When
Counting Conscious Subjects, the Result Needn’t Always Be a Determinate Whole
Number
Eric
Schwitzgebel
Department
of Philosophy
University
of California, Riverside
Riverside,
CA 92521
USA
Sophie
R. Nelson
Department
of Philosophy
New
York University
New
York, NY 10003
USA
November
19, 2024
Invited submission
to a special issue of Philosophical
Psychology on the philosophy of Daniel C. Dennett
When
Counting Conscious Subjects, the Result Needn’t Always Be a Determinate Whole
Number
Abstract:
Could there be 7/8 of a conscious subject, or 1.34 conscious subjects, or an
entity indeterminate between being one conscious subject and seventeen? Such
possibilities might seem absurd or inconceivable, but our ordinary assumptions on
this matter might be radically mistaken. Taking inspiration from Dennett, we
argue that, on a wide range of naturalistic views of consciousness, the
processes underlying consciousness are sufficiently complex to render it
implausible that conscious subjects must always arise in determinate whole
numbers. Whole-number-countability might be an accident of typical vertebrate
biology. We explore several versions of the inconceivability objection,
suggesting that the fact that we cannot imagine what it’s like to be 7/8 or
1.34 or an indeterminate number of conscious subjects is no evidence against
the possibility of such subjects. Either the imaginative demand is implicitly
self-contradictory (imagine the one, determinate thing it’s like to be an
entity there isn’t one, determinate thing it’s like to be) or imaginability in
the relevant sense isn’t an appropriate test of possibility (in the same way
that the unimaginability, for humans, of bat echolocation experiences does not
establish that bat echolocation experiences are impossible).
Word
Count: ~8000 words
Keywords: Artificial Intelligence; consciousness; Dennett, Daniel;
personal identity; split-brain; subjectivity
When Counting Conscious Subjects, the Result Needn’t
Always Be a Determinate Whole Number
1.
Introduction
People
typically assume that conscious subjects come in discrete, countable wholes. Either
there are no conscious subjects in the seminar room, or there are two, or six,
or twenty-three. It seems bizarre to say that there might be 9.382 subjects, or
7/8 of a subject, or 3i subjects, or that the number of subjects might
be indeterminate between five and seventeen or best represented by a nine-dimensional
non-Euclidian surface. What could such remarks even mean, unless as a wry
comment about a shy student with 30% of their head poking through the door?
We
will argue that this ordinary assumption is false. When counting conscious
subjects, the result needn’t always be a single or determinate whole number.
Ordinary counting might fail, or yield a mathematical representation other than
a whole number, or yield a set of whole numbers among which the result is
indeterminate. At best, discrete countability is an accident of typical
vertebrate biology, which needn’t apply to invertebrates, AI systems, or
atypical humans. If it’s part of our concept of consciousness that conscious
subjects necessarily come in determinate, whole bundles, then our ordinary
concept of consciousness requires repair. Just as the mathematics of whole
numbers might fail us if we attempt to count the eddies of a turbulent stream,
it might also fail us in attempting to count the conscious subjects in a flow
of experiences.[1]
We
start by clarifying our notion of a conscious subject. After arguing that the
complexity of the processes underlying consciousness renders our thesis
plausible, we argue for the possibility of cases indeterminate or intermediate
between zero subjects and one, as well as the possibility of cases
indeterminate or intermediate between one subject and whole numbers greater
than one. We conclude by addressing objections concerning inconceivability.
Our
position is partly inspired by Dennett, and we believe he would have endorsed
it. According to his “Multiple Drafts” theory of consciousness, not only do
different “drafts” of experience exist at different times (generating his
famous “Orwellian” vs. “Stalinesque” dilemma); they also exist simultaneously.
He writes, “At any point in time there are multiple drafts of narrative
fragments at various stages of editing in various places in the brain” (1991,
p. 135). The narratives that constitute our “selves” “issue forth as if
form a single source” encouraging us “to (try to) posit a unified agent” (1991,
p. 418, emphasis in original). While discussing split-brain and multiple
personality cases, Dennett says that we typically want “to preserve the myth of
selves as brain-pearls, particular, concrete, countable things, rather than
abstractions… refusing to countenance the possibility of quasi-selves,
semi-selves, transitional selves” (1991, pp. 424-425).[2]
2.
Our Main Claim
Marcel
sips tea containing the crumbs of a madeleine cookie and reflects back on his
days in Combray. In that moment, he simultaneously experiences the warmth of
tea in his mouth, the taste of the madeleine, and recollections of Combray.
These three experiences (or experience-parts or experience aspects) all belong
to the same field of consciousness. They are phenomenally unified.
There’s something it’s like to have them together. Perhaps, as Bayne and
Chalmers (2003) suggest, they are subsumed within a more complex experience of
tea-with-madeleine-with-recollection. Perhaps, as Dainton (2000) suggests,
they’re united by a basic, not-further-analyzable relation of co-consciousness.[3] We take no stand on how to
analyze phenomenal unity, but we assume that the core idea is clear: two
experiences might belong either to the same, or to different, fields or streams
of conscious experience.[4]
What
does it mean to be determinately one conscious subject? Conscious subjects,
as we’ll understand them here, are just such bundles of experiences,
individuated by maximal relations of phenomenal unity. If experience A is
unified with experience B, and if experience B is unified with experience C,
and if experience A is unified with experience C, then there is one conscious
subject with a unified experience of A-with-B-with-C.[5] If experience D is unified
with no other experiences, then there is one conscious subject experiencing
only D.
This
notion of a “conscious subject” is unusual but not unprecedented.[6] We choose it not because
we endorse it as the best approach to subjecthood from the point of view of
theories of selfhood or personhood, or because we think that “subjects” on this
conception are identical to cognitive systems, bodies, or persons, but rather
because it targets a specific phenomenon of special interest. Broader definitions
of “subject” that appeal to more than conscious experiences at a moment—for
example, diachronic relations between conscious states; or causal threads of
memory and inference; or values, personality traits, and nonconscious mental
processes; or bodies—probably make it easier to defend our thesis. Temporally
extended views, for example, appear to permit discussion of Parfitian (1984)
cases of merging, splitting, and slow change. Views that rely on synchronous
nonconscious processes appear to permit hypothetical AI or alien cases of
synchronous partial unity or overlap due to shared nonconscious mechanisms.[7] Similarly, bodies can
plausibly overlap. By focusing on “conscious subjects” in our narrow sense, we
address the countability issue in its starkest form, where skeptical interlocutors’
intuitions seem to run strongest against our view.
On
this notion of a “conscious subject”, is at least conceptually possible for
multiple conscious subjects to exist in the same body (one experiencing
A-with-B-with-C, another experiencing D-with-E-with-F), perhaps even
coordinating to operate as a single person.[8] On some accounts of
personal identity, you might be nothing but a conscious subject, perhaps
extended over time. But even if you aren’t strictly identical to a conscious
subject, you are intimately related to one. If you are, right now, experiencing
the warmth of tea, the taste of madeleine, and recollections of Combray, then
there is a conscious subject in your spatiotemporal vicinity undergoing exactly
that set of token conscious experiences, and that conscious subject is
certainly not someone other than you. Perhaps it is a part of you, an aspect of
you, a process within you, or in some other way ontologically adjacent.
Our
thesis is that conscious subjects, in the sense just articulated, needn’t
always come in determinately whole-number units. Experiences don’t always
bundle neatly.
3.
Plausibility
Considerations
For
the purposes of this argument, we assume a broadly naturalistic approach to
consciousness on which human beings have conscious experiences in virtue of
something about the complex structure and composition of their bodies and
brains. (We don’t assume materialism. Some forms of neutral monism, property
dualism, and even panpsychism are naturalistic in the relevant sense.) The
correct naturalistic theory of consciousness is far from settled. However, on a
wide range of plausible theories, it appears possible to construct cases that
defy whole-number countability, even if such cases are rare among vertebrates.
Consider
Global Workspace theories, for example, according to which information is
conscious if it is broadcast through a “global workspace” for potential use by
downstream cognitive systems.[9] How large must a workspace
be, and how much information must it be capable of feeding downstream, before
it is appropriately “global”? Is there some minimum workspace size or quantity
of connectedness below which an entity is not at all conscious and above which
an entity is conscious, with no intermediacy or indeterminacy? Could workspaces
be partial or overlapping? If information is available for 85% of downstream
processes, is that enough? 51.578103%? Two? Imagine an architecture with
downstream processes in two clusters, A1, A2, and A3 vs. B1, B2, B3, and B4.
What if some information is available to all of A and B while some is available
only to A or only to B or only to A1 and B3? Must there be a bright line
between cases of a single unified conscious subject with imperfect downstream
information uptake and two discrete subjects with limited or indirect
information sharing? The model seems to allow in principle for a diverse range
of messy cases where subjecthood and unity would either be partial or best
captured with more complex mathematical representations such as vectors or
regions.
Consider
Higher-Order theories of consciousness, according to which an experience is
conscious if it’s the target of a higher order representation of the right
sort.[10] Perhaps in typical
vertebrate cases, there’s a single higher-order system that does all of the
tracking and unifies all of the represented lower-order states. But as with
Global Workspace theory, we can imagine considerably messier architectures. The
same lower-order state might be targeted by different higher-order systems that
link to different or partially overlapping output systems. Partly overlapping
sets of lower-order states might be targeted by different higher-order systems
that are partly integrated and have different downstream influences on the
organism. It might be only in cases at the extremes that there exists either
one unified conscious subject or many sharply distinct subjects. The majority
of possibilities might lie in the middle.
Consider
Dennett’s (2005) “fame in the brain” view, according to which a cognitive
process is conscious to the extent that it is “famous”—that is, influential
on—other cognitive processes. Fame among humans is a complex phenomenon. People
can be famous in some circles, unknown in others. Fame circles can nest and
overlap. Fame relationships can correlate imperfectly, so that if Person A is
known to Person X, they are 85% likely to be known to Person Y but only 10%
likely to be known to the average member of the population. While it seems to
be typical in the human case that if a process—say a representation of the
color red in some region of the visual field—is “famous” in the centers that
govern verbal report, it will also be famous in the centers that govern
long-term planning and control of the fingers. But widespread dissociations do
occur—for instance, in split-brain patients.[11] As Dennett (1991)
emphasizes, dissociations even occur in ordinary humans. This suggests a
complex range of partial cases that defy characterization as exactly “one
conscious subject” or two, or three, or seventeen.
Similar
considerations apply to virtually all naturalistic theories of consciousness.
Almost inevitably, they ground consciousness in processes or structures that
can be implemented in fuzzy, indeterminate, or partly overlapping ways,
suggesting mechanisms for unity that can be implemented in fuzzy,
indeterminate, or partly overlapping ways. Embodied theories of consciousness
are no exception, despite the fact that we usually imagine embodied organisms
as discrete individuals. Sponges, lichen, grasses, and birch forests connected
at the root are not as readily divisible into discrete individuals. Octopus
arms operate partly independent of the head: is there one conscious subject or
nine?[12] The Hogan Twins have
overlapping brains and differ in personality while having the capacity to
report each other’s sensory experiences.[13] AI architectures might similarly
admit of various types and degrees of integration. Must it really always be the
case, for every possible pair of craniopagus twins, that there is either
determinately one conscious subject or two?
In
general, if consciousness has a complex, naturalistic basis, it seems
correspondingly plausible that cases could arise where the number of conscious
subjects is similarly complex, defying determinate whole-number countability.[14] Those who would argue
otherwise owe us an explanation of why conscious subjectivity must always be
simple and countable despite the complexity and multidimensionality of the
processes that give rise to it.
4.
Between Zero and One
Start
with a system that is not and does not have a brain. Posit a series of changes
that render it, eventually, an apparently conscious system that determinately
is or that determinately has a brain. Maybe the system begins as a fertilized
embryo and ends as a newborn child. Maybe the system begins as a simple form of
artificial intelligence and ends as an extraordinarily sophisticated one. Evaluate
the changes at arbitrarily precise time scales. Theories of conscious
subjecthood then face a quadrilemma. Either (1) the system is a conscious
subject the whole way through, even when it lacks a brain entirely; (2) the
system is never a conscious subject; (3) there is a sharp, stepwise distinction
where the system suddenly becomes a conscious subject; or (4) there is a
non-sharp or non-stepwise distinction between when the system is not a
conscious subject and when it is.[15]
For
any particular transformation of this sort, option (1) will always be available
to certain kinds of radical panpsychists, who hold that conscious experience is
present not only in all fundamental entities but also in all composites of
fundamental entities. Such a panpsychist could say that the collection of fundamental
particles that constitutes the initial, non-brain system possesses a unified
field of conscious experience, despite lacking spatial and functional unity. Similarly,
option (2) will be available to radical eliminativists, who hold that conscious
subjects don’t exist at all.[16] However, for present
purposes, we assume that options (1) and (2) won’t apply universally to all
such gradual series. Such radical forms of panpsychism and eliminativism lie
outside the scientific mainstream. We must then sometimes choose between (3)—saltation—and
(4)—indeterminacy or intermediacy. Note that intermediacy differs from
indeterminacy. The number of conscious subjects could be intermediate (for
example, exactly 0.3589) without being indeterminate. Conversely, the number
could be indeterminate (for example, not quite one and not quite three) without
being intermediate.
Saltation
is unattractive on broadly the grounds discussed in Section 3. It would be
surprising if, in general, atop smooth gradations of gradual structural change,
conscious subjecthood suddenly jumps in, with no indeterminacy or intermediacy at
all. Are we to imagine, for example, that lizards of one genus determinately
are conscious subjects while lizards of another genus, the tiniest bit less
sophisticated, are not? Nature does admit of sudden phrase transitions. Water
freezes at exactly 0.0°. Beams suddenly snap under loads. But, except in
quantum cases, even such phase transitions aren’t perfectly sharp. Close
inspection reveals intermediate states. Must there always be an exact moment,
down to the millisecond, down to the nanosecond, at which conscious subjecthood
suddenly pops in, with no intermediate or indeterminate phase? Furthermore,
must all such sequences lack any intermediate or indeterminate
phases? This is a bold claim! Only a powerful argument could justify it, and we
are aware of no published arguments within the framework of scientific
naturalism that attempt to do so.[17]
Accepting
that the number of conscious subjects can be indeterminate or intermediate
between zero and one doesn’t settle the best numerical means for representing
that possibility. The best approach in some cases might be a real value between
zero and one. For example, if we knew that a global workspace of size 1000 constituted
exactly zero conscious subjects, a global workspace of size 2000 constituted exactly
one conscious subject, and all intermediate workspace sizes were determinately
intermediate between zero conscious subjects and one, we could use values
between 0 and 1 to represent the number of subjects present. (It might remain
open whether the number of subjects related linearly, logarithmically,
sigmoidally, or in some other way to the size of the workspace.) Similarly, a
real value could measure how close a case of indeterminacy lies to the border
of determinacy (e.g., an indeterminate case much closer to being determinately
one conscious subject than zero might be represented by the number 0.9). On the
other hand, real numbers might suggest implausible precision, unless construed
as mere approximations.[18] A less commissive
representation might simply be the open interval (0,1) or a set of
possibilities among which the number is indeterminate {0, 1}. Or one might opt
for more structure: a vector or region that represents several independent
dimensions of intermediacy or indeterminacy. Even imaginary numbers might be
applicable if consciousness involves quantum states represented by complex
numbers.
5.
Between One and N
Luke
Roelofs (2019) constructs a similar slippery-slope case between two subjects
and one. Start with two conscious brains, wholly distinct. Slowly join them,
one neural connection at a time, until they form a single, unified subject of
experience.[19]
Either (1) the same, non-zero number of conscious subjects is present the whole
way through; (2) there aren’t, in fact, any conscious subjects during any stage
of the process; (3) there’s a sudden, sharp change in the number of conscious
subjects; or (4) there’s a gradual, non-sharp change in the number of conscious
subjects.
Again,
we assume the falsity of (1) and (2), although (1) is available to radical
panpsychists while (2) is available to radical eliminativists.[20] Option (3) seems just as implausible
here as in the zero-to-one case. If each step of integration is sufficiently
tiny, the architectural and functional differences will be correspondingly
tiny, and it’s unattractive to suppose that the seemingly huge metaphysical
difference between one and two conscious subjects would be grounded in a tiny
architectural or functional difference. And recall that the saltationist is
committed to a negative universal: There cannot be any way of slowly
connecting any two conscious subjects such that there is a single
moment of indeterminacy or intermediacy. Such a bold claim requires
compelling support.
If
N > 1, the best numerical representation of indeterminacy or intermediacy is
unlikely to be a single real number value. For example, in earlier work
(Schwitzgebel & Nelson 2023), we describe a case that allows a slippery
slope between 1 and 201. Imagine a conscious AI, perhaps employing a futuristic
technology very different from silicon chips. The entity is composed of a
large, orbiting AI system plus 200 robotic bodies on a planetary surface, each
with their own local AI processors. If the entity is massively interconnected
in the right way, it is plausibly a single conscious subject with multiple
bodies or one spatially discontinuous body.[21] If the entity is sparsely
connected, or connected in the wrong way, there are plausibly 200 or 201
distinct conscious subjects in communication with one another (201 if the
orbiting system is conscious, 200 if not). Between these extremes lies
approximately a continuum of possibilities, some of which may constitute cases
indeterminate or intermediate between 1 and 201. However, it would be misleading
to numerically represent the number of conscious subjects in an AI system indeterminate
between 1 and 201 in exactly the same way we represent the number when 101
typical humans gather in a room. Furthermore, such cases can be structured to
involve multiple independent dimensions of intermediacy or indeterminacy,
depending on the degree of integration between the orbiting AI system and each
individual robot, thus inviting multidimensional mathematical representation.
We
can also construct a zero to N case as follows: Start with our orbiter
and robots, all simple enough that none is conscious. Improve them all
simultaneously, one arbitrarily small step at a time. By analogy with our non-saltationist
reasoning above, there should be a range of cases indeterminate or intermediate
between zero and N.
6.
“But It’s Inconceivable!”
As
we descend further into such unfamiliar ways of thinking, we expect that many
readers will stop somewhere short, with a worry along these lines: It is inconceivable,
and therefore metaphysically impossible, that conscious subjects exist in
anything other than determinately countable wholes. At least, some readers may
be concerned that conscious subjects lacking determinate or discrete countability
are not “positively” conceivable, constituting grounds to doubt that
indeterminate or intermediate cases of conscious subjects are metaphysically
possible.[22]
And, of course, no plausibility consideration or slippery-slope argument can
establish a metaphysical impossibility. No Euclidian figure is indeterminate or
intermediate between being a scalene and isosceles triangle, no matter how
small the jump between one and the other. Similarly, an entity either has a
spatiotemporal extension, or not. Extremely small objects aren’t somehow only partly or
indeterminately or intermediately possessed of spatiotemporal extension.
Sometimes, there just are metaphysical bright lines. Conscious subjecthood
might be such a bright line case. In what follows, we’ll consider three
distinct inconceivability challenges for our view.
6.1. Between
Zero and One
To conceive of a case intermediate or
indeterminate between zero and one—a case in which there is, say, approximately
0.89 of a conscious subject—we must conceive of indeterminately or
intermediately conscious mental states (see Figure 1). After all, if there’s a
single, wholly conscious mental state present, there’s at least one conscious
subject. Can we imagine indeterminate or intermediate consciousness? Return to
Marcel’s experience of warm tea, a taste of madeleine, and recollections of
Combray. 
Now, subtract the
experience of warm tea and the taste of madeleine. Marcel's mental state is not
one-third conscious, and consequently Marcel has not been reduced to one third
of a conscious subject. He’s still a conscious subject, just with fewer
experiences. Now, subtract Marcel’s recollections of Combray. No conscious
state remains, and therefore, no conscious subject does either (at least at
that moment, according to our definition). This constitutes a discrete jump from
one to zero. Could we somehow subtract approximately half the experience
of recollection? Could we somehow imagine Marcel as only half conscious?
We might imagine first a vivid recollection of his bedroom in Combray with the
glimmering flame of the nightlight in its bowl of Bohemian glass, hung by
chains from the ceiling; and then we might reduce the experience. Forget the
chains, forget the glass, recall only the glimmering flame. Still, that memory
seems determinately to be an experience, and thus, one conscious subject
determinately exists. Perhaps the flame can be remembered only vaguely—what was
its shape? Its color? Was it even a flame, or only a glowing coal? However
faint we imagine Marcel’s phenomenology, it seems we still have some
phenomenology, until we remove the experience altogether and thus conscious
subjecthood altogether. No intermediate state seems conceivable. Either there’s
something it’s like to be Marcel in that moment—no matter how simple—or there’s
nothing it’s like. No conceptual space stands open between something and nothing.
A half-something is already a something, unless it is nothing.
We
acknowledge the pull of this way of thinking. However, we reply that there’s an
implicit self-contradiction in any attempt to imagine what it’s like to be an
entity indeterminate or intermediate between zero and one. Necessarily, there’s no one determinate thing
it’s like to be a borderline case of a conscious subject. No one, regardless of
their cognitive architecture, can grasp what it’s like to be such an entity any
more than they can grasp what it would be like to perceive a square circle. The
more you try to vividly imagine the phenomenology of something that, by nature,
lacks even a single wholly conscious, determinate experience, the worse you
miss the mark.
That
said, entities who regularly enter intermediate or borderline conscious states
might have no trouble discerning or self-representing such states, and they
might develop corresponding concepts. For example, they might be able to think,
“I spend a considerable period of time in that mizzy state between being
neither determinately unconscious nor determinately conscious” (alternatively,
partly conscious, if intermediacy is possible). They might be able to conceive
of mizzy states through imaginative episodes that are themselves mizzy.
Nonetheless, just like us, they would fail to conceptualize the full, determinate
experience of borderline or partial conscious subjecthood, because there is
no full, determinate experience of borderline or partial conscious subjecthood.[23]
6.2. Between
One and N
What
would be required to conceive of an indeterminate or non-whole-number of subjects
between one and N (where N is a whole number greater than one)—for instance, 1.34
conscious subjects? We see two possibilities between which we remain neutral.
6.2.1.
Indeterminate or intermediate unity among determinately conscious experiences. First,
in order to imagine subjects indeterminate between one and N, one might attempt
to imagine determinately conscious experiences that are indeterminately
or intermediately phenomenally unified. Rather than determinately
one or several distinct, unified bundles of conscious experience—for example,
A-with-B-with-C and D-with-E-with-F—we might conceive of something in-between
(see Figure 2). Perhaps the relation of phenomenal unity admits of degrees, or there
can be cases in which its presence is vague. On this picture, if Marcel were a
cognitive system intermediate or indeterminate between one and two subjects, he
would need to have both a determinate experience of the warmth of tea and a
determinate experience of the taste of madeleine, without those experiences
being either fully (that is, determinately and not intermediately) unified into
a conscious whole nor fully disunified into two separate wholes. He would need
to feel both experiences simultaneously, but neither entirely together nor entirely
apart.
Trying to conceive of what that would
be like, we might imagine the experience of the warmth phenomenally unified
with a hazy, faint, or peripheral-seeming experience of the taste (or vice
versa). But this isn’t a case of warmth indeterminately or intermediately
unified with the more robust taste from the original scenario; it’s just a case
of warmth determinately phenomenally unified with a hazy, faint, or
peripheral-seeming taste—a determinately conscious but less vivid experience. A
worry potentially arises: However much we try to imagine conscious experiences
being only partially severed from one another, it seems we’re always left imagining
wholly unified experiences, and therefore a single conscious subject—that is,
until we sever the tie altogether and are left with determinately multiple
conscious subjects. We imagine Marcel having his experiences conjointly, or we
imagine the experiences being felt in isolation. Those are, it seems, the only
conceivable options.
Such
an objection seems, again, to rely on an implicitly self-contradictory
imaginative demand. Our hypothetical objector seeks an act of imagination that
joins together, into the objector’s own, fully unified imaginative experience,
two experiences that aren’t fully unified. But, of course, it isn’t like any
one fully unified thing to feel two indeterminately or intermediately unified
experiences simultaneously. If the experiences were determinately disjoint,
the incoherence of the imaginative demand would be obvious: We can’t expect to
imagine what it’s like to have Marcel’s experience of the warmth of tea jointly
with Odette’s experience of a piano sonata. Clearly, there’s no one thing it’s like to have these two
disjoint experiences. The same holds, though less obviously, when the two
experiences are indeterminately or intermediately conjoint. The conceivability
objection articulated above relies on a standard of conceivability that
requires imagining, fully and determinately, the one thing it’s like to
have two experiences that are not fully or determinately like one thing
to have.
This
isn’t to say that indeterminate or intermediate phenomenal unity is inherently unimaginable.
An indeterminately or intermediately phenomenally unified conscious subject with
an indeterminately or intermediately unified imagination might have no
trouble introspecting and reflecting on such mental states. They might be able
to think, “When my tentacles with neurons at their tips are only partly
connected to my body, I start having dissy experiences that aren’t fully
unified with one another.” Although they couldn’t imagine dissy
experiences as being like one thing any better than we can, they might
be able to conceive of dissy states through imaginative episodes that
are themselves dissy. Suppose Marcel
experiences the warmth of tea in one tentacle and experiences memories of
Combray in another tentacle, and these experiences are only partly unified.
Odette—or Marcel himself later—might imagine or remember this phenomenology by
means of an imaginative structure that is itself distributed among different
tentacles and not fully unified. This would not (we assume) be much like normal
human imagination, but what is alien to us needn’t be impossible.[24]
6.2.2.
Intransitive unity. Alternatively, subjects might be intermediate
or indeterminate between one and N because they have overlapping fields of
consciousness that share token experiences. This would require the relation of
phenomenal unity to be intransitive. Most philosophers have assumed that
if an experience A is unified with another experience B, and if B is unified
with a third experience C, then A and C are themselves unified. However, if intransitive unity—or, as many have called it,
partial unity—is possible, then A and B might be unified, and B and C might be
unified, without A and C being unified as well (see Figure 3).[25]
To
understand how subjects intermediate or indeterminate between one and N would
look if phenomenal unity were intransitive, first consider two cases: Tiny
Overlap and Massive Overlap. In Tiny Overlap, two alien brains (or AI systems)
share a tiny bit of tissue. At the target moment, each alien has a million
experiences distinctive to them—vast turbulences of vivid, unified experiential
activity—plus one tiny shared experience: the faint sound of a distant motor. Plausibly,
Tiny Overlap should be conceptualized as a case of two conscious subjects who
happen to share one token experience. Massive Overlap is the complementary
case: a million experiences are shared, but two experiences are not—a green dot
in the left visual periphery and a red dot in the right visual periphery. The green
dot is unified with everything but the red dot, and the red dot is unified with
everything but the green dot. Plausibly, Massive Overlap should be
conceptualized as a case of a single conscious subject who is ever-so-slightly
disunified. Now, imagine that, like in Section 5, Tiny Overlap gradually becomes
Massive Overlap as the aliens’ brains slowly fuse. In the middle of this
process, there would be two partially overlapping fields of experience—for
instance, one with experiences 1 to 678,000 and another with experiences
315,000 to 1,000,000—that would plausibly count as neither determinately one
nor two subjects.
Again, intransitive unity might seem
impossible because we’re unable to imagine what having an intransitively
unified perspective would be like.[26] If we try to imagine how it
would feel to experience the warmth of tea alongside the taste of madeleine,
and the taste of madeleine alongside recollections of Combray, while the warmth
of the tea and the recollections of Combray remain disunified, we draw a blank.
Once again, however, the demand is paradoxical. The hypothetical objector seeks
to imagine, in a transitively unified way, what it would be like to have intransitively
unified experiences. They seek to bring into their unified imagination an
experience of A with B with C that is somehow simultaneously an experience of A
with B and B with C but not A with C. This self-contradictory imaginative
standard is inappropriate to the case.[27] Intransitively unified
experiences aren’t like any one thing, or part of any one
perspective, at all.
Still, we see no reason to believe
that a creature with intransitively unified consciousness couldn’t imagine, in
an intransitively unified way, intransitively unified experiences. Maybe
Marcel’s Arm 1 is unified with his head, and his head is unified with Arm 6,
but Arms 1 and 6 are not unified. Even though Marcel can’t join the experiences
of his head and arms in one phenomenally unified act of imagination, he might
imagine, think about, introspect, or recall them by means of a similarly
distributed imagination.
Our
response to each of the three conceivability objections is the same. The
objections, we suspect, turn on our wanting to imagine these extraordinary
cases in the ordinary, unified way. It is of course often fine to want to
imagine things in the ordinary way. That’s why the imaginative demands
superficially seem reasonable. We feel like we can’t quite get our head around
an experience if we can’t imaginatively construct or recreate it in the way we
imaginatively construct or recreate an experience of seeing a sunlit mound of
gold while feeling its warm, smooth texture. The ordinary way we imagine
experiences is as determinate experiences (perhaps with some indeterminate contents) that are wholly,
determinately, transitively unified. It is inappropriate and paradoxical to
apply this standard of imagination to the non-whole-number cases at hand.
More
reasonably, one might alter the standards of imagination to appropriately match
the target cases. The types of imagination required—mizzy, dissy, or
intransitive—may seem alien to us, but only in the same way that color is arguably
unimaginable to people blind from birth and bat echolocation seems unimaginable
to ordinary humans. Human limitations, not metaphysical or nomological
impossibility, explain our inability to concretely imagine conscious subjects
that don’t come in determinate, countable whole numbers.
6.2.3
Countability partly recovered?
If we accept the intransitivity approach
to conceiving of subjects indeterminate or intermediate between one and N,
there still might be a sense in which fields of experience are countable. After
all, overlapping entities can come in determinate whole numbers. A = {x ∣ 1 ≤ x
≤ 999,999} and B = { x ∣
2
≤ x ≤ 1,000,000} aren’t indeterminate between two sets; rather,
they’re determinately two sets that share 99.9999% of their contents. The shapes
in Figure 4 don’t occupy somewhere between one and two regions of space. They
simply occupy massively overlapping regions. If it’s possible in principle to
measure or quantify the degree of overlap between two fields of consciousness, it
might be possible in principle to count up a whole number of overlapping conscious
fields, just as it’s possible to count up a whole number of overlapping sets
and an overlapping number of bounded, continuous regions of space.
One
might worry that understanding subjects this way would once again force us to
posit a sharp, inelegant jump atop a complex physical base. However, we see no
reason for concern: This approach would still allow for gradual phenomenological
transitions alongside gradual increases and decreases in functional integration.
Consider again an analogy to sets: suppose I pull out a piece of paper and list
the sets of numbers [1, 2, 3] and [2, 3, 4]. I now have two mathematical
objects instantiated on my paper. Suppose that I then erase the number one from
the first set and the number four from the second set. Now, I only have one
mathematical object instantiated. We could, at this point, be puzzled. The
physical world is messy and complicated—how bizarre that the transition from
one entity to two on my page was so clean! But this clearly wouldn’t be the
right approach to thinking about the case. Abstract objects can be distinct,
even when the differences between them are tiny, and they can collapse into one
when those tiny differences are erased. The same goes, potentially, with
“conscious subjects” if we define them in terms of overlapping sets or fields
of experience.
However,
generalizing this approach to counting subjects generates what would seem to be
intuitively, pragmatically, and functionally the wrong result in the Massive
Overlap case: The tiniest bit of intransitivity would generate two discretely
different “subjects” even if the system is functionally, practically, and
introspectively almost identical to a single subject. This would be especially
worrying if, as Dennett suggests, ordinary humans are themselves often not
fully unified. Even if it’s possible in principle to count up massively
overlapping fields of experience, calling each one a “subject” seems bizarre. Furthermore,
this restoration of countability, if it works at all, works only for the
intransitive unity case. Zero-to-one and indeterminate or intermediate unity
cases will still ruin any strict countability principle. So we might as well
reconcile ourselves.
In Section 2, we defined “conscious subjects” as
bundles of experience, individuated by maximal relations of
phenomenal unity. If, as we’ve just suggested, unity can come in degrees or be
intransitive or indeterminate, the relevant relation might be sufficient rather
than all-or-none unity and there might not always be a single best individuation
scheme.
7.
Conclusion
Dennett
challenged readers to leave behind their presuppositions about the features of
consciousness. We celebrate this aspect of his work. Our ordinary conception of
consciousness is grounded in a specific evolutionary, developmental, and social
history, mostly focused on typical human cases and a few familiar vertebrates,
as commonly understood. Even if typical humans are normally fully and
determinately phenomenally unified,[28] typical humans are a tiny
corner of the architectural possibility space. What seems metaphysically
necessary, as viewed from this corner, may prove instead to be a matter of
contingent fact.[29]
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