewed in this way, Leibniz’s argument for primitive concepts comes across as a close relative of a more familiar one in which he argues that there could not be aggregates unless there were simples, since otherwise there would be nothing from which they could derive their reality. 36 “Ad Ethicam Benedicti de Spinoza,” A VI iv 1769/L 199. See, e.g., Leibniz to Arnauld, 30 April 1687, GP II 96-97/AG 85-86; “New System of the Nature and Communication of Substances,” GP IV 478/AG 139. We claimed at the outset that no obvious reason exists for thinking that Leibniz ever gave up his argument for primitive concepts. One might doubt our claim, however, on the ground that he later came to advance a theory of contingent truths on which not every complex concept ultimately resolves into primitives. According to this well-known theory, contingent truths differ from necessary ones in that the former can be analysed without end, whereas the latter can be resolved into identities in a finite number of steps. But since analysing a truth involves analysing the concepts that enter into it, this theory apparently entails that the concepts of many things we actually conceive are composed of other concepts ad infinitum. In that case, however, Leibniz’s argument for primitive concepts would entail that we do not conceive of these things. The theory of contingent truths therefore appears to conflict rather straightforwardly with his argument for primitive concepts. Since he endorses the theory many times over the last thirty years of his life, but does not advance the argument even once during that period, the most likely reason is that he perceived the incompatibility and rejected the argument in favour of the theory. Though this line of reasoning has some prima facie plausibility, we consider it erroneous. Providing a full account of the issue would go well beyond the scope of this paper, but one point to consider is that throughout his mature period, Leibniz consistently maintains that composites could not exist unless there were simples which entered into them and from which they could derive their reality, even whilst holding that composites always divide into smaller composites ad infinitum. If he sees this position as consistent, then we should be reluctant to conclude that he sees any inconsistency in the view that complex concepts could not exist unless there were primitives which entered into them and from which they could derive their content, even whilst holding that 36 35 13 4. An alternate proposal The foregoing criticisms cast considerable doubt on the plausibility of Plaisted’s attempt to rescue Leibniz from inconsistency. In light of this, we want to propose a different solution to the interesting problem that has been highlighted. One point on which we agree with Plaisted is that Leibniz’s argument for primitive concepts, properly understood, does not commit him to (15). However, we think revising the argument itself is not the correct way to block this commitment. Instead, we propose to understand Leibniz as denying the auxiliary assumption that conceiving involves awareness, i.e., (13). If we eschew the approach of revising Leibniz’s argument, and take it at face value, the logic of the situation leaves us with only one possible way of blocking the move to (15). As we showed in Section 1 above, (15) follows from the trio of assumptions (4), (7), and (13). Yet Leibniz clearly affirms (4) in the Ars Magna passage and elsewhere, and though he nowhere endorses (7) explicitly, he clearly seems to hold that some complex concepts are actually conceived, as Plaisted himself convincingly argues. 37 Given that we have reconstructed the argument correctly, then, only one way remains for Leibniz to avoid commitment to (15): he must reject (13). On our view, that is precisely what he did. The thought that Leibniz denied (13) is not one we should find difficult to accept. For, though conceiving may naturally strike us as an essentially conscious activity, the same could be said of perceiving, thinking, striving to satisfy an appetite (i.e., appetition), and even knowing. And yet Leibniz explicitly indicates that all these activities can be performed unconsciously. 38 It therefore seems hardly a stretch to think that he also believed the same thing about conceiving. In fact, he appears to view conceiving as a kind of thinking. He writes in the Ars Magna: “Whatever is thought [cogitatur] by us is either conceived through itself, or involves the concept of another.” 39 And in his Introduction to a Secret Encyclopaedia, he divides the category of the thinkable into concepts (or notions) and propositions. 40 Texts such as these suggest that conceiving is the thinking of a concept, in which case Leibniz’s acceptance of unconscious thinking makes it plausible to suppose that he also believes conceiving can be unconscious. Several other passages suggest that Leibniz would have denied (13). As we have already seen, his claim in the Ars Magna that “what is conceived only through others will be conceived insofar as those others are conceived” (i.e., (4)) logically implies that a complex concept cannot complex concepts always resolve into simpler concepts ad infinitum. Perhaps he thinks, or at least came to think, that primitive concepts enter into infinitely complex ones in a way analogous to the way in which simples enter into composites, which are also infinitely complex. Cf. D. Blumenfeld, “Leibniz’s Ontological and Cosmological Arguments,” in The Cambridge Companion to Leibniz, N. Jolley, ed. (Cambridge: Cambridge University Press, 1995), 361-62, 378n.21. 37 Op. cit., 334. 38 See, e.g., NE 53-58, 76-78, 83-84, 90-91, 113-18, 134, 161-66, 173, 178, 188-95. 39 A VI iv 157/MP 1. 40 A VI iv 528/MP 6; see also A VI iv 157/MP 1. 14 be conceived at all unless its primitive components are also conceived. We believe Leibniz was well aware of this implication; indeed on our reading this is precisely why he thinks (5)—that a complex concept is conceived in actuality only if it is ultimately composed of primitives— follows from (4). But Leibniz also clearly believes that we can conceive a concept without consciously conceiving any of its primitive components—something he admits even in the Ars Magna. Hence, he appears to hold both that we can conceive of these primitives and that we cannot consciously conceive of them. But, if so, then he must think conceiving does not require awareness. In the Introduction to a Secret Encyclopaedia, Leibniz again claims that “we can have no derivative concepts except by the aid of a primitive concept.” 41 But whereas in the Ars Magna he takes no firm stance on the identity of these primitive concepts, here he insists that ultimately only one thing can be conceived through itself, namely God. This leads him to conclude that in reality nothing exists in things except through the influence of God, and nothing is thought in the mind except through the idea of God, even though we do not understand distinctly enough the way in which the natures of things flow from God, nor the ideas of things from the idea of God. This would constitute ultimate analysis, i.e., the adequate knowledge of all things through their cause. 42 The key claim here is that “nothing is thought in the mind except through the idea of God.” If Leibniz views conceiving as a type of thinking, as we suggested above, then this remark entails that nothing can be conceived except through the idea or concept of God, that is, the one and only (positive) primitive that enters into every complex concept. Leibniz is therefore, in effect, claiming that nothing can be conceived through a complex concept unless it is conceived through that concept’s primitive constituent(s). But then this passage shows that Leibniz sees no essential connection between conceiving and consciousness. 43 For he goes on to acknowledge that many of our derivative ideas are inadequate and not ultimately analysable, and that we do not understand well how the ideas of things flow from the idea of God. In other words, we are not ordinarily aware of how, or even that, the concept of God enters into our concepts of things. Still, we cannot conceive these things without conceiving God. Hence, we conceive God in a way whenever we conceive anything, though typically without realizing that we are doing so. Conceiving can therefore take place even without awareness of everything being conceived. Support for our position can also be found in the New Essays, where in Book I Leibniz tackles Locke’s objection that many innate principles or truths do not enjoy universal consent: As for your point that there is not universal approval of the two great speculative principles which are the best established of all: I can reply that even if they were not known they would still be innate, because they are accepted as soon as they have been heard. But I shall further add that fundamentally everyone does know them; that we use the principle of contradiction (for instance) all the time, without 41 42 43 A VI iv 529/MP 7. Ibid. It would also seem to rule out the possibility of partial conception, as does (4). 15 paying distinct attention to it; and that the conduct of a liar who contradicts himself will be upsetting to anyone, however uncivilized, if the matter is one which he takes seriously. Thus we use these maxims without having them explicitly in mind. 44 [G]eneral principles enter into our thoughts, serving as their inner core and as their mortar. Even if we give no thought to them, they are necessary for thought, as muscles and tendons are for walking. The mind relies on these principles constantly; but it does not find it so easy to sort them out and to command a distinct view of each of them separately, for that requires great attention to what one is doing, and the unreflective majority are hardly capable of that. 45 According to these passages (and others in the vicinity) we all know and utilize the fundamental principles of reasoning all the time, even though many of us do so unconsciously. If we can know and use these principles without doing so consciously, however, it is natural to infer that we can conceive a concept without doing so consciously. For we evidently cannot know or use such maxims without conceiving the concepts involved in them. For example, we could not employ the principle of contradiction (i.e., that it is impossible for something to be and not be at the same time) in our reasoning without having concepts such as those of impossibility, being, time, sameness, and so forth. But clearly we must do more than just have these concepts in order to use the principles into which they enter: it seems that we must actually conceive them. Yet those who use these principles unconsciously will be equally unaware of any conceivings involved in their use. So Leibniz appears to be suggesting, at least implicitly, that we can conceive something without being aware of our conceiving it. Though these texts do not provide absolutely overwhelming support for our position, we have been unable to find any clear justification for Plaisted’s contention that Leibniz thinks conceiving “requires some amount of conscious awareness of the concept.” 46 Plaisted himself provides only one text in support of this claim. It comes from §27 of the Discourse on Metaphysics, where Leibniz remarks on the distinction between ideas and concepts: “these expressions that are in our soul whether we conceive them or not can be called ideas, but those we conceive or form can be called notions, concepts.” 47 According to Plaisted, Leibniz is here “saying essentially that the latter are ideas of which we conceive (i.e., take some conscious notice of).” 48 However, we fail to see how Leibniz’s remark establishes any connection between conceiving and awareness. What he says is that concepts are ideas that we actually conceive or form. But only if we assume that conceiving or forming an idea requires awareness does it follow from his statement that conceiving is an essentially conscious activity. It would of course be question-begging in this context to assume that conceiving a concept requires awareness; for that is precisely what this text is being used to establish. As for the process of forming an idea, it is unclear exactly what Leibniz has in mind. He may intend the ‘or’ joining ‘conceive’ and 44 45 46 47 48 NE 76. NE 83-84. Cf. NE 90-91 and GP V 22-23. Op. cit., 338. A VI iv 1572/AG 59. Op. cit., 338. 16 ‘form’ as copulative, in which case forming would just be conceiving and it would again beg the question to assume that forming requires consciousness of the concept formed. Alternatively, the ‘or’ may be disjunctive. In that case there would be nothing illicit about supposing that forming requires awareness; however the text does not require this reading either. In fact, Leibniz’s drawing the distinction between ideas and concepts as he does in the Discourse fits perfectly with our supposition that he rejects (13). For it could be that to conceive or form an idea is just to employ that idea in our thinking, whether consciously (as when we clearly conceive the colour green) or unconsciously (as when in conceiving green confusedly we conceive the various things that enter into green, all the way down to those that are conceived through themselves, without realizing that we are conceiving them). A mere idea would then be any idea that has never been employed even unconsciously in our thinking. Given the availability of this plausible interpretation, we conclude that Leibniz’s characterization of concepts in the Discourse provides no reason for thinking he accepted (13). So on balance, we think the texts provide much stronger support for the view that Leibniz rejected (13) than for the position that he accepted it. Add to this the difficulties facing Plaisted’s view and the fact that rejecting (13) is the only way to save Leibniz whilst taking his argument at face value, and the result is a very strong case for favouring our position over Plaisted’s. A further advantage of our view is that we have no difficulty explaining how there can be confused conception, that is, conception in which none of the components are consciously conceived. We saw this was a major problem for Plaisted’s account, but on our view there is no problem at all. Anytime something is conceived, it is conceived fully in the sense that all its ingredients are conceived. But since on our reading conceiving need not involve awareness, we can maintain that some (even all) of these ingredients are conceived only unconsciously. If we consciously conceive none of them, then our concept will be confused; if we are aware of some but not all the ingredients, then our concept will be distinct but not adequate; and if we conceive all the components with awareness, the concept will be adequate. In this way, our reading reconciles Leibniz’s apparent belief that conceiving is all-or-nothing with his oft-repeated claim that we can be conscious of more or fewer of the ingredients within our complex concepts. One loose end remains. In the previous section we argued that Leibniz effectively rules out the possibility of partial conception, that is, conceiving some but not all of a concept’s components. He does so when he claims in the Ars Magna that “what is conceived only through others will be conceived insofar as those others are conceived, and so on.” 49 Plaisted, however, whilst conceding that the Ars Magna passage seems to portray conceiving as an all-or-nothing affair, claims to find “too many textual indications to the contrary” in other discussions of concepts. He therefore concludes that, despite what the Ars Magna passage may suggest, “It is fairly clear … Leibniz did not see things this way.” 50 We are now in a position to see why the textual indications to which Plaisted alludes do not in fact show that Leibniz believed in partial conception. What Plaisted has in mind are those passages in which Leibniz distinguishes between the various levels of conception (i.e., obscure, clear but confused, clear and distinct, adequate). Of particular significance is Leibniz’s belief that distinct ideas admit of degrees of adequacy. “I put degrees in ideas, according to which I call those adequate in which there is 49 50 A VI iv 157/MP 1-2. Op. cit., 336-37. 17 nothing more to explain, much the same as in numbers.” 51 “[D]istinct knowledge has degrees, for ordinarily the notions that enter into the definition would themselves need definition and are known only confusedly.” 52 Recall that an adequate idea or concept is one that we can analyse fully, i.e., down to the primitives. But since concepts have many levels of constituents, the extent to which we can analyse a concept clearly admits of degrees, and this is what Leibniz means by degrees of adequacy. According to Plaisted, Leibniz’s belief in degrees of adequacy shows that he accepts the idea of partial conception. For if we can have concepts that are distinct but less than adequate, that means we can conceive some but not all of its components. However, notice that in drawing this conclusion, Plaisted once again assumes that Leibniz accepted (13). Only if this is assumed can we infer from Leibniz’s talk of degrees of adequacy that he believed that there could be partial conception. For if conceiving need not be a conscious activity, one could conceive all the constituents of a complex concept even if unable to analyse it completely; that is, one could both conceive some complex concept fully, in the sense that all its ingredients were conceived, and yet not conceive it adequately, in the sense that not all its ingredients were consciously conceived. In that case, conceiving something less than adequately would not amount to conceiving it partially. So Plaisted’s conclusion that Leibniz accepts partial conception relies on his contention that Leibniz embraces (13). Yet we have shown that there is no good reason to think Leibniz accepted (13), and moreover good reason to think he did not. We therefore see no evidence for partial conception in Leibniz’s talk of degrees of adequacy. In saying this, we are not, to be sure, denying that Leibniz believes in degrees of conception. Clearly he admits various levels of conception (obscure, clear but confused, clear and distinct, adequate), and these can be thought of as representing degrees. Further, Leibniz explicitly indicates that there are degrees of conceptual clarity and that distinct concepts admit of degrees of adequacy; he probably would allow degrees of obscurity too. 53 No doubt these are all degrees of conception of a sort. But notice that this degreed character of conception is best interpreted as qualitative. That is, Leibniz’s thought is that conception can be better or worse. Clear conception is better than obscure, distinct better than confused, adequate better than inadequate. Further, very obscure conception is worse than slightly obscure, somewhat clear worse than very clear, less adequate worse than more. This is the sense, we contend, in which there are degrees of conception. However, Leibniz gives no indication that he countenances degrees of conceiving in the quantitative sense. Conception can be better or worse, he thinks, but not more or less: it is, contra Plaisted, an all-or-nothing affair. Either we conceive a thing through all its concept’s constituents, or we do not conceive it at all; that is precisely the import of Leibniz’s claim in the Ars Magna that “what is conceived only through others will be conceived insofar as those others are conceived, and so on.” 54 GP V 17-18. Discourse on Metaphysics, §24, GP IV 449/AG 56. 53 See NE 255. 54 In this respect conceiving resembles perceiving. As Leibniz explains in Monadology §60, “since the nature of a monad is representative, nothing can limit it to represent only a part of things…. Monads are limited, not as to their objects, but with respect to the modifications of their knowledge of them. Monads all go confusedly to infinity, to the whole; but they are limited and differentiated by the degrees of their distinct perception” (GP VI 617/AG 220-21). In other 52 51 18 5. Conclusion Whereas Plaisted’s attempt to save Leibniz meets with insuperable difficulties, the alternative we have advanced coheres nicely with all the relevant texts and receives considerable support from others. Further, it allows us to solve in straightforward fashion the interesting puzzle identified by Plaisted, even whilst taking Leibniz’s argument at face value. In view of all this, we consider our approach to the problem both highly plausible and superior to Plaisted’s. If we are on the right track, then our view has the further virtue of drawing attention to an important aspect of Leibniz’s thought that – as evidenced by Plaisted’s reading of the argument for primitive concepts – has not been sufficiently appreciated: namely that Leibniz believes we may conceive of concepts, i.e., ideas that have been formed and are playing a role in our thinking, without their being available to us as objects of awareness. 55 words, monads differ not with respect to what they perceive, since they all perceive the whole universe, but with respect to how well they perceive the various parts of that universe. 55 We would like to thank Antonia LoLordo, Gonzalo Rodriguez-Pereyra, and an anonymous reviewer for this journal for their helpful comments on earlier versions of this paper. 19