## 1. Ontological Naturalism


### 1.1 Making a Causal Difference


A central thought in ontological naturalism is that all
spatiotemporal entities must be identical to or metaphysically
constituted by 
physical[3] 
entities. Many ontological naturalists thus
adopt a physicalist attitude to mental, biological, social and other such
"special" subject matters. They hold that there is
nothing more to the mental, biological and social realms than
arrangements of physical entities.


The driving motivation for this kind of ontological naturalism is
the need to explain how special entities can have physical effects.
Thus many contemporary thinkers adopt a physicalist view of the mental
realm because they think that otherwise we will be unable to explain
how mental events can causally influence our bodies and other
physical items. Similar considerations motivate ontologically
naturalist views of the biological realm, the social realm, and so
on.


It may not be immediately obvious why this need to account for
physical effects should impose any substantial naturalist constraints
on some category. After all, there seems nothing *a priori*
incoherent in the idea of radically unscientific
"supernatural" events exerting a causal influence on
physical processes, as is testified by the conceptual cogency of
traditional stories about the worldly interventions of immaterial
deities and other outlandish beings.


However, there may be *a posteriori* objections to such
non-natural causal influences on the physical world, even if there are
no *a priori* objections. We shall see below how modern
scientific theory places strong restrictions on the kinds of entities
that can have physical effects. Given that mental, biological and
social phenomena do have such effects, it follows that they must
satisfy the relevant restrictions.


Note how this kind of argument bites directly only on those
categories that do have physical effects. It places no immediate
constraints on categories that lack any such effects, which arguably
include the mathematical and modal realms, and perhaps the moral
realm. We shall return to the question of whether there are any
further reasons for ontologically naturalist views about such putatively
non-efficacious categories in sections 1.7
and 1.8 below.


### 1.2 Modern Science and Causal Influence


There is an interesting history to modern science's views
about the kinds of things that can produce physical effects (Papineau 2001). It will
be worth rehearsing this history in outline, if only to forestall a
common reaction to ontological naturalism. It is sometimes suggested
that ontological naturalism rests, not on principled grounds, but on
some kind of unargued commitment, some ultimate decision to nail
one's philosophical colours to the naturalist
mast.[4] And
this diagnosis seems to be supported by the historical contingency of
ontologically naturalist doctrines, and in particular by the fact that they have
become widely popular only in the past few decades. However,
familiarity with the relevant scientific history casts the matter in a
different light. It turns out that naturalist doctrines, far from
varying with ephemeral fashion, are closely responsive to received
scientific opinion about the range of causes that can have physical
effects.


A short version of this history runs like this: (1) the mechanistic
physics of the seventeenth century allowed only a very narrow range of
such causes; (2) early Newtonian physics was more liberal, and indeed
did not impose any real restrictions on possible causes of physical
effects; (3) however, the discovery of the conservation of energy in
the middle of the nineteenth century limited the range of possible
causes once more; (4) moreover, twentieth-century physiological
research has arguably provided evidence for yet further
restrictions.


Let us now rehearse this story more slowly.


(1) The "mechanical philosophers" of the early
seventeenth century held that any material body maintains a constant
velocity unless acted on, and moreover held that all action is due to
impact between one material particle and another. So stated, the
mechanical philosophy immediately precludes anything except impacting
material particles from producing physical effects. Leibniz saw this
clearly, and concluded that it discredited Descartes'
interactive dualism, which had a non-material mind influencing the
physical world (Woolhouse 1985). (Of course, Leibniz did not therewith
reject dualism and embrace the physicalist view that minds are
composed of material particles, but instead opted for
"pre-established harmony". Views which avoid ontological
naturalistic views of the mind by denying that mental events have any physical
effects will be discussed further in
section 1.6 below.)


(2) At the end of the seventeenth century Newtonian physics
replaced the mechanical philosophy of Descartes and Leibniz. This
reinstated the possibility of interactive dualism, since it allowed that
disembodied forces, as well as impacts, could cause physical
effects. Newtonian physics was open-ended about the kinds of forces
that exist. Early Newtonians posited fundamental mental and vital
forces alongside magnetic, chemical, cohesive, gravitational and
impact forces. Accordingly, they took *sui generis* mental
action in the material world to be perfectly consistent with the
principle of physics. Moreover, there is nothing in the original
principles of Newtonian mechanics to stop mental forces arising
autonomously and spontaneously, in line with common assumptions about
the operation of the mind (Papineau 2001: Section 7).


(3) In the middle of the nineteenth century the conservation of
kinetic plus potential energy came to be accepted as a basic principle
of physics (Elkana 1974). In itself this does not rule out fundamental
mental or vital forces, for there is no reason why such forces should
not be "conservative", operating in such a way as to
compensate losses of kinetic energy by gains in potential energy
and *vice versa*. (The term "nervous energy" is a
relic of the widespread late nineteenth-century assumption that mental
processes store up a species of potential energy that is then released
as kinetic energy in action.) However, the conservation of energy does imply that any
such special forces must be governed by strict deterministic laws: if
mental or vital forces arose spontaneously, then there would be
nothing to ensure that they never led to energy increases.


(4) During the course of the twentieth century received
scientific opinion became even more restrictive about possible
causes of physical effects, and ruled out any *sui generis*
mental or vital causes, even of a law-governed and predictable
kind. Detailed physiological research, especially into the operation of nerve cells,
gave no indication of any physical effects that cannot be explained
in terms of basic physical forces that also occur outside living
bodies. By the middle of the twentieth century, belief in *sui
generis* mental or vital forces had become a minority view. This
led to the widespread acceptance of the doctrine now known as the
"causal closure" or the "causal completeness of
the physical", according to which all physical effects have
fully physical causes.


### 1.3 The Rise of Physicalism


This historical sequence casts light on the evolution of
ontologically naturalist doctrines. In the initial seventeenth-century
mechanical phase, there was a tension, as Leibniz observed, between
the dominant strict mechanism and interactive dualism. However, once
mechanism was replaced by a more liberal understanding of forces in the second Newtonian phase, science ceased to raise any objections to
dualism and more generally to non-physical causes of physical effects.
As a result, the default philosophical view was a non-naturalist
interactive pluralism which recognized a wide range of fundamental
non-physical influences, including spontaneous mental influences (or
"determinations of the soul" as they would then have been
called).


In the third phase, the nineteenth-century discovery of the
conservation of energy continued to allow that *sui generis*
non-physical forces can interact with the physical world, but
required that they be governed by strict force laws. *Sui
generis* mental and vital forces were still widely accepted, but
an extensive philosophical debate about the significance of the
conservation of energy led to a widespread recognition that any such
forces would need to be law-governed and thus amenable to scientific
investigation. We might usefully view this as a species of
ontological naturalism that falls short of full physicalism. Mental
and other special forces were still *sui generis* and non-physical, but even so they fell within the realm of
scientific law and so could not operate spontaneously. (As many commentators
at the time recognized, this weaker form of naturalism already
carried significant philosophical implications, particularly for the
possibility of free 
will.[5]) 


In the final twentieth-century phase, the acceptance of the causal
closure of the physical led to full-fledged physicalism. The causal
closure thesis implied that, if mental and other special causes are to
produce physical effects, they must themselves be physically
constituted. It thus gave rise to the strong physicalist doctrine that
anything that has physical effects must itself be physical.


In support of this understanding of the twentieth-century history, it is
noteworthy how philosophical arguments in favour of physicalism began to appear from the 1950s onwards. Some of these arguments appealed
explicitly to the causal closure of the physical realm (Feigl 1958,
Oppenheim and Putnam 1958). In other cases, the reliance on causal
closure lay below the surface. However, it is not hard to see that
even in these latter cases the causal closure thesis played a crucial
role.


Thus, for example, consider J.J.C. Smart's (1959) thought
that we should identify mental states with brain states, for otherwise
those mental states would be "nomological danglers" which
play no role in the explanation of behaviour. Or take David
Lewis's (1966) and David Armstrong's (1968) arguments
that, since mental states are picked out by their causal roles, and
since we know that physical states play these roles, mental states
must be identical with those physical states. Finally, consider Donald
Davidson's (1970) argument that, since the only laws governing
behaviour are those connecting behaviour with physical antecedents,
mental events can only be causes of behaviour if they are identical
with those physical antecedents. At first sight, it might not be
obvious that these arguments require the causal closure thesis. But a
moment's thought will show that none of these arguments would
remain cogent if the closure thesis were not assumed, and it were thus
left open that some physical effects (the movement of matter in arms,
perhaps, or the firings of the motor neurones which instigate those
movements) were not determined by prior physical causes at all, but
by *sui generis* mental causes.


Quantum mechanics is often taken to involve a departure from
determinism. Sometimes it is suggested that indeterminism of this
sort creates room for *sui generis* non-physical causes to
influence the physical world. However, even if quantum mechanics
implies that some physical effects are themselves undetermined, it
provides no reason to doubt a quantum version of the causal closure
thesis, to the effect that the *chances* of those effects are
fully fixed by prior physical circumstances. And this alone is enough
to rule out *sui generis* non-physical causes. For such *sui
generis* causes, if they are to be genuinely efficacious, must
presumably make an independent difference to the chances of physical
effects, and this in itself would be inconsistent with the quantum
causal closure claim that such chances are already fixed by prior
physical circumstances. Once more, it seems that anything that makes a
difference to the physical realm must itself be physical.


### 1.4 Reductive and Non-Reductive Physicalism


It will be worth being explicit about the way the causal closure
principle supports physicalism. First we assume that mental causes
(biological, social, ...) have physical effects. Then the causal
closure principle tells us that those physical effects have physical
causes. So, in order to avoid an unacceptable proliferation of causes
for those physical effects (no "systematic
overdetermination"), we need to conclude that the mental
(biological, social, ...) causes of those effects are not
ontologically separate from their physical causes.


However, even if this general line of argument is accepted, there
is room for differing views about exactly what its denial of
ontological separateness requires. Let us agree that causes are
"events" (or "facts") that involve
instantiations of 
properties.[6]
 So, if some special cause is not
ontologically separate from some physical cause, the property
instantiations that it involves cannot themselves be ontologically
separate from the property instantiations involved in the physical
cause. At this point, however, there are divergent views about how
tight a constraint this imposes.


One school holds that it requires type-identity, the strict
identity of the relevant special properties with physical
properties. On the other side stand "non-reductive"
physicalists, who hold that the causal efficacy of special causes will
be respected as long as the properties they involve are
"realized by" physical properties, even if they are not
reductively identified with them.


Type-identity is the most obvious way to ensure the
non-separateness of special and physical causes: if exactly the same
properties comprise the special and physical cause, the two causes
will themselves be fully identical. Still, type-identity is a very
strong doctrine. Type identity about thoughts, for example, would
imply that the property of thinking about the square root of two is
identical with some physical property. And this seems highly
implausible. Even if all human beings with this thought must be
distinguished by some common physical property of their
brains--which itself seems unlikely--there remains the
argument that other life-forms, or intelligent androids, will also be
able to think about the square root of two, even though their brains
may share no significant physical properties with ours (Fodor 1974,
Bickle 2013).


This "variable realization" argument has led many
philosophers to seek an alternative way of reconciling the efficacy of
mental and other special causes with the causal closure thesis, one
which does not require the strict identity of non-physical and
physical properties. The general idea of this "non-reductive
physicalism" is to allow that instantiations of a given special
property will always be grounded in or metaphysically determined by
instantiations of physical properties, but to add that these
"realizing" physical properties might be different in
different cases. So, for example, any being who thinks about the
square root of two will do so in virtue of instantiating some physical
properties, but these can be different physical properties in
different cases--in one human being it may be one set of neural
arrangements, in another a different set, and in other life forms it
might involve nothing like neural properties at all.


There are various more detailed ways of filling out this idea of
non-reductive physicalism. A common feature is the requirement that
special properties should metaphysically supervene on physical
properties, in the sense that any two beings who share the realizing
physical properties will necessarily share the same special
properties, even though the physical properties which so realize the
special ones can be different in different beings. This arguably
ensures that nothing more is required for any specific instantiation
of a special property than its physical realization--even God
could not have created your brain states without thereby creating your
feelings--yet avoids any reductive identification of special
properties with physical ones. (This is a rough sketch of the
supervenience formulation of physicalism. For more see Stoljar
2015.)


Some philosophers object that non-reductive physicalism does not in
fact satisfy the original motivation for physicalism, on the grounds
that it does not really reconcile the efficacy of mental and other
special causes with the causal closure thesis (Kim 1998, Robb and Heil
2014: Section 6). According to non-reductive physicalism, special
properties are not type-identical with any strictly physical
properties, even though they supervene on them. And this then seems to
imply that any given special cause will be distinct from the
physical cause that realizes it, since it involves the
instantiation of a different property. (The property of thinking about
the square root of two is definitely a different property from the
neural property that realizes it in me, say, since another being could
share the former property without sharing the latter.)


The opponents of non-reductive physicalism then insist that this
gives us an unacceptable proliferation of causes for the physical
effects of special causes after all--both the physical cause
implied by the causal closure thesis and the distinct special
cause. In response, advocates of non-reductive physicalism respond
that there is nothing wrong with such an apparent duplication of
causes if it is also specified that the latter metaphysically
supervene on the former.


The issue here hinges on the acceptability of different kinds of
systematic overdetermination (Bennett 2003). All can agree that it
would be absurd if the physical effects of special causes always had
two metaphysically independent causes. Plugging this into the causal
closure argument for physicalism, we can conclude that there can be
no metaphysically independent non-physical causes (such as Cartesian
dualist mental causes) for effects that already have full physical
causes. However, even if "strong overdetermination" by
two ontologically independent causes is so ruled out, this does not
necessarily preclude "weak overdetermination" by both a
physical cause and a metaphysically supervenient special cause.
Advocates of non-reductive physicalism argue that this kind of
overdetermination is benign and consistent with the causal
argument's denial of strong overdetermination, since now the
two causes are not metaphysically distinct--the special cause
isn't genuinely additional to the physical cause (nothing more
is needed for your feelings than your brain states).


### 1.5 Physicalist Downwards Causation


Some recent writers have explored a different way of upholding the
causal efficacy of non-reduced mental and other special causes. Where
the "benign overdetermination" option says certain effects
have a special cause *as well as* a physical cause, these
writers urge that some effects have a special cause *instead*
of a physical cause.


Suppose a pigeon pecks at crimson tiles. Is the pecking caused by
the specific shade, crimson, or the more generic colour, red? The
natural answer is that it depends. If the pigeon pecks only at crimson
tiles, and not at other shades of red, then it is the crimsonness that
is causing the pecking; but if the pigeon pecks at any shade of
red, it is the redness. Examples like these have led a number of
writers to require that causes be *proportional* to their
effects (Yablo 1992; Menzies 2008; List and Menzies 2009, 2010). We
should attribute the effect to that property that is specific enough
to suffice for it, but no more specific than that.


This suggests that sometimes special causes and *not* their
physical realizers might be responsible for physical effects. Suppose
I want to hail a taxi, and that this desire is realized by some brain
state, and that I then wave my arm. It seems that it will then be the
desire that is proportional to the waving, not the brain state, in
that I would still have waved my arm if my desire had been differently
realized, though not if I hadn't had the desire at all.


Some will say that in such cases the desire
causally *explains* the waving, but that it is still the brain
state that *causes* it. This thought appeals to the intuition
that real causal relations are always constituted by basic physical
interactions, by bits of matter bumping into each other. But this
intuition is not decisive, and a number of theoretical considerations
speak against it. For instance, the "difference-making"
account of causation developed by James Woodward implies that generic
properties often eclipse their more specific realizations as
causes (Woodward 2005), as does the view that causation is a
relatively macroscopic phenomenon whose temporal asymmetry is
analogous to the temporal asymmetries of thermodynamics (Loewer 2007,
Papineau 2013).


It is worth observing that physicalists who advocate this kind of
downwards special causation are in some danger of sawing off the
branch they are sitting on, in that they now seem to be advocating
counter-examples to the causal closure of the physical. If my
arm's waving is caused by my desire and not by my brain state,
it would seem to have a mental cause and not a physical cause, and thus run counter to
the closure thesis that every physical effect has some fully physical
cause. Since the original rationale for embracing physicalism was
supposed to be science's discovery that the physical realm is
causally closed, this may seem to leave physicalists in an awkward
position.


However, even if the examples of "downwards" causation
do undermine the thesis of the causal closure of the physical, it
may still be possible to rework the original argument for
physicalism in terms of closure under nomological determination,
rather than causal
 closure.[7]
 Nothing in the idea of proportional
causation threatens the idea that modern physics shows that all
physical effects (or their chances) are fully nomologically
determined by physical antecedents, even if they aren't always caused by them. And this in itself argues that metaphysically independent special causes would imply an unacceptable strong overdetermination of physical events.


### 1.6 Conscious Properties and Closure Arguments


Some philosophers take there to be compelling arguments against the
view that *conscious* states are metaphysically constituted by
physical states. This rejection of physicalism about conscious properties certainly
has the backing of intuition. (Don't zombies--beings who
are physically exactly like humans but have no conscious
life--intuitively seem metaphysically possible?) However,
whether this intuition can be parlayed into a sound argument is a
highly controversial issue, and one that lies beyond the scope of
this entry. A majority of contemporary philosophers probably hold
that physicalism can resist these
arguments.[8]
But a significant minority take the other side.


This minority has a number of options. One is to hold that conscious properties are "epiphenomenal" and do not exert any influence on brain processes or subsequent behaviour (Jackson 1982, 1986; Chalmers
1996).[9] Another is to embrace the "overdeterminationist" view that the physical results of conscious causes are always strongly overdetermined , both by their normal physical antecedents and by the metaphysically independent conscious causes (Mellor 1995, Kroedel 2015). Still, neither of these positions is attractive. They require us to posit odd causal structures, either involving a species of effects that are never themselves causes, or a species of effects that are always strongly overdetermined. Given that nature displays no other examples of such causal structures, general principles of theory choice would seem to argue against both epiphenomenalism and overdeterminationism.


In consequence, a yet further option has become increasingly popular among those who are persuaded that consciousness must transcend the physical realm. This is the Russellian monist option that locates conscious properties among the basic categorical properties that play the dispositional roles described by physical science. This option has the virtues of separating consciousness from the world described by physics without positing any special causal structures operating in the brain (Alter and Pereboom 2019).


It is an interesting question whether Russellian monism is necessarily opposed to physicalism rather than a special case of it (Montero 2015, Brown 2017). In any case, we should note that Russellian monism is designed to conform to the causal (or determinational) closure of the physical realm, as indeed are epiphenomenalism and overdeterminationism. It is striking that nearly all contemporary views of the mind-brain relations are naturalist at least to the extent that they respect this closure thesis. Strongly interactionist views that allow the conscious mind to make an independent difference to the physical world have few defenders nowadays (but see Lowe 2000, 2003; Steward 2015).


### 1.7 Moral Facts


G.E. Moore's well-known "open question" argument
is designed to show that moral facts cannot possibly be identical to
natural facts. Suppose that the natural properties of some situation
are completely specified. It will always remain an open question,
argued Moore, whether that situation is morally good or bad (Moore
1903).


Moore took this argument to show that moral facts constitute a
distinct species of non-natural fact. However, any such non-naturalist
view of morality faces immediate difficulties, deriving ultimately
from the kind of causal closure thesis discussed above. If all
physical effects are due to a limited range of physically-grounded
natural causes, and if moral facts lie outside this range, then it
follow that moral facts can never make any difference to what happens
in the physical world (Harman 1986). At first sight this may seem
tolerable (perhaps moral facts indeed don't have any physical
effects). But it has awkward epistemological consequences. For beings
like us, knowledge of the spatiotemporal world is mediated by physical
processes involving our sense organs and cognitive systems. If moral
facts cannot influence the physical world, then it is hard to see how
we can have any knowledge of them.


The traditional non-naturalist answer to this problem is to posit a
non-natural faculty of "moral intuition" that gives us
some kind of direct access to the moral realm (as explained in Ridge
2014: Section 3). However, causal closure once more makes it
difficult to make good sense of this suggestion. Presumably at some
point the posited intuitive faculty will need to make a causal
difference in the physical world (by affecting what people say and
do, for example). And at this point the causal closure argument will
bite once more, to show that a non-natural intuitive faculty would implausibly imply that some of our actions are strongly overdetermined by two metaphysically independent antecedents.


Moral non-naturalism has had something of a revival in recent years, with defenders including Russ Shaffer-Landau (2003), Ralph Wedgwood (2007), Derek Parfit (2011) and David Enoch (2011). Still, the challenge of accounting for our access to non-natural moral facts remains, and it is debatable whether any of these writers has found a satisfactory alternative to a causally problematic faculty of intuition. Perhaps the most developed suggestion is Enoch's (2011) appeal to the indispensability of non-natural moral facts to moral reasoning, a line of argument that is analogous to Hilary Putnam's case for non-natural mathematical objects, to be discussed in the next section below. But Enoch's appeal arguably faces many of the same general objections as Putnam's argument, as well as objections specific to the moral realm (see Leng 2016).


In light of the difficulties facing moral non-naturalism, most
contemporary moral philosophers opt instead for some species of
naturalist view. We can divide the naturalist options here into two
broad categories: irrealist and realist. Irrealist moral naturalists
aim to account for moral discourse by offering naturalist accounts of
the social and linguistic and practices that govern it, but without
supposing that moral utterances report on moral facts with a
substantial independent existence (Joyce 2015). By contrast,
naturalist moral realists agree with moral non-naturalists that
substantial moral facts exist, but seek to locate them in the natural
realm rather than in some *sui generis* non-natural realm
(Lenman 2014).


Both these broad categories have further sub-divisions. Among the
irrealists, we can distinguish explicitly non-cognitivist views like
emotivism and prescriptivism which deny that moral judgements express
beliefs (Hare 1952, Blackburn 1993, Gibbard 2003) from cognitivist
views that accept that moral judgements do express beliefs but deny a
substantial reality to the putative facts to which they answer; and
among the latter cognitivist views we can distinguish error-theoretic
fictionalist options which view moral judgements as simply false
(Mackie 1977, Kalderon 2005) from projectivist options which hold that
moral discourse is sufficiently disciplined for its judgements to
qualify for a species of truth even though they do not report on
independently existing causally significant facts (Wright 1992, Price
2011). 


Naturalist moral realism also comes in different varieties. In
recent debates two versions have figured prominently; "Cornell
realism", which includes moral facts among the causally
significant facts but resists their type-reducibility to non-moral
facts (Sturgeon 1985, Boyd 1988), and "moral
functionalism" which is happy to equate moral facts with
straightforwardly descriptive facts (Jackson 1998). 


Any kind of moral naturalist realist needs to reject Moore's
open question argument. There are two alternatives here. One is to
insist that Moore's posited openness is relatively superficial,
and that there is no principled barrier to inferring moral facts *a
priori* from the non-moral natural facts, even if such inferences
will sometimes require a significant amount of information and reflection. The
other is to argue that the constitution of moral facts by non-moral
natural facts is an *a posteriori* matter, akin to the relation
between water and H2O, and that therefore Moore's
openness only points to a conceptual gap, not a metaphysical one
(Ridge 2014: Section 2).


This sub-section has focused on morality. But there are other
topics which arguably involve matters of value, such as aesthetics, the normativity of theoretical and practical reason, and so on. The constraints placed
on theories of moral facts by naturalist considerations will
apply, *mutatis mutandis*, in these areas too, militating
against theories that posit non-natural value-bearing facts and in
favour of naturalist alternatives, of either a realist or irrealist
stripe.


### 1.8 Mathematical Facts


Mathematics raises many of the same issues for ontological
naturalism as morality. Mathematical claims typically involve a
commitment to abstract objects like numbers and sets, eternal entities
outside space and time. This might seem cogent at first sight, but
once more epistemological difficulties quickly arise. Abstract objects
can have no effects in the spatiotemporal world. How then can
spatiotemporal being like ourselves come to know about them?


However the mathematical case does not fully parallel the moral
one. One of the options in the moral case was naturalist realism,
which reads moral claims as about natural facts which play causal
roles in the spatiotemporal world. However, given the explicit
commitment of mathematical claims to abstract objects without
spatiotemporal location, this option does not seem available in the
mathematical case (but see Maddy 1990). So we seem required to choose
between non-naturalist realism about non-spatiotemporal mathematical
entities or naturalist irrealism.


As in the moral case, non-naturalist realism faces epistemological
challenges, to which one response is to posit a
faculty of intuition which gives us access to the abstract
mathematical realm. Kurt Godel arguably favoured a view along
these lines (Parsons 1995). However, once more this only seems to push
the problem back. There seems no good way for the posited faculty to
bridge the causal gap between the abstract and the spatiotemporal
realms without generating implausible overdetermination.


An alternative version of non-naturalist realism aims to vindicate
mathematical and modal claims as essential parts of our best overall
theories of the world. According to this line of thought, defended by
Hilary Putnam, our empirically best-supported scientific theories
commit us to mathematical entities; ergo, we are entitled to believe
in such entities (Putnam 
1971).[10]


However, it is contentious whether our best-supported empirical
theories do commit us to abstract mathematical entities. The most
prominent version of naturalist irrealism about mathematics, Hartry
Field's fictionalism, disputes precisely this claim. According
to Field, we can construct "nominalist"
versions of scientific theories that avoid commitment to abstract
mathematical objects yet are explanatorily
superior to the "platonist" alternatives. Field argues
that we do not have to regard mathematics itself as literally true in
order to understand its use in science and other applications. Rather
it can be viewed as a "useful fiction" which facilitates
inferences between nominalistic scientific claims, but is not itself
implicated in our most serious beliefs about the world (Field 1980,
1989).


Not all philosophers of mathematics are convinced that Fieldian
nominalizations are available to replace all scientific references to
abstract mathematical objects. In particular, some have argued that
certain explanations of nominalist facts make essential reference to
abstract objects (Baker 2005, Batterman 2010). In response, others
have sought to show that there are in fact good nominalist
explanations of the facts in question (Daly and Langford 2009,
Butterfield 2011, Menon and Callender 2013). In any case, it is not
clear that Field's metaphysical stance requires a full execution
of his nominalizing programme, as opposed to a case for its cogency:
difficulties in constructing nominalist theories can always be
attributed to limitations of human ingenuity rather than the reality
of abstract mathematical objects (Leng 2013).


Perhaps the most popular contemporary alternative to fictionalism
is the version of non-naturalist realism offered by the neo-Fregean
thesis that abstract mathematical beliefs can be justified as analytic
truths that follow from logic and certain meaning stipulations. The
idea has been most fully developed in connection with arithmetic,
where Crispin Wright has shown how Peano's postulates can be
derived within the framework of second-order logic from nothing except
the Humean principle that the same number attaches to equinumerous
concepts. According to Wright, this principle can be viewed as an
implicit definition of our concept of number. If this is right, then
it has indeed been shown that arithmetic, and therewith the existence
of numbers as abstract objects, follows from logic and definition
alone (Wright 1983, Hale and Wright 2003). There has also been some
attempt to extend the programme to mathematical analysis (Shapiro
2000, Wright 2000).


One query that might be put to this programme is whether the Humean
principle and analogous assumptions can really be viewed as analytic
definitions. If they commit us to numbers and other abstract objects
whose existence cannot established without them, then they are
arguably doing more than definitions should. A related issue is
whether the overall neo-Fregean position is properly viewed as
realist. From its perspective, the role of abstract mathematical
objects in the overall scheme of things seems to be exhausted by their
making our mathematical statements true; given this, it might seem
better to classify it as a species of irrealism (MacBride 2003).


To complete this discussion of ontological naturalism, let us
briefly consider the realm of modality, understood as the subject
matter of claims that answer to something more than
actuality. Modality raises many of the same issues as mathematics, but
the topic is complicated by the prior question of the content of modal
claims, and in particular about whether they quantify over non-actual
possible worlds. Whereas there is little dispute about the initial
semantic analysis of mathematical claims--they purport to refer
to abstract numbers, sets, functions and so on--there is somewhat
less unanimity about the possible worlds analysis of modal claims
(Nolan 2011b).


To the extent that modal claims do quantify over possible worlds,
the ontological points made about mathematics apply well here too.
Since non-actual worlds do not inhabit our spatiotemporal realm, an
ontologically naturalist realism seems to be ruled out from the
start. The remaining alternatives are irrealism or non-naturalist
realism. The former alternative has been explored in recent years by
modal fictionalists (Rosen 1990; Nolan 2011a). The options under
the latter heading meet the same epistemological challenges as in
the mathematical case: brute intuition faces causal problems; it is
contentious whether we should take our best scientific theories to
commit us to possible worlds; and, if modal knowledge is to be
analytically *a priori*, on the model of mathematical
neo-Fregeanism, then it is not obvious that it can take us to
knowledge of possible worlds construed realistically. 


## 2. Methodological Naturalism


### 2.1 Philosophy and Science


In what follows, "methodological naturalism" will be
understood as a view about philosophical practice. Methodological
naturalists see philosophy and science as engaged in essentially the
same enterprise, pursuing similar ends and using similar methods.


Among philosophers of religion, "methodological
naturalism" is sometimes understood differently, as a thesis about natural
scientific method itself, not about philosophical method. In this
sense, "methodological naturalism" is the view that religious
commitments have no relevance within science: natural science itself
requires no specific attitude to religion, and can be practised just
as well by adherents of religious faiths as by atheists or agnostics
(Draper 2005). This thesis is of interest to philosophers of religion
because many of them want to deny that methodological naturalism in
this sense entails "philosophical naturalism", understood
as atheism or agnosticism. You can practice natural science in just
the same way as non-believers, so this line of thought goes, yet
remain a believer when it comes to religious questions. Not all defenders of religious belief endorse this kind of
"methodological naturalism", however. Some think that religious
doctrines do make a difference to scientific practice, yet are
defensible for all that (Plantinga 1996). In any case, this kind of
"methodological naturalism" will not be discussed further
here. Our focus will be on the relation between philosophy and
science, not between religion and science.


What exactly is involved in adopting a methodologically naturalist attitude to the relation between philosophy and science? In order to focus what follows, let us understand methodological naturalism as the specific claim that philosophy and science are both concerned to establish
synthetic knowledge about the natural world, and moreover to achieve
this by *a posteriori* investigation.


Methodological naturalists will of course allow that
there are some differences between philosophy and science. But they
will say that these are relatively superficial, a matter of focusing on different
questions rather than any radical difference of approach. For one thing, philosophical questions are often
distinguished by their great generality. Where scientists think about
viruses, electrons or stars, philosophers think about spatiotemporal
continuants, properties, causation or time, categories that
structure all our thinking about the natural world. Another common feature of philosophical questions is that they involve some kind of
theoretical tangle. Our thinking supports different lines of thought that lead
to conflicting conclusions. Progress requires an unravelling of
premises, including perhaps an unearthing of implicit assumptions
that we didn't realize we had.


For both these reasons, philosophical issues are rarely resolved by new observational data. The normal philosophical predicament is that we have all the observational data we could want, but aren't sure of the best way of accommodating them. Still, methodological naturalists will urge, this doesn't mean that a posteriori synthetic theories are not the aim of philosophy. A theory produced by unravelling the theoretical tangles surrounding some general category can still be an a posteriori synthetic theory, even if no new observational findings went into its construction.


From the methodological naturalist perspective, then, philosophical views are synthetic claims that answer to the overall tribunal of a posteriori observational evidence. The obvious objection to this view, however, is that it does not accord with philosophical practice. In particular, it seems in tension with the central role that *intuitions* play in philosophy. The typical way to assess philosophical views is arguably to test them against intuitive judgements about possible cases, not against *a posteriori* observational data. So, for example, the description theory of names is challenged by our intuitions about Kripke's imagined counterexamples, the tripartite theory of knowledge by our intuitive reactions to Gettier cases, and so on. At first pass, this certainly suggests that philosophy is centrally concerned with the analysis of everyday concepts, not the construction of synthetic theories: it is using intuitions about possible cases to uncover the structure implicit in our concepts. The reliance on intuitions thus argues that, far from delivering synthetic *a posteriori* knowledge, philosophy uses a priori methods to deliver analytic conclusions.


Methodological naturalists can respond to this challenge at a number of points. For one thing, they can ask whether intuitions really do play a central role in philosophy. For another, they can query whether, even if they do, they are really *a priori* intuitions. And finally, they can dispute whether, even if the intuitions are *a priori*, they are genuinely analytic. It will be convenient to consider these different responses in reverse order.


### 2.2 The Canberra Plan


One influential strand in contemporary philosophy is quite explicit in claiming that analytic intuitions play a central role in philosophy. Inspired by David Lewis, and led by Frank Jackson and David Chalmers, this is widely known as the "Canberra Plan". On this conception, philosophy starts with an initial analysis
of concepts employed by everyday thought, such as *free will*,
say, or *knowledge*, or *moral value*, or *conscious
experience*. Once this stage has been completed, philosophy
can then turn to "serious metaphysics" to demonstrate how
a limited number of ingredients (for example, physical ingredients)
might satisfy these everyday concepts. This second stage is likely to
appeal to synthetic *a posteriori* scientific knowledge about
the fundamental nature of reality. But the purely analytic first
stage, according to the Canberra plan, also plays an essential part in setting the
agenda for the subsequent metaphysical investigation.(Jackson 1998, Braddon-Mitchell and Nola 2009, Chalmers 2012.)


An initial question about this programme relates to its scope. It
is by no means clear that all, or indeed any, philosophically
interesting concepts can be subject to the relevant kind of
analysis. Jackson himself assumes that pretty much all everyday
concepts can be analysed as equivalent to "the kind which
satisfies such-and-such folk
assumptions".[11] 
But it is arguable that many everyday
concepts are not so constituted, but rather have their semantic
contents fixed by observational, causal or historical relations to
their referents.


Still, we can let this point pass. Even if we suppose, for the sake
of the argument, that a range of philosophically interesting everyday
concepts do have their contents fixed in the way the Canberra
programme supposes, there are further objections to its understanding
of philosophical method.


Let us look a bit more closely at the posited initial
agenda-setting stage of the Canberra programme. Upon closer
examination, it is not clear that this makes any essential appeal to
analytic knowledge. Defenders of the Canberra plan
characteristically explain their strategy in terms of "Ramsey
sentences" (e.g., Jackson 1998: 140). Suppose \(T(F)\) is the
set of relevant everyday assumptions involving some philosophically
interesting concept. For example, *F* may be the concept
belief, and the assumptions in *T* may include
"characteristically caused by perceptions",
"combines with desires to generate actions", and
"has causally significant internal structure". Then the
Ramsey sentence corresponding to \(T(F)\) is "\(\exists!\Phi
(T(\Phi))\)".[12] 
For the concept belief, this would say: there is some unique kind that is characteristically caused by perceptions, combines with desires to generate actions, and has causally significant internal structure.


 The Canberra suggestion is then that, once we
have articulated the relevant Ramsey sentence, we will be in a
position to turn to serious metaphysics to identify the underlying
nature of the F that plays the relevant role.


However, if this is the Canberra procedure, then there is no reason
to think of it as appealing to analytic knowledge at any stage. A
Ramsey sentence of the kind at issue says that there actually exists
some entity satisfying certain requirements (there is a kind of state
that is caused by perceptions ...). Sentences like this make
eminently synthetic and falsifiable claims. It is not a matter of
definition that humans actually have internal states that play the
causal role associated with the concept of belief. The Canberra
strategy thus seems no different from the prescription that philosophy
should start with the synthetic theories endorsed by everyday thought,
and then look to our more fundamental theories of reality to see what,
if anything, makes these everyday theories true. This seems entirely
in accord with methodological naturalism--philosophy is in the
business of assessing and developing synthetic theories of the
world.


The crucial point here is that Ramsey sentences don't define
concepts like belief, but eliminate them. They give us a way of saying
what our everyday theories say without using the relevant concept
(there is a kind of state that is caused by perceptions ...) If
we want definitions, then we need "Carnap sentences", not
Ramsey sentences (Lewis 1970). The Carnap sentence corresponding to
"\(\exists!\Phi(T(\Phi))\)" is "If
\(\exists!\Phi(T(\Phi)\), then \(T(F)\)". (*If* there is
a kind of state that is caused by perceptions ..., *then*
it's belief.) Carnap sentences can plausibly be viewed as akin
to stipulations that fix the reference of the relevant concepts, and
to that extent as analytic claims that can be known *a
priori*. But this certainly does not mean that Ramsey sentences,
which make substantial claims about the actual world, are also
knowable via *a priori* analysis. (Note how you can accept a
conditional Carnap sentence even if you reject the corresponding
unconditional Ramsey sentence. You can grasp the folk concept of
belief even if you reject the substantial folk theory of belief.)


Can't defenders of the Canberra programme argue that it is
the analytic Carnap sentences that are crucial in setting
philosophical agendas, not the synthetic Ramsey sentences? But this
seems wrong. We will want to know about the fundamental nature of
belief if we suppose that there is a kind of state that is
characteristically caused by perceptions, and so on. That is certainly
a good motivation for figuring out whether and how the fundamental
components of reality might constitute this state. But the mere fact
that everyday thought contains a concept of such a state in itself
provides no motivation for further investigation. (In effect, the
function of a Carnap sentence is to provide a shorthand for talking
about the putative state posited by the corresponding Ramsey
sentence. It is hard to see how any important philosophical issues
could hang on the availability of such a shorthand.)


To emphasize the point, consider the everyday concept of a soul,
understood as something that is present in conscious beings and survives
death. This concept of a soul can be captured by the analytic Carnap
sentence: "If certain entities inhabit conscious beings and
survive death, then they are souls". Accordingly, this Carnap
sentence will be agreed by everybody who has the concept of soul,
whether or not they believe in souls. Yet this Carnap sentence will
not *per se* raise any interesting metaphysical questions for
those who deny the existence of souls. These deniers won't start
wondering how the fundamental constituents of reality realize
souls--after all, they don't believe in souls. It is only
those who accept the corresponding Ramsey sentence ("There are
parts of conscious beings that survive death") who will see a
metaphysical issue here. Moreover, the Ramsey sentence will pose this
metaphysical issue whether or not it is accompanied by some analytic
Carnap sentence to provide some shorthand alternative terminology. In
short, the methodological naturalist can insist that anybody
interested in "serious metaphysics" should start by
articulating the substantial existential commitments of our folk
theories, as articulated in their synthetic Ramsey sentences. Any
further analytic conceptual commitments add nothing of philosophical
significance.


The point generalizes beyond the contrast between Ramsey and Carnap
sentences. On reflection, it is hard to see why any purely
definitional analytic truths should matter to philosophy. Synthetic
everyday truisms can certainly be philosophically significant, and so
their articulation and evaluation can play an important philosophical
role. But there is no obvious motive for philosophy to concern itself
with definitions that carry no implications about the contents of
reality. 


### 2.3 Synthetic *A Priori* Intuitions?


It is worth noting that not all philosophers who advertise themselves as engaging in "conceptual
analysis" are committed to the idea that this involves analytic a priori knowledge. In many cases philosophers who describe themselves in this way go on to explain that in their view "conceptual
analysis" is a matter of articulating synthetic claims and assessing them against a posteriori evidence. A particularly clear version of this picture of conceptual analysis is offered by Robert Brandom (2001). Similarly, recent advocates of "conceptual engineering" are explicit that in their view "concepts" embody substantial commitments which are open to criticism on a posteriori grounds (Cappelen 2018, Cappelen, Plunket and Burgess 2019). In the end, it is not clear what differentiates "conceptual analysis" in this sense from the a posteriori assessment of theories. In any case, this species of conceptual analysis seems perfectly consistent with methodological naturalism. (See also Goldman 2007.)


Other philosophers are also explicit that "conceptual
analysis" issues in synthetic claims, but simultaneously regard
it as a source of *a priori* knowledge (e.g. Jenkins 2008,
2012). This combination of views is less straightforward. In
particular, it seems open to the traditional query: how is such
synthetic *a priori* knowledge possible? If some claim is not
guaranteed by the structure of our concepts, but answers to the nature
of the world, then how is it possible to know it without *a
posteriori* evidence?


Yet other philosophers distance themselves from talk of conceptual
analysis, but even so feel that philosophical reflection is a source
of synthetic *a priori* intuition (Sosa 1998, 2007). They too
would seem to face the traditional query of how synthetic *a
priori* knowledge is possible.


In this context, Timothy Williamson has recently argued that the
traditional distinction between *a priori* and *a
posteriori* knowledge is less than clear-cut, and in particular
that it breaks down in connection with the intuitions on which
philosophers rely. In Williamson's view, there is a distinctive
philosophical method in which intuitive judgements play a central
role, but there is no warrant for classifying the relevant intuitions
as *a priori* rather than *a posteriori* (Williamson
2013).


However, it is arguable that this does not so much address as
by-pass the underlying question. Perhaps philosophical intuitions are
not best classified as clearly "*a priori*". But,
if philosophy's distinctive methodology relies on synthetic
intuitions, this still seems to call for some explanation of their reliability.


Doubts about the reliability of philosophical intuitions have been
amplified over the past few years by the findings of
"experimental philosophy". Empirical studies have
indicated that many central philosophical intuitions are by no means
universal, but rather peculiar to certain cultures, social classes and
genders (Knobe and Nichols 2008, 2017). This variability of intuitions is in
obvious tension with their reliability. If different people have
opposed philosophical intuitions, then it cannot be that intuitions of
this kind are always true.


Timothy Williamson has responded to this challenge from
experimental philosophy by suggesting that, while the intuitions of
ordinary people on philosophical matters might be unreliable, those of
philosophers in particular can be trusted. In his view, a proper
philosophical training winnows out mistaken philosophical reactions
(2007: 191; 2011). However, this position still seems to call for a
positive explanation of how synthetic philosophical knowledge might be
established without *a posteriori* evidence, even if it is
restricted to trained philosophers.


The possibility of such an explanation is not of course to be
dismissed out of hand. There is no contradiction in
the idea of experience-independent access to synthetic truths. After
all, until the eighteenth century no modern philosopher doubted that
God had bestowed on us powers of reason that would enable us to
arrive at perception-independent knowledge of a range of synthetic
claims. Even if few contemporary philosophers would still appeal to
God in this context, there are other possible mechanisms that could
play an equivalent role.[13] It is not to be ruled out that our
biological heritage, for example, has fixed a range of beliefs in us
whose reliability owes nothing to our individual ontogenetic
experience. Indeed there is a case for viewing certain aspects of
our cultural heritage as playing a similar role, imbuing us with
certain beliefs whose justification rests on ancestral rather than
individual experience.[14]


However, it is one thing to point to the general possibility of
biological and cultural mechanisms constituting
experience-independent sources of reliable knowledge, another to
show that such mechanisms operate within philosophy. Even if there
are areas of thought which rest on such foundations, this does not
show that the intuitions of philosophers in particular have a
similar backing. Moreover, there is arguably direct reason to doubt
that they do. It is not just the intuitions of everyday people on
philosophical matters that have a poor track record. The same applies
to philosophers through history. It is not hard to think of
deep-seated intuitions appealed to by past philosophers that have
since been discredited. (A purely mechanical being cannot reason;
space must be Euclidean; an effect cannot be greater than its cause;
every event is determined; temporal succession cannot be relative.)
In the next section we will see that there is reason to suppose that
this unreliability is intrinsic to the nature of philosophy.


### 2.4 A Role for Intuitions


The challenge to philosophical intuitions is clear enough. Either
they are analytic, in which they contain no substantial information,
or they are synthetic, in which case they are of dubious
reliability.[15] 
 Given this, a number of philosopher of
naturalist inclinations advocate a revisionary attitude to
philosophical method. Philosophy should turn away from intuitions, and
instead engage directly with proper observational evidence. (Kornblith
2002, Knobe and Nichols 2008.)


However, this is not the only possible reaction. We would do well to remember that intuitions arguably plays a role in science as well as philosophy. The history of science displays a number of important thought experiments, like Galileo's analysis of free fall, or the Einstein's argument against the completeness of quantum mechanics. And intuition functions here very much as it does in philosophy. The scientist imagines some possible situation, and then makes an intuitive judgement about what would happen.


In such cases, it is clearly not mere analytic definitions that are at issue. An eminently synthetic claim--say, that heavier bodies fall faster--is undermined by a contrary intuition--if a big and small body are tied together, they will be heavier than the big one, but will not fall faster. This thought is clearly not guaranteed by concepts alone, but by synthetic assumptions about the way the world works.


Still, this kind of example still faces the second horn of the dilemma about intuitions. If the intuitions involve substantial synthetic claims, why should we take them to be reliable? The historical track record of intuitions is scarcely any better in science than in philosophy. In both realms it would seem wiser to avoid unreliable intuitions and engage directly with observational evidence.


However, there is a way of understanding the role of intuitions in both science and philosophy that evades this worry. Instead of viewing them as designed to elicit authoritative judgments to which philosophical theories must defer, they can instead be seen as devices
which help us to articulate our implicit assumptions when we are
threatened with paradox and have difficulty finding a solution.


Recall a point made at the beginning of our discussion of
methodological naturalism. Philosophical problems are typically
occasioned by some kind of theoretical tangle. Different but equally
plausible lines of though lead us to conflicting conclusions.
Unraveling this tangle requires that we lay out different theoretical
commitments and see what might be rejected or modified. A useful
heuristic for this purpose may well be to use intuitions about
imaginary cases to uncover the implicit synthetic assumptions that are
shaping our thinking. This can help us better to appreciate our
overall theoretical alternatives, and assess which gives the best
overall fit with the *a posteriori* evidence.


This perspective on philosophical thought experiments shows why we
should positively expect many of the intuitions they elicit to prove
wanting. Perhaps there are contexts outside philosophy where various
kinds of *a priori* intuitions can be relied upon. But if
philosophical problems typically arise because we are unsure about
what exactly is amiss in the overall set of synthetic claims we bring
to the world, then it would seem only to be expected that the fault
will often lie in the implicit intuitions driving our judgements about cases.


It is worth noting that this often happens with scientific thought
experiments too. Galileo's intuition that light bodies fall as
fast as heavy ones was vindicated by subsequent physics. But the
verdict can also go the other way. For example, the assumption behind
the Einstein's argument against the completeness of quantum
mechanics is nowadays rejected. But this certainly did not mean that
his thought experiment was worthless. On the contrary, it led J. S.
Bell to the derivation of the eponymous inequality whose experimental
confirmation ruled out local hidden variable theories.


It is not hard to think of similar philosophical cases. The worth
of philosophical thought-experiments does not always require that the
intuitions they elicit are sound. Consider the classic Lockean set-up
where someone's memories are transferred to a new body. We all
have an intuition that the person goes with the memories, not the old
body, as evidenced by our reactions to the many fictions which trade
on just this kind of scenario. But few philosophers of personal
identity would nowadays hold that this intuition is decisive in favour
of Lockeanism. Again, consider the intuition that conscious properties
are ontologically distinct from physical ones, as displayed in our
immediate reaction to zombie scenarios. Here too, few would suppose
that these intuitions by themselves decide the case. Still, even those
who reject Lockeanism and dualism will allow that reflection on
memory-switching and zombie cases has played a crucial role in
clarifying what is at issue in the debates. The evocation of
intuitions by philosophical thought experiments is important, not
because they provide some special kind of *a priori* evidence,
but simply because they need to be made explicit and assessed against
the overall *a posteriori* evidence.[16]


This perspective on thought experiments shows that there is a sense
in which recent developments within "experimental
philosophy" can be viewed as complementing traditional armchair
methods. In the previous section we saw that some of the findings of
experimental philosophy carry the implication that everyday intuitions
are not generally reliable. But in addition to this
"negative" message, there is also room for experimental
philosophy to make a positive philosophical contribution, even in
cases where there is no variation in intuitions.


Careful experimental probing can helpfully augment traditional
armchair methods as a way of identifying the structure of implicit
assumptions that drive intuitive judgments about test cases.
Sometimes thought experiments may be enough. But in more complicated
cases systematic questionnaires and surveys may well be a better way
of identifying the implicit cognitive structures behind our
philosophical reactions.


Note that experimental philosophy, even when viewed in this
positive light, is at most an addition to our philosophical armoury,
not a new way of doing philosophy. For once we have sorted out the
intuitive principles behind our philosophical judgements, whether by
armchair reflection or empirical surveys, we still need to assess
their worth. Even if the claim that we think a certain way is
supported by hard empirical data, this doesn't make that way
of thinking correct. That can only be shown by subjecting that way
of thinking itself to proper *a posteriori* evaluation.


### 2.5 Mathematical, Modal and Moral Knowledge


Methodological naturalism fits more naturally with some areas of
philosophy than others. It is perhaps not hard to understand, at least
in outline, how work in areas like metaphysics, philosophy of mind,
meta-ethics and epistemology might be aimed at the construction of
synthetic theories supported by *a posteriori* evidence. But in
other philosophical areas the methodologically naturalistic project
may seem less obviously applicable. In particular it might be unclear
how it applies to those areas of philosophy that make claims about
mathematics, first-order morality or modality.


One possibility would be for methodological naturalists to make
exceptions for these areas of philosophy. It would still be a
significant thesis if methodological naturalism could be shown to
apply to a number of central areas of philosophy, even if some specialist
areas call for a different methodology.


This final subsection will address two issues raised by this suggestion. The first relates specifically to the idea that modal claims constitute a specialism within philosophy. Perhaps mathematical investigation and even first-order moralizing can be regarded as specialist subfields within philosophy. But it is arguable that a concern with the modal realm runs through all of philosophy. If so, then a challenge to the naturalist status of modal claims will threaten the naturalist status of all philosophy.


The second issue will be more directly about the methodologically naturalist status of the three areas mentioned--including mathematics and morality, along with modality. How far do methodological naturalists need to allow that mathematics, morality and modality constitute exceptions to their position in the first place?



On the first issue, Bertrand Russell said



>  [A philosophical proposition] must not deal
> specially with things on the surface of the earth, or with the solar
> system, or with any other portion of space and time. ... A
> philosophical proposition must be applicable to everything that exists
> or may exist. (1917: 110)
> 
> 


 However, one can agree with Russell that
philosophy automatically has implications for the modal realm
("everything that ... may exist"), without accepting
that the aim of philosophy is to explore the modal realm as such. We
need to distinguish here between an interest in claims which, as it
happens, have modal implications, on the one hand, and an interest in
those modal implications themselves, on the other. It is
uncontentious that most of the claims of interest to philosopher have
modal implications. But it does not follow from this that most of
philosophy is interested in the modal realm itself.


Philosophy is largely concerned with claims about identity and
constitution, claims which as it happens will be necessary if they are
true. When philosophers ask about knowledge, names, persons,
persisting objects, free will, causation, and so on, they are seeking
to understand the identity or constitution of these kinds. They want
to know whether knowledge is the same as true justified belief,
whether persisting objects are composed of temporal parts, and so
on. And so any truths they might establish about such matters will
inevitably be necessary rather than contingent, and so carry
implications about a realm beyond the actual.


But the fact that *p* implies *necessarily p* does
not mean that anyone who is interested in the former must be
interested in the latter, any more than someone who is interested in
John's age being 47 must be interested in its being a prime
number.


This makes room for methodological naturalists to insist that most
primary philosophical concerns are synthetic and *a
posteriori*, even if they imply additional modal claims which are
not. Natural science provides a good analogy here. Water is
H2O. Heat is molecular motion. Stars are made of hot
gas. Halley's comet is made of rock and ice. Since all these
claims concern matters of identity and constitution, they too are
necessary if true. But science is interested in these synthetic *a
posteriori* claims as such, rather than their modal
implications. Chemistry is interested in the composition of actual
water, and not with what happens in other possible
worlds. Methodological naturalists can take the same line with
philosophical claims. Their focus is on whether knowledge is actually
the same as true justified belief, or whether persisting objects are
actually composed of temporal parts--issues which they take to be
synthetic and *a posteriori*--and not with whether these
truths are necessary--issues which may well have a different
status.


Let us now turn to the second issue flagged above. How far do
methodological naturalists in fact need to allow that
modality--and mathematics and first-order morality--do have
a different status from the synthetic *a posteriori* character
they attribute to philosophy in general?


The issues here are by no means clear-cut. In
sections 1.7 and 1.8 above
we saw how the arguments for ontological naturalism placed general
constraints on the epistemological options in these area. By and large, these constraints tend to favour naturalism about philosophical method. There is no
question of exploring these epistemological issues fully here, but
some brief comments will be in order.


For mathematics and modality, the epistemological possibilities
were restricted to irrealism and ontologically non-naturalist
realism. In the moral case, there were again irrealist options, and
also ontologically naturalist realisms that identified moral facts
with causally significant spatiotemporal facts.


For those who endorse irrealist options in any of these areas,
there would seem to be no tension with methodological
naturalism. After all, irrealist analyses deny that there is any
substantial knowledge to be had in mathematics, modality or morality,
and so will not think of object-level claims in these areas as
themselves contributing to philosophy. (This is consistent with
thinking that a meta-understanding of the workings of mathematical,
modal or moral discourse is important to philosophy; but then there
seems no reason why such a meta-understanding should be problematic
for methodological naturalism.)


Similarly, there seems no reason why the naturalist realist options
in the moral case should be in tension with methodological naturalism.
The details deserve to be worked through, but on the face of things we
might expect knowledge of causally significant spatiotemporal moral
facts to be synthetic and *a posteriori*.


This leaves us with non-naturalist realist accounts of mathematical
and modal knowledge. As we saw earlier, the best options here appeal
to the neo-Fregean programme of grounding knowledge of the
mathematical and modal realms in *a priori* analytic
principles. If this programme could be vindicated, then it would
indeed violate the requirements of methodological naturalism. But, as
observed earlier, it seems at best an open question whether analytic
principles have the power to take us to realist knowledge of the
mathematical and modal realms.