Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi 1. Introduction Contemporary analytic metaphysics largely ignores idealism.1 When analytic metaphysicians do mention it, typically in a footnote, they often do so merely to note its existence and explain why they will not discuss it any further. In the case of transcendental idealism, and various forms of post-Kantian idealism (e.g., Hegel's absolute idealism), this neglect is almost total. This is not merely the result of analytic philosophy's relative lack of interest in the history of philosophy. Aristotelian and Spinozistic views are now widely discussed and defended in contemporary metaphysics, in some cases by the same philosophers engaged in historical and interpretive work on these figures. The neglect of transcendental idealism is no doubt partly due to lack of clarity about what, precisely, transcendental idealism is.2 The exact meaning of transcendental idealism, and how it differs from other forms of idealism (e.g., that of Berkeley), has been controversial since the publication of the first edition of the Critique of Pure Reason (CPR) in 1781, and this controversy continues to this day in Kant scholarship.3 The contemporary metaphysician might think, not unreasonably, that if scholars cannot agree on what Kant's idealism amounts to, then one is justified in ignoring it. In the case of post-Kantian figures like Hegel, the difficulty of the primary texts, and the disagreements among scholars, pose even greater hurdles. This essay is an attempt to explain Kantian transcendental idealism to contemporary metaphysicians and make clear its relevance to contemporary debates in what is now called 'meta-metaphysics.' It is not primarily an exegetical essay, but an attempt to translate some Kantian ideas into a contemporary idiom. I will not attempt to ground 1 The words 'idealism' and 'idealist,' for instance, do not appear in the Oxford Handbook of Metaphysics. 2 There may also be historical and systematic reasons for the unavailability of idealism within contemporary analytic metaphysics. I will pass over that issue here for reasons of space. 3 For my take on the status controversiae see Stang 2016a. 6 Transcendental Idealism Without Tears Nicholas F. Stang 0003203408.INDD 82 10/23/2017 8:46:19 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi transcendental idealism without tears 83 my claims about Kant rigorously in his texts, and will keep quotation of those texts to an absolute minimum; readers interested in knowing more about the reading of Kant on which this essay partly rests are referred to the footnotes. The Kantian idealism on which I will focus is a second-order or meta-ontological form of idealism: the concept of an object is to be explicated as the concept of what can be the referent of an intuition by some intellect. This by itself does not entail any 'firstorder' or 'ontological' mind-dependence at the level of objects; it does not entail any controversial claims to the effect that some set of properties (e.g., spatiotemporal ones) or objects are identical to, or dependent upon, minds or states of minds. I am not denying that Kant is committed to such object-level mind-dependence; I am arguing that there is a separable thread of Kant's thought, deriving from his analysis of the concept <object>,4 that establishes a quite interesting and substantive kind of idealism independent of that more robust form of mind-dependence. In concert with plausible epistemic premises it also entails limits in principle on the ambitions of metaphysics: we can achieve explanatory understanding (i.e. understanding why something is the case) only if our quantifiers are restricted to objects we can intuit (so-called 'phenomena'). That is the thread on which I focus in this essay. It may not be immediately recognizable to some readers as idealism; I address this issue at the end of §2. In §2 I introduce some Kantian ideas about what objects are, and argue that we understand the concept <object> through understanding what can be the referent of singular mental reference by some intellect (what Kant calls an 'intuition'), human or otherwise. §3 introduces the epistemic virtue of understanding and argues that explanatory understanding (e.g., understanding why ∃xFx) requires the ability to understand instances of relevant concepts (e.g., claims of the form Fx) which requires the ability to intuit objects that instantiate relevant concepts (e.g., an x that is F). This places a constraint on our ontology: we can have explanatory understanding only if our quantifiers are restricted to objects we can intuit (so-called 'phenomena'); philosophical ontology must be limited to phenomena if it is to provide us with explanatory understanding. §4 examines a Kantian view about the limits of intuition-we intuit only spatiotemporal concreta that are wholes (they have proper parts) but not totalities (they are proper parts of larger wholes)-and shows how this Kantian thesis, combined with the views about objects and explanatory understanding from §§2 and 3, entails that we lack explanatory understanding of some of the more recherché objects of contemporary metaphysics (e.g., instantaneous temporal parts, physical simples, etc.). I refer throughout the essay to 'explicating' one concept through another, so I want to preface my discussion with a brief note explaining what I mean by this term. The classic program of conceptual analysis ran afoul of certain problems, one of which is 4 I follow the convention in Kant scholarship (established, to my knowledge, by Anderson 2004) of using italicized expressions in brackets to refer to concepts. E.g., <water> is the concept expressed by the term 'water' in predicative position (e.g., in 'This is water'). 0003203408.INDD 83 10/23/2017 8:46:19 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi 84 Nicholas F. Stang known as the 'paradox' of analysis: if a given putative analysis of a concept is correct, how could competent users of that concept fail to know that analysis, and how could they disagree about it once it is articulated? I intend to sidestep these difficult issues by talking about one concept explicating another: the explicating concept provides us with greater understanding of the explicated concept. One can possess and competently use a concept without being able to explicate it; on pain of regress, there must be some concepts that cannot be explicated in terms of others. I do not pretend that this is a satisfactory theory of what concepts are, or what conceptual explication or understanding is, or that it avoids the paradox of analysis; I merely want to flag to readers that for the purposes of this essay I am assuming the intelligibility of these notions and the distinction between possessing a concept and understanding it, and between analysis and explication.5 2. Objects Most contemporary metaphysicians operate with the quantificational concept of an object: an object is an admissible value of a bound first-order variable. This means that an object is something that can be assigned to the variable x in the quantified sentence '∃xFx' such that the open sentence 'Fx' has a truth value relative to that assignment. The quantificational concept of an object goes hand in glove with the quantificational view of existence: existential claims are quantified claims of the form ∃xFx. To say that an F exists is just to say that something is an F, which is true if and only if at least one object is an F ('Fx' is true with respect to at least one assignment of a value to x). Kant, I believe, developed a proto-version of the quantificational theory of existence.6 A judgment of existence, according to Kant, is equivalent to a judgment of 'absolute positing': judging that there is an object in the extension of the concept. According to Kant, to say that an F exists is just to say that there is at least one object that falls under the concept F. To say that an F exists is not to say that there is a species of F (some sub-concept of F falls under F) or to say that Fs have some further property; it is to say that F is instantiated by an object. This entails that all and only objects are what fall under concepts.7 If there were a non-object that fell under a concept F then to say there are Fs would not be identical to 5 For more on the difference between explication and analysis, see Carnap 1947 and Jackson 1998. 6 A598/B626–7; Kant 1992, 118/Ak. 2:72–3. I follow the customary format of citing the CPR by the page in the 1781 edition (A) followed by the page in the 1787 edition (B). For works other than the CPR I give the volume and page number in the Akademie edition ('Ak.' for short), Kant 1902–. Given the intended audience of this volume, I also give the page number in widely available English translations (full citations can be found at the end of this chapter). For more on my interpretation of Kant on existence, see Stang 2015 and 2016a. My interpretation is by no means granted by all scholars; Rosenkoetter 2010, for instance, rejects the idea that Kant's theory of existence anticipates Frege's. 7 Restricting ourselves to first-order concepts, concepts which cannot be predicated of other concepts. There is some reason to think that Kant was aware of second-order concepts, for some passages can be read as making the proto-Fregean claim that existence is a second-order concept (see Ak. 2:73); I argue in 0003203408.INDD 84 10/23/2017 8:46:19 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi transcendental idealism without tears 85 absolutely positing an object that falls under F. Likewise, the hypothesis that there are objects that fall under no concept is self-defeating. If there are objects that do not fall under any concept then trivially they do not fall under the concept <object> (or the concept <self-identical>) so they are not objects, contra the hypothesis. Objects are what fall under concepts, and when we say there is an x that falls under concept F the only thing that can meaningfully be filled in for x is an object. Kant does not have Frege's function-argument conception of judgment (though there might be grounds to think he has a proto-version of that as well),8 so he does not yet have all the materials at his disposal to realize that quantifier expressions like 'There is' bind variables, much less that variables have a range of admissible values and that there may be different kinds of variable, distinguished by their different ranges of admissible values (the idea of higher-order quantifiers, etc.). But if we abstract from these points we can see that Kant is operating with a certain concept of object in these passages: objects are what can be absolutely posited (as I argued above, all and only objects can be absolutely posited). We can expand this thought slightly, while still remaining within the domain of what is thinkable for Kant, to the following: objects are what can make true acts of absolute positing of the form There is an x that falls under the concept F. But this just is the thought that would be expressed in modern lingo as: objects are all and only the admissible values of bound variables. Kant not only has a forerunner to the quantificational notion of existence; he also thereby has a forerunner to the quantificational notion of an object. To be an object is to be (able to be) the value of a variable. But what is it to be the value of a variable? One influential answer, that of Frege and Quine, is that to be (able to be) the value of a variable is to be (able to be) the referent of a singular term.9 This means that to be something that can be assigned as the value of a variable is to be something that can be referred to by a singular term, the singular term that assigns it as the value of that variable.10 Stang 2016a that, while the view that existence is second-order is part of Kant's theory, Kant's claim that existence is not a 'real predicate' cannot be reduced to that proto-Fregean claim. 8 For the function-argument conception of judgment see Frege's essay "Function and Concept" (Frege 1997: 130–48). While judgment, according to Kant, is a concept-concept relation, he thinks that the subsumption of an object under a concept is irreducible to the judgmental relation between concepts, so his overall logical theory is not as far from Frege as might initially appear. For a reading of Kant on judgment that emphasizes the distinction between object-concept and concept-concept relations, see Longuenesse 1998. 9 Since variables are the only singular terms he accepted, for Quine it is trivial that to be (able to be) the value of a bound variable is to be (able to be) the value of a singular term. 10 A skeptical reader might argue that to be assigned as the value of a variable is merely to be the output of an assignment function, where an assignment function is simply a set of ordered pairs of variables and objects. No mention of singular terms or reference is necessary. A semantics equipped with an assignment function (understood as a set of ordered pairs) that supplies an object for every variable in the object language is fine for the purposes of giving a model-theoretic semantics for a language that contains quantifiers. On its own, the model theory (the domain, the assignment function, etc.) remains just another piece of uninterpreted symbolism. But 'assignment' is an intentional notion: it is the notion of letting one thing (a singular term) stand for another (its referent). If we want to think of this model theory as giving the 0003203408.INDD 85 10/23/2017 8:46:19 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi 86 Nicholas F. Stang What are the singular terms in question? According to Quine they are linguistic, and according to Frege they are abstract constituents of Thoughts (akin to what are now called propositions). I think Kant would agree that to be an object is to be the referent of a singular term. This may sound grossly anachronistic, but notice that there is a third alternative to linguistic and to abstract singular terms: mental singular terms.11 Kant, like many early modern (and many analytic) philosophers, takes mental representation to be explanatorily prior to linguistic representation. The possibility of linguistic singular terms is explained by mental singular terms, which Kant calls intuitions. I will briefly explicate this Kantian view and then attempt to motivate it as at least a coherent alternative to Quine and Frege. The first step in understanding the Kantian notion of an intuition is the notion of a referential (or de re) thought: a referential thought is a thought of some particular object that it instantiates a concept.12 For instance, my thought This is a red cube is a referential thought.13 The contents of referential thoughts are partly individuated by their referents. If I think of the red cube in front of me (call it a) that it is red, and moments later this red cube is replaced (unbeknownst to me) by an indistinguishable red cube (call it b) and I think of that cube that it is red, then my two thoughts have different contents: one is about a, the other about b. By contrast, the contents of what I will call descriptive thoughts are not individuated by their referents. In the two situations above, if I had thought Whatever is in front of me is red my thoughts would not have had different contents, although I would have referred to different objects on the two occasions (a and b, respectively).14 Objects are 'given' to us, Kant says, by what he calls intuition. There is an ongoing scholarly controversy about what intuition is, what the 'givenness' of objects consists in, and why intuitions give us objects. I will not engage with that interpretive meaning of the existential quantifier in the object language we need to think of the assignment function as using singular terms to denote the objects which it assigns as values of object-language variables. In other words, if we are looking for an informative explication of the concept of an object we must go beyond mere model theory and the bare Quinean definition of an object (to be an object is to be the value of a bound variable) and invoke the notion of reference: to be an object is to be the referent of a singular term. 11 In fact, Kant is closer to Quine than one might think. Kantian judgments are composed of concepts and concepts are inherently general (Kant 1992: 589/Ak. 9:91). What is more, the general form of a judgment, according to Kant, includes the variable binding expression "to everything x to which the concept . . . (a+b) belongs" (Kant 1992: 607/Ak. 9:111). Since judgments in general involve variables and concepts (and logical connectives), and variables are singular terms while concepts are inherently general, Kant agrees with Quine that the only singular terms in judgment (i.e. in logic) are variables. The relation between variables in judgments and intuitions is explained in the main text. 12 Throughout this essay, 'thought' (uncapitalized) refers to the psychological act of entertaining or assertorically judging a content; I reserve 'Thought' (capitalized) for Fregean Gedanken. 13 I call them 'referential' thoughts to avoid confusion with Kantian singular judgments, which are different. A Kantian singular judgment has a subject concept (e.g., <cup of coffee>) and a predicate concept (e.g., <cold>), but the subject concept (which is intrinsically general) applies to only one object, e.g., This cup of coffee is cold. The role of a referential thought, and Kantian intuition, lies one level prior: it is the mental act by which we subsume this object under the concept <cup of coffee>. Cf. Hanna 2004: 194. 14 There is an extensive literature on the notion of referential thought (or 'singular' thought, as it is usually called). Russell 1910, Strawson 1959, and Evans 1982 are the classic sources (the latter two being especially relevant in a Kantian context). Jeshion 2010 and Dickie 2016 represent the state of the art. 0003203408.INDD 86 10/23/2017 8:46:19 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi transcendental idealism without tears 87 controversy directly but will simply state my own view: the givenness of an object consists in its availability to my mind for referential thought (thoughts of that object), and intuition describes the relation between a mind and an object of which that mind can have referential thought.15 Intuition is the 'presentational vehicle' for referential thought. The Kantian notion of intuition is thus close kin to the Russellian notion of acquaintance,16 though Kant does not share many of Russell's distinctive views about acquaintance (e.g., that we are acquainted with abstract universals17). According to Kant, to be an object is to be able to be absolutely posited. In other words, an object is what can be assigned the value of x in an act of absolute positing, whose general form is: There is an x such that Fx. This means that an object is what can be assigned the value of x in 'Fx' such that the latter attains a determinate truth value. What is it to be assignable as the value of x in 'Fx' (so that the latter is determinately true or false)? The formula 'Fx' expresses the content of a referential thought, a thought that subsumes a particular object under a concept, not the content of a descriptive or general thought (e.g., 'Whatever is G is F.'). Intuition is the presentational vehicle for referential thoughts, the vehicle by which values of x become available to be subsumed under concepts in thoughts whose content is of the form Fx. Since the form of a referential thought content is Fx,18 to be a possible value of absolute positing (to be an object in the quantificational sense) is to be a possible referent of a referential thought (one that subsumes its referent under the concept F). Since intuition is the presentational vehicle for referential thought, it follows that to think of an admissible value of an act of absolute positing we have to think of it as intuitable. In other words, to think of objects in general we must think of them as potential referents of intuition. The concept of an object is to be explicated as the concept of the referent of an intuition. I hope to have made some conceptual space for the Kantian alternative to the Fregean-Quinean concept of an object: an object is an admissible referent of a singular term, where the singular terms in question are mental (intuitions).19 I will now try to 15 On this reading, it is part of the definition of 'intuition' that objects are given to us by intuitions. What is not definitional is that objects are given to us passively, as in sense perception; a mind that actively generates the objects of its awareness (so-called 'intellectual intuition') is at least prima facie conceivable. My interpretation is closely related to that of Allais 2015. 16 In Fregean terms, intuition is the relation of a mind to any object such that there is an expression that refers to that object whose de re sense can be grasped by that mind (can be a constituent of the sense of some thought by that mind). See Evans 1982 and McDowell 1984 for the idea of a de re Fregean sense. 17 Nor does he share the idea that we must be acquainted with all of the constituents of a proposition to entertain it in thought. 18 I am not assuming the Russellian view that objects are literal constituents of the contents of referential thoughts (singular propositions). On the Fregean view, the content (sense) of a thought is composed of a mode of presentation of a function (concept) and a mode of presentation of an object; the syntactic form of such a thought is given by Fx. On one reading, Frege has room for the notion of a de re sense, a mode of presentation that is essentially the presentation of its object (if that object did not exist, that sense would not exist either). I am attempting to remain neutral between a Russellian and a de re Fregean construal of referential thoughts. For the notion of de re senses in Frege, see Evans 1982 and McDowell 1984. 19 Some care is required if we call intuitions singular mental 'terms,' for this very naturally carries the (mistaken) connotation that intuitions are constituents of (i.e. terms in) judgments. This is not Kant's view: the only singular terms in Kantian judgments are variables (see note 11). 0003203408.INDD 87 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi 88 Nicholas F. Stang motivate this alternative by arguing that it is more attractive than the Quinean or (one influential reading of) the Fregean answers. Against Quine's identification of the singular terms involved in the quantificational concept of an object with linguistic singular terms, I will merely point out that mental singular reference appears to be explanatorily prior to linguistic singular reference. There are beings (non-human animals, prelinguistic human infants) that can have thoughts about (which refer to) individual objects without understanding the linguistic singular terms that refer to them. Furthermore, it seems intuitively plausible that the possibility of linguistic singular representation is generally explained by mental singular representation: it is because we can mentally refer to objects in our environment that we can name them linguistically, and not vice versa.20 With respect to the Fregean view that the singular terms in question are abstract constituents of abstract Thoughts, it is important how we construe this Fregean view, in particular how we construe the relation between abstract Thoughts (which I will refer to as propositions to avoid confusion) and psychological states of thinking by subjects (which I will refer to as thoughts, as opposed to propositions). In particular, it will matter whether we explicate the concept of a proposition as the content of a sentential thought by some intellect, or whether we think of the concept of a proposition as intelligible without this explication. (By a 'sentential' thought I mean a thought with a truth value.) I will refer to these as the moderate and extreme Platonist views, respectively. The distinction is not between two different views about the ontology of propositions but about the correct explication of the concept of a proposition. On the extreme Platonist view, claims like 'Propositions are the contents of sentential thoughts' are merely hints used to get us to grasp the notion of a proposition; once we have grasped this notion we can think about propositions directly, without the hints. On the moderate Platonist view, this is an explication of the concept of a proposition: our understanding of the concept of a proposition flows from our understanding of the more basic concept of the content of a sentential thought. Against the extreme Platonist view I have three interrelated points to make. First, it is telling, I think, that the very terms we use for propositions (e.g., the word 'proposition' itself, as well as Frege's 'Gedanken' and 'Satz', a term Kant sometimes uses) are originally linguistic and psychological terms. This is at least prima facie evidence that the conceptual home of these notions is in the realm of thought, and that our use of them to talk about the abstract realm of propositions (Thoughts) is to be explicated in terms of their relation to thought (i.e. as contents of thoughts by intellects). Secondly, if abstract propositions are not explicated as contents of thoughts then we are left with two distinct intentional relations that are conceptually irreducible to one another: the relation between an intellect's thought and the abstract proposition that is its content, and the relation between that abstract proposition and the objects in the world it refers to. It would be preferable to have a more parsimonious ideology. Thirdly, abstract 20 To someone with Quine's behaviorist leanings, though, this line of reasoning will not carry much weight. 0003203408.INDD 88 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi transcendental idealism without tears 89 propositions are explanatorily redundant unless they are intrinsically representational, i.e. unless they represent their objects but not in virtue of standing in any relation to thoughts. But how much sense can we make of intrinsically representational items that are not in any way psychological? This problem is partly occluded by giving them names whose conceptual home is linguistics and psychology (propositions, Gedanken). If we called them instead something neutral, e.g., the Life Givers, and then said "The Life Givers are abstract mind-independent entities that intrinsically represent concrete objects," I think there would be reasonable grounds to wonder whether we understand what we are saying.21 The point of this is not an ontological reduction of propositions to thought (e.g., to equivalence classes of synonymous thoughts) but that the concept of a proposition is to be explicated as the concept of what can be the content of some intellect's ( sentential) thought. In fact, the Kantian view about objects I have sketched is perfectly compatible with moderate Platonism: the concept of an object is to be explicated as the concept of what can be the referent of the content of some thought by an intellect (e.g., a structured Fregean sense). The dependence of objects on thought is conceptual not ontological, and there is no assumption there that every object is referred to by some intellect. This also shows how to answer an objection that will have occurred to some readers. Some will suspect my earlier argument that the concept of an object is to be explicated as the concept of the referent of an intuition rests on a simple fallacy of overgeneralization. From the fact that referential thoughts have the form Fx it does not follow that propositional contents of the form Fx are, in general, contents of referential thoughts. Consequently, it does not follow that the concept of an object of absolute positing in general (being the value of x in Fx) can be explicated as the concept of the referent of a referential thought. Within a moderate Platonist framework, however, this objection can be easily dispatched. The propositional content Fx is to be explicated as a thought content whose form is Fx, that is to say, the content of a referential thought. Therefore, the conclusion from earlier holds: the concept of an object is to be explicated as the concept of the referent of a referential thought, and therefore of an intuition. This is not to say that the concept of an object is to be explicated as the concept of an actual or even metaphysically possible referent of a singular mental term. I am claiming only that when we think about something as an object we are thereby (insofar as our thought can be rendered intelligible) implicitly thinking of it as something that is conceivably referred to by some intuition, even if there is no mind that does so refer to it, and even if such a mind is metaphysically impossible. The concept of an object requires the conceptual possibility of an intuition that refers to it. Thus the form of my claim has a nested modality: □C(there is an object x → ◇C(x is intuited)), where the 21 It does not help if the referents of these abstract Life Givers are constituents of them, for this fails to explain why Life Givers are about those constituents. E.g., I am a constituent of the mereological sum of myself and the property of being a prime number, but that sum is not about me. 0003203408.INDD 89 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi 90 Nicholas F. Stang subscript C indicates conceptual necessity/possibility. Readers will wonder, rightly, what is meant by 'metaphysical' and 'conceptual' possibility. In a short piece like this I obviously cannot offer a whole theory of metaphysical and conceptual possibility, so let me say something briefly about how I understand these notions and the difference between them. I take metaphysically necessary truths to be those truths grounded in the essences of things and their logical consequences. I take conceptually necessary truths to be those truths grounded in the essences of concepts and their logical consequences. By the standard interdefinition of necessity and possibility, this entails that every metaphysical possibility is conceptually possible, but not that every metaphysical necessity is conceptually necessary. So it may be metaphysically possible that there is an object that is metaphysically necessarily not intuited-from which it follows that it is conceptually possible there is such an object-but it does not follow that that object is conceptually necessarily not intuited.22 Some readers may wonder why we should explicate the concept <object> in the first place, rather than taking it as primitive. But this doubt does not really affect my arguments, for they can easily be reformulated directly in terms of 'admissible values of bound first-order variables,' bypassing the term 'object' entirely. As long as we retain three core commitments of ontology as it has been practiced since Quine 1948-that ontology is the study of what exists, that existence is a quantifier, and that we are ontologically committed to the values of our bound first-order variables-we will retain the important conclusion: the concept of an admissible value of a bound first-order variable-the 'unit,' so to speak, of ontological investigation-is to be explicated by the concept of the referent of an intuition. 3. Understanding I think the best way to appreciate the relevance of Kant's idealism for contemporary metaphysics is to focus on the epistemic virtue of understanding. I will reconstruct 22 Williamson (2007: 17) argues, contra idealism and verificationism, that "elusive objects" are possible; in my terminology, elusive objects are objects that are not possibly intuited by any intellect. If the possibility in question is metaphysical possibility, elusive objects present no counterexample to this form of idealism. If the possibility in question is conceptual possibility then Williamson is baldly asserting that it is conceivable that there is something that is not conceivably intuited. I have argued that this is not conceivable; at most we have different intuitions about what is conceivable. I would note, however, that what is conceptually possible is usually adjudicated by further explication of a concept. So Williamson owes us an account of the concept of elusive objects that explains why they are inconceivably intuited. It is not enough simply to point out that we are conceiving of them as elusive objects, for this will ground only the de dicto conceptual necessity that elusive objects are elusive. Williamson needs to explain why we are conceiving of them as de re conceptually necessarily elusive objects. If he does so by saying something about the natures of such elusive objects, this will itself provide us with the materials to construct a conception of a mind that would intuit them (e.g., by creating them-see the end of §3). Williamson is assuming either that elusive objects can be values of bound variables, even though no singular term thinkable by an intellect can ever refer to them, or that the existential idiom (there is an elusive object) is intelligible without recourse to the quantificational idiom (for some value of x, x is an elusive object). I have argued against the former assumption in the main text; in this essay I am taking the latter assumption (the quantificational theory of existence) for granted. 0003203408.INDD 90 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi transcendental idealism without tears 91 Kant's critique of the ambitions of metaphysics as a critique of our capacity to achieve understanding in metaphysics. Much has been written recently on understanding and how it differs from knowledge.23 While I believe this salutary development brings analytic epistemology into closer dialogue with Kant and the pre-Kantian rationalist tradition, in which understanding is conceived of as a distinctive epistemic achievement,24 I do not have the space here to trace the connections between eighteenthand twenty-first-century epistemology. Instead, in this section, I will formulate my argument directly in twenty-first-century terms. We can distinguish several different kinds of understanding in terms of what is understood. I will focus on three such kinds: (a) explanatory understanding (understanding why p), (b) propositional understanding (understanding p), and (c) conceptual understanding (understanding a concept).25 For example, I can understand why gold melts at 1,064 °C, I can understand the proposition 'Gold melts at 1,064 °C' and I can understand the concept <gold>. This naturally raises the question of the relation among these different epistemic accomplishments, which I take to be strict logical entailment: (i) understanding why p requires understanding p (and not vice versa), (ii) which requires understanding F, where F is any concept in p (and not vice versa).26 For example, I do not understand why gold melts at this temperature unless I understand the proposition that it does; and I do not understand that proposition unless I understand the concepts in it (i.e. <gold>, <melting>, <degree Celsius>, etc.). I think this also holds where p is not the explanandum but the explanans, i.e. understanding q because p requires understanding p, which (by (ii)) requires understanding the concepts in p.27 For instance, I do not understand that gold melts at this temperature because of its atomic structure unless I understand the proposition that it has that atomic structure, and I understand the concepts involved in that proposition (i.e. <atom>, <structure>, etc.). I will restrict my attention to cases where p is a non-negated quantified proposition (i.e. one of the form ∃xFx or ⱯxFx) that is not a logical truth and is not vacuously true.28 I do so because the focus of this essay is on what transcendental idealism has to do specifically with (meta-)ontology, and because the interesting claims in philosophical ontology are neither logically nor vacuously true. Understanding comes in degrees. What degree of understanding of a proposition is required for explanatory understanding? What degree of understanding of a concept 23 'Understanding' now has its own specialist literature; see Zagzebski 2001, Kvanvig 2003, Elgin 2004 and 2009, Grimm 2006, Riggs 2009, and Pritchard 2010. 24 Cf. Kant 1992: 570/Ak. 9:65. 25 What I am calling 'explanatory understanding' is slightly different from the 'objectual' understanding (e.g., understanding physics) that much of the literature (following Kvanvig 2003) has focused on. 26 If p is a logical truth, conceptual understanding may not be required; see below. 27 We need to distinguish understanding q on the basis of p (an instance of explanatory understanding) from merely understanding the proposition q because p. For instance, I might understand the proposition q because p, without being able to use p to understand why q is the case. It is the latter epistemic achievement I call explanans understanding in the main text. 28 A vacuous universal quantified sentence is one that has no true instances, e.g., 'All round squares are red.' 0003203408.INDD 91 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi 92 Nicholas F. Stang is required for explanatory understanding of a fact involving that concept? I will stipulatively refer to these as determinate propositional understanding and determinate conceptual understanding, respectively. By definition, determinate propositional and conceptual understanding are necessary for explanatory understanding; it does not follow that they are sufficient. Where p has the form above, I think it is very plausible that determinate propositional understanding requires the ability to understand instances of the open sentence Fx; if you do not understand open sentences of the form Fx then you may have some understanding of the quantified propositions ∃xFx and ⱯxFx, but you cannot have explanatory understanding of them. You cannot understand why ∃xFx or ⱯxFx or deploy your understanding of those facts to understand other facts (explanans understanding). For instance, if you cannot understand the open sentence 'x is a Hilbert space' then you may possess some understanding of true propositions involving the concept <Hilbert space> but you are unable to understand why those propositions are true, or to use those facts to understand other facts about Hilbert spaces (e.g., in a proof). Likewise, I think it is very plausible that determinate conceptual understanding of the concept F requires that you be able to understand instances of the concept having the form Fx. If you lack the ability to understand instances of the concept, then you may have some understanding of the concept, but you are unable to have explanatory understanding of the fact that ∃xFx or ⱯxFx or to deploy your understanding of those facts to understand further facts.29 For instance, you might possess the concept <Hilbert space>, but due to your inadequate understanding of it, you are unable to think of any of its instances (i.e. you are unable to think of anything that it is a Hilbert space); in my terminology, you would lack determinate understanding of that concept. In such a case, then, you would lack explanatory understanding of facts about Hilbert spaces. Before continuing with my main argument, I want to address some difficult questions about the scope of the capacity to understand instances of concepts required for determinate conceptual understanding. Impossibilities. If it is impossible for a concept to have instances (e.g., <counterexample to Goldbach's conjecture>, assuming the conjecture is true) then it is impossible for there to be instances I understand. Does this entail that I lack determinate understanding of that concept? While I do think we can have determinate understanding of concepts of metaphysical impossibilities (as long as these concepts are prima facie coherent, i.e. their objects are prima facie conceptually possible) I do not have to argue for that here, for I am concerned with the case where p has the form ∃xFx or ⱯxFx and is neither logically nor vacuously true. If I understand why p is the case then p is the 29 I think the very same requirements that hold for explanatory understanding (understanding why p) also hold for explanans understanding (understanding why q based on p): one must have determinate propositional understanding of p and one must have determinate conceptual understanding of the concepts contained in p. 0003203408.INDD 92 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi transcendental idealism without tears 93 case, and if p has this form then F is instantiated (for then it would be either false or vacuously true) so it is not the concept of an impossibility. Restriction of understanding. The requirement on determinate conceptual understanding-that one be able to understand instances-does not require that one be able to understand every instance of a concept. One's determinate understanding of a concept can be restricted in the following sense: one can understand instances of F only under the condition that they are also instances of P. This restriction on my understanding of F entails a corresponding restriction on my understanding of quantified sentences involving F. In the existential case, what I can determinately understand is ∃x(Px&Fx) or ∃x∈PFx; in the universal case, what I understand is Ɐx(Px → Fx) or Ɐx∈P(Fx). 30 The subscript indicates that the quantifier is restricted to values of x in the extension of P. Predicates and their negations. Does determinate understanding of the concept F confer determinate understanding of its negation ~F? It might seem obvious that if I can understand instances of the form Fa I thereby have the capacity to understand instances of the form ~Fa, but this does not follow where the predicate F expresses the conditions under which I can understand instances of concepts at all. To fully explain this, I must say more about what it is to understand an instance of a concept, to which I now turn. Determinate understanding of a concept F, I have argued, requires the capacity to understand instances of the form Fa. The capacity to understand instances of the form Fa is the capacity to entertain the thought, of some a, that it is F. This requires the capacity to mentally refer to some object a (in the quantificational sense of 'object') and entertain the thought of it that it is F. This may seem like a very weak requirement. I can entertain the thought, of my desk, that it is a Hilbert space. Is this an exercise of the capacity to think of instances that I have in virtue of determinately understanding <Hilbert space>? No, because as a matter of conceptual necessity, my desk is not a Hilbert space.31 The concept of a Hilbert space is the concept of a fundamentally different kind of thing than my desk. The capacity to have referential thoughts about objects requires (but is not exhausted by) the capacity to 'intuit' them (in Kant's terminology). So determinate understanding of a concept requires the capacity to intuit instances.32 If it is impossible for an object a to which I have singular mental reference (intuition) to be an instance of the concept F, then I cannot understand of a given object a that it is F, and, while I may be 30 The difference between these formulations (unrestricted quantifier with restricting predicate vs. restricted quantifier) will not matter to my argument. 31 Fully defending this claim would require a worked-out theory of de re conceptual possibility, which for reasons of space I cannot provide here. 32 This requires only the conceptual possibility that there be intuitable objects that instantiate the concept, but not the metaphysical possibility of such objects; it requires only that it not be impossible, as a matter of conceptual necessity, that objects intuitable by me are instances of the concept. 0003203408.INDD 93 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi 94 Nicholas F. Stang said to possess some limited understanding of the concept, I cannot have explanatory understanding of claims involving it that meet the conditions above.33 Can we not be said to understand a proposition of the form Fa when our understanding of that proposition consists in our understanding of its inferential relation to other propositions (e.g., it entails ∃xFx)? On the contrary, if our understanding of Fa were exhausted by our understanding of its inferential relations to other propositions then we would not understand this system of propositions as anything more than uninterpreted symbols. We would not understand that the proposition Fa, as well as the propositions to which it is inferentially related, are about objects. One does not understand the concept <object> merely in virtue of understanding the introduction and elimination rules for quantification.34 To understand the concept <object> one must understand that objects are what quantified propositions are about, that is, the values of bound variables. This allows us to infer, from conditions on what kinds of objects I can intuit, conditions on what concepts I can determinately understand, and hence of which claims I can have explanatory understanding. Let us assume that I cannot intuit objects except those in the extension of predicate P. In this case I determinately understand a concept P-that is, I can think of instances of it-but I cannot determinately understand its negation ~P. This means I cannot have referential thoughts about non-Ps, and so I cannot think of any individual such object that it falls under a concept (including ~P). I can have determinate understanding of a concept only under the restriction that I think of its instances as Ps. I determinately understand ∃xFx, where F is a concept that is not specifically a concept of Ps (it is not conceptually necessary that Fs are Ps) only under the restriction that its instances are Ps, i.e. what I determinately understand is either ∃x(Px&Fx) or ∃x∈P(Fx). Likewise, where ⱯxFx is logically contingent and non-vacuous, since I determinately understand the predicate F only restricted to phenomena, what I determinately understand is either Ɐx(Px → Fx) or Ɐx∈P(Fx). This does not mean that we lack any understanding of the unrestricted propositions or of the unrestricted concept. We can mentally entertain thoughts with this content and there may even be epistemic reasons to accept some such claims and reject others; for instance, considerations of ontological parsimony, simplicity, and coherence with background theory may provide epistemic warrant for some such claims and against others. It is even possible that our epistemic warrant to accept and reject such claims will, in some cases, amount to knowledge. But what we will lack in all such cases is determinate understanding of these claims, because we lack determinate understanding of these concepts when their extensions are not restricted to phenomena. Due to our lack of determinate understanding, we will lack explanatory understanding of these claims; we will fail to understand why they are true.35 33 Non-negated quantified claims that are neither logically nor vacuously true. 34 Cf. the 'uninterpreted symbolism' objection in note 10 above. 35 Can we use them in explanatory understanding of other truths? No, for the same requirements on explanatory understanding (understanding why p) hold for explanans understanding (understanding why q through p). See the discussion of 'elusive objects' in section 1. 0003203408.INDD 94 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi transcendental idealism without tears 95 Before I continue I want to address a global strategy that a metaphysician might use to extend our determinate understanding of objects we cannot intuit. The metaphysician might argue that we can have determinate understanding of a concept F in virtue of being able to think of an instance using a definite description, e.g., 'The G is F' (FɩxGx). But if a definite description has the form 'the G' (ɩxGx) then determinate understanding of propositions involving this description requires determinate understanding of this expression, which requires determinate understanding of the concept G. That is to say, determinate understanding of propositions involving definite descriptions requires being able to think of instances of the concept over which the definite description operator has scope. This entails that definite descriptions cannot expand the range of concepts you determinately understand, because determinate understanding of definite description-involving propositions depends upon precisely that determinate understanding.36 4. Phenomena and Noumena What I have called 'explanatory understanding' is not new to philosophy, for it is the ambition of metaphysics, both traditional and contemporary. In the German rationalist tradition in which Kant was educated, metaphysics is understood as the science of all beings as such. The aim of metaphysics is not fundamentally knowledge that all beings have certain properties, but explanatory understanding of what all beings as such have in common. Paradigmatically this takes the form of a systematic hierarchy of the predicates of all possible beings, at the top of which we find the most fundamental or basic predicates that explain, and allow us to understand, all the possible predicates lower in the hierarchy. While contemporary metaphysicians typically conceive of their project in less grandiose terms, they nonetheless often conceive its methodology in explicitly explanatory terms: seek the theory that is the best (simplest, most economical, most powerful, etc.) overall explanation of the subject (e.g., modality, persistence of objects, etc.).37 In my terminology this means that the enterprise of metaphysics aims at explanatory understanding, or understanding why. The aim of metaphysics is not merely to know that various propositions are true, but to deploy that knowledge in explanatory understanding of its subject matter. In §3 I argued that constraints on what objects we can intuit put in-principle constraints on the bounds 36 Neo-Fregeans hold that we can expand the range of objects to which we can refer (objects that can be the referents of singular terms) via Hume's Principle, which involves definite descriptions: the number of Fs = the number of Gs ↔ F and G are equinumerous. My Kantian reply to this is that linguistic representation of objects is not fundamental. Referring to numbers is not, contra the neo-Fregean, merely a matter of introducing syntactically singular number terms into our language in a logically consistent way. To understand sentences as involving singular terms as representing we must understand them as contents of thoughts, which requires understanding those syntactically singular terms as standing for objects we can think about (i.e. mentally refer to, i.e. intuit). So the bounds of intuition put an in-principle bound on the range of linguistic singular terms, including definite descriptions, that we can determinately understand. For discussion see Wright 1983, Hale and Wright 2001, and McBride 2003. 37 Notably Williamson 2013: 423–6. 0003203408.INDD 95 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi 96 Nicholas F. Stang of our explanatory understanding. If the aim of metaphysics is explanatory understanding, then constraints on what objects we can intuit put in-principle constraints on the ambitions of metaphysics. In this section I am going to explore Kant's own views on the limits of our intuition, and consequently on the limits of explanatory understanding in metaphysics. I will try to motivate them as intrinsically plausible views about intuition without giving explicit arguments in their favor. This is because rigorously grounding a particular view about intuition is dialectically quite tricky, a point to which I will return at the end. We can conceive of various alternatives to our mode of intuition of objects, and therefore abstractly conceive of various kinds of objects we cannot intuit (and of which we therefore lack explanatory understanding). This means that in determining the limits of 'our' intuition of objects (determining the value of the restricting predicate P from §3), we thereby form various correlative concepts of alternate forms of intuition and alternate kinds of objects. In determining the limits of our mode of intuition (assuming there is such a limit) we are to abstract from the contingent facts about our sense organs; we are not determining the limits of intuition of Homo sapiens but of the fundamental kind of intellect we possess.38 On Kant's account, our basic mode of intuition of objects is this: we intuit objects that are (i) spatiotemporal, (ii) concrete, and (iii) wholes but not totalities. Clause (i) I take to be clear enough for our purposes. Clause (ii) means that the objects we intuit stand in cause-effect relations with one another and with our minds, and we intuit them partly in virtue of their causal effect on our minds.39 Clause (iii) means that the objects we intuit are wholes (they possess proper parts) that are proper parts of yet further wholes. We do not intuit either simples, objects that lack proper parts, or what Kant calls 'totalities,' objects that are not proper parts of any larger whole (e.g., the cosmos). I will call these wholes discursive wholes. Borrowing another piece of Kantian terminology, I will refer to any intuition that meets these three conditions as sensible intuition. Before continuing, I want to note that clause (ii) does not mean that sensible intuition is limited to what we can directly perceive. If some object (e.g., an unobservable scientific posit) causally interacts with our minds, for instance, by causally interacting with objects we directly perceive, it falls within the scope of sensible intuition as long as it is spatiotemporal, causally efficacious, and is a discursive whole (i.e. not a simple, not a totality); if our sense organs were finer, or different, we could directly 38 A skeptical reader might wonder: how do we know which aspects of our mode of intuition are 'contingent' and which are 'fundamental'? This objection gets to the very heart of Kant's philosophy; it has no easy or quick answer. It was originally pressed against Kant and K. L. Reinhold by G. E. Schulze in a short book titled Aenesidemus, oder über die Fundamentale der von Professor Reinhold in Jena gelieferten Elementar-Philosophie (1792); an English translation of selections can be found in Di Giovanni and Harris 1985. For a Kantian response to Schulze's skeptical objection see Pereboom 1991 and my own unpublished manuscript "Answers for Aenesidemus." 39 I am ignoring, for the purposes of this essay, our practical awareness of our own actions, for in that case Kant rejects (ii); my awareness of my action is among the causes of the action, not vice versa. 0003203408.INDD 96 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi transcendental idealism without tears 97 sense it.40 Some readers might reject (ii) out of hand for they think we intuit (are directly acquainted with) abstract objects such as mathematical objects.41 Rather than engage that view directly, I am going to simply limit the scope of Kant's theory of intuition: (i)–(iii) represent the limits of our intuition of concreta. The Kantian term for objects that meet these constraints is 'phenomena' (objects of sensible intuition). If we let P stand for the predicate 'is a phenomenon' then, by the argument of §3, the quantified sentences of which we can have determinate understanding are accordingly restricted: ∃x(Px&Fx) and Ɐx(Px → Fx). We can have determinate understanding in metaphysics that, for instance, all concrete objects have some property (e.g., being causally efficacious) or that some property is instantiated by a concrete object (e.g., substantiality), but only if this is implicitly restricted to the domain of concrete objects we can intuit, that is, phenomena. This is an interesting conclusion only if it imposes substantive constraints on metaphysics. To show this I will have to show that some of the more recherché concrete objects whose existence is debated in contemporary philosophical ontology are objects that cannot be sensibly intuited. Consequently, we lack determinate understanding of them; and lacking determinate understanding, we also lack explanatory understanding of propositions that quantify over them. (a) Instantaneous temporal parts. Because we have spatiotemporal sensible intuition our intellect is temporal. This means that it intuits objects in time, and the intellectual acts by which it understands objects have temporal duration. Consequently, we cannot intuit an object with zero temporal duration. For any arbitrarily small temporal interval, it is possible for an intellect such as ours to intuit an object that exists only for that very short interval. But an instantaneous object, one that exists for an interval of zero temporal extent, cannot be intuited by such an intellect. Consequently, objects with zero temporal extent are (as a matter of conceptual necessity) not objects that our form of intellect can intuit. They are not phenomena. We cannot determinately understand concepts of them, and propositions that quantify over them cannot figure in our explanatory understanding. Consequently, the concept of an instantaneous temporal part of an object that persists through a non-zero temporal interval is a concept that we cannot determinately understand. Thus, while we may be able to entertain the thought that persisting objects have instantaneous temporal parts, we cannot deploy this thought in explanatory understanding. In particular, we cannot understand why objects persist through time by citing their instantaneous temporal parts. (b) Concrete atoms. The spatial analogues of instantaneous temporal parts are nonextended simples: concrete objects that inhabit a region of zero spatial extent. Just as we intuit only objects of non-zero temporal extent, we intuit only objects of non-zero spatial extent. For any region of non-zero spatial extent it is possible for an intellect 40 A225–6/B273–4/Kant 1998: 325–6. 41 Historically, this view was upheld by Plato and the Platonic tradition, as well as Descartes. Chudnoff 2013 is a contemporary articulation and defense of such a view. 0003203408.INDD 97 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi 98 Nicholas F. Stang like ours to be given an object in that region; the nature of spatiotemporal sensible intuition puts no finite lower bound on the spatial extent of objects. But objects of zero spatial extent, physical objects that occupy only a point, cannot be intuited by intellects like ours. (c) The world-whole. At the opposite end of the spectrum from (a) instantaneous objects and (b) point-sized objects are 'maximal' objects: (a*) the totality of all events in time and (b*) the totality of all objects in space. We can intuit neither. An intellect with spatiotemporal sensible intuition is successively given proper parts of these totalities and its cognitive task is to combine them into an understanding of ever greater wholes containing those parts and to analyze them into an understanding of ever smaller parts of those wholes. The totality of concrete objects in space and time is the idealized limit of the former combinatory process, just as the instantaneous temporal parts or point-sized spatial parts of a thing are the idealized limit of a process of temporal and spatial analysis. Since this is the concept of an object we cannot intuit, it is a concept we do not determinately understand. Consequently, metaphysical claims about the totality of concrete objects in space and time are not claims of which we can have an explanatory understanding.42 According to the argument of §2 the concept of an object is to be explicated as the concept of the referent of an intuition, so to explicate concepts of non-phenomena we must conceive of alternate forms of intellect that would intuit them. The first such conception is that of an intuition that is like ours in being passively given discursive wholes (by being sensibly affected by concreta, clauses (ii)–(iii) above), but which is not given objects in space and time. This is what Kant would call 'non-spatiotemporal sensible intuition.' It is the conceptual tool by which we can explicate the concept of discursive (non-simple, non-total) concrete wholes that are non-spatiotemporal.43 Because Kant ties the spatiotemporality of our intuition so tightly to the discursive nature of the wholes we intuit (neither simples nor totalities) it is not clear that he can make coherent sense of an intellect that intuits a spatially or temporally non-extended object.44 If we want to go beyond Kant and render the concept of such an object fully intelligible, we will need to provide a more determinate concept of an intellect that is immediately 42 It is possible to construct an ersatz form of determinate understanding of such 'limit' concepts by determinately understanding propositions about arbitrarily long converging sequences of objects we can intuit (e.g., ever larger parts of the world, or ever smaller parts of an object). But while this gives us determinate understanding of whole propositions involving the terms 'whole world' or 'infinitely small part,' the true analysis of these propositions reveals these terms not to correspond to any singular term in the underlying logical form. This is comparable to understanding claims about real numbers as claims about converging sequences of rational numbers; one does thereby expand one's ontology in the sense at stake in this essay. 43 The primary purpose of this concept in Kant's system is to express the idea that, while objects are given to us in space and time, there may be other kinds of intellect that have sensible intuition, but which are given non-spatiotemporal objects. 44 It is not clear, for instance, where in the CPR Kant proves we are not given spatial or temporal simples, rather than merely assuming this, much less proving that no intellect with spatiotemporal intuition is given such simples. 0003203408.INDD 98 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi transcendental idealism without tears 99 given spatial or temporal simples (or both). Finally, the most important way of conceiving an alternate form of intuition, within Kant's system, is to modify or reject clauses (ii) and (iii) in the account of our intuition above. With respect to (ii), we can conceive of an intellect that is not passive with respect to the concreta it intuits, but actively generates the object of its intuition in intuiting it. With respect to (iii), we can conceive of an intellect that intuits, not a proper part of some larger whole, but the totality of all (concrete) objects all at once, 'in a single glance.' These are concepts of what Kant calls 'intellectual intuition' and 'intuitive intellect,' respectively.45 Unsurprisingly, these concepts of alternate forms of intellect are modeled on conceptions of God's intellect in the theological tradition.46 These concepts of alternate modes of intuition generate, given the conceptual dependence of objects on intuition, correlative concepts of objects, which Kant calls noumena. Because we cannot intuit them, we lack determinate, and hence explanatory, understanding of noumena. This does not entail that we lack any understanding whatsoever of concepts of noumena. We can entertain thoughts involving them, and we may acquire epistemic warrant for believing or rejecting such claims, though the nature of this epistemic warrant will be problematic, given that these concepts cannot figure in explanatory understanding, and thus our belief in them cannot be warranted by an inference to the best explanation. For instance, it may be that some theories about such objects are logically simpler or more elegant than others. This by itself may give us epistemic warrant to accept the simpler and more elegant theories; it may even be the case that we come to know certain claims involving these indeterminately understood concepts. But metaphysics, both traditional and contemporary, does not aim merely at knowledge or at entertaining theories that have greater degrees of rational coherence than their rivals. Metaphysics aims at understanding, and that is precisely what we cannot have with respect to such objects. I want to note something about the structure of this essay: the view of objects (§2) and the view of explanatory understanding (§3) are independent of the specifically Kantian view of the limits of intuition (§4). This means that, if we reject Kant's specific views on the limits of intuition, we can 'slot in' a different such view (e.g., perhaps one that allows intuition of abstracta) and derive correlative consequences about the limits (or lack of limits) of our determinate understanding in metaphysics. I point this out because the specifically Kantian limits on intuition I outlined above may strike some readers as unmotivated or false, in part because of their consequences for our explanatory understanding. In particular, it might be objected that they leave no room for explanatory understanding of abstract objects in mathematics. Kant thinks he can account for our explanatory understanding in mathematics without having to resort to abstract objects, but the larger point is a methodological one: since a view about 45 The concepts of intellectual intuition and intuitive intellect play important roles in Kant's philosophy. See Förster 2011 for extensive discussion. 46 E.g., Thomas Aquinas, Summa theologiae I, q. 14, art. 7, who cites Augustine, De trinitate 15: ch. 14. 0003203408.INDD 99 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi 100 Nicholas F. Stang intuition has consequences (according to §§2–3) for our explanatory understanding, the reach of our explanatory understanding can just as much be used to argue against a view of the limits of intuition, as vice versa. It is not obvious that claims about the nature and limits of intuition are epistemically or methodologically more secure than claims about the scope of our explanatory understanding. But the ontologist who thinks the Kantian limits on explanatory understanding are too narrow and so concludes by modus tollens that the Kantian limits on intuition are also too narrow owes us an explanation of how it is possible for us to have intuition of the non-phenomena quantified over in her theory. In other words, regardless of our view of the limits of intuition, if the arguments of §§1–2 are correct the non-Kantian ontologist owes us an explanation of how referential thought about her objects is possible and, what is more, how it is possible 'from the armchair.'47 5. Yes, But Is It Idealism? Some readers may wonder whether there really is a form of idealism at all. It is more of a semantic or epistemic thesis than a metaphysical one, and the only consequences it has for metaphysics are broadly epistemic ones: we cannot have explanatory understanding of noumena. What is this doing in a volume of essays on the metaphysics of idealism? First of all, there is a certain historical naivety in thinking that 'idealism' means one particular doctrine. Originally coined to refer to the Platonic view that what is ultimately real are 'ideas'-intelligible archetypes of which sensible objects are imperfect replicas-'idealism' came to mean, in the early modern period, the view that everything ontologically depends on minds and their ideas (states).48 This is correlated with a shift in the meaning of 'idea' itself: from intelligible Platonic archetypes (eidos) to the immediately available mental contents (often sensible ones) of the early modern 'way of ideas.' Whether something counts as a form of idealism should therefore be determined according to its intellectual continuity with one of the many strands in the tangled web of the history of idealism. By this criterion, the Kantian view I have outlined is definitely a form of idealism. First of all, it builds off an idea present in the central argument for what many consider the paradigm case of idealism as universal mind-dependence: Berkeley's 'master argument' in his Treatise Concerning the Principles of Human Knowledge.49 Very roughly, Berkeley's argument is that we cannot imagine an unperceivable object because in imagining it we are imagining how it would be perceived, because we are imagining its 47 This problem, how can we intuit (be acquainted with) an object a priori (independently of our sensory experience), is the very problem that Kant's doctrine of the ideality of space and time is supposed to solve. While Kant's solution is by no means unproblematic, it is far from clear to me that any alternative is superior. In the CPR see A26/B42 (Kant 1998: 176), but this emerges even more clearly in Prolegomena §§8–9 (Ak. 4:282/Kant 2002: 78). 48 For the vicissitudes of 'idealism' and cognate terms, see Dunham, Grant, and Watson 2014. 49 Berkeley, Treatise Concerning the Principles of Human Knowledge, Part One, §§ XXII–XXIII. 0003203408.INDD 100 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi transcendental idealism without tears 101 perceptual qualities. Because it is unimaginable, Berkeley claims, it is impossible. The Kantian argument I have sketched here is a descendant of this (I think, quite unsuccessful) Berkeleyan argument, but freed from certain implausible Berkeleyan assumptions and with a much weaker (and more plausible) conclusion. For one thing, it does not equate (as Berkeley does) the 'imaginable' with the possible. For another, it does not assume we conceive of possible objects by perceptually imagining them, but by conceiving of intuitions of them. Consequently, its conclusion is not that non-intuitable objects are impossible, but merely that we cannot have a determinate understanding of concepts of such objects. Nonetheless, it shares a core idea with Berkeley: the concept of an object is conceptually downstream of the concept of a mind's object awareness (sensible perception for Berkeley; intuition for Kant). It is also one strand in Kant's 'transcendental' idealism, one of the most important and influential moments in the whole complex history of idealism. As I mentioned in §1 there has been a scholarly controversy since 1781 about whether Kantian transcendental idealism is a form of Berkeleyan idealism. But if 'idealism' is to be equated with specifically Berkeleyan idealism (or some variant of it) then this would entail that if this controversy turned out a particular way then Kant's transcendental idealism would not be a form of idealism. I think that this conclusion is absurd (and not just because 'transcendental idealism' has the word 'idealism' in it!). Kant's transcendental idealism is an important enough moment in the history of idealism-it does, after all, influence the whole course of nineteenth-century idealism in Germany and Britain- that it has just as much right to the term 'idealism' as Berkeley does. The ideas I have explored in this essay constitute one strand in Kant's 'transcendental' idealism, but only one strand. In particular, I have reconstructed the negative part of Kant's theory: the limits of sensible intuition constitute limits on explanatory understanding. The positive part of Kant's theory involves his explanation of how we can have a priori explanatory metaphysical understanding of objects we intuit, i.e. phenomena. That part involves further 'idealist' commitments, in particular the ideality of space and time. While I have argued at length elsewhere that this positive part of Kant's theory does involve a substantive ontological form of idealism similar in some respects to that of Berkeley and (even more so) that of Leibniz, I cannot explore this point here.50 The positive part of Kant's idealism is significantly harder to motivate for a contemporary audience than the negative part, and it is that goal that has guided my discussion here.51 50 Stang 2016b and Stang forthcoming. 51 I would like to thank the editors of this volume, Kenny Pearce and Tyron Goldschmidt, for this opportunity to air my idealist views, and for their feedback on the essay. Karl Schafer and Damian Melamedoff took the time to read carefully, and comment upon, an earlier, inferior draft and for that I thank them. I am especially grateful to Jack Woods, who gave me detailed comments on this essay- twice!-and who encouraged me when my confidence in it was faltering. Thanks to Markus Gabriel, Eli Chudnoff, Otávio Bueno, Peter Lewis, and the rest of the audience at University of Miami for their comments on the talk in which I presented the core ideas of this essay. I would also like to thank an anonymous referee for this volume whose comments helped improve the essay. 0003203408.INDD 101 10/23/2017 8:46:20 PM Dictionary: NOSD OUP UNCORRECTED PROOF – REVISES, 10/23/2017, SPi 102 Nicholas F. Stang References Allais, L. 2015. Manifest Reality: Kant's Idealism and his Realism (Oxford: Oxford University Press). Anderson, R. L. 2004. "It Adds Up After All: Kant's Philosophy of Arithmetic in Light of the Traditional Logic." 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