Kant: Transcendental Ideality and the Kantian Noumenal

Introduction

At the heart of Kant’s project in the ‘Critique of Pure Reason’ is the contention that our necessary forms of sensibility, as well as understanding, do not give us knowledge of the world as it is in itself beyond these necessary modes of cognition. The thing-in-itself, beyond our necessary comprehension of it, is, by definition, unknowable, an ‘island, enclosed by nature itself within unalterable limits’ (Critique of Pure Reason (CPR), B295). And yet, the Transcendental Aesthetic contains the bold claim that both space and time are ‘nothing but’ (CPR B66) the forms of all outer appearances. It would seem that there is then at least one thing we can know of the thing-in-itself, that it is a-spatial and a-temporal. In this essay, I will argue that Kant has not contradicted himself. I will be arguing that, if we understand Kant’s claims about a-spatiality and a-temporality as a somewhat weaker epistemic claim, rather than a stronger ontological or metaphysical claim, then Kant can be saved from an apparent contradiction. I will maintain that Kant has invoked a paradox and not a contradiction and that this paradox is no more threatening than any other paradox in the history of philosophy. This conclusion will be loosely drawn from the work of Desmond Hogan and James Van Cleve as well as Saul Kripke’s ‘Naming and Necessity’. In §1 I will lay out Kant’s arguments concerning the ideality of space and time. In §2, I will be considering whether or not Kant is right in his ontological/metaphysical contention that space and time cannot be features of the external world as well as a feature of human understanding and will conclude that, yes, he is. Finally, in §2, I will consider whether or not negative epistemic assertions constitute a form of positive ontological/metaphysical knowledge about the world in-itself. My answer to this will be that, no, they do not.

§1 The Ideality of Space and Time

Kant begins his project by asking ‘How are synthetic a priori judgements possible?’  (CPR, B19). A priori knowledge, for example, ‘A is not the same as not A’ is knowable before and without experience; its truth (or falsity) is necessary and therefore requires no contribution from experience. By contrast, a posteriori knowledge, for example ‘my laptop is 5 years old’, is true (or false) contingently, that is, only by recourse to experience. (Ibid, B3). Analytic judgements, for example ‘all bachelors are unmarried’, are true by definition and necessarily so because the predicate (unmarried) is contained within the subject (bachelor) (B11). With synthetic judgements, the predicate lies entirely outside of the subject. Hence ‘all bachelors have long hair’ is true (or false) only in recourse to something outside of the terms within the proposition. Kant argues that analytic judgements must be knowable a priori and most synthetic statements are known a posteriori. There can be no analytic a posteriori judgments because judgements knowable through experience cannot be true by virtue of the terms contained within the judgement. Kant wishes to maintain that there is a third category of judgment: synthetic a priori judgements. Such judgements include those of pure mathematics such as ‘5+7 = 12’ (B15). These are knowable before experience (a priori) but are, nonetheless, synthetic because the predicate ‘12’ is not contained within the subject ‘5+7’. The same is true of geometrical truths, such as ‘a straight line is the shortest distance between two points’. This is knowable prior to experience but is, nonetheless, not knowable analytically, that is, through an analysis of its terms.

Kant’s project in the Critique of Pure Reason is thus to ask, what must the nature of our cognitive faculties be in order to account for the truth of these synthetic a priori judgements? Kant will conclude that such judgements can only be possible on the assumption that their object is not the ‘world’ outside of human experience (the noumenal) but the ‘world’ such as it necessarily must be cognised by the subject (the phenomenal). Thus we learn something genuinely new about our experience as we experience it through space and time, as well as further cognitive categories, and hence it is synthetic. And yet the conditions of such knowledge, the form in which it is packaged or given to us, is a priori in the sense that it is, by necessity, spatial and temporal. These are the forms of pure intuition by which he means the forms that our sensory input must take. This is not because the world ‘in-itself’ is spatial or temporal, but because these are the necessary conditions through which anything that can be classed as knowable can become knowledge for us in the first instance. Space and time cannot be features of a mind-independent reality because of their apodictic necessity. There are certain judgements about both space and time which are true with a priori necessity and therefore cannot be known empirically. They, therefore, can only be discovered in the epistemic subject and not in the world independent of the subject.  There are two forms of the argument at work here. One is a transcendental argument asking: What must be the nature of our cognitive faculties given that we have such knowledge of space and time at all? The other is an argument by elimination arguing that, given the nature of our knowledge of space and time, the only possible explanation is that they are transcendentally ideal and not a feature of a mind-independent reality. Kant demonstrates a number of apodictic necessary truths concerning space and time.  

Firstly, space and time cannot be empirical objects drawn from the senses because, in order to first recognise objects as external to me or temporally ordered in my experience, I must first have made the presumption that they are located spatially outside of myself or in a temporal sequence. Space and time are, therefore, not features of pure sensibility, the pure empirical datum given from experience, but mind-dependent impositions projected on to experience for experience to be possible in the first place (B38/B46). Kant’s next argument states that while I can imagine space and time without objects, I cannot entertain in thought, let alone in experience, objects without space and time. How would this be possible unless space and time are not features of sensibility but are instead necessary features of intuition and thus transcendentally ideal? (B39/B46). The next argument states that our knowledge of space and time is of one space and one time. While we can imagine different locations in space and time, we can only imagine experience through the presumption of one united holistic time and one united holistic space as the intuitive matrix within which objects subsist. Since, according to Kant, singular impressions such as these can only be intuitions, this points to the transcendental ideality of both space and time (A25/A32). Space and time also have infinite magnitudes because no matter how large the spatial or temporal field, we can always imagine a larger space or time that this is within. We, however, have no empirical basis upon which to make this assertion and this necessity must thus be because space and time are transcendentally ideal (B40/B48). Finally, geometrical truths appear to be a feature of our experience and yet they follow with apodictic certainty. It is a priori true that a straight line is the shortest distance between two points and yet this is also synthetic: The necessity of this judgement is not contained within the definition of the terms ‘line’, ‘shortest’, ‘straight’, or ‘point’. This is a truth which is contained within the possibility of thinking about these terms at all both within sensibility of the world and in abstract construction in thought. But pure experience can never provide a priori certainty and thus how can this truth of our experience be the case unless space and time are transcendentally ideal and thus mind-dependent? (B41) Next, Kant argues that we know before experience and with certainty that there are infinite determinations in space and time. There is no possible a posteriori experience that could persuade us that there is a smallest unit of space or of time - between any two instances of space and time we can always imagine a smaller space or time. Space and time, therefore, do not enter our cognition through a posteriori sensibility and are thus transcendentally ideal. Finally, experience, both in inner sense and in outer sensibility, is ordered in temporal succession. Different times cannot be ordered simultaneously. And yet this a priori truth is not analytic because it is not contained within the definition of time that it must be in succession, it is therefore synthetic. Knowledge of this truth would not be available either analytically or through a posteriori observation and thus could not be the case unless space and time are transcendentally ideal. (B47)

In his ‘Conclusions from the above concepts’ Kant argues that such necessity in geometric and temporal truths can only be the case if ‘intuition has its seat in the subject only’. (B42) To many readers, it now appears that Kant is no longer making an epistemic claim, he is making an ontological or metaphysical one. He believes he is not only describing the necessary features of our epistemic faculties but also the world as it is beyond these faculties. The argument here seems to be that we cannot possibly apply the conditions of sensible intuition to a noumenal mind-independent reality outside of those intuitions (A27). This is because they have a priori necessity, but a mind-independent reality could never have such a priori necessity. Therefore, space (and time) ‘comprehends all things that appear to us as external, but not all things in themselves…for…if our intuition had to be of such a nature as to represent things as they are in themselves, there would not be any intuition a priori, but intuition would always be empirical (Prolegomena, p 24). Therefore, as the world outside of appearance is not comprehended by the subject, it cannot therefore be spatial or temporal.

§2 Is Kant right in his ontological contention that space and time cannot be features of a mind-independent external world as well as a feature of human understanding?

In answer to this question I will argue that Kant is right. Firstly, and importantly, I view Kant’s arguments for the ideality of space and time as fundamentally sound. In so far as we are denoting ‘time’ and ‘space’ as necessary conditions of sensibility by the subject, they are a mind dependent feature of the subject. I believe Kant has successfully demonstrated that time and space as ‘inner intuitions’ do not ‘inhere’ in pure mind-independent sensibility in so far as their apodictic certainty sets the necessary limitations upon what we may consider sensible experience in the first place. I cannot even imagine a sensible intuition that is not at least temporal. There may be an exception for spatial intuition as I may be able to imagine a non-spatial internal thought or a non-spatial form of sensibility in so far as sound is non-spatial. However, at the very least, I cannot imagine a non-temporal form of sensibility. Therefore, temporality, though perhaps to a lesser extent, spatiality, do necessarily form the limits of potential experience. In my view then, they necessarily cannot have their origin in sensibility alone because pure sensibility only affords a posteriori and not a priori truths. Therefore, what Kant designates as time and space, our ‘pure forms of intuition’, because of their apodictic necessity, do arise in the subject.

Nonetheless, many have responded to Kant’s arguments with the ‘neglected alternative’ criticism. Trendelenburg argued that, even given the success of Kant’s arguments, we cannot presume that time and space do not also independently subsist outside of the subject and that, consequently, our epistemic faculties are not correctly mapping onto an ontological reality independently existent outside of ourselves (Bird, 2006).  I, however, believe that this misunderstands Kant’s argument in the Transcendental Aesthetic. There is an equivocation at the heart of the neglected alternative objection. I would like to propose that we borrow from Saul Kripke’s ‘Naming and Necessity’, and call the equivocated uses of the words ‘time’ and ‘space’ in the neglected alternative objection entirely different ‘rigid designators’ (Kripke, 2019). A rigid designator denotes a term in language which refers to one thing and one thing only in all possible worlds and, importantly, for Kripke at least, has a causal relation to its referent. By this he means that we must have a correct causal connection to the object facilitated through communities of language users; we must have epistemic access to it. When Kant speaks of ‘time’ and ‘space’, he is referring to time and space as our internal cognitive apparatus projected onto pure sensibility. For the sake of ease, let us call these rigid designators time1 and space1. The neglected alternative complaint states that there could be an existing time and space in the noumenal world which we do not have access to. Let us call these time2 and space2. When Kant states that time and space do not inhere in objects he is referring to time1 and space1. Our internal cognitive apparatus is not a feature of a world independent of our internal cognitive apparatus - ‘Intuitions which are possible a priori can never concern any other things than objects of our senses’ (Prolegomena, p. 24). This seems self-explanatory and logically uncontroversial. Therefore, time and space as we know them, as intuitions (time1 and space1), have their seat in the mind and not the thing-in-itself, existent beyond the mind.

As to the existence or non-existence of time2 and space2, this is something that Kant is not concerned with. It would be, necessarily, unknowable to a cognitive subject, and therefore not something we can speak about or have any knowledge of, as it exists, if at all, in the noumenal. Kant states ‘What objects may be in themselves, and apart from all this receptivity of our sensibility, remains completely unknown to us. (A42). To borrow from Kripke again, time2 and space2 would no longer be rigid designators as we do not have a causal epistemic relationship with them. Therefore, I believe that Kant is making a slightly weaker claim than some have imagined him to be. He is not arguing that time2 and space2 (whatever these would in fact be, as they are not rigid designators at all in our language, having no appropriate causal referent) as well as any number of other possibilities do not exist outside of the subject. This is because the noumenal world is simply unknowable, we have no access to it (at least in ordinary ways of knowing). He is making the weaker claim that time1 and space1, that is time and space as our necessary conceptual apparatus (which are rigid designators), cannot exist without a subject and therefore, by definition, do not exist in the noumenal. A complaint against my position may be that there is no equivocation in the neglected alternative hypothesis and that time and space as we conceive them, complete with their apodictic necessity, could exist outside of the subject. I, however, disagree. Time and space as we conceive of them are, by definition, only conceivable a priori and therefore, can only plausibly have their seat within the subject. What would an apodictic necessary time and space look like in a non-apodictic, non-necessary world? As soon as we abstract time and space outside of the subject they are no longer time and space as we ordinarily understand them in our rigid designation.

§3 Do negative epistemic assertions about the world in-itself constitute a form of positive ontological/metaphysical knowledge?

Let us assume the success of the proceeding arguments. We are still left with the objection that a negative assertion about the thing-in-itself is, nonetheless, a positive article of knowledge and hence the contradiction remains. I disagree; contentions concerning what the noumenal is not is not the same as to say what it is. Firstly, this form of negative designation, forming positive knowledge, may work for ordinary objects in our phenomenal experience because ordinary objects come under the analytic principle of non-contradiction and therefore cannot be two things at once. For example, ‘Ellie is not tall’ suggests that we know that ‘Ellie is medium height or short’. However, we cannot know that such analytic laws, for example non contradiction, hold for the noumenal. Therefore, saying what it is not, is arguably, not to say that we know anything about what it is. Furthermore, besides pure forms of intuition, we can presumably have much less controversial negative knowledge of the noumenal. For example, ‘the noumenal world is not colourful’. This would be indisputable to most philosophers because colour is a secondary property inhering in the subject and noumenal existence is subject independent. Is this negative assertion about the noumenal also a positive one? If so, then all philosophers, from Locke onwards are guilty of the same contradiction as Kant. Consequently, it is my view that denoting something negative about the noumenal is not the same as saying that we know anything positive about what the noumenal in fact is. Therefore, when we say that the noumenal cannot be in time1 and space1 (our cognitive apparatus), it does not follow that it cannot be in time2 and space2 (something of which I can have no conception whatsoever). We have not contradicted Kant’s assertion that we cannot know about the noumenal world because Kant is only making a negative assertion which holds with analytic certainty and is reasonably indisputable to most philosophers: the world outside of our ways of perceiving it is not like my ways of perceiving it. The more this is examined, even statements of the kind ‘we cannot know anything about the noumenal world’ appear to be saying at least one thing about the noumenal world. It is, however, a negative judgement and not a positive one. Thus, in truth, there is at least one thing we can know about the noumenal world and this is that we can abstract our conscious modes of thought away from it. Therefore, it cannot look like the world as it appears to me.

There is, however a further worry here: Is it not a positive judgement to say ‘I know that I can know nothing about the thing-in-itself’. Is this not a contradiction (indeed of the Socratic kind), knowing that we know nothing about the noumenal world is in fact admitting that we know something? I think this issue can be resolved if we make a distinction between epistemic truths and ontological/metaphysical truths. We know that the noumenal world cannot be epistemically as it is to us because, by definition, our epistemic faculties cannot cognize it. This appears to be a self-evident truth that is expressed in the negative ‘The noumenal cannot be known to us’. However, this does not mean that we know anything about the ontological/metaphysical nature of the noumenal. We simply know that it is a reality that has our knowing faculties abstracted from it. It is our epistemic questions which pre-disposes us to think of the noumenal and phenomenal as ontologically/metaphysically different, whereas, in fact, we can only really know that they are epistemically different.

James Van Cleve argues a similar point – Kant has not necessarily fallen into a contradiction, but instead a ‘pragmatic paradox’ (Van Cleve, p135). Such a paradox is not saying (ontologically) ‘P and not P’ but ‘(epistemically) P, but I do not know that P’. Van Cleve states that such an assertion is self-enfeebling but not an outright contradiction. Such a claim is akin to the Socratic ‘The only thing I know is that I know nothing’ which is a paradox rather than a contradiction. I agree with Van Cleve here. Kant, in my view, is not making claims about the ontological/metaphysical nature of the thing in itself, simply the epistemic nature: ‘It is such that I know that I know that it is not knowable as I ordinarily know’. This is a paradox but not an outright contradiction. The issue comes down to a more focused philosophical question: Is knowing that I do not know something a form of knowledge? My position is therefore in line with Desmond Hogan in his article ‘How to know unknowable things in themselves’. Hogan argues that Kant’s claim, that he knows that there is no way to know a non-empirical reality, may be a substantive metaphysical claim and therefore a positive statement about the nature of things in themselves. However, this does not contradict Kant’s skeptical claims about the noumenal but is rather ‘part of that denial’ (Hogan, 2009, p 60). 

Conclusion

I have endeavored to show that Kant has not contradicted himself. I have argued that, if we understand Kant’s claims about a-spatiality and a-temporality as somewhat weaker epistemic claims, then Kant can be saved from an apparent contradiction. I believe Kant has invoked a paradox and not a contradiction and that this paradox is no more threatening than any paradox in the history of philosophy. I have drawn on the work of Desmond Hogan and James Van Cleve as well as Saul Kripke’s’ ‘Naming and Necessity’. In summary, Kant has, in his exploration of the limits of cognition, come up against the edges of that ‘Island’ of the noumenal ‘surrounded by a wide and stormy ocean’ (CPR, B295) and, thus we should not expect his contentions about the noumenal to make perfect rational sense. There is, therefore, a sense in which finishing in a paradox, though certainly not a contradiction, is most fitting for Kant’s endeavor in the Critique of Pure reason.