ABSTRACT
This paper proposes a new metaphysical
framework for distinguishing between human and machine intelligence by drawing
on Kant’s incongruent counterparts as an analogy. Specifically, the paper posits
two deterministic worlds that are superficially identical but ultimately
different. Using ideas from Wittgenstein, Gödel, and Cantor, the paper defines
“deterministic knowledge” and investigates how this knowledge is processed
differently in those two worlds. The paper considers computationalism and
causal determinism for the new framework. Then, the paper introduces new
concepts to illustrate why human and machine agents display different causal
characteristics in processing verbal information. Overall, the paper’s
framework provides a theoretical basis for the uniqueness of the human mind.
Introduction
This paper
was motivated in part by asking questions that arose from Nietzsche’s concept
of amor fati (or “love of fate”) (Nietzsche 1990, 99). His suggestion to embrace and love
fate has resonated with many of his readers seeking guidance in life. However,
Nietzsche’s advice seems to have certain inconsistencies. For instance, how can
one learn to embrace fate if everything in one’s life has been predetermined?
If determinism is true, would it not be accurate to say that even an act of
learning to love one’s fate was also predetermined from the beginning? Was
Nietzsche himself, perhaps, predestined to admonish his readers to love their
fate? It is doubtful if it truly matters whatever people choose to believe or
say if everything was predetermined. Furthermore, when determinists assert that
the universe is deterministic, it is difficult to avoid the impression that
they are putting themselves away from the universe that they belong to.
Apparently, none of them have provided a convincingly strong basis for
justifying the significance of their assertion while situating themselves
within the universe.[i] In
other words, no qualitative distinction has been established between the act of
declaring the universe as deterministic and all the events of the universe that
should also comprise the very act of declaration.
One may
argue that such an issue has been addressed through compatibilism,
which proposes that one’s perceived sense of free will is compatible with
determinism. However, the compatibilist view of human nature still relies on
causal determinism, which is rooted in the notion of causality. This may
reinforce the idea that humans are not essentially different from computing
machines.[ii] Therefore, compatibilism itself may not be
particularly helpful in clarifying what significant distinction lies between
the determinist’s mind and the events of the universe that are within the
determinist’s scope. If compatibilism is true, it is possible that the human
mind differs from computers or other physical events of the universe only in
terms of complexity.
To address
this issue, this paper proposes a novel philosophical perspective by discussing
different types of deterministic worlds. These deterministic worlds are
carefully examined with respect to the human mind. Kant’s “incongruent
counterparts” (hereinafter, “ICs”) was a major inspiration for the development
of the metaphysical argument in this paper. The argument also builds upon the
idea of Cantor’s diagonal argument, Gödel’s proof strategy for his incompleteness
theorem, and Wittgenstein’s first proposition in Tractatus Logico-Philosophicus
(hereinafter, “TLP”). Admittedly, the use of ICs as an analogy may appear to be
far-fetched, since the original idea concerns absolute versus relational space.
In addition, given that Cantor’s and Gödel’s are mathematical theorems, their connections to
determinism might be initially difficult to grasp. Moreover, one may question
the relevance of the metaphysical argument to the empirical world. This paper
will address these concerns.
1. The
incongruent counterparts
Kant
devised the concept of ICs in order to address the issue of absolute versus
relational space (Kant 1994, 145-174). According to the theory of absolute
space, even if the universe had only one body and nothing else, that body would
still have a spatial background in which it could move (Asher 1987). However,
the relational view of space denies the existence of absolute space and defines
motion only in relation to other bodies.
Kant
begins his argument by imagining two worlds. One world includes only a left
hand (“LH world”). The other world includes only a right hand (“RH world”). If
the relational view is correct, there should be no difference between these
two. However, from an outsider’s viewpoint, it is clear that the two worlds are
different. Therefore, Kant concludes that the relational theory of space must
be incorrect.
However,
the objective of this paper is to use the IC analogy as a speculative tool for
discussing the nature of determinism in relation to human reasoning, rather
than address the absolute/relational space controversy. To accomplish this, the
paper will consider the following cases based on Kant’s original concept.
(LH1) A
right hand cannot enter into an LH world. Also, the right hand is inconceivable
in the LH world.
(LH2) A
right hand can enter into an LH world, and if it does it will be perceived no
differently than the existing left hand.
(RH1) A
left hand cannot enter into an RH world. Nevertheless, its attributes can be
hypothesized in the RH world.
(RH2) A
left hand can enter into an RH world. Also, the RH world can hypothesize the
attributes of the left hand before such entry takes place.
2. A
deterministic knowledge argument
This paper
will use the following three key definitions for the discussion:
(1) Deterministic knowledge (D
knowledge): The totality of facts associated with all the past, present, and
future events in a deterministic world. The totality coincides with every time
point of the world.
(2) Knowledge-in-hindsight (H
knowledge): The totality of facts associated with all the events in a world
ranging from the beginning up to a particular time point. The totality coincides
with the particular time point and the time thereafter.
(3) Metaphysically open deterministic
world: A deterministic world where there is a metaphysical sense in
assuming a scenario in which its deterministic knowledge is provided to a
cognitive agent of the world.
Definitions
(1) and (2) were influenced by Wittgenstein’s idea that the world is the
“totality of facts” (Wittgenstein 1922, 25). In Definition (3), the idea of the
cognitive agent receiving D knowledge bears a resemblance to the “circular-seeming idea of
substituting a string’s own Gödel number into the string itself” (Nagel &
Newman 2001, 89).
But what is a string? In a formalized
system of mathematics, “postulates and theorems” are “‘strings’ (or finitely
long sequences) of meaningless marks, constructed according to rules” (Nagel
& Newman 2001, 26). Further, a Gödel number is a “unique number [assigned]
to each elementary sign, each formula (or sequence of signs), [or] each proof
(or finite sequence of formulas),” which “serves as a distinctive tag or label”
(Nagel & Newman 2001, 69). D knowledge for the world can be likened to the
Gödel number assigned for a math theorem. Also, the cognitive agent can be
compared to a variable within the math theorem. Just as the Gödel number for the
theorem is substituted into the variable within the theorem, the D knowledge is
fed back into the cognitive agent’s information processing mechanism.
The result
of such feedback in (3) can be illustrated using Cantor’s diagonal argument as
another analogy. According to Cantor, the proposition that real numbers
correspond one-to-one with natural numbers is false because a distinct real
number can be created that is not included in a hypothetical list where real
numbers correspond to natural numbers (Simmons 2008, 20-22). See the following
simplified illustration.
Suppose
that natural numbers correspond one-to-one with real numbers within [0, 1]. For
instance:
n = 1 and
r1 = 0.[1]0010…
n = 2 and
r2 = 0.0[0]100...
n = 3 and
r3 = 0.11[1]00…
n = 4 and
r4 = 0.001[1]0…
n = 5 and
r5 = 0.1111[1]…
… and so
on.
rd
= 0.01000… can be generated by changing 0 to 1, or 1 to 0 in the digits in the
brackets. This real number does not exist in the existing list. This proves
that no one-to-one correspondence can be established between natural numbers
and the real numbers within [0, 1].
Imagine
what might happen when rd = 0.01000… is paired with a new natural
number and then added to the existing list of real numbers. Upon examination, a
new real number would emerge that is not included in the updated list. The
concept of D knowledge shows a similar characteristic. D knowledge should
include all the descriptions of the physical events related to the agent. The
verbal descriptions correspond one-to-one with the physical events. Suppose
that the agent gains access to the content of the D knowledge. However, this
access is not described in the existing verbal descriptions included in the D
knowledge. Also, gaining access to it would generate a new derivative version
of D knowledge that describes the agent’s access to the original D knowledge.
Undoubtedly,
the idea of the cognitive agent receiving the D knowledge is unconventional and
seemingly contradictory. How could someone know about one’s future if it was
preordained? One way of circumventing this contradiction is to assume that a
particular deterministic world is contained within a larger system and that
there exists a mathematical probability that the descriptions in the D
knowledge will be at a particular time point provided to the agent from the
larger system. Technically speaking, however, that would be an indeterministic
world. Accordingly, this paper proposes to examine a hypothetical situation
where the agent receives[iii]
the D knowledge in a metaphysical
sense.
Another
unconventional aspect of the argument is the assumption of two apparently
identical but different deterministic worlds. For example, Schwartz defines
determinism as the view “that [possible] worlds cannot be the same up to a
point and then diverge” (Schwartz 2012, 216). However, in this paper’s thought
experiment, it is possible for two
deterministic worlds to be computationally the same up to a point and then
diverge when D knowledge is provided to them. If one maintains that the human
mind cannot be fully reduced into an algorithm, then it is necessary to assume
that a divergence between the two worlds is possible. Specifically, this paper
presents the following two deterministic worlds that are established as “ICs”:
(i) The
original world, and
(ii) A
simulated world that replicates every aspect of the original world and realizes
the human mind through computationalism (i.e., the computational theory of
mind), characterized by an input-output system that may involve stochastic[iv]
elements.
These two
worlds are assumed to be metaphysically
open. From a computational viewpoint, both worlds are the same. However,
they are ultimately different as they produce different outcomes in response to
D knowledge.
2.1
Predefined deterministic knowledge
If the D
knowledge of the simulated world were provided to its cognitive agent, the
agent would process it simply as one of the available inputs that is closest to
the D knowledge and produce a corresponding output. This means that the agent’s
cognitive mechanism operates with rigid
processing, as the agent cannot process in any other way an input that it
was not configured to receive. Accordingly, this paper defines the simulated
world as trivially deterministic. This world is governed by predefined D knowledge. This knowledge dictates how things should occur.
Based on
the IC analogy, it is observed that the simulated world is physically
characterized by “LH1.” Recall that a right hand cannot enter into the LH1
world. Similarly, D knowledge cannot be provided to the simulated world.
Additionally, the simulated world is metaphysically characterized by “LH2.” If
a right hand enters into the LH2 world, it will be perceived no differently
than the existing left hand. Likewise, even if the D knowledge were provided to
the simulated world, it could not be identified by its cognitive agent as
distinct from all the other existing available inputs.
See below
the input-output mappings for the time point that the agent receives the D
knowledge. Since this is a deterministic world, the agent is originally
designed to receive only one input from I1 to In. The
other inputs are provided only as hypotheticals that could have been processed
from a computational viewpoint. Specifically, the other input-output pairs than
the actual input-output pair serve to illustrate counterfactual cases. These cases
are also described in the predefined D knowledge.
Input set:
I1, I2, …, In
Output
set: O1, O2, …, On
1 ≤ k ≤ n
ID
= D knowledge
ID
= Ik
OD
= Ok
However,
the above mappings are based on a non-stochastic model, which does not allow
for indeterminacy. Based on the notion of stochasticity, it is possible to
construct the mappings below. Each subset of the output set is constructed such
that the probabilities of the elements within each subset add up to 1.
I1,
I2, …, In
{O1[1],
…, O1[s1]}, {O2[1], …, O2[s2]}, …, {On[1],
…, On[sn]}
OD
= One element from {Ok[1], …, Ok[sk]}
In the
stochastic model as well, it is seen that the agent’s response to the D
knowledge remains trivial because its response cannot be anything other than
the predefined outputs.
In the
simulated world, suppose that there is an AI philosopher named Susan. She loves
coffee but often hesitates whether to have a coffee every morning. She loves
coffee for its taste. Besides, its caffeine helps fuel her insights when
developing a line of philosophical thinking. However, she also worries about a
potential side-effect of caffeine such as insomnia. One morning, she decides to
have a coffee anyway without knowing that it would cause her insomnia later
that night. She starts drinking it while reading her philosophical essay draft
through a tablet device. In this case, suppose that there is a 60% chance that
she will stop drinking her coffee if she is somehow convinced that she will not
be able to fall asleep at night. The following mappings are established for a
specific time point in the morning:
I1
= She feels thirsty (possibly due to the caffeine).
I2
= Nothing happens other than the continuous visual influx of texts from her
tablet.
I3
= She is convinced that she will not be able to sleep tonight because of her
coffee.
O1
= She drinks a glass of water on her desk.
O2
= She continues to read.
O31
= She stops drinking her coffee.
O32
= She continues to drink her coffee.
However,
since the world is deterministic, it can be assumed that only a particular
input such as I2 was configured to occur at the specific time point.
Meanwhile, in a metaphysical sense, it is possible to assume that specific
descriptions in the D knowledge could be provided to her at the specific time
point. For instance, suppose that her tablet suddenly displays detailed
descriptions involving all of her activities that occurred in the morning (such
as having breakfast or checking the weather outside), her inner thoughts and
emotions throughout the morning, and a subsequent scenario of the day to unfold
involving her loss of sleep due to the coffee. How would she respond to this?
She will most likely be “convinced that she will not be able to sleep tonight
because of her coffee.” Then, given the 60% chance, she will probably stop
drinking the coffee.
2.2
Reflective deterministic knowledge
If the D
knowledge of the original world were provided to its cognitive agent, the agent
would perceive it as a different input than the available inputs and generate a
new corresponding output. This means that the agent’s cognitive mechanism
exhibits emergent processing,[v]
as the agent can distinctly identify a particular input that it was not
supposed to receive. Accordingly, this paper defines the original world as non-trivially
deterministic. Using the IC
analogy, this world can be physically characterized by “RH1” and metaphysically
by “RH2.” Further, it is possible that
the above D knowledge is reflective D knowledge. This
knowledge only reflects every
physical event across time. Unlike predefined D knowledge, it does not describe
counterfactual cases. Also, reflective D knowledge is compatible with the block
universe theory.
In the block universe model, “[w]hether
past, present or future, all events ‘lie frozen’ in the four-dimensional block,
much like the scenes from a movie are fixed on the film roll” (Thyssen 2020,
6). If one were to see the events of the universe like fixed scenes on a film
roll from an omniscient viewpoint across time, that person might be able to
extrapolate counterfactual cases in relation to those events. However, the
scenes themselves do not include such information. In that sense, the
reflective D knowledge only mirrors the physical events.
Meanwhile,
it is assumed that emergence of a new output in response to D knowledge is necessary, considering that the agent’s
cognitive mechanism is usually assumed to be governed by causality. However, the content of the new output may be deterministic or
non-deterministic. This is highlighted by the question mark in the input-output
mappings below. The input-output pairs other than the actual input-output pair
are provided as dummies whose contents are unknown. “In+1” is
enclosed in the parentheses to indicate that it is only a latent input for the
agent.
I1,
I2, …, In, (In+1)
O1,
O2, …, On, (?)
ID
= In+1 OD
= ?
If the
Susan scenario happened in the original world, she might have been struck to
the core and asked, “Am I living in a Matrix?”
2.3 Causal
deterministic knowledge
Based on
the notion of causality, this subsection defines causal D knowledge. Specifically, the D knowledge of a causally
deterministic world is generated by the first cause of the world.
Causal
determinism holds that everything that has happened could not have happened
otherwise and that everything will happen the way it is supposed to (Hoefer
2023). Such an idea of strong causal connections is applicable to a non-trivial
world without inconsistency. Assume that everything is deterministic in the
metaphysical as well as physical realm of the non-trivial world. Then, in the
metaphysical realm, it follows that the agent should produce a new
corresponding output whose content is deterministic in response to each
derivative version of D knowledge (i.e., D’, D’’, and so on).
This paper
defines such property as hard causality. It renders deterministic both physical and metaphysical
scenarios at the very beginning. In that sense, it can be described as an
extreme version of causal determinism. Specifically, hard causality suggests
that infinitely many derivative versions of D knowledge are causally generated
at once, which would make it impossible
to construct a simulated world through computationalism. In Susan’s situation,
she would have to give a different response to each derivative version of D
knowledge. Specifically, she should not keep only saying “Am I living in a
Matrix?” with regard to every derivative version of D knowledge. If she does,
this would show she relies on rigid processing.
Accordingly,
there can be no predefined D
knowledge that dictates a non-trivial world. In order for such
knowledge to exist, the contents of new outputs would have to be predefined in
response to infinite derivative versions of D knowledge before the world could
begin. This is not a plausible idea. See the mappings below.
I1,
I2, …, In, In+1, In+2, … and so on
O1,
O2, …, On, On+1, On+2, … and so on
ID
= In+1, OD
= On+1
ID’
= In+2, OD’
= On+2
... ...
2.4 Knowledge-in-hindsight as a “fail-safe”
Unlike in the above cases, suppose now that
the original world is indeterministic. Then, the concept of D knowledge would
be useless, rendering the D knowledge argument futile. In this case, H
knowledge can be used as a replacement. In a metaphysical sense, a cognitive agent of the past would still
allow for generation of an output in response to the H knowledge that the
cognitive agent is subject to. Further, even if there were exceptional events
in the history of the universe
where causality failed, this problem can be addressed, because H knowledge
provides information on a continuous sequence of events regardless of whether
or not they were causally interrelated. As long as causality works in regards
to the agent’s reception of H knowledge, the thought experiment remains valid. The point is that H
knowledge would also be interpreted distinctly by the human agent that is
subject to the H knowledge.
3. Diagonalization through concatenation
This section introduces new terms that can
help explain different causal characteristics exhibited by human and machine
agents in processing verbal information. Additionally, it presents a
theoretical basis for the human agent’s way of processing verbal
information.
3.1 Definitions
When a sentence is input into a machine
agent, it processes the sentence as a mere concatenation of words.
The machine has no sense of a temporal flow when executing the process. It
simply moves from one bit to another during its information processing. On the
other hand, when a sentence is presented to the human agent, the agent forms a
mental image of the subject word and retains[vi]
it up to the point of recognizing the predicate. Ultimately, the images of the
subject and predicate are combined to create a holistic image of the sentence
itself. This process can be defined as diagonalization.[vii][viii]
3.2 Continuity of space and time
The process of “retaining” mental images
raises the question of how any spatial/temporal transitions can occur if space
and time are continuous. For instance, what does it mean to move within
continuous space when no immediately subsequent coordinate can be defined with
respect to an origin? This issue can be resolved through an “ontological”
argument. Specifically, transitions can happen because they should happen in
order for the notion of continuity to be established. As illustrated in Zeno’s
paradox, continuity is discovered retroactively[ix]
through endless transitions. Without relying on these transitions, it is
impossible to identify continuity. Therefore, transitions must exist. Moreover,
the very initial distance between the two points that is to be split in two
ensures the presence of a discrete leap in real space. Ultimately, it can be
proposed that the human agent’s perceptual mechanism proactively achieves a discrete leap in real space and time, by
retaining relevant information (e.g., perceptible spatial/temporal coordinates)
along the way. This enables the human agent to process verbal information in an
inherently different way.
4. Further
implications
This
section investigates one possible empirical case of using the metaphysical
concept of D knowledge.[x]
Further, it explores how the initial question posed in the introduction of this
paper – how is it possible that the determinist can declare the universe to be
deterministic while remaining part of the deterministic universe – can be
resolved based on the D knowledge argument.
4.1
Quasi-deterministic knowledge
Consider a prototype AI named “TARS.”
Assume that TARS relies on non-stochastic
processing, which simplifies the experimental setup. With regard to the
replicas TARS0 and TARS1, conduct the following experiment: (1) Place TARS0 in
a controlled environment, (2) provide it with various inputs from t=t0
to t=tn, (3) collect its corresponding outputs, and (4) compile the
data. Next, place TARS1 in the same environment and provide it with the same inputs
at the exact time points as TARS0 only up to t=tk (0<k<n).
Finally, at t=tn, provide TARS1 with the data compiled from TARS0.
The key idea is that the compiled data serves as an input that TARS1 was not
supposed to receive. If TARS1 produces an emergent output, as described in
Section 2.2 on emergent processing, it can be considered to have surpassed
conventional AIs.[xi]
In the above case, the compiled data can be
regarded as an approximation to a narrow breadth of D knowledge specific
to TARS1. While the compiled data partially constitutes H knowledge for
humans, it can serve as quasi-D knowledge for TARS1.[xii]
Admittedly, it must be very difficult to determine if the above output truly
represents a new response to an input other than the available inputs, due to
the technical difficulties involved. Nevertheless, the metaphysical argument
remains significant as it provides a standard for evaluating an AI’s level of
enhancement.
The TARS experiment has an advantage over
one existing method of testing an AI on its enhancement. In her book
"Artificial You," Schneider proposes an AI Consciousness Test (ACT).
To test if an AI has consciousness, she suggests "'boxing in' an AI –
making it unable to get information about the world" (Schneider 2019, 53).
Schneider emphasizes that "the AI's vocabulary must lack expressions like
'consciousness,' 'soul,' and 'mind'" (Schneider 2019, 54). Then, the AI
can be asked a question like "Could you survive the permanent deletion of
your program?" (Schneider 2019, 55). If the AI's answer is similar to what
a human being might provide, it can indicate some evidence that the AI is
conscious. However, in the TARS experiment, an AI can be taught all those words
and still be tested on whether it has achieved emergent processing.
Regarding the TARS experiment, consider
adding a third replica, which will be referred to as TARS2. If TARS2 is
provided with the same quasi-D knowledge that was received by TARS1, in the
same manner that it was provided to TARS1, will TARS2 produce the exact same
output as TARS1’s? The outcome will have to be interpreted differently
according to each world model (e.g., a metaphysically open/closed,
deterministic/indeterministic world).
4.2 The
determinist versus the deterministic universe
In
"Freedom Evolves," Dennett notes that "confusion [over
determinism] arises when one tries to maintain two perspectives on the universe
at once." One perspective is the "God's eye" perspective, and
the other is the "engaged perspective of an agent within the
universe" (Dennett 2003, 93). His description of the former perspective
coincides with the Parmenidean view of the universe. Specifically, he states
that "[f]rom the timeless God's-eye perspective nothing ever changes"
as "the whole history of the universe is laid out 'at once'" (Dennett
2003, 93). It appears that Dennett is giving equal weights to both perspectives
but cautions against assuming them at the same time. He stops short of
providing a philosophical scheme in which both perspectives can coexist. Also, he
does not explicitly state that when he is expressing support for determinism,
he is doing that from a provisional God's-eye perspective. As a matter of fact,
every philosopher and scientist who makes a declarative statement about the
universe at large assumes such a perspective. However, every such individual is
also part of the universe. How to reconcile this discrepancy?
According
to the D knowledge argument, a human agent is distinguished by its capacity to
process even “otherworldly but comprehensible” inputs (i.e., D knowledge).[xiii]
This temporarily sets a determinist apart from the objects of the determinist’s
investigation that are to include the determinist when the determinist declares
the universe to be deterministic. This relationship between the two creates a
dialectic circle[xiv] that
grows as the determinist and the objects/events continue to encircle each other
in an alternating manner. This expanding circle provides a more sophisticated
illustration of the dynamics involving the determinist and the universe,
compared to the diagram in Wittgenstein’s TLP of the metaphysical subject’s eye
that remains encapsulated within the world’s periphery (Wittgenstein 1922, 75).
It is this dialectic circle that provides a holistic scheme for investigation
of the universe.
5.
Conclusion
The major
ideas of this paper can be outlined as follows.
(1)
Deterministic knowledge (“otherworldly but comprehensible”)
l Predefined
D knowledge: dictates the world (computationalism)
l Reflective
D knowledge: reflects the world (block universe theory)
l Causal
D knowledge: generated by the world (hard causality)
(2)
Knowledge-in-hindsight
l A
“fail-safe” in case causal determinism fails
l Quasi-D
knowledge for an AI machine
(3)
Metaphysically open deterministic world
l Trivial
determinism: rigid processing (concatenation)
l Non-trivial
determinism: emergent processing (diagonalization)
Based on the above conceptual scheme, this
paper has sought to preserve the uniqueness of the human mind while allowing
for hard determinism. Instead of discrediting computationalism and causal
determinism, it has integrated them into a comprehensive framework. Recall that
the investigation in this paper began by critically questioning Nietzsche’s amor fati. As such, it has an underlying
humanistic motivation as well. Ultimately, the above metaphysical model can
provide a foundation for investigation of the human mind and its place in the
supposedly deterministic universe.
However, this paper is subject to
limitations, including heavy reliance on metaphysical speculation and lack of
empirical evidence. For instance, in Section 2.3, the idea that the human mind
is capable of providing a distinct response to each of the infinite derivative
versions of D knowledge may not be deemed plausible by several readers. Further,
the conception of D knowledge may face challenges from quantum physicists, who argue
that describing physical events through exact spatial/temporal coordinates on
the quantum level is impossible in principle. Additionally, the D knowledge
argument cannot explain the phenomenon of qualia or a sense of agency and free
will. These problems require further study.
[i]
Similarly, Wittgenstein expresses the view that the “[metaphysical] subject
does not belong to the world” (Wittgenstein 1922, 74). It appears that neither
Wittgenstein nor compatibilists fully addressed how to distinguish the
“metaphysical subject” from the world by
including the subject within the world at the same time.
[ii]
According to Piccinini
and Maley (2021, Section 3.4), some scholars support “pancomputationalism,”
which proposes that the whole universe is computational (Piccinini and Maley
2021, Section 3.4).
[iii]
It is assumed that the cognitive agent receives only a “small breadth” of D
knowledge that is relevant to the agent. The entirety of the D knowledge would
be too immense to be processed by any agent.
[iv]
Rescorla states that “[i]n a stochastic model,
current state does not dictate a unique next state. (Rescorla 2020, Section
3.0)”
[v]
Schneider observes that “current
chatbots [such as ChatGPT] use existing human writing to describe their
internal state” (Schneider 2023). She suggests that “one way to test if a
program is conscious” is to “not give it access to that sort of material and
see if it can still describe subjective experience” (Schneider 2023). This idea
inherently relies on the concept of emergent processing.
[vi]
Supposing that space and time are continuous, Husserl’s diagram can
provide
a useful illustration for
how the “retaining” takes place (Dodd 2005).
If this “retaining” process cannot be implemented in machines, no amount of
machine training may achieve consciousness for an AI.
[vii]
The word “diagonalization” has been coined in this paper by drawing inspiration
from Cantor’s diagonal argument again. As explained in Section 2.0, there is
always a new real number that turns out to be not included in a list where
every real number is supposedly matched with a corresponding natural number.
Note that all the existing real numbers have left their “marks” in the single
new real number. Similarly, in the process of diagonalization, the distinct
images of the subject and predicate are merged together to create a holistic
meaning of the entire sentence.
[viii]
One’s image of a word arises out of one’s subconscious corpus in which the word
has formed sophisticated interconnections with other words. These connections
are also established through diagonalization. Then how does one build a corpus
from scratch? It starts by matching a particular spoken word with a physical
object and on and on. This matching process must also rely on diagonalization.
[ix]
The
“ontological” argument was influenced by Žižek, who mentions “a retroactive
realization that the solution can be found in what we originally saw as the
problem” (Žižek 2014, 29).
[x]
The concept of an imaginary number contradicts common sense as it appears to be
an “intangible” number in the realm of human experience. Nonetheless, its use
has been instrumental in establishing quantum mechanics and telecommunications.
Although D knowledge is a purely metaphysical concept, it can meaningfully
relate to the empirical world.
[xi]
It is possible that the (human) experimenter, whose mind is characterized by
emergent processing, can coexist in the same non-trivially deterministic world
with an AI whose mechanism is characterized by rigid or emergent processing.
[xii]
The practical application of quasi-D knowledge as an incomplete representation
of D knowledge specific to the AI can be likened to the conventional use of
3.14 as an approximation for the mathematical constant π.
[xiii]
D
knowledge is “otherworldly but comprehensible” in that it can never be accessed
but exists in comprehensible form. In that sense, D knowledge is unlike Kantian
things-in-themselves, which are “otherworldly and incomprehensible.”
[xiv]
This dialectic circle is associated with the
diagram of “The Absolute Idea” in Section 1 of Maybee’s
article on “Hegel’s Dialectics” (2020).
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