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The Human A Priori
Essays on How We Make Sense in
Philosophy, Ethics, and Mathematics
A. W. MOORE
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Contents
Preface
Publisher’s Acknowledgements
ix
xi
Introduction
1
PART I. THE NATURE, SCOPE, AND LIMITS OF
A PRIORI SENSE-MAKING
1. Armchair Knowledge: Some Kantian Reflections (2023)
23
2. On the Necessity of the Categories (written jointly with Anil
Gomes and Andrew Stephenson, 2022)
44
3. What Descartes Ought to have Thought about Modality (2019)
and Postscript
77
4. Varieties of Sense-Making (2013)
94
P A R T I I . H O W WE M A K E S E N S E I N P H I L O S O P H Y
5. Sense-Making from a Human Point of View (2017)
107
6. Not to be Taken at Face Value (2009)
117
7. Carving at the Joints (2012)
127
8. The Concern with Truth, Sense, et al.—Androcentric or
Anthropocentric? (2020)
135
PART III. HOW WE M AKE S ENSE IN ETHICS
9. A Kantian View of Moral Luck (1990)
149
10. On There Being Nothing Else to Think, or Want, or Do (1996)
171
11. Conative Transcendental Arguments and the Question Whether
There Can Be External Reasons (1999)
189
12. Maxims and Thick Ethical Concepts (2006)
210
13. Quasi-Realism and Relativism (2002)
226
14. From a Point of View (2012)
233
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viii

15. Williams, Nietzsche, and the Meaninglessness of
Immortality (2006)
241
P A RT I V . HO W W E M A K E S E N S E I N M A T HEM A T I C S
16. On the Right Track (2003)
259
17. Wittgenstein and Infinity (2011)
273
18. Wittgenstein’s Later Philosophy of Mathematics (2017)
291
19. A Problem for Intuitionism: The Apparent Possibility of
Performing Infinitely Many Tasks in a Finite Time (1989–90)
306
20. More on ‘The Philosophical Significance of Gödel’s
Theorem’ (1999)
320
Bibliography
Index
337
353
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Publisher’s Acknowledgements
Essay 2, ‘The Necessity of the Categories’, written jointly with Anil Gomes and Andrew
Stephenson, was originally published in The Philosophical Review, 131 (2022): 129–68.
Essay 3, ‘What Descartes Ought to Have Thought About Modality’, was originally published in Sofia Miguens (ed.), The Logical Alien: Conant and His Critics (Harvard UP 2019).
Essay 4, ‘Varieties of Sense-Making’, was originally published in Midwest Studies in
Philosophy, 37 (2013): 1–10.
Essay 5, ‘Sense-Making from a Human Point of View’, was originally published in
Giuseppina d’Oro and Søren Overgaard (eds), The Cambridge Companion to
Philosophical Methodology (Cambridge UP 2017): 44–55.
Essay 6, ‘Not to be Taken at Face Value’, was originally published in Analysis, 69/1 (2009):
116–125.
Essay 7, ‘Carving at The Joints’, was originally published in the London Review of Books,
34/16 (30 August 2012): 21–23.
Essay 8, ‘The Concern With Truth, Sense, et al.—Androcentric or Anthropocentric?’, was
originally published in Angelaki 25/1–2 (2020).
Essay 9, ‘A Kantian View of Moral Luck’, was originally published in Philosophy, Vol. 65,
no. 253 (1990): 297–321.
Essay 10, ‘On There Being Nothing Else to Think, or Want, or Do’, was originally published
in Sabina Lovibond and S. G. Williams (eds), Essays for David Wiggins: Identity, Truth and
Value (Blackwell 1996): 165–84.
Essay 11, ‘Conative Transcendental Arguments and the Question Whether There Can Be
External Reasons’, was originally published in Robert Stern (ed.), Transcendental
Arguments: Problems and Prospects (OUP 1999): 271–92.
Essay 12, ‘Maxims and Thick Ethical Concepts’, was originally published in Ratio,
19 (2006): 129–147.
Essay 13, ‘Quasi-Realism and Relativism’, was originally published in Philosophy and
Phenomenological Research, Vol. 65, No. 1 (2002): 150–56.
Essay 14, ‘From a Point of View’, was originally published in Philosophical Quarterly,
Vol. 62, No. 247 (April 2012): 392–8.
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xii
 ’  
Essay 15, ‘Williams, Nietzsche, and the Meaninglessness of Immortality’, was originally
published in Mind, Volume 115, Issue 458 (2006): 311–30.
Essay 16, ‘On the Right Track’, was originally published in Mind, Volume 112, Issue 446
(2003): 307–22.
Essay 17, ‘Wittgenstein and Infinity’, was originally published in Oskari Kuusela and Marie
McGinn (eds), The Oxford Handbook of Wittgenstein (Oxford UP 2011): 105–21.
Essay 18, ‘Wittgenstein’s Later Philosophy of Mathematics’, was originally published in
Hans-Johann Glock and John Hyman (eds), A Companion to Wittgenstein (Blackwell
2017): 319–31.
Essay 19, ‘A Problem for Intuitionism: The Apparent Possibility of Performing Infinitely
Many Tasks in a Finite Time’, was originally published in Proceedings of the Aristotelian
Society 90/1 (1989‒90): 17–34.
Essay 20, ‘More on “The Philosophical Significance of Gödel’s Theorem”’, was originally
published in Grazer Philosophische Studien, 55/1 (1999): 103–126.
Permissions to republish are gratefully acknowledged.
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Introduction
Part of the rationale for collecting these essays together is that they are all
concerned, in one way or another, with the a priori. But there is a more fundamental and more distinctive unifying theme: the essays all reckon, again in one
way or another, with what I see as something ineliminably anthropocentric in our
systematic pursuit of a priori sense-making.
I shall not try to provide a precise definition of the a priori. Given the range of
these essays, and given the extent to which their concern with the a priori is a
matter of unspoken background presupposition rather than direct engagement, it
suits my purposes to allow as much latitude as possible in how the term is to be
understood. This includes latitude in how its very domain is to be understood:
does the term apply to truths? to states of knowledge? to concepts? to modes of
investigation? to justifications for what is believed? possibly even to features of
reality? It is largely to accommodate this latitude that I have elected, in this
Introduction, to use the blanket term ‘sense-making’ as the complement of ‘a
priori’. For ‘sense-making’ can itself be understood in a suitably wide variety of
ways. And even if it does not capture all of what has been classified by philosophers as ‘a priori’, its own classification as ‘a priori’ allows for extension to other
cases: for instance, a truth may be said to be a priori if it can be known as a result
of a priori sense-making. All that really matters, for current purposes, is that
if something can be classified as ‘sense-making’, and if it manages to do whatever
it is intended to do independently of experience, then it can also be classified as
‘a priori’.
Just as I shall refrain from trying to provide a precise definition of the a priori,
so too I shall refrain from trying to provide a precise definition of the anthropocentric. Again all that really matters, for current purposes, is that the term
indicates what is from a human point of view, and that ‘human’ in turn is to be
understood in relation to Homo sapiens. This reference to Homo sapiens might
have been thought to go without saying. But it deserves to be made explicit, if only
because of a non-biological understanding of the term ‘human’ that we find, at
least arguably, and at least sometimes, in Kant. On that understanding the term
denotes finite rationality.¹ Interestingly, this makes the concept of the human itself
a priori—though, more interestingly still, there is an argument due to Michael
¹ See e.g. Kant (1996a), 4: 428 ff. and Kant (1996d), 6: 26 ff.
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2
   
Thompson that the concept of the human is a priori anyway, even when it is
understood biologically.² This raises some fascinating issues that are clearly
pertinent to what I have identified as the unifying theme of these essays. Even
so, I mention them principally to set them aside. For the question whether or not
the concept of the human is itself a priori is strictly orthogonal to the question
whether or not what is a priori is bound up with the human in the way I am
claiming. Either answer to the first question is compatible with either answer to
the second.
In order to give an initial indication of why I see the connection that I do
between the a priori and the human, I am going to present something that I will
call ‘the Basic Model’. In the Basic Model, there is some subject S who is in
possession of some concept c which is integral to some a priori sense-making that
S achieves, but there is also something radically parochial about S’s possession of c.
A simple example would be a subject who, by virtue of possessing the concept of a
wife, deduces a priori that there are at least as many women and girls as there are
wives. The a priority of S’s deduction is in no way compromised by the fact that
there is a complicated network of highly contingent social structures and values
that support the institution of marriage and that serve as a precondition of any
subject’s possessing any such concept in the first place. The Basic Model is therefore
already enough to indicate how the a priori can be grounded in the parochial. It is
not a huge leap from there to the thought that the a priori can be grounded in
peculiarities of an entire species; nor from there to the thought that there can be a
priori sense-making that may appropriately be said to be from the point of view of
that species; nor from there to the thought that we humans and what accrues from
our systematic pursuit of a priori sense-making are a case in point.
I mentioned in the Preface that Essay 10 has what I now see as an important
imperfection whereby it cuts across one of the main threads that links together
this volume as a whole. In the bulk of what follows in this Introduction I shall say a
little about each of the essays in the order in which they occur; but first I want to
amplify on what I had in mind when I made that comment about Essay 10, and
to draw on some related material in Essay 12, since this will help to clarify the
Basic Model.
Essay 10 is concerned with an idea that occurs in David Wiggins’s work: the
idea of there being nothing else to think.³ In that essay I explore a way of
construing this idea whereby the claim that there is nothing else to think but
that p is equivalent to the claim that it is true that p. This in turn involves the
following subsidiary idea: if it is true that p, then anyone who does not think that p
pays a price. But what is it not to think that p? It is easy to assume, and in the essay
I in effect did assume, that not thinking that p must take one of three forms:
² Thompson (2004).
³ For a fascinating discussion of this idea, and of other related ideas, see Diamond (2019).
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
3
thinking the opposite; being self-consciously agnostic about the matter; or not
even considering the matter, possibly not even being in a position to consider it.
But even at the time of writing the essay I was aware of what many people, Bernard
Williams in particular, would regard as an important fourth possibility. I gesture
towards this possibility in footnote 29 of the essay, albeit only to register my
disagreement with Williams. However, as I indicate in a parenthesis within that
footnote added for the reprint, I have subsequently arrived at a more sympathetic
view of what Williams has in mind.
To understand what Williams does have in mind we can exploit some of the
material that I present in Essay 12. I there offer a distinction between what I call a
‘disengaged’ grasp of a concept and an ‘engaged’ grasp of it—a distinction which
I fudge in footnote 29 of Essay 10 when I talk of ‘having’ a thought, and which for
that matter I fudge in Essay 10 as a whole when I talk of ‘thinking’ that something
is the case. This distinction applies when a concept is what Williams would call a
‘thick’ concept, that is a concept with both a factual aspect and an evaluative
aspect. An example is the concept of infidelity: if I claim that you have been
unfaithful, then I say something straightforwardly false if you have not in fact gone
back on any relevant agreement; but I also thereby censure you. Another example,
albeit one in which the evaluative aspect is somewhat subtler, is that which I used
to illustrate the Basic Model: the concept of a wife. To grasp a thick concept in the
disengaged way is to be able to recognize when the concept would correctly be
applied, to be able to understand others when they apply it, and so forth. To grasp
such a concept in the engaged way is not only to be able to do these things but also
to be prepared to apply it oneself and hence to share whatever beliefs, concerns,
and values give application of the concept its point. Talk of ‘having’ a thought, or
even of ‘thinking’ something, and other related talk, can then be understood in
two corresponding ways: in the engaged way whereby it requires having an
engaged grasp of all the relevant concepts; and in the disengaged way whereby it
does not. And if ‘thinking’ that p is understood in the engaged way, then there is
indeed a fourth form that not thinking that p can take: namely, ‘considering’ the
matter, where this is understood in the disengaged way, and possibly even
‘recognizing’ that it is true that p, where this too is understood in the disengaged
way, but not oneself being prepared to apply one of the relevant concepts
and thus not oneself thinking that p. Moreover, all of this may be completely
self-conscious. One may not think that p because one repudiates the concept in
question as somehow pernicious. The reason why this poses a particular threat to
my project in Essay 10 is that, if the concept is somehow pernicious, then the idea
that one pays a price for not thinking that p when it is true that p is clearly
compromised: the very perniciousness of the concept may mean that one is better
off not thinking that p, because one is better off not thinking in such terms at all.
The relevance of all of this to the Basic Model should be clear. I couched the
Basic Model in terms of ‘sense-making’, a term whose versatility I have already
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4
   
heralded, and in terms of ‘possession’ of a concept, a term on which I did not
expand. Importantly, the distinction between the engaged way of understanding a
term and the disengaged way of doing so apply to both of these. In particular, both
can be understood in the engaged way. And if they are, then the instance of the
Basic Model that I gave concerning wives turns out to be just one of a whole family
of instances that involve thick concepts. For there is certainly something parochial
about anyone’s possession of a thick concept, so understood; and such possession
can certainly be integral to a priori sense-making, so understood. In what follows
I shall frequently return to the Basic Model.
Now there are often thought to be three great exemplars of the systematic
pursuit of a priori sense-making: philosophy, ethics, and mathematics. The essays
in Parts II, III, and IV deal respectively with each of these. The essays that precede
them in Part I deal with the very nature of a priori sense-making and introduce the
anthropocentrism. Much of the attention throughout is devoted to the work of
other philosophers. But, even when it is, I take it to be of more than exegetical
interest. One of the lessons that I take to emerge, either in opposition to the views
of these other philosophers or by invocation of their views, is that we humans
achieve nothing of real significance in philosophy, ethics, or mathematics except
from a human point of view. In itself this does not force us to conclude that there
is anything ineliminably anthropocentric about our systematic pursuit of a priori
sense-making. After all, it may be that none of these three disciplines is the
systematic pursuit of a priori sense-making that it is taken to be. This is not in
fact my own conclusion, although it would be striking enough if it were the only
alternative. My own conclusion is that philosophy, ethics, and mathematics each
betoken what may reasonably be called ‘the human a priori’.
1. Part I: The Nature, Scope, and Limits
of A Priori Sense-Making
Given what I have said so far, Kant might be expected to figure in these essays as a
hero. Is he not the great champion of the human a priori? One of his primary
metaphysical projects is, after all, to account for a certain kind of a priori sensemaking; and the way in which he does so is by appeal to experience-independent
cognitive resources which we humans have and which, for all we know, only we
humans have. Not only are these integral to the a priori sense-making in question,
they are integral to it in a way that makes it entirely appropriate to say that such
sense-making is from a human point of view—possibly even from a peculiarly
human point of view.⁴
⁴ Cf. Kant (1998), A26/B42.
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5
In many ways Kant does figure in these essays as a hero. He is the focus of each
of the first two essays. Nevertheless, the principal lesson of Essay 1 is that there is
something badly wrong with Kant’s own vision of the human a priori. This vision
has three critical components:
(Necessity) When we make a priori sense of things from our human point of
view, we make sense of them as necessarily being a certain way.⁵
(Dependence)
Things’ being that way is dependent on that point of view.
(Inescapability)
We cannot make sense of things except from that point of view.
But there is an incoherence in supposing that we can acknowledge all three of
these. For to acknowledge Dependence is to acknowledge a contingency in things’
being that way. And, given Necessity, this is to make sense of things from other
than our human point of view (which presumably means, in this context, from no
point of view at all). But this is what Inescapability says we cannot do.
In the penultimate section of Essay 1 I argue that a significant part of Kant’s
problem is the nature of the experience-independent cognitive resources that he
invokes to explain our a priori sense-making. He includes aspects of how we think.
But he also includes aspects of how we receive material to think about. And he
does the latter in such a way that he also includes aspects of that very material,
specifically its spatiality and temporality. By the time he has done all of this he is
committed to Dependence. Had he only included aspects of how we think, any
anthropocentrism that this involves would not have infected the subject matter of
our thoughts and would not have compromised the necessity in how we make
sense of things as being. We can appreciate this by reconsidering the Basic Model.
However parochial the fact that a given subject thinks in terms of wives, to revert
to that example, this subject is in a position to see that there must be fewer of them
than there are women and girls.⁶
I said that, had Kant only included aspects of how we think in the resources that
he invokes to explain our a priori sense-making, ‘any anthropocentrism that this
involves’ would not have infected the subject matter of our thoughts. But what
anthropocentrism does this involve? Is it akin to the anthropocentrism involved in
the other resources that he invokes, that is to say in the spatiality and the
temporality that are operative in how we receive material to think about? In
their case, although Kant thinks they are part of our human point of view, and
although he thinks we can know this, this is the limit of what he thinks we can
⁵ This is not to be confused with the thesis labelled ‘Necessity’ in Essay 2.
⁶ In the final section of Essay 1 I moot another way in which the problem could be averted, albeit a
way that would take us even further from Kant’s own position. We could develop a conception of a
priori sense-making that allows for contingency in how things are thereby made sense of as being. But
I shall not now dwell on the many further issues that this raises.
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6
   
know. We cannot, in Kant’s view, know whether they are part of the point of view
of other finite sense-makers (if such there be) nor for that matter whether they are
part of the point of view of all possible finite sense-makers.⁷ The issue is whether
he adopts an analogous circumspection concerning the resources that are operative in how we think, or whether, in their case, he reckons that we can know more:
specifically, that they are part of the point of view of all possible finite sensemakers. This is the issue that Anil Gomes, Andrew Stephenson, and I address in
Essay 2.⁸ We end up mooting a second-order circumspection on Kant’s part
whereby the answer is neither—although there are reasons of principle why
Kant had better not explicitly endorse this position.⁹
In Essay 3 attention shifts to Kant’s predecessor Descartes. Descartes likewise
sees an anthropocentrism in our a priori sense-making. And he likewise embraces
a version of Necessity. Both of these are manifest when, in making a priori sense of
things, we at the same time make sense of them as necessarily being a certain way.
For, on Descartes’s conception, for things necessarily to be a certain way is for the
denial that things are that way to ‘conflict with our human concepts’.¹⁰
Not only is there a version of Necessity at work here, though. There is also what
appears to be a Kantian predicament in the offing, as we see when Descartes pits
his conception of necessity against his conception of God. For he is reluctant
to say that any necessity in how things are is necessity even for God. This is in
large part because he believes that ‘every basis of truth . . . depends on [God’s]
omnipotence’,¹¹ from which it follows that even those things that are necessarily a
certain way are ultimately that way only because God decrees that they are. From
this in turn it follows, or rather it seems to follow—I shall return to the significance of this qualification shortly—that the necessity in question is at most a
necessity for us, a necessity resting on a deeper contingency about our human
point of view and the play of our concepts there. This is not the contingency of
Dependence: the link here is between our human point of view and the necessity
itself, not between our human point of view and what the necessity attaches to. But
it makes for similar trouble. And it does mean that, if an analogue of Inescapability
is at work in Descartes, as it plausibly is, then the apparent Kantian predicament
to which I have referred is a real one.
In fact, however, it is the burden of Essay 3 to argue that it is merely apparent.
Descartes is at perfect liberty to deny that what I said seems to follow does follow;
and he is at perfect liberty to insist that the necessity in question is indeed
⁷ Kant (1998), A27/B43 and B72.
⁸ For those who have read my Preface and are curious to know what our disagreement was, I can add
that I originally thought that I could defend the former of these exegetical alternatives, while Gomes and
Stephenson originally thought that they could defend the latter.
⁹ Some readers familiar with other work of mine, on inexpressibility, may see the stamp of that work
on this conclusion. They would be wrong to do so. The silence required of Kant here has nothing to do
with inexpressibility. It is silence on an issue that I take myself to have just expressed.
¹⁰ Descartes (1984b), ‘Second Set of Replies’, p. 107.
¹¹ Descartes (1991), p. 359.
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
7
necessity even for God. He can do these things by doing what his a priori
reflections on these issues mean that he should only ever have been doing—
albeit, for reasons that I have indicated, he is sometimes diffident about doing—
namely, heeding the analogue of Inescapability and resting content with making
sense of things from our human point of view. This makes any claim that the
necessity in question is necessity even for God harmlessly anthropocentric. It does
nothing to gainsay the fact that even those things that are necessarily a certain way
are ultimately that way only because God decrees that they are. In saying that they
are necessarily that way we are saying only that it would conflict with our human
concepts to deny that that is how they are. (We are also alluding to our means of
coming to know that that is how they are.) In its own way, then, Essay 3 clearly
develops the theme of the human a priori. In a brief postscript to the essay
I correct a misunderstanding of the essay due to James Conant that precisely
fails to recognize this.
Of the four essays in Part I, Essay 4 is the one that is least obviously about the a
priori. It is targeted at what is commonly dubbed ‘the new atheism’. I use the essay
to explore a conception of theistic sense-making for which the new atheism makes
no allowance. As it happens I believe that this conception significantly overlaps
with my broad conception of a priori sense-making; I also believe that, where it
does, there is something fundamentally anthropocentric about it. So, although
none of this is explicit in Essay 4, it does mean that the essay is not the incongruity
which it may appear to be. Even so, the significance of the essay for the volume as a
whole lies elsewhere. I have included it because of the way in which it draws
attention to kinds of sense-making that are not characteristic of the natural
sciences. My hope is that it thereby serves as a helpful prelude to Parts II, III,
and IV. For I do not believe that we can properly grasp the anthropocentric
element in philosophy, ethics, or mathematics until we have come to appreciate
how deeply the sense-making involved in each of these differs from that involved
in the natural sciences (whose systematic pursuit can reasonably include the
aspiration to abandon the human point of view¹²). Part of the force of what is
to come in the remaining essays, therefore—as of Essay 4 itself—is an antiscientism.
2. Part II: How We Make Sense in Philosophy
Such anti-scientism is to the fore in Part II. Of the three disciplines around which
the essays in this volume are structured—philosophy, ethics, and mathematics—it
is philosophy that is in greatest danger of falling prey to scientism. In Essay 5
¹² This is something that I argue in A. W. Moore (1997), esp. ch. 4.
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   
I take as my starting point the view famously defended by Bernard Williams as
a safeguard against this danger: that philosophy is a humanistic discipline.
I consider some of the implications of this view. However, to the extent that
Essay 5 is written in opposition to anyone, it is written in opposition, not to those
philosophers, typically within the analytic tradition, who think on scientistic
grounds that we can abandon the human point of view when practising philosophy, but to those philosophers, typically not within the analytic tradition, who
think that we can do so on the very different grounds that ‘we’ do not have to
understand ‘ourselves’ as human beings at all and should embrace what is
sometimes called ‘the post-human’. If philosophers of the former kind are in too
much thrall of the natural sciences, then philosophers of the latter kind are in too
little thrall, it seems to me, of their own humanity. The sheer fact that they adopt
such a stance indicates that they have a greater aversion to philosophical conservatism than they have to philosophical loss of identity. And while I am certainly
conscious of the dangers of philosophical conservatism—to the extent that I agree
that we should be ready to embrace the post-human—nevertheless there is
something so important about our humanity that the dangers of philosophical
loss of identity strike me as being altogether graver.
It is in Essays 6 and 7 that my opposition to philosophers of the former kind—
those who think on scientistic grounds that we can abandon the human point of
view when practising philosophy—is most evident. Each of these essays is targeted
at a book by a philosopher in the analytic tradition. The target in Essay 6 is The
Philosophy of Philosophy by Timothy Williamson; the target in Essay 7 is Writing
the Book of the World by Theodore Sider.¹³ And each of these books is a defence of
what I see as just such a scientistic conception of philosophy—or rather, in the case
of Sider’s book, of metaphysics, although I take metaphysics to be a subdiscipline of
philosophy that is in relevant respects typical of the discipline as a whole.
My opposition takes a somewhat different form in each of these two essays. In
Essay 6 it takes a more piecemeal form. I there focus on a few characteristic
examples of how Williamson’s scientistic conception of philosophy manifests
itself, and I try to indicate in each case why I see things differently. It is worth
noting that one of the clearest ways in which it manifests itself is in the doubt that
Williamson casts, not on the view that philosophical sense-making is fundamentally anthropocentric, but rather on the view that it is fundamentally a priori.
(Williamson is in general suspicious of the significance that philosophers attach to
the a priori. He is even suspicious of the significance that they attach to it in
connection with mathematics. Some of what I say in Essay 6 is a foretaste of some
of what is to come in Part IV.) In trying to counteract Williamson’s conception of
philosophy I thus have my work doubly cut out.
¹³ Williamson (2007) and Sider (2011), respectively.
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In Essay 7 my opposition takes a more systematic form. Sider sees metaphysics
as continuous with physics; and he devotes some of his book to practising
metaphysics, some of it to the meta-metaphysical task of reflecting on what he
is thereby doing. Significantly, however, he acknowledges that some such reflection is already part of metaphysics itself. For he sees metaphysicians as standing in
a similar relation to physicists as meta-metaphysicians stand to them (metaphysicians). More specifically, he sees metaphysicians as reckoning with the propriety
and worth of what physicists are doing. The significance of this, as I urge in Essay 7,
is that there can be no reckoning with the propriety and worth of anything except
from a point of view that allows for due evaluation. In particular, there can be no
reckoning with the propriety and worth of what physicists are doing except
from a point of view that allows for due evaluation of various human endeavours, which is to say a human point of view. Sider’s acknowledgement that such
reflection is part of metaphysics therefore constitutes a crucial concession to
anyone who shares my conviction that there is something ineliminably
anthropocentric about metaphysics in particular, and about philosophy in
general. Not that Sider would agree. He would deny that the evaluation in
question is linked to a point of view in the way I claim. He has to deny this:
the alternative poses far too much of a threat, if indeed it does not deal a fatal
blow, to his vision of metaphysics as continuous with physics. But then so much
the worse, I say, for that vision.
The target in Essay 8 is the work of another philosopher, although this time a
philosopher less easily classified either as an analytic philosopher or as a nonanalytic philosopher: Pamela Sue Anderson. I believe that she errs in the opposite
direction. Much of my opposition in the three previous essays has been to the view
that philosophy can escape the human. Anderson advances reasons for opposing
the view that philosophy can escape the gendered human. In particular she argues
that some of my own philosophical work betrays my masculinity. I disagree,
although I acknowledge that she thereby raises some very important issues
about the relation between philosophy and the masculine, between philosophy
and the feminine, and between philosophy and the human. Towards the end of
Essay 8 I try to reinforce a recurring theme of all the essays in Part II by insisting
that it is the third of these—the relation between philosophy and the human—that
is overwhelmingly the most significant.
3. Part III: How We Make Sense in Ethics
The essays in Part III are concerned with ethics. Of the three disciplines—
philosophy, ethics, and mathematics—this is the one that is liable to provoke
least resistance to the thought that it is fundamentally anthropocentric. On
the other hand, it is also the one that is liable to provoke most resistance to the
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   
thought that it is fundamentally a priori. There is accordingly a kind of shift of
onus in these essays compared with those in Part II.
The first four essays of Part III direct us once again to Kant. One of the many
reasons why Kant is significant in this context is that he is, in the respect to which
I have just adverted, an outlier. On Kant’s view, ethics is not fundamentally
anthropocentric, but it is fundamentally a priori. In so far as Kant is a champion
of the human a priori, this is because of his views about a priori sense-making of
the theoretical kind that is characteristic of philosophy and mathematics, not
because of his views about a priori sense-making of the practical kind that is
characteristic of ethics. The latter, for Kant, is at root neither more nor less than an
exercise of pure reason. As such it can be implemented by any being whose
faculties include reason, be the rest of that being’s constitution as it may. This
means that it is not only a priori in a way that does not involve its being
anthropocentric; it is a priori in a way that precludes its being anthropocentric.
One of my aims in these four essays is to consider some of what makes the
opposed idea that ethics is fundamentally anthropocentric so attractive, and to
explore how much of Kant’s commitment to the a priority of ethics could survive
its assimilation. Given what I have said so far, the answer is obviously not all of it.
But it is not obviously not any of it. The upshot of these four essays is neither a
simple defence of that commitment nor a simple attack on it, but rather, in
keeping with the volume as a whole, a non-Kantian reconsideration of a priori
sense-making as itself, even in its practical form, inextricably bound up with the
human.
In Essay 9 I consider some of the consequences of Kant’s view that, even though
ethics is not fundamentally anthropocentric, there is something fundamentally
anthropocentric, possibly even peculiarly anthropocentric, about the way in which
its demands appear to us as obligations. The fact that we are not just rational
beings, but rational animals—with all the needs, desires, and drives that this
entails—means that we are not always inclined to do what it would be purely
rational to do. Hence, as Kant himself points out, what we would willingly do if we
were purely rational appears in the guise of what we ought to do.¹⁴ And when we
do not do it, there are issues that arise, and that create a certain awkwardness for
Kant, about what kind of a failing this is, about what kind of control we have over
what we do instead, and about what kind of relationship there is between such
control—or lack of control—and our blameworthiness. St Paul takes an extreme
view in his letter to the Romans: ‘[W]hat I do is the wrong which is against my
will; and if what I do is against my will, clearly it is no longer I who am the agent,
but sin that has its lodging in me.’¹⁵ Kant is under pressure to say something
similar. But it is pressure that he resists. (This is the primary reason for the
¹⁴ E.g. Kant (1996a), 4: 449.
¹⁵ Romans 7: 19–20.
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11
awkwardness to which I referred.) On Kant’s view, if I incur blame for doing
something other than what I ought to do, then there is no question but that
I myself am the agent.
In exploring all of this, I am playing out a curious variation on the theme of
Essay 3 concerning Descartes, in as much as I am directing attention, not at the
content of any of our a priori insights, but at the kind of necessity that attaches to
them from our human point of view. There is even a hint of something else from
Essay 3: the idea that we can do greatest justice to the resultant position by
adhering resolutely to the human point of view and not trying to make sense of
any of this except from there. No matter how much justice we do to the resultant
position, however, it will still contain elements that are mysterious, counterintuitive, or both, for instance the idea, which is related to the pressure that
Kant is under malgré lui to align himself with St Paul, that there is no such
thing as a totally free act of wrong-doing. It will also contain elements, as I finish
the essay by briefly expounding, that reflect further discomfort on Kant’s part with
what St Paul says. In particular, Kant will not want to join St Paul in saying that a
person’s blameworthiness for doing something other than what they ought to do
can be annulled by divine grace. For just as it goes against the Kantian grain to say
that someone can incur blame as a result of something that sin does, so too it goes
against the Kantian grain to say that someone can forego blame as a result of
something that God does. For non-Christians this may seem a relatively arcane
matter. But for Christians and non-Christians alike it serves as a reminder of the
purity that Kant sees in our practical sense-making—while some of the other
elements in the resultant position serve as a reminder of the messiness that he
encounters in his attempt to make sense of that purity from our human point
of view.
But what about the question that I flagged above, about how much of what Kant
sees in our practical sense-making can survive if the purity is removed, that is if
such sense-making is itself reckoned to be from our human point of view? One
thing seems clear. Whatever survives, we shall encounter a similar messiness, if
not a much greater messiness, in trying to make sense of it from our human point
of view. What is not clear is whether this matters. Once we have relinquished the
view that our practical or ethical sense-making is an exercise of pure reason, we
shall be less beholden to the particular notions of freedom, control, wrong-doing,
and such like that made for mystery and counterintuitiveness in the messiness that
Kant himself encountered. The messiness that we encounter is liable to strike us as
simply the messiness of life. In fact there are some important lessons to be learned
here about how the combination of the a priori with the human is always
vulnerable to the interference with the a priori by the human. That is, there are
some important lessons to be learned about how the attempt to make a priori
sense of things from a human point of view has its own distinctive ways of meeting
with failure.
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Essays 10 and 11 are likewise concerned with the kind of necessity that attaches
to the ethical from our human point of view. Neither essay defends the view that
ethics is an arena for the human a priori. Neither, come to that, defends the view
that ethics is an arena for any kind of a priori. But both portray the necessity in
question as having some affinity with the kind of necessity that characterizes our a
priori sense-making, and both combine that with an indication of how such
necessity has the special force that it has from a human point of view. I have
already discussed the flaw in Essay 10, and the way in which this flaw, once
perceived as such, puts us in mind of the Basic Model and thereby prepares us for
the possibility of the human a priori. The significant point here, however, is that
Essay 10 manages to prepare us for that possibility anyway. The crucial work is
done by something that I refer to in Essay 10 as ‘the Basic Idea’—where that label,
incidentally, does not betoken any special connection with what I have been
calling ‘the Basic Model’. The Basic Idea is that human beings are finite, but
have an aspiration to be infinite.¹⁶ It is this that allows the necessity to have the
special force that it has from our human point of view; for the necessity is precisely
to be explained in terms of certain marks of the infinitude to which, according to
the Basic Idea, we aspire. Not that the details of the account (which are in any case
very sketchy in Essay 10) are what really matter in this context. Much more
important and much more fundamental than the Basic Idea itself—be the truth of
the Basic Idea as it may, and indeed be the interpretation of the Basic Idea as it
may—is the broader idea of some shared conative state among human beings that
influences our sense of necessity. If there is any such state, then there is scope for it
likewise to influence our a priori sense-making and to prepare the way once again
for a kind of human a priori.
That same broader idea plays a similarly crucial role, and a similarly relevant
role, in Essay 11—where the necessity has a new guise, as the necessity that
animates a kind of transcendental argument. More specifically, I argue in Essay
11 that, just as there may be transcendental arguments of a Kantian kind for the
conclusion that things are thus and so, proceeding via the intermediate conclusion
that it is necessary for us to believe that things are thus and so, so too there may be
‘conative’ variants of these transcendental arguments for the desirability that
things are thus and so, proceeding via the intermediate conclusion that it is
necessary for us to desire that things are thus and so (in some suitably broad
sense of ‘desire’). And it is the necessity of our desiring that things are thus and so
that exemplifies the broader idea: there is a conative state which, on the one hand,
we all have because we cannot help having it, and which, on the other hand,
influences our sense of necessity, including the very necessity of our having it.
Much of Essay 11 is concerned with tracing these elaborate interconnections.
¹⁶ Cf. Cavell (1979), p. 109; and Conant (1991b), p. 634.
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Neither Essay 10 nor Essay 11 is primarily about Kant. In fact Essay 10, as
I have already indicated, is primarily about David Wiggins, whose related idea of
there being only one thing that one can think about a given issue is an idea that he
would distance from anything peculiarly Kantian, or indeed from anything to do
with the a priori.¹⁷ Nevertheless, both essays have clear Kantian resonances. And,
in so far as they depart from Kant in what room they leave for an understanding of
the ethical as a priori, they do so precisely by allowing aspects of our humanity
back in. This they do by taking seriously the idea that we humans all share a
conative state that shapes all our ethical deliberations, a priori and empirical alike.
The fourth of the essays in this quartet is like the first in being more straightforwardly about Kant. And it is pivotal to the volume as a whole. For it is here, in
Essay 12, that we find the most graphic illustration of the Basic Model. (This is
why I had occasion to refer to Essay 12 earlier in the Introduction.) It is here too
that we most directly confront the question of how much of Kant’s own commitment to the a priority of ethics could survive assimilation of the idea that ethics is
fundamentally anthropocentric. Ethics, for Kant, is an exercise of pure reason. But
even Kant acknowledges that ethics is applicable to issues that can be framed only
in terms of concepts whose possession depends on highly contingent social
structures. (It had better be applicable to such issues, if the exercise of pure reason
in question is to be suitably practical.) Kant has no qualms, for example, about
drawing ethical conclusions about the marriage contract.¹⁸ And such applicability
is already an illustration of the Basic Model. For precisely what it involves is a
priori sense-making that is achieved through the implementation of concepts
whose possession is radically parochial. But now comes the twist. It would be
possible to maintain a broadly Kantian view of ethics, while nevertheless departing
from Kant himself and embracing the view that ethics is fundamentally anthropocentric, by conceiving of ethics as concerned not only with issues about how to
respect whatever concepts we possess but also with issues about what concepts to
possess in the first place—and, in particular, about what thick concepts to possess in
the engaged way. On this extended conception of ethics—I say some more about
the conception and about its rationale in the final section of Essay 12—ethics
would involve negotiating certain basic facts of human nature that determine what
concepts we are so much as capable of possessing. (This is not unrelated to Kant’s
own concession that the exercise of pure reason that constitutes ethics sometimes
involves negotiating certain basic facts of human nature that determine what we
are capable of willing.¹⁹) Ethical sense-making could then reasonably be viewed as
a prime example of sense-making that is both fundamentally a priori and fundamentally anthropocentric.
¹⁷ See Wiggins (1996).
¹⁸ Kant (1996c), 6: 279–80.
¹⁹ E.g. Kant (1996a), 4: 423–4.
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   
The remaining three essays in Part III are more concerned with the
anthropocentric than with the a priori. But they are concerned with the anthropocentric in a way that connects importantly with what has gone before and
continues to have implications for the human a priori.
Essay 13 is a critique of Simon Blackburn’s meta-ethical ‘quasi-realism’,
whereby ethical claims, though they are expressive of our conative states, also
admit of truth or falsity. In this essay I argue that, despite Blackburn’s insistence to
the contrary, he is committed to a relativism akin to what we have just witnessed
in Essay 12. Moreover, I do so in a way that directly relates back to the discussion
of Descartes in Essay 3. For Descartes’s conception of necessity and Blackburn’s
conception of desirability are variations on a single theme: each adverts to what we
are implicitly saying about ourselves when we make some claim about the notion
in question. On Descartes’s conception of necessity, when we make some claim
about how it is necessary for things to be, we are implicitly saying that it would
conflict with certain concepts that we human beings possess for things not to be
that way. On Blackburn’s conception of desirability, when we make some claim
about how it is desirable for things to be, we are implicitly saying that it would
conflict with certain conative states that we human beings have for things not to be
that way. The reason why I take Blackburn to be committed to a kind of relativism
is that I take it to follow from this that, had our conative states been relevantly
different, which I believe his own quasi-realism compels him to say they could
have been, then we would, quite rightly, have counted different things desirable.
Interestingly, however, there is no reason to think that Descartes is committed
to an analogous relativism. For, as I argue in Essay 3, there is not the same
compulsion for Descartes to say that our concepts could have been relevantly
different. Be that as it may, the label ‘anthropocentric’ looks entirely appropriate
in both cases. (Not that Blackburn need demur. The relativism that he eschews, as
the Cartesian case shows, is a separate matter.)
In Essay 14 I turn to Derek Parfit’s very different meta-ethical views and
reproach him for precisely failing to advert to, in fact for failing to respect, some
of what we are implicitly saying about ourselves when we make ethical claims—or,
in his extended discussion of these issues, when we make normative claims more
generally. These claims, I urge, are irreducibly from some point of view: in making
them we are implicitly saying something about our occupancy of that point of
view. (This places me closer to Blackburn than to Parfit.) And, although there is
nothing in Essay 14 to suggest that ‘we’ here means ‘we human beings’—the reach
of the pronoun in any specific case may be either wider or, more probably,
narrower—there is still something fundamental about the human at stake, if
only because making ethical sense of things is itself an essential part of being
human. For that matter, there is something fundamental about the human at stake
in the very idea that making ethical sense of things involves making sense of things
from some point of view, because we—however wide or narrow the reach of that
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15
pronoun—cannot make sense of things from any point of view that human beings
are incapable of occupying. This is reminiscent of the way in which Essay 12
allowed for a conception of ethics as anthropocentric. What mattered in that case
were the constraints imposed on our ethical sense-making by the fact that our
ethical sense-making needs to involve concepts that human beings are capable of
possessing.
The final essay in Part III, Essay 15, is concerned with one very radical version
of the idea that making ethical sense of things involves making sense of them from
some point of view, a version that can be found in Nietzsche. This is the idea that
making ethical sense of things involves making sense of them from ever different
points of view. Not that this is the main focus of Essay 15. The main focus of Essay
15 is something quite different: Bernard Williams’s argument for the meaninglessness of immortality. Nietzsche’s relevance to this lies in an argument that I give
to the effect that he (Nietzsche) can be seen as an unexpected ally of Williams, in
as much as even to acknowledge our immortality, let alone to rejoice in it, would,
on a Nietzschean conception, and contrary perhaps to appearances, thwart this
continual making of new ethical sense of things from new points of view.
This indicates one of many ways in which the human a priori needs to reckon
with our very finitude (a reckoning that assumes even greater significance if we
accept what I called in Essay 10 ‘the Basic Idea’: that human beings are finite, but
have an aspiration to be infinite). This in turn is a good cue for the next section,
where attention shifts from ethical sense-making to mathematical sense-making.
For if the latter is an example of the human a priori, then it too must indicate how
the human a priori needs to reckon with our finitude. This is because one of the
most elemental tasks that we confront, when we engage in mathematical sensemaking, is to make sense, in particular, of the infinite; and this requires that we
leverage our finite resources to achieve a grasp of that which precisely cannot be
grasped by any straightforward use of any finite resources. Each essay in Part IV is
concerned, to a greater or lesser extent, with what it takes for us to do this.
4. Part IV: How We Make Sense in Mathematics
I said above that, of the three disciplines—philosophy, ethics, and mathematics—
ethics is the one that is liable to provoke least resistance to the thought that it is
fundamentally anthropocentric and most to the thought that it is fundamentally a
priori. Mathematics is its polar opposite in this respect. Certainly there is liable to
be great resistance to the thought that mathematics is fundamentally anthropocentric. The essays in Part IV go some way towards motivating the view that even
so, in some sense, it is.
This is not the crude relativist view that, when we humans claim that, say, twice
two is four, what we mean is that twice two is four for us although it may have
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   
some other value for other beings. It is rather the view that, when we humans
claim that twice two is four, even if what we claim holds both universally and
necessarily, there are nevertheless some facts of human nature that not only enable
us to make such sense of things but that enable such sense to be made of things at
all. One exponent of this view is Kant. Kant would certainly deny that twice two
may have some value other than four for other beings. But he does hold that, when
we humans claim that twice two is four, we are making use of concepts that have
been formed ‘through successive addition of units in time’;²⁰ and he also holds, as
we noted earlier, that time is a feature of our human point of view. So any being
that did not share this point of view and that knew nothing of it would not be able
to make such sense of things. What this means is that the question of what twice
two is would not so much as arise for such a being. It does not mean that the
question would arise and somehow receive an alien answer. Nor does it mean that
the sense-making involved in answering the question is anything less than a priori:
it really just casts mathematical sense-making as an instance of the Basic Model.
Call the view that mathematics is anthropocentric in this way the Anthropocentric
View. I tried to indicate earlier why I think that Kant himself, by assigning time
the role that he does in his own version of the Anthropocentric View, lapses into
incoherence. But ‘his own version of the Anthropocentric View’ is the key phrase.
The structure of the Anthropocentric View, and in particular the casting of
mathematical sense-making as an instance of the Basic Model, is not in itself
problematical. Kant’s critical error is to include in the experience-independent
cognitive resources that he invokes to explain our mathematical sense-making
aspects of what we think about, not just aspects of how we think. Had he done
only the latter, he would have avoided any such incoherence. To the extent,
therefore, that we can construe the experience-independent resources that equip
us to engage in mathematics as a matter of how we think, not a matter of what we
think about, we too shall avoid any such incoherence. This gives us scope to adopt
an acceptable alternative to Kant’s version of the Anthropocentric View. On what
I take to be the most attractive version, mathematics consists in developing,
refining, consolidating, and implementing the very experience-independent cognitive resources that equip us to engage in it. Mathematics is a formation of
mathematical concepts. But the concepts, once formed, exhibit a rigid interrelatedness that is made not a whit less rigid by whatever peculiarly human sensibilities
and faculties were integral to their formation. Not only is twice two four: twice two
must be four, always, everywhere, and for everyone.²¹
This view is essentially Wittgensteinian. Wittgenstein regards mathematics as a
formation of mathematical concepts.²² He also has an acute sense of how the
²⁰ Kant (2002a), 4: 283.
²¹ This once again calls to mind the discussion of Descartes in Essay 3.
²² E.g. Wittgenstein (1978), pt IV, §§29–33.
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17
human is at work in sustaining our use of mathematical language.²³ Wittgenstein
accordingly features prominently in Part IV. The first three essays in this part
consist of more or less direct exegesis of his work—albeit, in the case of Essay 16,
through the lens of Crispin Wright’s discussion and appropriation of it.
Essay 16 includes a brief discussion of (Wright’s tentative defence of )
Wittgenstein’s argument against the possibility of a private language; but its
primary focus is Wittgenstein’s later philosophy of mathematics, which is also
the subject matter of Essay 18. In between, Essay 17 provides an overview of
Wittgenstein’s treatment of the infinite. In all three essays I try, however subliminally, to motivate Wittgenstein’s version of the Anthropocentric View. One of the
issues that I address in Essay 16 is that of how to avoid allowing self-conscious
awareness of the anthropocentrism at stake to instil in us needless sceptical
worries about whether our mathematical sense-making is as robust as it should
be. In Essay 17 I address the more specific issue, adumbrated in my remarks at the
end of the previous section, of how to avoid allowing that same self-consciousness
to instil in us needless sceptical worries about whether our mathematical treatment of the infinite is as robust as it should be. I suggest that Wittgenstein himself
does not always succeed in this respect. For he is led by these reflections into what
I see as unacceptable fussing about standard mathematical accounts of the infinite.
In fact he is led into outright disdain of them. This theme is pursued in Essay 18,
where I place Wittgenstein’s scepticism about these accounts in a broader context.
In particular, one thing that I do in Essay 18 is to highlight a tension that there
appears to be between Wittgenstein’s philosophy of mathematics and his philosophy of philosophy. Wittgenstein’s philosophy of philosophy, familiarly, casts
philosophy as a therapeutic exercise aimed at combating various confusions to
which our mishandling of our own ways of making sense of things exposes
us. There is no need, on this conception, for philosophers to reform how we
make sense of things: indeed they had better not do so, for they simply run the
risk of generating more such confusion if they do. It is in this connection that
Wittgenstein says that philosophy ‘leaves everything as it is’²⁴—to which he
immediately adds, in amplification, ‘It also leaves mathematics as it is.’ The
apparent tension lies in the fact that his philosophy of mathematics seems not
to respect this precept. Not only in his reflections on the infinite but elsewhere in
his philosophy of mathematics, we find Wittgenstein taking continual philosophical exception to actual mathematical practice, and thereby to actual mathematical
sense-making. (Another example will occur in Essay 20, on Gödel’s theorem.)
To be sure, there is an obvious get-out clause for Wittgenstein: when he insists
that philosophers had better not interfere with our ways of making sense of things,
there is a tacit restriction to our legitimate ways of making sense of things. It is
²³ E.g. Wittgenstein (1967a), pt I, §§240–2, and pt II, pp. 226–7; and Wittgenstein (1978), pt I, §142.
²⁴ Wittgenstein (1967a), pt I, §124.
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18
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entirely possible that the ways that mathematicians have of making sense of
things are not always legitimate, but are sometimes corrupted, say by mathematicians’ view of the nature of their own discipline.²⁵ Whenever this is the case,
mathematical sense-making is precisely ripe for philosophical interference on a
Wittgensteinian conception.
But, for reasons that I try to make clear in Essay 18, I do not myself believe that
this get-out clause ultimately prevents the apparent tension between
Wittgenstein’s philosophy of philosophy and his philosophy of mathematics
from being real. And I end the essay by saying (albeit without elaborating) that
I take the principal fault to lie with his philosophy of philosophy. Given what
I have said so far in this Introduction, this may come as a surprise. Have I not been
suggesting the very opposite: that the principal fault lies rather with his philosophy
of mathematics?
Not exactly. The point is this. Even when some mathematical way of making
sense of things is legitimate, there may be an alternative that has certain practical
advantages. Suppose there is. The fact remains that the sheer legitimacy of the
original way of making sense of things means that Wittgenstein’s philosophy of
philosophy requires philosophers simply to accede to it. And that seems to me
unduly conservative. True, there is a risk that adopting the alternative will
generate new philosophical confusion. But there is a risk that retaining the original
will do that too. Indeed precisely one of the practical advantages of the alternative
may be that it is less susceptible than the original to being mishandled in a way that
throws us into confusion. And if that is the case, then not only is it entirely
reasonable to advocate for the alternative, it is entirely reasonable to do so on
philosophical grounds.²⁶ And this returns us to the main theme of this volume. For
deciding which of the two ways of making sense of things is less susceptible to
being mishandled in that way will require sensitivity to the various human
sensibilities and faculties that are involved in our implementing each of them.
The final two essays in Part IV are concerned with specific applications of the
Wittgensteinian version of the Anthropocentric View. But the starting point of
Essay 19 is provided by a non-Wittgensteinian version of the view, closer in many
ways to what we find in Kant: namely, the view endorsed by intuitionists whereby
the facts of human nature that enable mathematical issues to arise in the way in
which they do are facts about our experience of the pure structure of time. Quite
how closely or distantly this is related to Kant’s view is an issue that I touch on
very briefly in §4 of the essay: perhaps distantly enough for intuitionists to avoid
some of problems that afflict Kant himself. For, rather than casting time as the
subject matter of our mathematical sense-making, they can arguably be seen as
doing something more innocuous: casting temporally informed concepts as
²⁵ Cf. Wittgenstein (1967a), pt I, §254.
²⁶ For further discussion see A. W. Moore (forthcoming), esp. §5.
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19
among the primary tools of our mathematical sense-making. Nevertheless, intuitionists do confront a problem, which it is the main burden of Essay 19 to address.
The problem is that their view completely loses its force if we allow ourselves to
apply the concept of the infinite in a certain way. To solve this problem, and thus
to prevent ourselves from applying the concept of the infinite in that way, what we
need to do, I argue, is to pit such applications of the concept against the
Wittgensteinian version of the Anthropocentric View and, more specifically, to
pit them against some of the lessons of Essay 17.
Finally, in Essay 20, I apply the Wittgensteinian version of the Anthropocentric
View to consideration of the philosophical significance of Gödel’s theorem, in the
context of a discussion of Michael Dummett’s essay on the same topic.²⁷ Not that
Essay 20 is unreservedly Wittgensteinian. In the final section of the essay I discuss
some of Wittgenstein’s own remarks on Gödel’s theorem, in the course of which
he recoils from one standard way of stating the theorem. This way of stating the
theorem is as follows: given any sound axiomatization of arithmetic, there are
arithmetical truths that the axiomatization cannot be used to prove. Wittgenstein
advocates a relativization of mathematical truth to some axiomatization which
makes this way of stating the theorem inappropriate.²⁸ While I am more sympathetic to what Wittgenstein is doing here than most commentators, I nevertheless
urge that this is another example of unacceptable meddling with actual mathematical sense-making. The bulk of Essay 20, however, is devoted to arguing that we
can make best philosophical sense of Gödel’s theorem in broadly Wittgensteinian
terms. In particular, it is in broadly Wittgensteinian terms that we can make best
philosophical sense of what is involved in our advancing from acceptance of some
axiomatization A of arithmetic to acceptance of the consistency of A, and thereby
to acceptance of certain arithmetical truths that A cannot be used to prove.
The forces that are at work here are the forces that are at work in the very
formation of all the relevant mathematical concepts, such as the concept of a
natural number, the concept of addition, and the concept of consistency. And they
depend, as I try to indicate in Essay 20, on shared human reactions. Gödel’s
theorem can thus be seen as a further illustration of the Anthropocentric View—
as it can, therewith, of the human a priori.
²⁷ Dummett (1978c).
²⁸ Wittgenstein (1978), pt I, app. III, esp. §8.
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PART I
T H E NA T U R E , S C O P E , A N D L I M I T S
OF A PRIORI SENSE-MAKING
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1
Armchair Knowledge
Some Kantian Reflections
Abstract
This essay considers a puzzle associated with ‘armchair knowledge’, that is to say,
knowledge that is not warranted by experience. The puzzle is that each of the
following claims seems true although they also seem mutually incompatible: there
is armchair knowledge; some armchair knowledge, if such there be, concerns what
is beyond the subject; and armchair knowledge does not involve any appeal to any
particular encounter with anything beyond the subject. The Kantian solution to
this puzzle, namely transcendental idealism, is a view whereby some of what the
subject has knowledge of has a form that depends on the subject. After discussion
of the scope and limits of this solution, it is argued both that it is the only available
solution when the armchair knowledge in question is synthetic and that it is
incoherent, from which it is concluded that there is no such thing as synthetic
armchair knowledge. But this is all on the assumption that the armchair knowledge in question is knowledge of what is necessary. In the final section of the essay
consideration is given to other solutions to the puzzle that may be available if the
knowledge in question is knowledge of what is contingent.
1. A Kantian View of Armchair Knowledge
One of the oldest of philosophical puzzles is to account for what I shall call
‘armchair knowledge’. By ‘armchair knowledge’ I mean knowledge that is independent of experience, in the sense that it is not warranted by experience. The
rationale for the label is clear enough: a subject¹ who has such knowledge could
have had it while remaining seated in an armchair.² I might just as well have used
¹ There will be frequent references in this essay to the ‘subject’. For remarks that are very pertinent
to my use of this term see Kant (2000), 5: 401.
² That is, the subject could have had it while remaining seated in an armchair granted possession of the
concepts involved: it is not precluded that the subject had to leave the armchair to acquire those concepts
in the first place (cf. Kant (1998), B3). And it is important that the armchair should be nothing more than
an inessential prop: one thing that a subject could know while remaining seated in an armchair is how
comfortable the armchair is, but this, I hardly need say, is not an example of what I have in mind. (In the
first and the most famous discussion of armchair knowledge in Western philosophy—a discussion that
predates armchairs—the only significant prop involved is some sand: see Plato (1961d), 82b–85b.)
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24
the more familiar label ‘a priori knowledge’. But ‘a priori knowledge’ is sometimes
applied more broadly—not just to knowledge that is independent of experience,
but to knowledge that could have been independent of experience.³ I hope that my
use of the less familiar label, along with my stipulative definition of it, helps to
avoid confusion on that score.⁴ I also hope that it helps to highlight a crucial
feature of such knowledge, or at least what appears to be a crucial feature of such
knowledge: it does not involve any appeal to any particular encounter with
anything beyond the subject.
The puzzle to which I have referred arises from the fact that not only does there
appear to be such knowledge, but some of it appears to concern what is beyond the
subject. For how can it?—given that what is beyond the subject is irrelevant to it in
that way. The puzzle is exacerbated by the fact that some of the knowledge in
question appears to concern, not just some of what is beyond the subject, but all of
what is beyond the subject; indeed, not just all of what is beyond the subject, but all
of what could possibly be beyond the subject.⁵
To repeat, the puzzle arises because each of the following appears to be the case:
(i)
there is armchair knowledge;
(ii)
some armchair knowledge, if such there be, concerns what is beyond the
subject;
and
(iii)
armchair knowledge does not involve any appeal to any particular
encounter with anything beyond the subject.
Some philosophers think that the puzzle can be solved by denying the appearances. Thus certain empiricists simply deny (i). Other empiricists accept (i), but
deny (ii): they hold that all armchair knowledge concerns the subject’s command
of language, or the subject’s conceptual repertoire, or something of the sort.
Certain Platonists accept (i) and (ii), but deny (iii): they hold that armchair
³ Thus my own knowledge that every natural number is the sum of four squares is based on an
appeal to authority. So it is not included in what I am calling ‘armchair knowledge’. But it is included in
what, on this broad usage, would be called ‘a priori knowledge’, since it is knowledge of a mathematical
truth that could in principle have been independent of experience. A further complication is that the
term ‘a priori’ is also sometimes applied, not to knowledge, but to truths: those that, in my terms, are
potential items of armchair knowledge, in other words those that are knowable independently of
experience (cf. Kant (1996b), 5: 31, and Frege (1980), §3). A yet further complication, which will prove
to be pertinent in §6, is that the term ‘a priori’ is also sometimes applied to non-propositional entities,
such as concepts.
⁴ For a second possible advantage of my use of the less familiar label—pertaining this time to the fact
that ‘a priori knowledge’ is sometimes applied, not more broadly, but more narrowly—see n. 57 below,
together with the accompanying text.
⁵ Cf. Kant (1998), B3–4.
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25
knowledge is acquired through, and involves appeal to, acquaintance with one or
more Platonic idea or universal.⁶
But there are also philosophers who think that the puzzle can be solved without
denying the appearances. They accept (i), (ii), and (iii). The way in which they
solve the puzzle is by espousing some version of idealism, whereby some of what
the subject has knowledge of, including, in this version, some of what is beyond
the subject, has a form—a range of essential features—that depends on the subject.
The armchair knowledge in question pertains to this form. Thus some of it is
knowledge to the effect that whatever has the form is of such and such a kind;
some of it is knowledge to the effect that whatever is of such and such a kind has
the form. This means that it does indeed concern what is beyond the subject; for
the form is the form of what is beyond the subject. But it also means that the
knowledge does not involve any appeal to any particular encounter with anything
beyond the subject, precisely because the form to which the knowledge pertains
depends on the subject.
This is Kant’s view.⁷ Its attractions are not confined to the fact that it can
be used to account for armchair knowledge of what is beyond the subject. It
can also be used, if Kant is right, to account for (some) knowledge of what is
necessary—Kant’s own view being that all armchair knowledge, simply qua
armchair knowledge, is knowledge of what is necessary.⁸ Indeed it can be used
to account for (some) knowledge of what is necessary as necessary. Thus if some
of the armchair knowledge in question is knowledge to the effect that whatever has
the given form is of such and such a kind, then some of it is also, in Kant’s view,
knowledge to the effect that whatever has the given form must be of such and such
a kind. How to account for knowledge of what is necessary, as necessary, is
another old philosophical puzzle. The puzzle this time arises from the sheer
fact that we, finite contingent creatures that we are, can have epistemic access to
all the ways things might have been. Many philosophers think that they can
solve this puzzle, or at least that they can begin to solve it, by finding a
grounding for necessity in contingency, where finding a grounding for necessity
in contingency is more than simply discovering, with respect to some apparent
necessity, that there is a contingency underpinning it—so that it no longer
appears necessary. Doing that is not especially remarkable, nor does it have any
great philosophical purchase. In fact it is an important part of growing up.
⁶ For the label ‘Platonist’ cf. Plato (1961a), 73–6. Whatever the exact nature of the relationship
between this view and Plato, the fact that there is such a relationship helps to explain why W. D. Hart is
emboldened to say, in Hart (1988), p. 158, that ‘we are all of us empiricists in our bones (even, or
especially, Plato)’. Whether or not the view can be attributed to Plato, it can certainly be attributed to
Russell: see Russell (1959), ch. 10.
⁷ Kant (1998), Bxvi.
⁸ See again the material in Kant (1998), B3–4, cited in n. 5; see also Axv and Bxii. I shall not, for the
time being, query Kant’s view that all armchair knowledge is knowledge of what is necessary, although
in section 7 I shall explore some of the implications of rejecting this view.
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Finding a grounding for necessity in contingency is doing something more
delicate than that: it is discovering, with respect to some apparent necessity,
that there is a contingency underpinning it without disrupting the appearance of
necessity. This, if it can be done at all, does have philosophical purchase. And it
is what Kant tries to do.⁹
Kant espouses a version of idealism whereby that part of the subject’s
armchair knowledge which pertains to the given form is knowledge from a
particular point of view.¹⁰ And a point of view, by its very nature, admits of
alternatives. So the fact that there is knowledge from this point of view is the
relevant contingency, the contingency in which the relevant necessity is
grounded. But Kant does not think that the necessity is thereby compromised.
For he does not think that there is anything in his idealism to preclude the
subject’s continuing to have, and continuing to exercise, knowledge from the
given point of view: it is just that such knowledge cannot itself include acknowledgement of the idealism.
This explains why Kant’s idealism is, in his own terminology, ‘transcendental’
idealism rather than ‘empirical’ idealism. Kant uses these two terms to register a
distinction between two views about the nature of space and time.¹¹ For our
purposes, however, it will help to extend his usage and to work with a broader
distinction. Let us refer to the dependence posited by the idealist—the dependence of the form of what the subject has knowledge of on the subject—as the
i-dependence. Then we can construe transcendental idealism as idealism in
which the i-dependence is not itself included in whatever has this form; and
we can construe empirical idealism as idealism in which it is.¹² The reason
why Kant’s idealism is transcendental is that it assigns contingency to the
i-dependence (for it allows that there might not have been any such subject,
nor therefore any such form depending on any such subject), and this contingency, simply qua contingency, must transcend the necessity attendant on
whatever has the form in question.¹³
⁹ On a popular reading of Descartes, it is what he tries to do too—by taking the necessity of any
given necessary truth, say that twice four is eight, to lie in the contingent fact that human beings are
incapable of grasping any other possibilities. If this is Descartes’s strategy, however, then all that he
succeeds in doing is providing a very graphic illustration of why finding a grounding for necessity in
contingency is such a delicate matter. For if it really is necessary that twice four is eight, then there are no
other possibilities, hence no other possibilities for human beings to be incapable of grasping. I should
add, however, that I am not persuaded that the popular reading of Descartes is correct, certainly not as a
reading of his fully considered view: see Essay 3 in this volume, which is in turn indebted to Bennett
(1994).
¹⁰ See Kant (2000), 5: 403. Cf. also Kant (1996a), 4: 452.
¹¹ See Kant (1998), A369.
¹² I have elsewhere construed the two doctrines slightly differently: see A. W. Moore (1997), p. 116,
and (2012), ch. 5, appendix. But the differences, which are tailored to the demands of their specific
contexts, are relatively insignificant.
¹³ We can extract, from these considerations, a general test for whether any given idealism is
transcendental or empirical. Let TI be some version of transcendental idealism; let EI be some version
of empirical idealism; let FTI be the form involved in the i-dependence that is posited in TI; and let FEI
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2. The Distinction between Analytic Armchair
Knowledge and Synthetic Armchair Knowledge,
and Two Associated Questions
Now Kant famously distinguishes between two kinds of armchair knowledge: that
which is analytic and that which is synthetic. This distinction is related to another
that he draws, between intuitions and concepts. Intuitions are products of
the subject’s receptivity: there is something passive about them. Concepts are
products of the subject’s spontaneity: there is something active about them. It is by
means of intuitions that the subject is given various objects of knowledge. It is
by means of concepts that the subject thinks about these objects, as thus given.¹⁴
Any knowledge, at least if it has what Kant calls ‘content’,¹⁵ must make use of
both. It must involve an exercise of concepts, whereby something is thought. But
these concepts must in turn relate ultimately to intuitions, whereby what is
thought has whatever content it has.¹⁶ What distinguishes analytic knowledge is
that, in this case, the exercise of concepts does all the relevant work: the subject
knows, simply by appeal to the concepts involved, and in particular by analysis of
them, that what is being thought is true. By contrast, in the case of synthetic
knowledge, the subject also appeals to the intuitions involved.¹⁷
Does it follow that no analytic armchair knowledge testifies to (ii), in other
words that no armchair knowledge that is analytic concerns what is beyond the
subject? It looks as though it does follow, because it looks as though what analytic
armchair knowledge concerns, on this view—and here we are reminded of the
empiricist view that I flagged in §1—is the subject’s conceptual repertoire. In fact,
however, I do not think that we are forced to say this. There is a perfectly good
be the form involved in the i-dependence that is posited in EI. Then, whereas an exposition and/or
defence of TI is bound to reckon with the distinction between what transcends FTI and what has FTI, an
exposition and/or defence of EI need not reckon with any such distinction concerning FEI. Moreover,
there are family resemblances between claims about what transcends FTI and claims about what has FTI
whereby it is natural to use the same language to express them—albeit not with exactly the same
meaning—not least because we are liable to lack independent linguistic resources to talk about what
transcends FTI. This means that, in practice, an exposition and/or defence of TI is liable, sooner or later,
to include a claim that is to be deemed true when construed as a claim about what transcends FTI but as
false when construed as a claim about what has FTI. (Paradigm cases include various claims that Kant
considers whose truth is sensitive to the ambiguity in the expression ‘outside us’ that he notes in Kant
(1998), A373.) The same is not true of an exposition and/or defence of EI. Here it might be objected
that Berkeleian idealism, which is empirical if any idealism is, counts as transcendental by this
(admittedly inconclusive) test because it does involve such equivocation, in particular where phrases
such as ‘perceiver-independent’ are concerned: see e.g. Berkeley (1962), pp. 200–1. To pursue this
matter is far beyond the scope of this essay, although it is worth noting that any problem about the
application of this test to Berkeleian idealism may be a problem with Berkeleian idealism rather than a
problem with the test.
¹⁴ Kant (1998), A19/B33.
¹⁵ Kant (1998), A51/B75. The significance of this qualification will be clear in due course.
¹⁶ Kant (1998), A50–1/B74–5.
¹⁷ Kant (1998), A47/B64–5, B73, and Kant (2002a), §2. (But see below, n. 49, for some complications
in this connection.)
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sense of ‘concern’ in which the subject’s analytic armchair knowledge that all
vixens are female, say, concerns vixens, not the subject’s concept of a vixen, nor
any other part of the subject’s conceptual repertoire. There is a perfectly good
sense of ‘concern’, in other words, in which it concerns what is beyond the subject.
Indeed, my own view is that Kant allows for analytic armchair knowledge that
lacks content, that is to say, analytic armchair knowledge in which the concepts
involved do not relate to intuitions,¹⁸ and that even knowledge of this kind can, in
the relevant sense of ‘concern’, concern what is beyond the subject. An example
might be the subject’s knowledge that things in themselves are things irrespective
of how they are given to us, knowledge which concerns things in themselves.¹⁹
But whether or not we adopt this attenuated sense of ‘concern’ and say that
some analytic armchair knowledge concerns what is beyond the subject, two
associated questions arise. We can begin to appreciate the force of these questions
by noting that, to whatever extent it is appropriate to say that some analytic
armchair knowledge concerns what is beyond the subject, to that extent it is
likewise appropriate to regard such knowledge as part of the original puzzle—
the puzzle that Kant tries to solve by invoking transcendental idealism, or rather,
the puzzle part of which Kant tries to solve by invoking transcendental idealism.
For, although Kant holds that transcendental idealism is needed to solve the
puzzle with respect to synthetic armchair knowledge,²⁰ he also holds that it is
needed to solve the puzzle only with respect to synthetic armchair knowledge.²¹
And, whatever his reasons for holding this, they were not apparent in anything
I said in the previous section. The two questions are these.
(1) Would Kant allow that transcendental idealism can be invoked to solve the
puzzle with respect to analytic armchair knowledge too, even if it does not
have to be?
(2) What is it about synthetic armchair knowledge that makes Kant think that
transcendental idealism must be invoked to solve the puzzle with respect to it?
3. Invoking Transcendental Idealism to Account for Analytic
Armchair Knowledge
Let us begin with question (1). Kant certainly thinks that the puzzle with respect to
analytic armchair knowledge can be solved without recourse to transcendental
¹⁸ This is what I had in mind in n. 15. For arguments against the view that Kant would acknowledge
any such knowledge see Kreis 2023, esp. §6. I remain unpersuaded.
¹⁹ See e.g. Kant (1998), A258–60/B314–15. Note that the distinction between knowledge and cognition
that many Kantian exegetes draw is very pertinent to what I am suggesting here and may help to make
what I am suggesting appear less exegetically contentious: see A. W. Moore (2012), ch. 5 n. 13.
²⁰ See Kant (1998), B41 and A92/B124–5.
²¹ See e.g. Kant (2002a), §5.
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29
idealism. It is enough, Kant thinks, to note that the subject can have such
knowledge just by analysing the concepts involved.²² In effect, then, Kant is saying
that, even if analytic armchair knowledge does concern what is beyond the subject,
the sense in which it does so is sufficiently attenuated—it really just comes down
to the fact that the concepts involved apply to what is beyond the subject²³—that
there is no need, in accounting for such knowledge, to relate the form of what
the subject has knowledge of to the subject in any way, still less to acknowledge the
i-dependence, still less to acknowledge the i-dependence in such a way that some
of the subject’s knowledge is to be seen as knowledge from a particular point of
view that admits of alternatives.
There is no need to do this. But the question is whether Kant would have any
quarrel with a philosopher who, perhaps in an attempt to give a unified account of
all armchair knowledge, does do this. Thus imagine a philosopher who urges that
the form of what is beyond the subject, which depends on the subject and to which
the subject’s armchair knowledge pertains, is not confined to those of its essential
features that Kant famously fastens on—its spatio-temporality, its subjection to
causal laws, et cetera—but extends to all those of its essential features that are in
any way conceptual, such as the feature of being, if a vixen, female; and that the
contingency of the i-dependence is no less a mark of the subject’s general
conceptualization of things than it is of the subject’s spatio-temporal intuition
of them. Such a philosopher does not have to disagree with Kant’s claim that, in
order to have analytic armchair knowledge, the subject need only analyse the
concepts involved: this extension of Kant’s transcendental idealism might be
intended as an explication of that claim, not as a challenge to it. So to repeat:
would Kant have any quarrel with such a philosopher?
In fact he would. For Kant holds that the subject can have thoughts concerning
things in themselves. I earlier suggested that some analytic armchair knowledge
could serve as an example; but, even if that suggestion is open to dispute, there are
uncontentious examples, such as the thought that we are free.²⁴ And a philosopher
who holds that the subject’s conceptualization of things contributes as much to the
contingency of the i-dependence as the subject’s spatio-temporal intuition of
things must, in Kant’s view, hold that the subject’s thinking, no less than the
subject’s intuiting, is always of appearances rather than of things in themselves.
But to say that Kant would have a quarrel with such a philosopher is not to say
that he would be justified in having it. The question remains what error, in Kant’s
own terms, such a philosopher would be committing; and why Kant is not forced
²² Kant (1998), A7/B11.
²³ And it comes down to this, of course, only when the concepts involved do apply to what is beyond
the subject. The subject’s knowledge that mermaids have fishes’ tails is arguably another example of
analytic armchair knowledge and can arguably be said, in the same attenuated sense of ‘concern’, to
concern mermaids. Cf. Kant (1998), A290–2/B346–9.
²⁴ Kant (1998), Bxxvi–xxx.
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to conclude, again in his own terms, albeit against his own conviction, that the
subject’s thinking is always of appearances rather than of things in themselves. We
can put it this way: when Kant argues from the existence of armchair knowledge
concerning what is beyond the subject to the truth of transcendental idealism, at
what point in his argument does he make crucial appeal to the fact that the
armchair knowledge is synthetic and what, in his own terms, would preclude
someone’s extending the argument to armchair knowledge that is analytic?
This question is surprisingly unstraightforward. To be sure, there are, in Kant’s
presentation of his argument, frequent appeals to the fact that the armchair
knowledge is synthetic.²⁵ But if the argument were reworked to eliminate these
appeals, it is not obvious what would prevent it from continuing to meet with
success; or rather, it is not obvious what would prevent it from continuing to meet
with whatever success it meets with in the first place.²⁶
Here are two responses that Kant might give at this point. First, he might say
that his own argument for transcendental idealism is an inference to the best
explanation (in fact, an inference to the only possible explanation) and that what
would prevent it from meeting with the same success if extended to analytic
armchair knowledge is the fact that, although it would still count as an inference
to an explanation—of how we can have such knowledge—it would no longer
count as an inference to the best explanation, because the simpler explanation
involving nothing but the subject’s analysis of the concepts involved would still be
available. Second, he might say that, not only does he want to allow for thoughts
about things in themselves, which the extended version of the argument would
rule out, but he is obliged to allow for thoughts about things in themselves,
‘otherwise there would follow the absurd proposition that there is an appearance
without anything that appears’.²⁷
Neither of these responses is entirely satisfactory however. The first may beg
crucial questions about the relative virtues of rival explanations. Why do the unity
and the power of an explanation that applies to all armchair knowledge not count
for more than the simplicity of an explanation that applies only to analytic
armchair knowledge? To be sure, there would be an obvious answer to this
question if the first response were buttressed by the second. But the second may
beg crucial questions of its own about the coherence of Kant’s transcendental
idealism: if the extended version of his argument leads to a contradiction, it may
be a contradiction to which Kant is destined, eventually, to be led anyway.
These are enormous issues. I shall say no more about them at this juncture
(though I shall return to the issue of the coherence of transcendental idealism in
section 5). Instead I want to take a slight detour that will bring us back to
question (2).
²⁵ See e.g. Kant (1998), ‘Transcendental Aesthetic’, §8.
²⁶ See e.g. the summary of the argument in Kant (1998), Bxvi–xviii.
²⁷ Kant (1998), Bxxvi.
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4. Invoking Transcendental Idealism to Account for Synthetic
Armchair Knowledge
We have seen that one of the attractions of Kant’s transcendental idealism is that
it accounts for (some) knowledge of what is necessary, as necessary, by locating
a grounding for the necessity in contingency. But there are views other than
transcendental idealism, indeed views that are not versions of idealism at all,
that have title to the same claim. Consider, for instance, the view according to
which the subject’s knowledge that vixens are female consists in command of a
particular rule of representation, namely the rule that prohibits counting a
creature as a vixen without also counting that creature as female. As before,
there is an issue about whether such knowledge can be said to concern what is
beyond the subject, in however attenuated a sense, or whether it is better described
as concerning the subject’s conceptual repertoire or something of that sort. Be that
as it may, there is certainly a sense in which it is knowledge of a contingency. For
there might never have been any such rule (at least not if rules are conceived as
social institutions, which is how I am conceiving them in this essay). The point,
however, is that the necessity concerned is not thereby compromised. If there had
never been any such rule, vixens would not have failed to be female. Rather, what
sex vixens are would not have been an issue for anyone: no one would have
thought in those terms. Vixens would not have failed to be female, because vixens
must be female. And this ‘must’ is as hard as it either can or need be.²⁸
Now any view of this kind—any Wittgensteinian view, as I shall say²⁹—would
be a variant of Kant’s view of analytic armchair knowledge. There would be
differences, to be sure. Indeed there would be differences large enough for it to
count as a rival view.³⁰ But there would also be a clear family resemblance which
there assuredly would not be where Kant’s view of synthetic armchair knowledge
is concerned. And, in exploring why not, we shall be helped on our way towards
addressing question (2).³¹
On a Wittgensteinian view, there is a clear sense in which, given any item of
knowledge to which the view applies, such as the knowledge that vixens are
female, sheer familiarity with the concepts involved ensures that one can see the
truth of what is known. (This is not because one can derive the truth of what is
known from familiarity with the concepts involved. The order of derivation, in so
far as there is one, is rather the reverse: one does not count as familiar with the
²⁸ Cf. Wittgenstein (1978), pt VI, §49, and McDowell (1993), pp. 282 ff.
²⁹ But I shall make no attempt to justify the exegesis here. For discussion see A. W. Moore (2019b), §1.
³⁰ For discussion of why it would count as a rival view, possibly even to the extent of having no truck
with the notion of analyticity, and for some relevant references to Wittgenstein, see again A. W. Moore
(2019b), §1.
³¹ Some of what follows, both in this section and the next, is based on A. W. Moore (2016), which is
in turn a response to Baiasu (2016). I am grateful to Sorin Baiasu for the stimulus provided by his
excellent essay.
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   
concepts involved unless one has command of the relevant rule.) But on Kant’s
view of synthetic armchair knowledge, there is no clear sense in which, given any
item of knowledge to which the view applies, sheer familiarity with the concepts
involved ensures that one can see the truth of what is known; precisely not. Kant
insists that one cannot see the truth of what is known, in such a case, without
appeal to the intuitions involved.
What Kant would accept, even in such a case, is that sheer familiarity with the
concepts involved ensures that one can see how things must be for what is known
to be true. In other words, it ensures that one can see, not the truth of what is
known, but the truth conditions of what is known. This is in contrast to sheer
familiarity with the logical form of what is known, which leaves the truth
conditions of what is known undetermined.³² This in turn explains why, if one
wanted to show that what is known is not an analytic truth, one could not avail
oneself of any analogue of a procedure that would be available to show that what is
known is not a logical truth. If one wanted to show that what is known is not a
logical truth, one could specify a false proposition with the same logical form. If
one wanted to show that what is known is not an analytic truth, by contrast, one
would have to reckon with alternatives to that very truth. And this of course
means that, as far as the concepts involved are concerned, there had better be
alternatives to that very truth. Suppose, for instance, that the truth in question is
that the sum of the angles in a triangle is equal to two right angles. Then there had
better be alternatives in which the sum of the angles in a triangle is something
other than two right angles. If no such alternative existed—if no such alternative
existed, mind, not just if no such alternative were realized—then no such alternative would remain to be ruled out by anyone familiar with the concepts involved.
And then there would be a sense, a clear sense, in which sheer familiarity with the
concepts involved would ensure that one could see the truth of what is known.
But now we are in sight of an answer to question (2), about why Kant thinks
that transcendental idealism is needed to solve the original puzzle with respect to
synthetic armchair knowledge. On Kant’s view, synthetic armchair knowledge,
qua synthetic, is knowledge of a truth that admits of alternatives in the way just
outlined; but, qua armchair, it is knowledge of a truth that in some sense admits
of no alternatives. It is knowledge, somehow, both of a contingency and of a
necessity. Now so too, as we have seen, is the subject’s knowledge that vixens are
female, on the Wittgensteinian view. The difference is that, in the Wittgensteinian
case, there does not even appear to be any conflict between the contingency and
the necessity: the necessity attaches to the known truth itself, that vixens are
³² Here and subsequently in this paragraph, I am prescinding from the fact that, strictly speaking,
there is no such thing as ‘the’ logical form of what is known: if what is known is a conjunction, for
example, then, even so, it has as one of its logical forms simply ‘p’. Properly formulating the main point
that I wish to make in this paragraph, so as to take this fact into account, would involve (tendentious)
considerations about complete logical analysis that need not detain us now.
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female; the contingency attaches to the second-order truth that there is a rule in
force whose statement consists in an enunciation of that first-order truth. The
relevant alternatives are not alternatives to vixens’ being female; they are alternatives to that rule’s being in force, hence to anyone’s having thoughts about vixens.
But on Kant’s view of synthetic armchair knowledge, the relevant alternatives are
alternatives to the known truth itself: in the example considered above, they are
alternatives to triangles’ having angles whose sum is equal to two right angles. So,
in the Kantian case, there does appear to be a conflict between the contingency
and the necessity. And the only way that Kant can see to resolve this apparent
conflict is by introducing some appropriate relativization. He holds that the truth
in question is necessary from a particular point of view, the very point of view
that the subject’s knowledge is from, constituted, in part, by the intuitions to
which the subject appeals in having the knowledge. But when the truth is not
considered from that point of view—when a step back is taken to reflect on why
appeal to these intuitions is necessary to have knowledge of the truth, which is
done precisely by not appealing to them but rather by duly prescinding
from them—then Kant thinks that the truth can be conceived as admitting of
alternatives. And to make this work, in particular to explain how the subject can
have armchair knowledge of what admits of such alternatives, Kant espouses an
idealism whereby the necessity in question itself depends on the subject: this is
the i-dependence. But the idealism has to be transcendental idealism. The
i-dependence has to be conceived as transcending the necessity in question. For
the i-dependence cannot so much as be entertained until that step back is taken
from the original point of view. Both on Kant’s view and on the Wittgensteinian
view, then, there is an attempt of sorts to ground necessity in contingency. But on
Kant’s view, unlike on the Wittgensteinian view, the attempt assumes the form
that it is peculiarly given by transcendental idealism, so as to allay what would
otherwise be a simple conflict between a claim of necessity and a claim of
contingency with respect to one and the same truth.
5. The Incoherence of Transcendental Idealism
Kant is vindicated, then, as far as question (2) is concerned; or at least, he is
vindicated up to a point. But that point comes quickly. In fact it is a point that
I anticipated in the discussion of question (1) when I alluded to the possibility that
Kant is destined, eventually, to lapse into contradiction, given the way in which he
allows us thoughts about things in themselves. I think we are now witnessing such
a lapse. For the step back that we have just been considering is not a shift from
considering things from one point of view to considering them from another; it is
a shift from considering things from one point of view to considering them from
no point of view at all, from thinking about how things appear to thinking about
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how they are in themselves. (It involves thinking of how things appear as how they
appear and, concomitantly, as different from, albeit dependent on, how they really
are, something that we are required to do if we are to avoid ‘the absurd proposition
that there is an appearance without anything that appears’.) This would be all very
well if such thinking were only ever mere thinking. Kant is not involved in any
internal inconsistency simply in allowing us thoughts about things in themselves.
The problem is that, by Kant’s own lights, such thinking sometimes amounts to
knowledge. Consider, for example, his own thought that there is synthetic armchair knowledge, which cannot be accounted for except by appeal to the distinctive i-dependence that is the hallmark of transcendental idealism. This, by his own
lights, is a piece of knowledge—if only because he has arrived at it as a result
of what he takes to be a decisive argument³³—and indeed not just a piece of
knowledge, but a piece of synthetic armchair knowledge. For Kant would surely
deny that it depends on sheer analysis of the concepts involved; but he would also
surely deny that it depends on experience. The upshot is that Kant is, by his own
lights, forced to accede to the very thing that it is his business to deny, synthetic
armchair knowledge of how things are in themselves.³⁴
If this is right, Kant does eventually lapse into contradiction then. Not that this
invalidates the argument that he advances from the existence of synthetic armchair knowledge to the truth of transcendental idealism. When I claimed earlier
that, as far as question (2) is concerned, Kant is vindicated ‘up to a point’, precisely
what I had in mind was the validity of this argument.³⁵ The crux, however, is that
we can acknowledge the validity of this argument without lapsing into the same
contradiction. For we do not have to conclude that transcendental idealism is true.
Where Kant applies a modus ponens, we can apply a modus tollens instead and
conclude that there is no such thing as synthetic armchair knowledge. This may be
because there is no armchair knowledge at all, or because all armchair knowledge
is analytic, or because there is something wrong with the very distinction between
analytic armchair knowledge and synthetic armchair knowledge, or . . . But whatever the explanation, something, somewhere, must give.
6. A Priori Intuitions and Pure Concepts
My own view is that what should give, first and foremost, is the Kantian thesis, to
which I adverted in §4, that there are a priori intuitions, that is to say intuitions
³³ Kant himself uses the phrase ‘indubitably certain’ in this connection: see Kant (1998), A48/B66.
Cf. Kant (1996b), 5:12.
³⁴ See A. W. Moore (2012), ch. 5, §§9–10, and A. W. Moore (2016), for further discussion and
references.
³⁵ There is an important qualification to this claim that I shall pass over for now but to which I shall
return in section 7.
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35
that the subject already possesses in the armchair, intuitions that are partly
constitutive of the subject’s point of view. It is by appeal to such intuitions,
Kant believes, and only by appeal to these, that the subject can have synthetic
armchair knowledge.³⁶ He holds that space and time are two of them—and the
form of all of them.³⁷
Suppose I am right to target this thesis—call it the Intuition Thesis. Suppose (in
other words) that there are no a priori intuitions. There may yet be a priori
concepts, that is to say concepts that the subject already possesses in the armchair.
Of course, Kant himself believes that there are a priori concepts because he
believes that there are concepts such as that of a triangle, or that of motion,
which the subject possesses by virtue of possessing the two specified a priori
intuitions. Importantly, however, Kant also believes that there are a priori
concepts that are not thus dependent on those two intuitions. He labels these
‘pure’ concepts. The thesis that there are pure concepts—call it the Concept
Thesis—could, as I have said, survive the Intuition Thesis.
Kant has a long and elaborate story to tell about how pure concepts and a priori
intuitions combine in structuring the subject’s point of view. This story is part of
his transcendental idealism. But suppose we accept the Concept Thesis without
the Intuition Thesis. Then we need have no truck either with transcendental
idealism or with anything like it. Indeed this holds true even if we accept a variant
of the Concept Thesis—call it the Relativized Concept Thesis—which allows for
the possibility that different subjects, humans and extraterrestrials say, possess
different pure concepts. I say ‘even if ’, because Kant expressly holds the corresponding variant of the Intuition Thesis—call it the Relativized Intuition Thesis—
which allows for the possibility that different subjects possess different a priori
intuitions,³⁸ and we might think that this is what makes his commitment to
transcendental idealism mandatory. In fact, however, as I tried to indicate in §4,
what makes his commitment to transcendental idealism mandatory is not any
contingency that he endorses in the subject’s possessing such and such a priori
intuitions; it is rather the contingency that he endorses in those intuitions’ being
the way they are.
As for any contingency in the subject’s possessing such and such pure concepts,
this will be akin, in some respects, to the contingency in the subject’s abiding by
such and such rules on the Wittgensteinian View. It will not force us to reckon
with any relativization in any associated necessities that the subject acknowledges.
Thus suppose that the subject’s possessing such and such pure concepts both
³⁶ For references—but also for discussion of some complications—see n. 49.
³⁷ See e.g. Kant (1998), A20–2/B34–6 and B73.
³⁸ See e.g. Kant (1998), B72. Note, however, that the only possibility to which Kant ever commits
himself is an epistemic one. He is careful not to commit himself to what he elsewhere calls a ‘real’
possibility (e.g. Kant (1998), A244/B302). Quite what Kant means by a ‘real’ possibility is a large and
difficult question, which does not matter for current purposes.
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involves and is involved in the subject’s acknowledging that things must be thus
and so. It does not follow that things might not be thus and so for subjects not
possessing those concepts. All that follows is that, for subjects not possessing those
concepts, whether things are thus and so is not an issue: they do not think in those
terms. Transcendental idealism is not beckoning.
I have said that Kant expressly holds the Relativized Intuition Thesis. I have not
committed myself one way or the other on whether he holds the Relativized
Concept Thesis. I have described the latter as a variant of a thesis that he does
hold, the Concept Thesis simpliciter, but I have left open the question whether he
subscribes to the variant too. Does he?
This is a fascinating exegetical issue in its own right, and I shall spend the rest of
this section saying a little about how it might be addressed.³⁹ But I hope that this
will also steer us back to some of the important questions about transcendental
idealism and Kant’s argument for it that we have been considering. Concerning
the exegetical issue, we can distinguish very roughly between textual evidence and
philosophical evidence, that is between what Kant actually says and philosophical
considerations that can be marshalled to make best sense of what he says.⁴⁰ The
textual evidence is unexpectedly inconclusive. There are a few passages in which
Kant suggests allegiance to the Relativized Concept Thesis. There are a few
passages in which he suggests allegiance to its opposite—call it the Unrelativized
Concept Thesis—that all concept-possessing subjects must possess the same pure
concepts; or, more specifically, that all concept-possessing subjects must possess
‘our’ pure concepts, where by ‘our’ pure concepts Kant means the twelve fundamental pure concepts that he calls ‘categories’ together with all those that can be
derived from them.⁴¹ For the most part, however, when he commits himself to
the Concept Thesis simpliciter, he does so in such a way as to suggest nothing
whatsoever about which of these variants he holds.
Two of the passages in which he suggests allegiance to the Relativized Concept
Thesis are Critique of Pure Reason, B145–6, and Prolegomena, 4: 350–1. In the
former he refers to the ‘peculiarity’ of the subject’s conceptual faculty, that what it
achieves by means of the twelve categories it achieves only by their means and
only through such and so many of them; and he says that there is just as little
prospect of explaining this peculiarity as there is of explaining the peculiarity of
the subject’s intuitive faculty that its only two forms are space and time. In the
³⁹ I have been greatly helped in this part of my essay by discussion with Anil Gomes and Andrew
Stephenson. See our joint essay, Essay 2 in this volume, for an extended discussion of the issue. Note
that what follows in this section is not especially germane to the rest of the essay, whose main thread
I pick up again in section 7.
⁴⁰ It is worth remembering, in connection with this distinction, Kant’s own claim that ‘it is not at all
unusual to find that we understand [an author] even better than he understood himself, since he may
not have determined his concept sufficiently and hence sometimes spoke, or even thought, contrary to
his own intention’ (Kant (1998), A314/B370).
⁴¹ Kant (1998), A64–5/B89–90, A79–83/B104–9, and B306.
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37
latter he likens the ‘absurdity’ of thinking that there is only one possible way of
understanding things, namely in accord with our pure concepts, to the absurdity
of thinking that there is only one possible way of intuiting things, namely spatiotemporally. Neither passage settles anything, however. As far as the first is
concerned, failure to admit of further explanation is not the same as contingency:
some necessities are surd. And as far as the second is concerned, Kant seems to be
adverting here, not to subjects whose understanding of things involves pure
concepts other than ours, but to subjects such as God whose understanding of
things does not involve concepts at all.⁴²
The passage in which Kant most strongly suggests allegiance to the Unrelativized
Concept Thesis is Critique of Pure Reason, B148. He there contrasts the limited
range of space and time, which he says extend only to ‘objects of the senses’, hence
only to objects capable of being given by means of spatio-temporal intuitions,⁴³ with
the unlimited range of our pure concepts, which he says extend to any objects
capable of being given by means of any intuitions whatsoever.⁴⁴ But this too fails to
settle anything. True, Kant can be interpreted as saying that, for any subject S who is
given objects by means of intuitions (whether these intuitions be spatio-temporal or
not), S must, and may, use our pure concepts to think about those objects. But he
can just as well be interpreted as saying that, for any subject S who is given objects by
means of intuitions and who possesses our pure concepts, S must, and may, use those
concepts to think about those objects. There is even an interpretation on which he is
saying that, for any subject S who is given objects by means of intuitions, and for any
subject S* who possesses our pure concepts, S* must, and may, use those concepts to
think about those objects. Admittedly, if S’s intuitions are not spatio-temporal
though S*’s are,⁴⁵ then there will not be much that S* is able to think about such
objects; and there will be even less that S* is able to know about them. Even so, S*
can use (for example) the category of causality-and-dependence to wonder whether
every such object depends on some other such object as its cause; and the category
⁴² Cf. Kant (1998), B145.
⁴³ This is not quite the tautology that it appears to be, although it would not matter for current
purposes even if it were.
⁴⁴ There is a phrase towards the end of this passage that is ambiguous in the original German and
that translators render differently. The phrase is die jene allein enthalten. In Kant (1998) this is
rendered as ‘which they alone contain’, while in Kant (1933) it is rendered as ‘which constitutes the
whole [of their] content’—which I take to be equivalent to ‘which is all they contain’. The ‘which’ refers
to ‘the synthetic unity of apperception’. The ‘they’ refers either to ‘the pure concepts of the understanding’, which Kant explicitly mentions in the previous sentence, or to the ‘forms of thought’ with
which he subsequently identifies these. The first version (‘which they alone contain’) is the one that
better supports the suggestion that he subscribes to the Unrelativized Concept Thesis. (For further
discussion of this matter, see Essay 2 in this volume, §5.2.)
⁴⁵ That S’s intuitions are not spatio-temporal does not, I think, preclude S’s being spatio-temporal,
or rather S’s appearing spatio-temporally, say as an inhabitant of some distant planet. Who is to say
that S’s non-spatio-temporal intuitions may not facilitate the successful negotiation of spatio-temporal
objects in S’s environment? For there may be some deep isomorphism between how the objects of those
intuitions are and how those spatio-temporal objects are, perhaps based on some yet deeper isomorphism between how they both are and how things in themselves are.
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of negation to rule out any such object’s violating the principle of contradiction.
And if S does not possess any of our pure concepts, then all that follows, as before,
is that S does not think in these terms: S never confronts these issues.⁴⁶
So far, so inconclusive, then. What happens when we invoke philosophical
evidence? One reason to think that we can make better sense of what Kant says
by ascribing the Relativized Concept Thesis to him than by ascribing the
Unrelativized Concept Thesis to him is this. If we ascribe the Unrelativized
Concept Thesis to him, that is if we credit him with the belief that all conceptpossessing subjects must possess our pure concepts, then we confront awkward
questions about the nature of this ‘must’. Given that it is (presumably) the kind of
‘must’ that is characteristic of armchair knowledge, what sort of armchair knowledge? Analytic? Or synthetic? Neither answer is entirely satisfactory.
The ‘analytic’ alternative is unsatisfactory because it is in tension with Kant’s
suggestion that the necessity in question is some kind of surd that fails to admit of
further explanation. This alternative can also appear straightforwardly implausible. Could Kant really think that sheer analysis of the concepts involved would
suffice to determine the truth of a thesis as recondite as this, whose very ascription
to him is such a bone of exegetical contention?⁴⁷
If we opt for the ‘synthetic’ alternative, however, then we are in danger of opting
for something too weak. There is supposed to be a contrast here between our pure
concepts and our a priori intuitions. But when the ‘must’ is interpreted in the
‘synthetic’ way, it is no less true, for Kant, that all subjects that are given objects in
intuition must be given them spatio-temporally:⁴⁸ the Unrelativized Concept
Thesis no longer marks the requisite contrast.⁴⁹
⁴⁶ I should however record an objection to this third interpretation (to which I paid insufficient
attention when I endorsed the interpretation in A. W. Moore (2012), ch. 5 n. 40). The objection is this.
There is a clause in the passage—‘as long as [the intuition] is sensible and not intellectual’—which, on
this interpretation, amounts to an explicit refusal on Kant’s part to say the same thing about a subject
such as God, whose understanding of things does not involve concepts, as he says about S. For by an
‘intellectual’ intuition Kant means an intuition of the kind that such a subject would possess, that is to
say, an intuition that itself brings objects into existence rather than serving as the means by which
objects are given (see Kant (1998), B71–2). But it is unclear why Kant would refuse to say the same
thing about such a subject as he says about S; for would he not think that our pure concepts are as
applicable to the objects of such a subject’s intuition as they are to the objects of S’s intuition? On each
of the two other interpretations, by contrast, it is clear why such a subject has to be exempted from the
claim that Kant is making: the claim that Kant is making is a claim about subjects that need to make
use of concepts. All I can offer in response to this objection is the observation that, in a later work,
namely Kant (2002b), Kant seems straightforwardly to contradict the offending clause and to say
something much more conducive to the given interpretation: he writes, ‘[Our pure concepts] are
merely thought-forms for the concept of an object of intuition as such, of whatever kind that may be,
and even if it were a supersensible [i.e. intellectual] intuition’ (Kant (2002b), 20: 272, emphasis added; cf.
Kant (1996b), 5: 54).
⁴⁷ This is a genuine question, not a rhetorical question. However implausible the view may appear, it
is not outrageous. For further discussion see Essay 2 in this volume, §6.1.
⁴⁸ See e.g. Kant (1998), A24/B38–9 and A31/B46.
⁴⁹ Note: I do not deny that different kinds of necessity can answer to synthetic armchair knowledge.
But unless and until we are given some reason to draw the relevant distinction between the two claims
at stake here, that is the claim that all concept-possessing subjects must (in the ‘synthetic’ sense) possess
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None of this, however, is decisive against ascribing the Unrelativized Concept
Thesis to Kant. And if we ascribe the Relativized Concept Thesis to him instead—
that is, if we say that there is, for Kant, a contingency in the subject’s possessing
‘our’ pure concepts—then this in turn gives pause. For in so far as it is appropriate
to talk about ‘the’ subject,⁵⁰ then surely the fact that the subject possesses these
pure concepts counts as an item of armchair knowledge for Kant. And if it does,
how can ascription of the Relativized Concept Thesis to him be reconciled with his
belief, to which I referred in §1, that all armchair knowledge is knowledge of what
is necessary?⁵¹
Note, however, that this may be a philosophical problem for Kant rather than
an exegetical problem for anyone ascribing the Relativized Concept Thesis to him.
True, the aim of the current exercise is to make best sense of what Kant says. But it
would be setting the bar too high to insist that one cannot make best sense of what
Kant says unless one absolves him of all internal inconsistency. And there are
reasons to think that, even in his own terms, Kant ought not to believe that all
armchair knowledge is knowledge of what is necessary. Indeed there are reasons to
think that, inchoately and in spite of himself, he already recognizes counterexamples. Thus consider certain remarks that he makes concerning my consciousness
our pure concepts and the claim that all subjects that are given objects in intuition must (in the
‘synthetic’ sense) be given them spatio-temporally, then the former, in mimicry of the latter, cannot but
allow for the possibility of concept-possessing subjects who do not possess our pure concepts. An
advocate of the Unrelativized Concept Thesis needs to be able to rule out this possibility. That is to say,
an advocate of the Unrelativized Concept Thesis needs to be able to rule out the possibility that what
makes it true that all concept-possessing subjects must possess our pure concepts is some peculiarity of
the understanding akin to the peculiarity of the sensibility that makes it true that all subjects that are
given objects in intuition must be given them spatio-temporally. There is a further concern about the
‘synthetic’ alternative which relates to something that I said in the opening paragraph of this section,
namely that it is only by appeal to a priori intuitions that Kant believes the subject can have synthetic
armchair knowledge. For what appeal to a priori intuitions is being made here? However, I concede that
an advocate of the ‘synthetic’ alternative has things to say in response. For one thing, there is room for
doubt about whether it is Kant’s view that only by appeal to a priori intuitions can the subject have
synthetic armchair knowledge. When I attributed this view to him, I had in mind such texts as Kant
(1998), A47–8/B64–6, B73, A62/B87, A155–6/B194–5, and B289, and Kant (2002a), §2, final paragraph. (See also the second of the two notes added by Kant in his own copy of the first edition of
Critique of Pure Reason at A158, mentioned by his translators in Kant (1998), p. 283 n. c.) But
elsewhere Kant does in fact suggest the opposite, e.g. in Kant (2000), 5: 197 n. 1, and in connection
with the fundamental law of morality in Kant (1996a), 4: 420, and Kant (1996b), 5: 31 and 42–3. This is
all complicated by the fact that my very talk of synthetic armchair knowledge (as opposed to synthetic a
priori cognition, or synthetic a priori propositions) already involves a departure from Kant’s own way
of framing these ideas. These issues are far too large for me to address within these confines. I shall
merely comment, specifically in connection with Kant (2000), 5: 197 n. 1, that Kant seems to be
adverting to the distinction that he draws elsewhere between the way in which mathematicians achieve
synthetic armchair knowledge, through the actual exhibition of relevant a priori intuitions, and the way
in which philosophers do so, through appeal to the role that a priori intuitions play in the very
possibility of experience: see Kant (1998), A713/B741 and A766/B794.
⁵⁰ See again n. 1 above.
⁵¹ This problem is somewhat mitigated by the fact that the contingency in question is epistemic—but
only somewhat.
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that I exist,⁵² or concerning what he calls ‘the sole fact of pure reason’.⁵³ Consider,
for that matter, his commitment to the Relativized Intuition Thesis.
Not that any of these reasons is the primary reason for thinking that there may
be a philosophical problem for Kant here. The primary reason for thinking that
there may be a philosophical problem for him here is that the problem in question
would be a version of the basic problem with transcendental idealism which I tried
to identify in the previous section. The contingency in the subject’s possessing our
pure concepts, like the contingency in the subject’s intuiting things spatiotemporally, would be one of the contingencies in which the transcendental idealist
claims to find a grounding for the various necessities that stand in the relation of
i-dependence to the subject. The transcendental idealist must acknowledge
these contingencies—but cannot do so from the subject’s point of view. (From
the subject’s point of view, there is, as I remarked above, no other way of intuiting
things than spatio-temporally, nor any other way of understanding things than in
accord with our pure concepts.) To acknowledge these contingencies, the transcendental idealist must therefore take a step back from that point of view. But to
credit the transcendental idealist with the capacity to do this is to credit the
transcendental idealist with the capacity to gain an insight into how things are
in themselves of just the sort that Kant insists is impossible.⁵⁴
7. Accounting for Armchair Knowledge without
Invoking Transcendental Idealism
I said in §5 that I took Kant’s argument from the existence of synthetic armchair
knowledge to the truth of transcendental idealism to be valid. But in the light of
the discussion that we have just been having, it is worth emphasizing that I was
presupposing a Kantian conception of armchair knowledge whereby such knowledge is always of what is necessary.⁵⁵ Kant’s argument crucially relies on this.⁵⁶ If
we admit armchair knowledge of what is not necessary, that is if we admit
armchair knowledge of what straightforwardly and unambiguously admits of
alternatives, then the argument fails. This is clear as soon as we reflect on one of
the contenders mentioned in the previous section. The sheer fact that I can be
⁵² E.g. Kant (1998), B157–9. Here (cf. n. 19) it is important that I am talking about knowledge, not
about cognition.
⁵³ Kant (1996b), 5: 6, 31, 42, 43, 55, and 194, and Kant (2000), 5: 468.
⁵⁴ Question: Just as an advocate of the Unrelativized Concept Thesis can be pressed on the issue of
what kind of necessity the thesis involves, cannot an advocate of the Relativized Concept Thesis be
pressed on the issue of what kind of contingency the thesis involves? And might there not likewise be
reasons for thinking that no answer—not even an ‘epistemic’ answer—is satisfactory? Answer: Maybe
so, but then this too can be regarded as Kant’s problem. For he is already committed to just such a
contingency in his endorsement of the Relativized Intuition Thesis.
⁵⁵ See nn. 8 and 35 above.
⁵⁶ See e.g. Kant (1998), ‘Transcendental Aesthetic’, §8, esp. A46–9/B64–6.
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41
credited with armchair knowledge of my own existence, if I can, clearly provides
no support for transcendental idealism.⁵⁷
But my knowledge of my own existence does not concern what is beyond me.
What happens if, at the same time as we admit armchair knowledge of what is not
necessary, we prescind from all knowledge except that which concerns what is
beyond the subject? Is there then a valid argument from the existence of synthetic
armchair knowledge to the truth of transcendental idealism? Even then, I think
not. I think it is possible to account for such knowledge by other means. By what
other means?
I have two suggestions. Each draws inspiration from the work of a great
philosopher—albeit only in the sense of being a variation on one of the themes
played out by that philosopher. In neither case is there any reason to think that the
philosopher in question would be sympathetic to the suggestion. In neither case,
come to that, is there any reason to think that sympathy for the suggestion is
warranted. For my purposes, this does not matter. Neither suggestion need be
plausible to ensure the invalidity of the argument in question, the argument from
the existence of synthetic armchair knowledge (appropriately construed) to the
truth of transcendental idealism. All that is required, in each case, is that the
suggestion cannot be ruled out.
My first suggestion, drawing inspiration from the work of Spinoza, is that there
is some common feature of things, including the subject, which the subject can
knowledgeably self-ascribe in the armchair and which, in Spinoza’s memorable
phrase, ‘is equally in the part as in the whole’.⁵⁸ It is a difficult question what
Spinoza himself means by this phrase. But what I mean by it is this: for a feature to
be equally in the part as in the whole is for that feature to be like Euclidean
spatiality in that its very possession by some given finite thing testifies to its
possession by some larger thing of which that finite thing is a part. If there were
such a feature, and if the subject could knowledgeably self-ascribe it, then the
subject could, by extrapolation, have knowledge that some larger thing possessed
the feature, and hence could have knowledge concerning what lies beyond the
subject—all in the armchair.⁵⁹ This admittedly presupposes that the knowledge in
question is not compromised by the existence of alternatives, that is by counterparts of non-Euclidean spatiality. For there must be such alternatives. If there were
not—if the knowledge in question were knowledge of what is necessary, à la
⁵⁷ This is an apt point at which to signal another advantage that my use of the label ‘armchair
knowledge’ has over the more familiar ‘a priori knowledge’. Among those who would be prepared to
credit me with armchair knowledge of my own existence, there are many who would have qualms
about classifying such knowledge as ‘a priori’. What rationale there would be for such qualms need not
concern us here: I merely note that my use of the label ‘armchair knowledge’ ensures that I do not beg
any questions in this regard.
⁵⁸ Spinoza (2002a), pt II, prop. 38.
⁵⁹ Cf. Spinoza’s argument in the proof of Spinoza (2002a), pt II, prop. 38. Not that I deny that there
are important differences between Spinoza’s argument and mine.
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42
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Kant—then there would once again be the problem of reconciling this lack of
alternatives with the syntheticity of the knowledge.
My second suggestion, drawing inspiration from the work of Aristotle, has
three components: first, that the subject’s mind shares a form with certain things
that are beyond the subject; second, that the subject thereby understands what it is
for those other things to have this form and thereby has knowledge concerning
those other things; and third, that none of this requires the subject to leave the
armchair. Aristotle’s own view lacks the third component. He does not believe
that the subject’s mind can share a form with other things in this way unless and
until the subject has duly investigated those other things, and he believes that
this does require the subject to leave the armchair.⁶⁰ But, even on Aristotle’s
view, there is a sense in which the subject is eventually able to access knowledge
concerning those other things through a kind of introspection. (Aristotle himself
says that ‘the mind . . . is then able to think itself ’.⁶¹) All I am envisaging is that the
subject’s mind has this form as a result of a pre-established harmony rather than
as a result of investigation. As in the case of the first suggestion, this presupposes
that the resultant knowledge is not compromised by the existence of alternatives
in which some of the particularities of what the subject knows about the things
that have the form do not hold.
I referred just now to a pre-established harmony. This helps to highlight the
most important difference between Kant’s own account of synthetic armchair
knowledge and these two rivals. Kant, to repeat, thinks that such knowledge must
be knowledge of what is necessary. Not only that; as I have more than once
emphasized, he thinks that such knowledge must be knowledge of what is
necessary as necessary. The necessity is revealed in the fact that the subject, at
least while considering things from the point of view that the knowledge is from,
cannot entertain alternatives. This means that the range of possibilities for how
things are corresponds to the range of possibilities that the subject, considering
things from that point of view, can entertain for how they are. And unless this is
just some brute coincidence, there are only three possible explanations: that the
former range is determined by the latter; that the latter range is determined by the
former; or that the two ranges have some common determinant, in other words
that there is a pre-established harmony. But only the first of these, that the former
range is determined by the latter, serves to explain how the subject can have
armchair knowledge of the coincidence; that is, armchair knowledge of the coincidence, of the fact that things not only are, but must be, thus and so.⁶² And to
invoke the first of these, that is to accept that the range of possibilities for how
things are is determined by the range of possibilities that the subject can entertain
⁶⁰ See Aristotle (1941d), bk3, chs 4–5.
⁶¹ Aristotle (1941d), bk 3, ch. 4, 429b8–9, emphasis in original.
⁶² Kant (1998), A92–3/B124–6 and B166–8.
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43
for how they are, is to appeal to the i-dependence that is characteristic of
transcendental idealism.
But this does not, I hardly need say by now, provide any ultimate vindication of
Kant. Kant’s belief that the knowledge at stake is knowledge of what is necessary is
precisely the thing which, as we have seen in the two previous sections, creates
insuperable difficulties for him. My own view, as I intimated in §5, is that the
primary casualty of these reflections is Kant’s very idea that there is synthetic
armchair knowledge.⁶³
⁶³ I am very grateful to Anil Gomes, Andrew Stephenson, Robert Stern, and participants at a
workshop on ‘Kant on A Priori Knowledge and the Necessity of the Categories’, at the University of
Fribourg, for valuable discussion of the issues that I have pursued in this essay.
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