00:06
good afternoon
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i'm michelle moody adams i'm the strauss
00:10
professor of political philosophy
00:12
and legal theory at the in the
00:15
department of philosophy at columbia
00:17
and i'm pleased to welcome you to this
00:19
panel discussion
00:20
of a new book by my colleague justin
00:23
clark doan
00:24
entitled morality and mathematics
00:27
published by oxford university press in
00:29
2002
00:31
justin is currently associate professor
00:33
of philosophy at columbia
00:35
and in addition to this forthcoming book
00:37
his work has been published in numerous
00:39
journals
00:40
in philosophy including news and ethics
00:44
our speakers beyond justin today
00:47
are david papano who's professor of
00:49
philosophy
00:50
of science at king's college london and
00:53
visiting presidential professor at the
00:55
cuny graduate center
00:56
he's the author of knowing the score
00:59
what sports can teach us
01:01
about philosophy and what philosophy can
01:04
teach us about sports
01:06
as well as philosophical devices proofs
01:09
probabilities possibilities and sets and
01:12
thinking about consciousness
01:13
among other published works katya maria
01:16
vote is professor of philosophy
01:18
at columbia university she is the author
01:22
of numerous books and articles
01:23
including desiring the good belief
01:26
and truth law reason and the cosmic city
01:31
and skepsis and laban's proxies she's
01:34
also the co-editor of a book entitled
01:36
epistemology
01:37
after sexist empiricus and the editor
01:41
of peyronian skepticism in diogenes
01:43
laertes
01:45
she's received many honors and awards
01:47
including fellowships from the templeton
01:49
foundation
01:50
and the princeton council of the
01:51
humanities and finally michael harris
01:54
is professor of mathematics at columbia
01:57
university
01:59
he is the author of mathematics without
02:01
apologies
02:03
and co-author with richard taylor of the
02:05
geometry and co-homology
02:08
of some simple shimura varieties and
02:11
he's received a number of prizes
02:13
including the clay research award which
02:16
he shared
02:16
in 2007 with richard taylor
02:20
and after our panelists have spoken
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we'll have some time
02:24
for questions from the audience you
02:26
should see a question and answer a q a
02:28
box at the bottom of your screen
02:30
where you'll be able to submit questions
02:33
for me
02:34
to read aloud and without further ado
02:38
do i ask justin to give us a wonderful
02:41
account of his book
02:45
uh thanks so much michelle and thanks to
02:48
david michael uh katya and everyone at
02:51
the hyman center
02:53
for making this possible i feel really
02:55
privileged to be able to
02:56
to think through these issues with all
02:57
of you um
02:59
philosophy has traditionally had
03:01
systematic ambitions
03:03
to understand as wilford sellers
03:05
famously put it how things in the
03:06
broadest possible sense of the term hang
03:08
together in the broadest possible sense
03:10
of the term
03:11
however as philosophy has become
03:13
increasingly specialized these ambitions
03:15
have become
03:15
increasingly threatened a case in point
03:18
concerns the question of realism
03:20
to what extent are the subjects of our
03:22
thought and talk independent of us
03:24
independent of our minds and languages
03:25
and practices
03:28
a common naturalist position combines
03:30
realism about science with anti-realism
03:32
about
03:32
value but realism about science
03:36
presupposes realism about mathematics
03:38
and indeed
03:39
logic and modality the theory of
03:41
possibility necessity
03:42
so whether we can be naturalists turns
03:45
on whether we can be mathematical
03:46
realists but moral anti-realists
03:49
despite its importance for systematic
03:51
philosophy the debate over the question
03:53
has been mostly limited to trading
03:55
impressions
03:57
um the problem is specialization
03:59
morality and mathematics are such
04:01
different subjects and philosophies
04:02
become so specialized
04:04
that nobody really knows whether one can
04:06
be a moral anti-realist and a
04:08
mathematical realist or whether ethics
04:09
in the philosophy of mathematics have
04:11
anything else to teach each other
04:13
my book morality mathematics seeks to
04:15
rectify the situation
04:17
it explores arguments for and against
04:19
moral realism and mathematical realism
04:21
and how they interact
04:22
it concludes with surprising lessons for
04:24
philosophy generally
04:26
among other things it shows that
04:27
practical questions as opposed to
04:29
questions of fact
04:31
are the ones that are really at stake in
04:33
traditional philosophical controversies
04:36
uh let me briefly uh summarize the
04:38
chapters
04:39
uh in chapter one i clarify the concept
04:42
of realism and distinguish it from
04:44
related concepts with which it's often
04:46
conflated
04:47
i show that properly conceived realism
04:49
has no ontological implications and the
04:52
common objections to realism
04:53
fallaciously assume otherwise
04:55
that is it has nothing to no
04:56
implications for what exists
04:59
uh i conclude by distinguishing realism
05:01
from objectivity
05:02
in a certain sense objective questions
05:05
in my sense are those that admit
05:06
a single answer by contrast in a
05:09
disagreement over a non-objective
05:10
question we can both be right
05:13
i use the parallel postulate understood
05:15
as a claim of pure geometry as a
05:17
paradigm claim that fails to be
05:18
objective in the relevant sense
05:20
even if mathematical realism is true
05:22
conversely i explain
05:24
how realism about claims of a kind may
05:25
be false although they are objective
05:28
in a sense that the parallel postulate
05:30
is not
05:32
in chapter 2 i argue that our
05:33
mathematical beliefs have no better
05:35
claim to being a priori
05:37
justified than our moral beliefs that's
05:39
the way they're commonly thought to be
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justified
05:41
in particular they have no better claim
05:43
to being self-evident
05:45
provable plausible analytic or true by
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definition
05:49
um or even initially credible than our
05:51
moral beliefs despite widespread
05:53
allegations to the contrary
05:54
i consider the objection that pervasive
05:56
and intractable moral disagreement
05:58
betrays an obvious lack of parity
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between the cases
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and argue that there is no important
06:03
sense in which there is more moral
06:05
disagreement than mathematical
06:06
disagreement or in which it is less
06:08
tractable than mathematical disagreement
06:10
a common argument to the contrary simply
06:12
confuses logic that is
06:14
the question of what is true if
06:16
something else is true or what is true
06:17
if the axioms are true
06:19
with mathematics proper the the
06:22
nonlogical
06:23
part i conclude with the suggestion that
06:25
the extent of disagreement in an area in
06:27
any familiar sense is of doubtful
06:29
epistemic significance
06:31
in chapter 3 i argue that our
06:33
mathematical beliefs also have no better
06:35
claim to being a posteriori
06:37
or in other words empirically justified
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than our moral beliefs i focus on
06:41
gilbert harmon's influential argument to
06:43
the contrary
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harmon argues that since the truth of
06:46
our mathematical beliefs is
06:47
indispensable to our scientific theories
06:49
while the truth of our moral beliefs is
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not
06:52
only the former are empirically
06:53
justified
06:55
i show that even if this argument were
06:57
sound it would at most establish that a
06:59
subset of our mathematical beliefs
07:02
has better claim to being empirically
07:03
justified than any of our moral beliefs
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and i argue that it does not even show
07:07
that
07:08
surprisingly however the full range of
07:10
our moral beliefs could be empirically
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justified albeit in a different way
07:14
unlike mathematics there's no apparent
07:16
ground on which to rule out so-called
07:18
moral perceptions
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as being on an epistemic par with
07:21
ordinary judgments describing high-level
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properties like
07:25
there's a chair i conclude with the
07:27
prospect that
07:28
there may be no principle distinction
07:30
between intuition and perception
07:32
and hence between our priori and our
07:34
posteriori justification
07:37
having shown that our mathematical
07:38
beliefs have no better claim to being
07:40
defeasibly justified than our moral
07:42
beliefs in chapter four i consider
07:43
attempts to undermine the latter by
07:45
appeals of their genealogy what have
07:47
become known as genealogical debunking
07:49
arguments
07:50
i argue that a standardly formulated
07:51
such arguments misunderstand the
07:53
epistemic significance of
07:55
explanatory indispensability debunkers
07:58
observed that whether the proposition
08:00
that p
08:00
is implied by some explanation of our
08:02
coming to believe that p
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is predictive of its having
08:05
epistemically desirable qualities
08:07
when the fact that p would be causally
08:09
efficacious if it obtained the problem
08:12
is that these things are independent
08:14
when the fact that p would be causally
08:15
inert
08:16
and genealogical debunking arguments
08:18
fallaciously assume
08:19
otherwise i formulate a principle that i
08:21
call modal security which entails a
08:23
criterion of adequacy on genealogical
08:25
debunking arguments a criterion they
08:28
fail to satisfy
08:29
but even if modal security is false i
08:32
argue that such arguments have little
08:33
force absent account of the epistemic
08:35
quality they're supposed to threaten
08:38
i conclude that the real problem to
08:39
which genealogical debunking arguments
08:41
point is the so called the nasser f
08:43
problem that is the problem of
08:45
explaining the reliability of our moral
08:47
beliefs
08:48
realistically construed however this
08:50
problem has nothing to do
08:52
with whether the contents of our moral
08:53
beliefs are implied by some explanation
08:55
of our coming to have them nothing to do
08:57
with their genealogy
08:58
in chapter five i consider the
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banasseraf problem or what i call the
09:02
reliability challenge in detail i
09:04
consider various ways to understand the
09:06
challenge i show that its most
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promising formulations involve
09:09
variations of the truths or variations
09:12
of our beliefs the best version of the
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former is the challenge to show that our
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beliefs are sensitive in the
09:18
epistemologist sense that is roughly
09:20
that had the truths been different our
09:22
beliefs would have been correspondingly
09:23
different
09:24
this challenge is widely supposed to
09:26
admit of an evolutionary answer in the
09:28
mathematical case but not in the moral
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i argue that on the contrary the
09:32
sensitivity challenge may admit of an
09:33
evolutionary answer in the moral case
09:35
and not the mathematical
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but in any case i argue that this is an
09:39
inadequate formulation of the challenge
09:41
so this leaves only
09:42
analyses in terms of the variation of
09:44
our beliefs the best version of this
09:46
is the challenge to show that our
09:48
beliefs sorry our beliefs are safe in
09:50
the epistemologist sense
09:51
roughly that we could not have easily
09:53
had systematically false ones
09:55
understanding the reliability challenge
09:57
is the challenge to show that our
09:58
beliefs are safe explains the otherwise
10:00
mysterious conviction
10:02
that the view that i will call
10:03
mathematical pluralism
10:05
affords an answer to the reliability
10:07
challenge it also illuminates the
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significance of genealogy
10:10
in a certain sense uh and disagreement
10:14
i conclude that whether the reliability
10:15
challenge is equally pressing in the
10:17
moral and mathematical cases
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thus turns on whether pluralism is
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equally viable in the two areas
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the rough idea to pluralism about an
10:26
area f is that any f
10:27
like theory that we might have accepted
10:29
is true of the entities which it is
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about independent of human minds and
10:33
languages
10:34
in chapter 6 i show that while standard
10:36
formulations of pluralism are dubiously
10:38
coherent the view can be refined and the
10:41
resulting theory does seem to answer the
10:42
reliability challenge for f realism
10:45
understood as the challenge to show that
10:47
our f beliefs are safe
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uh it does so by giving up on the
10:51
objectivity of the truths in the sense
10:53
of chapter one but not on their
10:54
independence not on the realism
10:57
however there's a key difference between
10:59
the mathematical and moral cases
11:01
under the assumption of mathematical
11:02
pluralism peculiarly mathematical as
11:05
opposed to logical questions get
11:07
deflated
11:08
they become verbal in roughly the sense
11:10
in which the parallel postulate question
11:12
is verbal
11:12
understood as a question of pure
11:14
mathematics
11:16
by contrast under the assumption of
11:18
moral pluralism all the pressing
11:19
questions remain
11:21
those are the practical questions what
11:23
to do we can frame the point as a
11:25
radicalization of moore's famous open
11:27
question argument
11:29
practical questions remain open even
11:31
when the facts
11:32
including the evaluative ones if there
11:34
are any
11:35
are closed this means that mathematics
11:37
and morality if it is practical
11:40
do differ but the concept of realism
11:42
alone is too crude to do justice to the
11:44
difference
11:45
although practical realism is false
11:46
practical questions are objective in a
11:48
paradigmatic respect and while
11:50
mathematical realism is true
11:52
mathematical questions fail to be one
11:54
upshot of the discussion is that the
11:56
concepts of realism and objectivity
11:59
uh are not only distinct but are
12:01
actually in tension
12:03
i conclude by sketching the broader
12:04
significance of the book's conclusions
12:07
i suggest a general partition of areas
12:09
of philosophical interest
12:10
into those that are more like
12:12
mathematics and those that are more like
12:13
morality
12:14
in the former category are questions of
12:16
modality grounding
12:18
essence logic and meriology in the
12:20
latter are questions
12:22
of epistemology political philosophy
12:24
aesthetics and prudential reasoning
12:27
i argue that um the former questions are
12:29
like the question of whether the
12:30
parallel postulate is true understood as
12:32
a question of
12:33
a pure mathematical conjecture they're
12:35
verbal but not because they're literally
12:37
about words
12:39
they're verbal because reality is rich
12:41
enough as to witness any view we might
12:42
have given
12:43
on them i illustrate this conclusion
12:46
with questions of modality
12:47
i argue that just as there are different
12:49
concepts of geometrical point in line
12:51
all independently satisfied
12:53
there are different concepts of modality
12:55
or counterfactual possibility
12:57
while it is say metaphysically
12:58
impossible that you could have had
13:00
different parents a famous argument from
13:02
sal kripke is
13:03
is sound it's logically possible that
13:05
you could have
13:06
and there's nothing more real uh about
13:09
metaphysical possibility than logical
13:10
possibility
13:11
in general while typical questions of
13:13
modal metaphysics are not about the word
13:15
possible they might as well be because
13:18
all we learn in answering them is how we
13:19
happen to be using modal vocabulary
13:21
rather than learning what modal reality
13:23
contains
13:25
by contrast a value of questions insofar
13:27
as they are practical are immune to
13:29
deflation in this way
13:30
but the reason that they are is that
13:32
they don't answer to the facts
13:34
so their objectivity is not compromised
13:36
if the facts are abundant
13:37
i conclude that the objective questions
13:39
in the neighborhood of questions of
13:41
modal metaphysics grounding essence and
13:43
so forth are therefore practical
13:44
questions as well
13:46
practical philosophy should therefore
13:48
take center stage
13:49
thanks
13:57
david so i go straight in now thank you
14:01
i'm
14:01
waiting for a prompt that's fine that's
14:04
great thank you very much justin
14:06
and i should say from the start that i
14:09
really enjoyed reading your book it's a
14:10
kind of
14:11
novel approach to a set of traditional
14:13
issues and
14:15
made me think a lot i learned a lot it's
14:16
great great stuff
14:19
so i want i want to make a few comments
14:22
and
14:22
and raise a query at the end and maybe a
14:26
little suggestion about how to
14:28
how to deal with the query so
14:32
as you explained you you you set it up
14:34
by posing a challenge to
14:38
naturalism i'm going to query this uh
14:41
terminology of networks in a second but
14:43
but uh that's not an important thing
14:44
that
14:45
that your target is is a standard view
14:48
that's
14:48
that's uh in philosophy that's that's
14:52
realist about science and there with
14:56
about mathematics but uh
14:59
non-realist anti-realist about about
15:02
morality and that's kind of the standard
15:04
naturalist humanism
15:05
the hard stuff there's science and then
15:07
there's all this kind of opinion they're
15:08
not
15:09
serious about that you have some you
15:10
have some nice quotes illustrating it
15:13
and the the main body of your book uh
15:16
uh attacks this stance by by
15:20
arguing uh uh by a number of roots that
15:23
there's no
15:24
good episodical basis for this this
15:27
analogy that it looks
15:28
as if all the pistol arguments uh make
15:31
mass immorality stand or fall
15:34
together indeed indeed by and large
15:38
make them stand together now
15:42
i'm i'm i'm all for this attitude in
15:45
fact when it comes to me you'll be
15:46
you're pushing at an open door in fact
15:48
more than an open door
15:50
ah i'm somebody who's always been
15:54
rather suspicious about pure mathematics
15:57
but
15:57
uh not so suspicious about morality i
16:00
mean
16:01
so i might challenge you on whether
16:03
whether
16:05
it's part of naturalism that they should
16:07
uh
16:08
be pro-mass and anti-morality i mean
16:12
i'm a naturalist i wrote a book called
16:14
philosophical naturalism
16:16
uh and uh i'm i'm rather the other
16:20
other way around but uh uh
16:23
no i mean the the terminology doesn't
16:25
doesn't matter the question is uh
16:27
uh do they stand or fall together
16:31
in fact i've been rather more suspicious
16:34
of mathematics than
16:37
morality because
16:41
of the abstractness of mathematics so
16:46
there's no question but that
16:47
mathematical entities sets
16:49
numbers real numbers are outside space
16:52
and time they have no special
16:54
temporal location they don't enter into
16:56
cause relationships everybody
16:57
everybody agrees about that
17:01
so and morality not so much is that
17:04
outside space and time one would think
17:06
that the
17:07
you know being good being bad is a
17:10
characteristic of of acts uh
17:14
that take place inside space and time
17:16
it's not it's not at all so obvious that
17:18
uh moral facts aren't on part of the
17:22
concrete world kind of things that can
17:23
enter into causal relations
17:26
and that's always made me feel you know
17:28
finally
17:29
following hartree field that that
17:32
shawnee mass should be dispensable
17:34
in giving uh characterization of what's
17:38
going on
17:38
in the concrete world right i mean
17:42
i agree that the fact is it's
17:43
dispensable for describing the concrete
17:45
world doesn't mean we have to be
17:46
anti-realist about it that doesn't
17:48
follow but still it's an interesting
17:49
disadvantage between the mass
17:51
and the morality which seems to count
17:53
against
17:55
can't against the mass
17:58
i mean you chuck in at one point that uh
18:01
mass might be dispensable for describing
18:03
the concrete world but it's not
18:04
dispensable for doing
18:06
metallogic uh interesting line of
18:11
line of thought but that kind of
18:12
reminded me of
18:14
david lewis at some point says i'm in in
18:17
a different context but about what you
18:19
ought to be using
18:20
i'm not ready to take lessons in
18:21
ontology from quantum mechanics as it is
18:24
now
18:25
i.e quantum mechanics is a bit of an
18:27
ontological
18:28
uh quagmire and i feel slightly to say
18:31
about metallogic i'm
18:32
i'm never quite clear about what's the
18:35
ontological commitments of the things
18:37
that get said in mental logic
18:39
so i'm not too quick to think that uh
18:42
you can you can read off commitments
18:45
from
18:46
the use of certain uh uh devices in
18:49
metal logic
18:51
but still right and enough enough uh
18:56
about what i think about these matters
18:58
let me have a look at
18:59
your ending point because it's very it's
19:02
very
19:03
interesting so so you save
19:06
mathematical realism by going
19:09
pluralistic
19:10
i mean is is the is the parallel posture
19:14
true uh yes in some abstract geometries
19:18
yes you click in geometry in others
19:22
not uh all these geometries
19:25
exist there's no real issue about which
19:28
is the right geometry
19:29
they're all kind of geometry like uh
19:33
uh subject matters and
19:36
the only real issue is which do we want
19:39
to
19:39
talk about so we we save realism all
19:42
these geometries exist
19:44
by giving up on objectivity there's no
19:46
there's no need to decide
19:48
which is the right one
19:55
okay and then you make the point the
19:57
same line isn't going to work
19:59
with morality i mean so we might say
20:03
um is it is it right to allow
20:08
immigration and then somebody might say
20:10
well yes it's it's it's
20:12
it's it's right it's right one it's
20:14
right according to
20:16
to the uh
20:20
code of liberal cosmopolitanism and it's
20:22
it's and it's
20:23
it's not right to it's not right
20:26
according to
20:27
uh the code of the traditionalist
20:31
nationalist and you might say why can't
20:34
we just
20:35
rest like that like you know parallel
20:37
prostitutes
20:38
parallel postulates true according to
20:40
one one notion of geometry not according
20:43
to another
20:44
but of course as you point out that that
20:46
can't be a happy
20:48
resting point because there's still the
20:50
question about what to do
20:53
should we have immigration or not and
20:55
that
20:56
that hasn't gone away and you say that
20:58
means that morality
21:00
is objective in a way that
21:03
that mathematics is not we have to
21:06
we have to answer answer that question
21:10
and you conclude that because we have to
21:13
answer that question
21:14
we can't be realistic about morality we
21:17
can't think
21:18
that moral judgments answer to to some
21:21
set of independent facts
21:23
they're they're just about what to what
21:26
to do
21:29
it's okay that's that that's all very
21:30
cogent argument but i'm
21:32
i was slightly left
21:36
feeling i didn't know what to think at
21:37
that point about
21:41
about moral discourse or more generally
21:45
discourse about what to do look people
21:49
are discussing what to do they will give
21:52
give reasons in favor of this course of
21:54
action or that reasons for lying or
21:57
immigration
21:57
or or not and it's not clear to me on
22:00
your account that you can give any good
22:02
account of what
22:03
they are aiming to do they mean of
22:06
course
22:07
you mean as the expressive is kind of
22:08
that they're just kind of
22:10
expressing their preferences but that
22:12
doesn't look like a happy account of
22:14
of what's what's going on one offers
22:16
when offers
22:17
reasons but i mean if on your account
22:21
the giving of reasons i mean this is the
22:23
right thing to do is not
22:24
doesn't answer to any facts i don't
22:26
quite understand what to make of that
22:28
kind of discourse
22:29
and at that point i wondered whether one
22:31
should go
22:34
go back and
22:39
feel that maybe there's one
22:43
one kind of right that's right for us i
22:46
mean
22:47
in the case of geometry if we go back
22:50
down to the concrete world
22:51
and away from the world of of abstract
22:54
geometries
22:55
there is a fact of the matter uh uh uh
22:59
and an objective one about which is i
23:02
mean
23:03
are real lines uh do they satisfy the
23:05
parallel posture
23:06
no no i mean that's a pretty
23:08
straightforward uh
23:09
non-pluralist answer uh which is
23:11
simultaneously realist when we ask a
23:13
concrete question
23:15
and it wasn't clear to me what would be
23:16
wrong with taking the line
23:19
that uh when we're asking about
23:22
uh moral matters or questions of what to
23:25
do
23:26
generally that we aren't talking about
23:29
about uh values or reasons whichever way
23:32
you want to set it
23:33
up for us uh
23:37
for the community that we're part of
23:40
uh uh perhaps perhaps a human community
23:44
and then we can see it as citing citing
23:47
facts features of the situation
23:50
perfectly
23:51
naturalistically acceptable facts that
23:54
that we know will move move the people
23:56
in our community
23:59
that's a way of making sense of moral
24:00
moral discourse that
24:03
goes back to it's being both objective
24:06
and realistic now of course that
24:08
presupposes that that
24:10
we're in a community where people are
24:11
going to be moved by the same things
24:13
and uh maybe
24:17
if we were speaking to martians uh then
24:20
we wouldn't be
24:21
with a community uh uh of that kind
24:24
and we'd be talking past each other uh
24:28
just like people arguing about
24:31
lines when in fact they're thinking in
24:33
terms of different abstract geometries
24:36
but it's not obvious to me that that
24:40
we're in that situation with human
24:42
beings maybe we are
24:43
maybe they're different communities of
24:44
human beings who are incommensurably
24:47
different in terms of what moves them
24:48
and then
24:49
and then we'll be talking past each
24:52
other in those cases too and if so
24:54
so be it but at least that gives us some
24:56
account of what we're doing when we
24:57
engage in evaluative discourse that seem
25:00
to me to be missing
25:01
on your story so i'll stop i'll stop
25:05
there i mean nothing nothing uh uh very
25:08
much to disagree about
25:09
except uh there seems to be a gap leave
25:11
left at the end
25:12
but i'll stop there thank you david
25:16
michael thank you very much for
25:19
inviting me and for giving me the
25:21
opportunity to read justin's
25:23
justin's book and uh to
25:26
put up with my misconceptions and my
25:30
fuzzy terminology for the next uh eight
25:33
minutes or so
25:34
when i first saw justin's title i
25:36
assumed his book was about
25:38
the immorality that is rife in
25:40
mathematics
25:42
that is a very timely topic but justin's
25:44
book
25:45
is about timeless philosophical
25:48
questions
25:48
that we mathematicians have trouble
25:50
formulating
25:51
coherently on our own i found it covers
25:54
an amazing range of such questions for
25:56
such a short book
25:57
and in my time i'll just touch on two
26:00
about which i can hope to say something
26:02
coherent
26:03
the question of mathematical pluralism
26:05
of course which is raised
26:07
explicitly as part of a solution to the
26:10
question of realism
26:11
in morality versus mathematics i
26:14
should say i'm convinced by this
26:16
solution which corresponds to my
26:18
practice although i
26:20
would draw different conclusions i
26:23
try to make that clear then the question
26:25
of morality within mathematics in the
26:27
sense of what mathematicians
26:28
should do which is implicit throughout
26:31
the book but is sometimes
26:32
obscured by treating ethical matters as
26:35
metaphysics
26:37
there's a tradition going back to plato
26:39
at least of philosophers complaining
26:41
about the thoughtlessness and confusion
26:43
of mathematicians and a more recent
26:45
tradition
26:46
of philosophers taking the attitude that
26:48
of course mathematicians should not
26:50
worry about the issues
26:51
that concern philosophers because we
26:53
have more important things to do
26:57
i've heard that this hints at an uneasy
26:59
superiority complex which is easily
27:01
matched
27:01
on the mathematician's side where the
27:04
unease as you might imagine comes to the
27:06
surface when we wake up in the middle of
27:07
the night as i
27:08
actually did last night wondering
27:10
whether there is anything real
27:12
about what we're doing a handful of
27:14
mathematicians deal with this sort of
27:16
anxiety by more or less
27:18
loudly proclaiming their platonism since
27:21
they include some familiar names
27:23
people like stephen pinker quoted in the
27:25
book assume that mathematicians on the
27:27
whole are realist
27:29
justin doesn't make that mistake
27:30
although occasionally he displays more
27:33
realism about mathematicians than i
27:35
would
27:36
uh using language that suggests that we
27:39
are a natural kind for example at one
27:41
point he writes that
27:42
mathematicians want to know what is true
27:44
if the axioms are true
27:46
this is valid as folk philosophy as a
27:49
rough way
27:50
of distinguishing the priorities of
27:52
mathematicians from those of ethicists
27:54
and helps to explain why episodes of
27:56
metaphysical night sweats are so
27:58
infrequent among mathematicians
28:00
and it's a plausible explanation of why
28:03
we do what we do but as a definition of
28:05
mathematicians it ascribes wants
28:07
differently than i would the
28:09
mathematicians i know
28:11
want to prove theorems and then and this
28:13
is also important want to know
28:15
why the proof works the word truth
28:18
appears rarely in mathematics and then
28:21
only as a convention like
28:23
qed i would replace want in the above by
28:27
a moral descriptor like
28:29
virtue of mathematical practice
28:32
even though we use the word exist
28:34
constantly it's possible to embarrass
28:36
some mathematicians by asking whether
28:38
our objects really exist
28:40
i avoid embarrassment by limiting my
28:42
ontological commitment to the reality of
28:44
mathematical ideas here i paraphrase
28:47
ian hacking if you can steal ideas then
28:51
they are real
28:53
and i wish more philosophers could
28:55
explain how it's possible for the ideas
28:57
to be real
28:58
when the reality of the objects to which
29:00
the ideas refer
29:01
is left unresolved because ideas really
29:03
are stolen
29:04
i can tell you some stories and all the
29:07
time
29:08
and while this is naturally considered
29:10
immoral
29:11
it's not incompatible with the morality
29:14
of mathematics as a discipline
29:17
as a practice maybe but as a but as a
29:21
discipline though
29:21
but there's another way to restore
29:23
realism to mathematics and that's by
29:25
entrusting it to machines
29:28
these days more prominent mathematicians
29:30
far more
29:31
worry that we will be replaced by
29:32
machines than worry about the accident
29:34
the truth of the axioms of set theory
29:36
i have a question for justin in
29:38
particular what does the correct
29:40
operation of mechanical proof
29:41
verification
29:43
say about mathematical realism or truths
29:46
or beliefs does this count as putnam's
29:49
if then ism which
29:51
justin calls anti-realist but if the
29:54
machine is entrusted with the standards
29:56
for the ideal mathematician does that
29:58
not make
29:58
questions about mathematical pluralism
30:00
mood unless there are
30:02
competing apple and android versions
30:04
each guaranteeing better than 95 percent
30:07
modal security
30:10
someone has actually already imagined a
30:11
mechanical morality verifier
30:13
and proposed it in something called the
30:16
nsf 2026 idea machine
30:19
uh can a driverless car be programmed to
30:21
follow moral rules strictly
30:23
about choosing between running over 10
30:25
university professors or
30:27
10 school children and would we want to
30:29
program
30:30
it in that way or would pluralism more
30:32
pluralism be desirable
30:34
a virtue in both situations
30:37
with regard to mathematical pluralism
30:40
mathematical practice may well look
30:42
pluralistic to outsiders
30:44
non-euclidean versus euclidean geometry
30:46
has long ceased
30:47
to be a matter of controversy there's
30:49
just differential geometry which
30:50
includes euclidean is one of many
30:52
uncountably many possibilities
30:55
contemporary mathematics is more
30:56
opportunistic when it comes to
30:58
to set theory to construct a talk
31:01
homology grotenbic introduced his
31:03
universes
31:04
which require inaccessible
31:07
cardinals which quine called the
31:10
recreational mathematics i
31:11
discovered vyovock's universal univalent
31:14
foundation
31:15
even require an infinite increasing
31:18
sequence of
31:19
inaccessible cardinals every topologist
31:21
and algebraic geometer works with a
31:23
category of sets which is too big to be
31:25
a set
31:25
and most number theorists i've asked
31:27
claim neither to know nor to care about
31:29
these or miller franco axioms
31:31
but this doesn't lead to something like
31:33
a mathematical multiverse
31:35
on the model of a moral multiverse where
31:37
setting cats on fire is immoral in one
31:39
world but no big deal
31:40
in another if two groups of
31:42
mathematicians come up with incompatible
31:44
solutions to a problem
31:46
then the community's moral obligation is
31:48
to swoop in and begin a process
31:50
not an algorithm which is uh as
31:54
justin refers to one uh late in the book
31:57
much like the one dramatized in
31:58
nakatosh's proofs and refutations that
32:00
will persist
32:02
until consensus is achieved so pluralism
32:05
about what is considered correct
32:06
mathematics is impossible with a
32:08
socially social structure of actually
32:10
existing human
32:11
not to mention mechanical mathematics so
32:14
this reveals the moral content of the
32:16
question of realism about mathematicians
32:18
are actually existing mathematicians
32:21
even
32:22
the world experts justin quotes at one
32:24
point acceptable substitutes for the
32:26
morally ideal
32:27
stewards of mathematical truth i
32:29
conclude by saying maybe
32:31
if what i just described illustrates in
32:33
practice the reflective equilibrium
32:36
discussed in the early part of the book
32:38
i would have liked to see
32:39
related to pluralism and finally is this
32:41
is this a practical question
32:46
thanks very much michael and now we turn
32:47
to katya
32:52
i want to thank justin for the
32:54
invitation to join this panel and
32:56
michelle for the kind introduction it's
32:58
a pleasure for me to participate
33:00
justin and i have discussed the ideas
33:02
that figure in his book many times and
33:04
he kind of knows where i'm coming from
33:07
but i i keep enjoying the discussion i
33:09
sort of want to thank him for for all
33:11
the
33:12
you know amazing conversations over the
33:14
years about the material in the book i
33:16
i really enjoyed and feel i learned a
33:18
lot from them
33:19
now justin writes with deep insight
33:21
about both morality and mathematics and
33:24
i think that is a huge
33:25
accomplishment most of us know a lot
33:27
more about one or the other
33:29
um so so i'm i think that is that is a
33:31
big deal but i want to invite you justin
33:34
to talk
33:34
a little more about the morality side of
33:37
things and
33:38
i have kind of three topics or questions
33:41
that i want to pose and one is
33:43
about just sort of the nature of
33:46
normativity or how you see
33:48
moral normativity relate to other kinds
33:50
of normativity
33:52
the second is about what you think of
33:55
the like theoretical framework
33:59
that people may bring to bear or not
34:02
when they have moral disagreements
34:05
and the third is about whether you think
34:08
there is an
34:08
affective dimension to disagreement
34:12
now the first question is going to take
34:14
a little longer than the other ones
34:16
but it kind of lays out a little bit
34:18
where i'm coming from and also something
34:20
that i think is important to your
34:21
project and your comparison
34:23
between morality and mathematics a lot
34:26
is about
34:27
how in both fields people disagree and
34:30
as you know that that interests me also
34:33
a lot
34:34
and i want to ask you sort of as the
34:37
first question
34:38
whether you think that ultimately
34:42
there are going to be kind of these two
34:44
domains as you describe them now
34:46
in your intro that there's going to be
34:48
like the practical domain on the one
34:50
hand and questions of fact as you call
34:52
it on the other hand and you were saying
34:53
in your intro now that
34:55
sort of in the same on the same side of
34:58
things where you put mathematics you
35:00
would also put modality and maybe also
35:02
some other things and on the side where
35:04
you put
35:05
morality you would also put political
35:07
philosophy and some other things and in
35:09
the book you you use
35:11
kind of traditional distinctions between
35:13
kinds of normativity so for example
35:16
moral versus prudential normativity or
35:19
moral versus epistemic normativity
35:21
and there is a kind of promise at the
35:23
end of the book that what you have to
35:25
say about
35:25
moral normativity either sort of carries
35:29
over to these other kinds of normativity
35:31
or at least has somehow implications
35:34
for it and i wanted to ask you about
35:37
another kind of normativity and how it
35:39
fits or doesn't fit into the picture
35:41
namely social
35:42
norms or or societal cultural norms
35:45
maybe even legal norms
35:47
because it seems to me that maybe they
35:49
are on the other side of your comparison
35:51
and that might pose a problem for a kind
35:54
of unified conception of normativity or
35:56
for this distinction between practical
35:58
questions
35:59
and questions of fact now think about a
36:02
customary norm
36:03
say i should wear black when i go to a
36:05
funeral in this
36:06
country and i should wear white when i
36:08
go to a funeral in another country
36:11
now to my mind that is a little bit like
36:13
different
36:14
answers to the parallel postulate
36:16
question in euclidean
36:18
and hyperbolic geometry i cannot do both
36:21
things at once
36:22
but i can travel between the two
36:23
cultures and i could can do one thing if
36:25
i'm in one culture and the other thing
36:27
when i'm in the other culture
36:29
and there's kind of nothing very
36:30
disturbing or puzzling
36:32
or complicated about it in the same way
36:34
in which you argue there isn't anything
36:36
really disturbing about
36:38
one answer to the parallel postulate
36:40
question euclidean geometry and another
36:42
answer
36:42
in hyperbolic geometry so i'm thinking
36:46
that there might be kinds of norms
36:48
that just sort of don't really fit into
36:51
the picture
36:53
and that is the question that i have
36:56
whether you would acknowledge that or
36:58
you know maybe then cultural norms or
37:00
societal norms
37:01
on your view aren't really sort of
37:02
properly speaking norms in the full
37:04
sense
37:05
but that would be an interesting thing
37:07
to learn more about the second
37:09
question is you assume
37:12
that when people disagree morally that
37:15
they bring to bear theoretical
37:16
frameworks and that is kind of part of
37:18
the comparison between morality and
37:20
mathematics in both fields you assume
37:22
that people who disagree
37:23
kind of think in theoretical frameworks
37:26
in in you know in geometry hyperbolic
37:28
or euclidean geometry in morality you
37:31
say as an example someone may think in a
37:33
consequentialist framework or
37:35
deontologist framework now i have to say
37:38
that i'm kind of
37:39
doubtful about this as a sort of general
37:41
description of moral
37:42
disagreement i think that a lot of times
37:44
people when they morally disagree
37:47
they don't necessarily sort of endorse
37:49
or
37:50
formulate for themselves as theoretical
37:52
framework
37:53
and on the country it kind of seems to
37:55
me that often when we disagree and also
37:57
also when we kind of
37:58
disagree in important ways say the
38:01
example that david mentioned about
38:03
immigration or you know very important
38:05
questions
38:05
i think we actually often share kind of
38:08
imprecise versions of general
38:10
ideas we're sort of in the same
38:13
framework
38:13
but we still disagree in in very you
38:16
know
38:17
seemingly irresolvable ways and i just
38:20
sort of wonder whether that
38:22
fits anywhere into your framework and
38:25
the third and last question
38:27
is about affective dimensions of this
38:29
agreement
38:30
now i've been sort of struck by the fact
38:32
that that doesn't come up in your
38:34
analysis of moral disagreement
38:36
and i tend to think that that is a very
38:38
salient dimension of disagreement that
38:40
peop you know there's a characteristic
38:42
set of
38:43
of attitudes that people have and they
38:44
disagree they are offended or
38:46
hurt or they fight or they
38:50
distance themselves from each other or
38:52
whatever
38:53
and then i was thinking you know maybe
38:55
you are not treating that
38:56
as a feature of your account because
38:58
maybe you think that is only on one side
39:00
of the comparison
39:02
and you're starting out from features of
39:04
morality and
39:05
and mathematics that they kind of at
39:07
least you know at the first glance have
39:09
in common
39:10
but then i'm thinking you know theorists
39:12
can also fight and what michael
39:14
was just saying seems to bear on that
39:17
question that theorizes you know either
39:19
they love the truth or maybe they put it
39:20
not quite that nobly maybe there's
39:22
something else
39:23
but theorizers can certainly also get
39:25
into fights when they disagree so maybe
39:27
that is not the way
39:28
to look at it and then i was thinking
39:30
that maybe you think
39:31
that this kind of affective dimension
39:33
doesn't bear
39:34
on the metaphysics and epistemology of
39:36
value and that is after all what the
39:38
book is about
39:40
but here i just sort of want to raise a
39:42
question because one could also think
39:44
that it is truly an insight about the
39:47
nature of value that it shows up for us
39:50
from the perspective of agency
39:52
and that it motivates and moves us and
39:55
that people
39:56
kind of you know want that which they
39:58
see as good
39:59
and so on and so forth and if that is
40:01
true then that actually does spare
40:03
immediately on the metaphysics and
40:05
episomology of value and i'm just sort
40:06
of interested whether that would fit
40:08
into the picture
40:12
thank you so much everyone katya that
40:14
was a wonderful
40:16
ending to the panel discussion i wonder
40:18
if we want to get justin a few minutes
40:21
to try to respond to these questions
40:24
that have been posed
40:25
before the audience questions maybe just
40:27
a few minutes
40:29
uh sure thanks i um uh
40:33
uh i didn't expect to have opportunities
40:35
so yeah
40:36
thank you for the fantastic uh questions
40:39
um
40:39
maybe i'll go in in reverse order um
40:43
so katya briefly my
40:46
um my thought on your question of
40:51
uh what's the difference between ethics
40:53
and other norms i'm with you in thinking
40:55
the notion of ethics is kind of a
40:57
hopelessly indeterminate notion
40:59
and that that should we we probably
41:02
shouldn't put too much emphasis on that
41:04
um my feeling is that there's basically
41:07
questions of what to do
41:09
um in a given concrete circumstance so
41:12
you know what dress am i gonna wear
41:16
today um uh and then there's basically
41:20
norms that can be laid out kind of like
41:22
different constitutions
41:24
and they become normative in some sense
41:26
only to the extent that i adopt them
41:28
as answers to the question of what to do
41:31
so in that in that sense nothing
41:34
morality
41:35
cultural norms epistemic norms nothing
41:38
is normative in the fact in that sense
41:40
as a as just
41:41
a bunch of constitutions or a bunch of
41:43
factual claims about what to do
41:45
um but but but you know
41:49
the activity of asking what to do and
41:51
answering
41:52
that question that is it seems to me
41:55
like
41:56
if anything deserves the name morality
41:57
it's that um
41:59
that's anyway what it seems to me that
42:01
we should be focused on it
42:02
as philosophers um so
42:05
about the frameworks thing um
42:08
so my feeling is that you're absolutely
42:11
right that sort of for simplicity i talk
42:12
about like the deontologist and the
42:14
consequentialists asking about whether
42:16
to kill the one to save the five as if
42:17
the
42:17
as if this were at all representative of
42:19
a normal conversation
42:21
um but i actually don't you're
42:23
absolutely i completely agree with the
42:25
point that people don't
42:26
walk around with moral frameworks in
42:27
their head um but i don't actually think
42:30
that establishes a dis analogy
42:31
so for example um among those
42:35
few who care about the question of for
42:37
example what axioms of set theory are
42:39
true
42:40
um very commonly the situation is both
42:44
parties agree
42:45
that the iterative concept of set is the
42:48
defining
42:49
uh concept and the question is what kind
42:52
of fills that out so
42:53
you know boolos famously thought
42:55
replacement is not part of that
42:56
conception whereas most people evidently
42:59
do because they're part of the zfc
43:01
axioms
43:02
um so so that's a case where we both
43:04
have this kind of in goa
43:05
in koa concept uh or encode
43:09
you know guiding picture but there's a
43:12
disagreement about a concrete
43:13
proposition
43:15
and it seems to me like that's enough to
43:17
get the problem going
43:18
um uh because in the moral case if we
43:22
have a disagreement about the concrete
43:23
question of whether to kill the one to
43:24
save the five we've either got to do it
43:26
or not
43:27
in the mathematical case i'm suggesting
43:30
but i want to ask
43:31
uh michael about this because i wasn't
43:32
totally sure i understood
43:34
what what his
43:37
view was in the mathematical case i was
43:39
suggesting
43:40
why not why don't we treat it like
43:42
geometry why don't we let there be kind
43:45
of why don't we distinguish different
43:46
kinds of iterative notions of set and we
43:49
have one that satisfies
43:50
all instances of replacement and another
43:52
that doesn't why why must
43:54
we choose um uh
43:57
okay and finally the thing about you
43:59
know the effective attitudes and
44:01
emotions
44:02
um so you're absolutely right i think
44:05
that's a
44:05
essential feature um i i did try to say
44:09
something about that
44:10
in the in the section on self evidence
44:12
and what i said was
44:13
if anything that seems to favor
44:17
moral realism over mathematical realism
44:19
because in the mathematical
44:20
case it's much harder to argue that
44:23
people are arguing because they have
44:24
personal investment or
44:26
religious commitments or distorting
44:28
influences
44:29
that are affecting their ability to have
44:31
a sort of careful conversation about the
44:34
the matter whereas in the ethical case
44:37
you know
44:38
ethical questions are so tied to all
44:40
these things that we care so much about
44:42
as you say they tend to get rapidly
44:43
heated and it's hard to you know
44:46
the the ideal would be one where it's
44:48
just kind of
44:49
an intellectual back and forth somebody
44:51
might say
44:52
um so i tried to talk about it a little
44:54
there and its relevance but but the
44:56
short
44:57
answer to the the question of what where
44:59
do i think it fits in is i think it
45:00
supports ultimately the non-cognitivism
45:03
i advocate at the end
45:04
about what to do because if practical
45:06
questions are non-factual questions
45:08
about what to do it's no wonder
45:10
that we're going to get very worked up
45:12
about it because it's about action and
45:14
what's going to happen to us and others
45:16
um rather than about you know the you
45:19
know the platoplasm
45:21
in in uh uh you know whatever
45:24
so um so anyway the obviously that's
45:26
just off the top of my head um
45:28
so so david um let's see
45:32
so um so your thought at the end was
45:36
that
45:37
um uh
45:41
that why why okay so i i'm advocating a
45:44
kind of non-cognitivism
45:46
and you know famous problem for
45:48
non-cognitivism is the freyja geech
45:50
problem
45:50
which is how to explain the apparent
45:52
rationality
45:54
of uh of ethics if it's really just a
45:57
way of expressing non-cognitive
45:58
attitudes
46:00
on that specific matter i'm inclined to
46:02
basically follow
46:03
gibberd so i think i think questions of
46:06
what
46:06
what we ought to do in the practical
46:09
sense are questions of what to do
46:11
this is a matter of hyper plans and
46:14
you know you can recover what looks like
46:17
standard logic
46:18
not understood in terms of truth
46:20
conditions in a heavy duty sense
46:23
um uh in just the way gibber doesn't
46:26
is and thinking how to live now why
46:29
prefer that to what you were suggesting
46:31
which is a sort of naturalist
46:34
um non-pluralist ethics or something
46:38
well my thought is that even if you're
46:41
right um the argument
46:43
for non-cognitivism one wasn't supposed
46:45
to turn on the actual
46:47
truth of moral pluralism it was supposed
46:50
to
46:50
just proceed from the assumption of it
46:53
the idea
46:54
is that if moral pluralism turned out to
46:57
be true
46:58
and by the way there is an argument in
47:00
there arguing that it's hard to see how
47:02
it could fail to be true actually once
47:03
you start to think about it i mean
47:05
surely there's mills properties and
47:07
cons properties and boyd's properties
47:09
out there we can ask the semantic
47:11
question of which we happen to be
47:12
referring to but at a metaphysical level
47:14
what's there to dispute um
47:17
the claim was if if pluralism
47:21
were assumed to be true there would be a
47:23
further question
47:24
now what would that question be suppose
47:26
i ought one to kill the five to
47:28
to kill uh to kill the one to save the
47:30
five i ought to not
47:32
now suppose i say the further question
47:33
is yeah well whether i all things
47:35
considered ought to kill the one to save
47:36
the five or something like that well
47:38
now i can just index the all things
47:39
considered things and re-ask the
47:41
question
47:41
there's always a further question and it
47:43
can't be a question of ought
47:45
on pain of triviality because i always
47:47
de ontological ought to do what i
47:49
deontological ought to do and i always
47:51
utilitarian ought to do what i
47:52
utilitarian not to do there seems to be
47:54
a question of all things considered
47:56
what i ought to do but that can't
47:57
literally be the right story for the
47:59
reason i just mentioned so
48:01
i call that remaining question the what
48:02
to do question
48:04
that doesn't mean that answering the
48:06
what to do question
48:08
in order to answer it we can't just get
48:10
by by consulting
48:12
these natural properties you you think
48:14
maybe that we all
48:15
feel moved by um and and adopting those
48:19
to use the language i just used in
48:21
response to katya as normative
48:23
but the point is that they're not gonna
48:25
settle the practical question by
48:27
themselves we have to ch
48:28
we have to adopt them and that's a
48:30
practical
48:31
move on our part that's uh what you know
48:34
whether to use the whether to consult
48:35
those properties
48:37
okay um finally uh
48:40
michael um uh so
48:43
um so uh
48:47
frankly i just had a couple questions
48:49
about your your questions because i i
48:51
really appreciated them
48:52
so um the the um the first question is
48:55
you started out by saying that you
48:57
yourself i as i understood it
49:01
consider yourself a pluralist um
49:04
but as i understood the end of your
49:07
comments they were sort of critical of
49:08
pluralism or worried about pluralism
49:10
because we have a moral imperative to
49:12
arrive at some kind of consensus rather
49:16
than
49:16
letting a hundred flowers blossom and
49:20
so so could i could you just i think i
49:22
didn't understand the position you were
49:24
you were
49:24
trying to ask me about or maybe this is
49:27
not the time but that's
49:29
i so okay so so i wonder what kind of
49:33
pluralism you
49:34
you feel sympathetic to um the
49:38
the the final question about um is this
49:40
a practical question
49:42
if this was referring to whether to
49:46
require convergence or something
49:50
um then yes i would say that's a
49:52
practical question
49:54
but i wasn't sure what this was
49:55
referring to when you said is this a
49:57
practical question
49:58
um uh the the proof checker thing is
50:01
very interesting but what i would
50:03
be inclined to say is that requires at
50:06
most
50:07
the actual truth preservation
50:10
of a system of logic and not even
50:14
the correctness of the logic because the
50:16
correctness of the logic would require
50:18
the validity
50:19
that is not just the actual truth
50:21
preservation but the truth preservation
50:23
in all logically possible cases
50:25
of the inference rules so this doesn't
50:27
require
50:28
of course we can program certain axioms
50:31
and so forth as well but i don't see why
50:33
that would in any way
50:34
vindicate the idea that there's a one
50:36
true
50:38
uh you know that that there's a one true
50:41
theory about the universe of sex or
50:43
something
50:44
so just um okay but that's it
50:47
sorry thanks so much let's take a couple
50:50
of questions from the audience one of
50:51
them is going to ask you um to follow up
50:54
a little bit on the non-cognitivism
50:56
issue so this comes from devin morse
50:59
is there a correct answer to the
51:00
question what to do if so
51:02
why doesn't this immediately give rise
51:05
to the existence of a certain moral
51:07
fact namely a is the thing to do
51:11
which is then subject to the same
51:13
deflationary pluralism i'll actually
51:15
stop there and let you
51:17
and let you take that up um good
51:20
so here's let me uh so i'm not
51:23
i don't have i can't take the time to
51:25
read the parenthetical things so let me
51:26
know if i'm missing something important
51:28
but um
51:29
uh so let me try to put your worry
51:32
in an even more worrisome way um
51:35
uh in order to deal with the freyja
51:37
geech problem that david brought up
51:39
i better be a deflationist about
51:41
semantic concepts
51:43
and so that means that there's nothing
51:45
to stop me
51:46
from introducing a truth predicate
51:48
whenever i have a declarative sentence
51:50
and whenever i'm willing to claim p
51:52
claim that p
51:53
is true and so forth well okay
51:56
so now suppose i stipulatively introduce
51:58
the term
52:00
that's the thing to do or you know
52:02
killing the one to save the five is the
52:03
thing to do
52:04
uh for the state of mind of intending to
52:07
do it roughly speaking
52:09
um well then it's true and now can't i
52:13
run pluralism because now i can say
52:15
that's the
52:15
that's the thing to do uh it's not the
52:19
thing to do
52:19
star and now there's a question of
52:21
whether to do the thing to do or the
52:23
thing to do star it seems like i can
52:24
just rerun the worry
52:26
in other words why doesn't the um the
52:29
kind of new open question style worry
52:31
just rearrives at the level of what to
52:32
do
52:33
and um my answer
52:37
to this though i agree that this is a
52:39
kind of deep
52:40
problem is that um
52:43
well yeah i can language is conventional
52:46
and i can use a declarative sentence to
52:48
express whatever i want to
52:50
but the question i'm asking is not a
52:52
question of fact
52:54
it's a question of intention and i can
52:57
only intend to do one thing at a time
52:59
so to the answer to the question is
53:01
there a right answer
53:02
certainly there's a right answer out of
53:04
my mouth
53:06
if you want some kind of god's eye
53:08
answer that requires somehow
53:10
um you know getting outside of morality
53:13
or
53:13
what to do questions and as a
53:16
deflationist i think
53:17
you know just like blackburn and gibbert
53:19
and all those people those are it's
53:20
going to be
53:21
morality all the way down so when we
53:23
start doing metaphysics of morality at
53:25
that level
53:27
it's just going to be more what to do
53:28
questions and so of course there's a
53:30
right answer
53:32
uh because do that and even if i hadn't
53:35
thought
53:36
to do that do that is what you know the
53:38
kind of thing that i would
53:40
uh say but this is a this is a deep
53:42
question uh
53:43
and i i agree it's a problem
53:46
thanks justin so we've got a sort of
53:48
historical question
53:50
um that you might want to try to to
53:52
answer what does
53:53
what do you think of locke's abandoned
53:55
promise
53:57
to provide a mathematical demonstration
53:59
of morality
54:00
in the essay concerning human
54:01
understanding
54:03
or you know you may not have a position
54:05
on it but just i think the
54:07
questioner is curious about that yeah so
54:10
you know i do
54:12
briefly talk about lock's discussion
54:14
it's in an
54:15
extended footnote that probably
54:16
everybody was like i don't have time for
54:18
this
54:19
um but um
54:22
so so look i don't have anything to say
54:26
about the bio
54:27
the biographical lock what i would say
54:29
though about the position
54:31
is that i think these kinds of positions
54:34
according to which
54:35
um the basic principles of ethics are as
54:39
self-evident as the basic principles of
54:41
math
54:42
um you know the the chapter two is
54:45
trying to defend
54:46
the view that yeah that's right but
54:49
not because they're self-evident but
54:51
because neither of them is
54:52
um so in other words they are on a par
54:56
lock was right to draw an analogy
54:58
between
54:59
between ethics and math
55:02
the the naive thought is not that
55:05
they're on a par
55:06
but that somehow the axioms of math
55:09
again the axioms i'm not talking about
55:11
logic for a second i'm not talking about
55:12
what is true if the axioms are
55:14
talking about things like that every
55:16
non-empty set has a choice function
55:18
or the replacement axiom or whatever um
55:22
the naive thought is that those are
55:24
self-evident
55:25
or that you know that there's an
55:26
inductive set is self-evident
55:28
so um so on the question
55:31
basically of like you know was lock
55:34
right i actually think he probably was
55:36
probably not for the reason he thought
55:38
he thought he was though
55:39
um yeah great
55:42
so we've actually got a questioner who
55:44
wants to hear uh professor
55:46
harris address the um questions
55:49
that justin raised about his commentary
55:56
well i i apologize for that the uh
56:00
uh first i mean the uh
56:03
i guess all of the questions uh
56:06
presuppose uh if i were to
56:10
give complete answers presuppose trying
56:12
to explain my thoughts about where the
56:14
line is drawn
56:15
between philosophy of mathematics and
56:16
sociology of mathematics
56:18
and whether there's a mathematics
56:22
that is the same for uh mathematicians
56:25
and philosophers
56:26
and brains in vats and martians or
56:29
whether
56:30
there's uh there when when
56:33
uh google or whoever gets the patent
56:37
for the future of mathematics then
56:39
that's that's the only one
56:41
that uh that's left and mathematicians
56:44
are replaced by machines then uh then
56:48
why would the philosophers even bother
56:50
asking about it but
56:51
so that's that's my that's my comment on
56:55
the
56:56
on the uh on the pluralism there now
56:58
it's from my own what i said about
57:00
pluralism i use the word
57:01
opportunism and so
57:04
whether that's uh the same as pluralism
57:07
or not
57:08
is a complicated question but in
57:11
practice
57:12
there are different groups of
57:13
mathematicians who at different times
57:15
decide
57:16
to uh stretch the axioms because
57:20
uh of that gets them where they want to
57:22
go
57:23
and then actually they they are they're
57:25
they you sometimes
57:26
see uh apologetic statements like well
57:30
in a very influential book this is a
57:32
nuisance
57:34
uh if if i had you know several thousand
57:37
more pages i could
57:38
i could avoid making this hypothesis but
57:40
you know i don't
57:42
you don't want to see them anyway uh as
57:45
but the uh but this whether the whether
57:48
the uh
57:51
requirement of convergence a
57:53
sociological
57:55
requirement a practical requirement or
57:57
somehow
57:58
it's whether that can be separated from
58:01
whatever mathematics
58:02
is is uh it's
58:06
i don't think it's in conflict in any
58:07
sense with
58:09
what i what i described as opportunism
58:12
now it so happens that i did
58:13
spend some time with uh set theorists
58:18
uh oh i'm not a set there's that that
58:20
marks me as an
58:22
outlier among number theorists i spent a
58:24
week with a bunch of set theorists
58:26
including
58:27
hugh wooden and my understanding was
58:29
that they wanted to find the axiom
58:31
that would get them the the answer uh to
58:35
the continuum hypothesis plus a whole
58:37
bunch of other things that
58:38
are special special interest to uh for
58:41
set theorists
58:42
and in that sense uh you know they
58:46
there's you could say call their either
58:48
tension
58:49
between pluralism and and uh
58:53
and it's opposite or maybe
58:56
maybe uh that they are working together
58:59
so that's i guess that's that's enough
59:01
of a uh
59:03
thanks so much so i'm going to suggest
59:05
that since it's 3 14 we have time
59:07
to go a little over for uh justin to
59:10
answer one more question from the
59:11
audience this is from siddharth krishna
59:13
several questions in mathematics have
59:15
been around for a lot longer before
59:18
there was a recognition
59:20
there could be alternative conflicting
59:22
sets of axioms
59:23
questions and number theory like
59:24
fermat's last theorem are like this
59:27
so what drove agreement about the
59:29
centrality
59:30
of these problems siddharth asks was the
59:33
acceptance
59:34
of one of many different axiomatic
59:36
systems just driven by intuition
59:39
or culture but even after the
59:41
recognition of alternative systems
59:43
don't we still think these questions are
59:46
central
59:47
um so i'll give you a chance to answer
59:49
that and then we'll we'll
59:52
yeah no that's a great question it's
59:54
actually i i do address
59:55
that question in in chapter two in
59:58
reference to pel's equation
60:00
um uh you know it's in
60:03
uh it's an interesting historical fact
60:06
that in
60:07
that um that you know isil
60:10
figures that were isolated across the
60:13
globe independently arrived
60:15
at the same conclusions about you know
60:17
certain like say number theoretic claims
60:20
um the you know there was a
60:24
there's a there's a suggestion in the
60:26
book that many claims of the form p
60:28
out of a mathematician's mouth are best
60:31
understood as if dentist claims like
60:33
you know if the axioms are true than
60:35
that like if you really press them no
60:37
i'm not trying to take a stand on
60:38
metaphysics or something i'm saying if
60:40
you know this this is a there's a valid
60:42
proof to this claim from the axioms
60:44
um but your point is that well what
60:46
about before
60:47
the time that there were any agreed upon
60:50
axioms i mean the axiomization of
60:51
arithmetic is a relatively recent event
60:54
how do we understand convergence on
60:56
certain claims at least
60:58
in number theory before that we can't
60:59
take them as shorthand for these sorts
61:01
of conditional claims
61:03
and my view on this is that this is an
61:06
interesting
61:07
fact and um you can start to give an
61:10
explanation of of the convergence on
61:13
arithmetic claims in terms of the
61:16
connection between arithmetic and first
61:18
order logic uh which would obviously be
61:21
uh useful to to do correctly
61:25
uh in in avoiding predators for example
61:27
uh first order logic about objects in
61:29
our environment
61:30
now that won't get you that far it's not
61:32
going to get you to things like about
61:33
primes and so forth
61:35
but that is something that's true also
61:38
in the moral case so
61:39
for example i mean michelle's own work
61:41
actually you know talks about
61:43
um you know uh the extent to which
61:47
um there are norms that are
61:49
cross-cultural and the extent to which
61:52
um uh you can find non-trivial claims
61:56
that it's it it seems like
61:58
uh people have independently arrived at
62:01
despite their mutual isolation what
62:03
would be really striking
62:06
is if beyond the kinds of claims we see
62:09
in the ethical case which of course
62:11
don't begin to settle all the kinds of
62:13
ethical
62:14
debates we have you saw this kind of
62:17
convergence on things like
62:18
choice among totally independent people
62:21
independent mathematics developing you
62:24
know there's a quote from
62:25
poodlock at the end about you know
62:26
determinacy versus choice i mean it
62:28
would be very interesting if you could
62:30
somehow establish that
62:31
but unfortunately i just don't think
62:33
that's true i think that there's a lot
62:34
of contingency about how the foundations
62:36
of math
62:37
arose and it could have gone differently
62:40
in my view anyway i
62:41
i it seems to me like there's no
62:43
compelling reason to think it couldn't
62:44
have
62:45
um so that's the short version but it is
62:48
something that i discuss and i think
62:50
it's a good point to
62:51
to to have in mind in in thinking of
62:53
thinking through the kind of
62:55
simplistic if then ism that that
62:57
sometimes i uh
62:58
i feel tempted to espouse that's great
63:02
justin it's also
63:03
a great conclusion to our discussion
63:05
today before we say
63:07
goodbye and thank the panelists i want
63:08
to just remind people that to follow up
63:11
on these issues that justin's just
63:13
raised you can go into the chat box
63:15
and find the link to the bookseller it
63:17
gives you a bit of
63:18
a discount on the book and now i'd
63:21
really like to thank our panelists
63:23
justin
63:23
it's a wonderful book and it's
63:24
provocative and challenging and you
63:26
reminded us of that
63:28
david and michael and katya i want to
63:30
thank all of you for wonderful
63:32
commentary and
63:33
and challenge to uh to our author um and
63:36
i want to thank the audience for
63:38
uh for being a wonderful um sort of
63:41
backdrop for this discussion thank you
63:43
all so much
63:44
and this will bring the public portion
63:46
of the event
63:47
to to a close thanks again
63:51
thank you