Rethinking Human and Machine Intelligence through Kant, Wittgenstein, and Godel
Abstract
This paper proposes a metaphysical
framework for distinguishing between human and machine intelligence. By drawing
an analogy from Kant’s incongruent counterparts, it posits two identical deterministic
worlds -- one comprising a human agent and the other comprising a machine
agent. These agents exhibit different types of information processing
mechanisms despite their apparent sameness in a causal sense. By postulating
the distinctiveness of human over machine intelligence, this paper resolves
what it refers to as “the vantage point problem” – namely, how to define the
determinist’s reasoning mind in relation to the universe where the determinist
belongs.
Keywords:
determinism; incongruent counterparts; simulation; state description;
counterfactuals
Introduction
This paper
was motivated by asking questions about the concept of amor fati (or “love of fate”) (Nietzsche, 1990, 99). This philosophy of life has inspired
many of Nietzsche’s readers seeking guidance in life. However, his advice seems
to have certain inconsistencies. For instance, how can someone learn to embrace
fate if everything in her life has been predetermined? If determinism is true,
would it not be accurate to say that even an act of learning to love her fate
was also predetermined? Was Nietzsche himself, perhaps, predestined to encourage
his readers to love their fate?
When determinists
assert that the universe is deterministic, this requires assuming a hypothetical
vantage point from which to describe the universe. However, that vantage point
should not belong in the universe.[1]
Meanwhile, the determinists themselves are part of the universe. This peculiar
relationship between the two appears to cause a contradiction. Therefore, they must
figure out how to justify the significance of their assertion by situating themselves
within the universe. This issue will
be referred to as the “vantage point problem” in this paper.
To address
the problem, this paper proposes to discuss two different types of
deterministic worlds by using Kant’s “incongruent counterparts” (hereinafter,
“ICs”) as an analogy. The paper also builds upon Gödel’s proof strategy for his
incompleteness theorem and Wittgenstein’s (1922) proposition that “the world is
the totality of facts” (p. 25). Admittedly, the use of Kant’s ICs may seem
far-fetched, since his original purpose was to resolve an absolute versus
relational space controversy. In addition, Gödel’s theorem belongs in the field of mathematics, so one
may question this paper’s approach for its potentially pseudo-philosophical utilization
of the theorem. However, these concepts are used for analogical reasoning only;
they are not meant to provide direct insights into the issue at hand. If readers
patiently follow this paper’s arguments to the end, they will see how it
establishes a plausible model allowing determinists to validly claim our
universe as deterministic while remaining part of it.
1. The Incongruent
Counterparts
Kant
devised the concept of ICs to address the issue of absolute versus relational
space (Kant, 1994, pp. 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, p. 447).
However, the relational view of space denies the existence of absolute space
and defines motion only in relation to other bodies.
Kant develops
his argument by discussing the left hand and right hand. Specifically, the left
hand observed from a perspective restricted to the property of the left hand
would be no different from the right hand observed from a perspective
restricted to the property of the right hand. However, their difference is apparent
“when both are considered in relation to some appropriate third thing”
(Remnant, 1963, p. 393). In other words, they are revealed to have different
orientations from an external perspective embedded in absolute space.
However,
the aim of this paper is to use the IC analogy as a speculative tool for
discussing the nature of determinism in relation to human reasoning. To achieve
this, by building upon Kant’s concept, this paper assumes a world where only a
left hand exists (an “LH” world) and another world where only a right hand
exists (an “RH” world). Specifically, it posits the following cases.
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. Deterministic
Knowledge
This paper
will use the following key definitions:
(1) Deterministic knowledge (D
knowledge): A totality of facts associated with all the past, present, and
future events in a deterministic world.
(2) 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.[2]
The
concept of D knowledge is
similar to Carnap’s (1947) “one state-description” (he notes that this idea was
inspired by Wittgenstein) (p. 10). Specifically, it “describes the actual state
of the universe” and “contains all true atomic sentences and the negations of
those which are false” (p. 10). However, Carnap primarily devised this concept in
relation to a semantical system for linguistic analysis. Meanwhile, D knowledge
relates to descriptions of a deterministic world. In this regard, these two notions
are different. Nevertheless, following Carnap, we will assume that D knowledge
is an entirety of atomic sentences that describe a deterministic world.
Regarding
Definition (2), 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, p. 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”
(p. 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” (p.
69). The D knowledge specific to the universe can be likened to the Gödel
number assigned to a string (or mathematical theorem). Also, the agent can be
compared to a variable in the theorem. Just as the Gödel number for the theorem
is substituted into the variable in the theorem, the D knowledge is fed back
into the agent’s information processing mechanism. Put simply:
Gödel number (representing a theorem) → D knowledge (describing the
universe)
Theorem → Universe
Variable (included
in the theorem) → Agent (included in the universe)
Substituting the Gödel number into the
variable →
Providing the D knowledge to the agent
Undoubtedly,
the idea of the agent receiving the D knowledge is unconventional and seemingly
contradictory. How could someone know about her future if it was predetermined?
One way of circumventing this contradiction might be 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 reception of D knowledge in
a metaphysical sense only.[3]
Another
unconventional aspect of this paper is the assumption of two apparently
identical but different deterministic worlds. For example, Schwartz (2012) defines
determinism as the view “that [possible] worlds cannot be the same up to a
point and then diverge” (p. 216). However, in our thought experiment, it is possible for two deterministic worlds
to be causally the same up to a point and then diverge when D knowledge is
provided to them. If one contends that the human mind cannot be fully reduced to
an algorithm, it is becomes necessary to assume that such a divergence is
possible.
For
further discussion, we define the following two metaphysically open deterministic
worlds that are established as “ICs.”
(i) The
original world like ours that comprises a human agent.
(ii) A
simulated world that replicates every aspect of the original world and comprises
a machine agent emulating the human agent in a causal manner.[4]
The
paper will discuss information processing through computational concepts. According
to Beraldo-de-Araújio, the essence of computation is “symbolic manipulation”
and concerns “mapping function between two sets of symbols” (Polak &
Krzanowski, 2019, p. 6). The human agent’s symbolic manipulation, for instance,
may take place through neural activities in the brain. Meanwhile, the machine
agent performs symbolic manipulation by processing machine-readable symbols. By
slightly changing Beraldo-de-Araújio’s definitions on p.6, this paper defines
computation as follows.
(1) A
process is a function P: I → O such that its domain I is a set whose elements
are called input events and its co-domain
O is a set whose elements are called output events,
while both I and O are subsets of a physical world. For all x∈I, y = P(x) (y∈O) is a corresponding output
event.
(2) A
computer is a function C: S → T from a set of input symbols S to a set of output symbols
T, such that C(x̅) is outputted by computing x̅. (x̅ is a symbolic
representation of x.) A process P: I → O is computational if P is generated by
a computer C.
In
the simulated world, we suppose that the mind is a “classical von Neumann
computer” and that “its representation-bearers [are] data structures” (Frankish & Ramsey, 2012, pp. 31-32).[5]
This world is intentionally designed to avoid being based on a “connectionist”
model.[6]
Specifically, it may not be feasible for the connectionist model to accurately
emulate the human agent due to its comparatively high stochastic nature. Such a
feature might hinder accurate realization of a scripted scenario in which
probabilities may be occasionally assigned to counterfactual input events.[7]
Although the classical model may be much less sophisticated, it can at least
robustly emulate human behaviors in hindsight if all the relevant information
is available.
2.1 Type 1
If the D
knowledge specific to the simulated world were provided to its agent, the agent
would process reception of the D knowledge simply as one of the existing
potential input events. This suggests that the agent executes rigid processing, as it cannot process
in any other way an input that it was not configured to receive. This world is trivially deterministic in
that it is governed by a predefined type of D knowledge (i.e., Type 1)
that dictates how things should
occur.
Through
the IC analogy, the simulated world can be physically characterized by “LH1.”
Recall that a right hand cannot enter into LH1. Similarly, D
knowledge cannot be provided to the simulated world. Additionally, the
simulated world can be metaphysically characterized by “LH2.” If a
right hand enters into LH2, it will be perceived no differently than
the existing left hand. Likewise, even if the D knowledge were provided to the
simulated world, its provision could not be identified by its agent as distinct
from all the other existing potential input events.
See the
following mappings.
I = {x1,
x2, …, xn}
O = {y1,
y2, …, yn}
Since this
is a trivially deterministic world, only one of the input events from x1
to xn is to occur. The pairs other than the actual input-output pair
serve to illustrate counterfactual cases. These cases are included in Type-1 D
knowledge. Now suppose that reception of D knowledge occurs immediately before
a particular event in the input event set does. Then:
xD
= xk (xD is reduced to xk.) 1 ≤ k ≤ n
xD
= reception of D knowledge
yD
= yk
yD
= response to reception of D knowledge
However,
the above mappings are based on a non-stochastic model, which does not allow
for indeterminacy. By supposing for now that the simulated world is
indeterministic, we can establish the following mappings.
I = {x1,
x2, …, xn}
O = {y1[1],
…, y1[s1]}, {y2[1], …, y2[s2]}, …, {yn[1],
…, yn[sn]}
xD
= xk (xD is reduced to xk.) 1 ≤ k ≤ n
yD
= One element from {yk[1], …, yk[sk]} (The probabilities
assigned to these stochastic outcomes add up to 1.)
The above
stochastic model is meant to show that, even in an indeterministic world, as
long as the agent relies on rigid processing, its response to reception of the
D knowledge could be nothing other than any one of the predefined output events.
To
illustrate the triviality of the simulated world, let us consider a hypothetical
scenario involving a clinical psychologist named “Millicent” (or simply “Millie”).
She loves coffee but often hesitates whether to drink it. One morning, she
decides to have a coffee anyway while watching a seminar video through a tablet
device. In this case, suppose that there is a 60% chance that she will stop
drinking her coffee if she happens to think that it will do her no good. The
following event mappings are
established for her in atomic-sentential form:
x1
= The seminar tires me.
x2
= The coffee does not convince me of insomnia.
x3
= The coffee convinces me of insomnia.
y1
= I stop watching.
y2
= I keep drinking.
y31
= I stop drinking.
y32
= I keep drinking.
However,
since the world is deterministic, only a particular event such as x1
(which does not allow a stochastic outcome) would have been configured to
occur. Meanwhile, in a metaphysical sense, it is possible to assume that
specific descriptions in the D knowledge could be provided to her immediately
before x1 happens. Suppose that her tablet displays not only the
above mappings but also a short history of her activities in the morning and
the events to unfold throughout the day. How would she respond?
From a
humanistic perspective, there must be a distinct mental representation corresponding
to the event of “I see the descriptions.” However, Millie’s rigid processing
mechanism would only be able to interpret the sight of the display as one of x̅1
to x̅3. Recall that Millie’s mind follows the classical
computer model whose representation-bearers are data structures. Since she only
executes rigid processing, a bit structure corresponding to her symbolic
representation of the event would most probably be translated to a particular
bit structure corresponding to one of x̅1 to x̅3. Suppose
that it is interpreted as x̅3. Then, her processing mechanism would
output either one of y̅31 and y̅32. Given the 60% chance,
it would probably output y̅31, which should be accompanied by y31.
In other words, she would probably stop drinking her coffee in response to
receiving the D knowledge.
2.2 Type 2
If the D
knowledge specific to the original world were provided to its agent, the agent
would process reception of the D knowledge as a different input event than all
the other previous potential input events. This means that the agent’s processing
mechanism exhibits emergent processing,
as it can distinctly identify a particular input event that was not supposed to
happen. This world is non-trivially deterministic. Using the IC analogy, it can be physically characterized by “RH1”
and metaphysically by “RH2.” Further,
it is possible (rather than necessary) that the D knowledge only reflects every physical event across
time. Unlike Type 1, this type of D knowledge (namely, Type 2) does NOT include
counterfactual cases. Also, this 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,
p. 6). If one were to see the events of the universe like fixed scenes on a
film roll from an omniscient viewpoint across time, she might be able to
extrapolate to a certain extent counterfactual cases in relation to those
events. However, the scenes themselves do not include such information. In that
sense, Type-2 D knowledge only mirrors the physical events.
Meanwhile,
we assume that emergence of a new output in response to D knowledge reception is
necessary, considering that the
agent’s processing mechanism is 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 pairs other than the actual input-output pair are provided
as dummies whose contents are unknown (i.e., the counterfactual cases are
unknown). “xn+1” (i.e., reception of D knowledge) is enclosed in
parentheses to indicate that it is only a latent
event in a metaphysical sense.
I = {x1,
x2, …, xn,(xn+1)}
O = {y1,
y2, …, yn, (?)}
xD
= xn+1 yD
= ?
If the Millie
scenario happened in the original world, she might have been struck to the core
and asked, “Am I living in a Matrix?” by emergently interpreting D knowledge
reception.
2.3 Type 3
Despite
its assertion that the past, present, and future all coexist, the block
universe theory does not demand absolute causality. Polkinghorne (2007) notes
that “[b]elievers in the block universe are not forced to commit themselves to
a deterministic account of its causal structure” (p. 977). However, assume that
the original world is thoroughly deterministic in a causal sense. Then, one can entertain the idea that its agent’s
decision-making processes are strictly deterministic in a metaphysical as well
as physical sense. Specifically, the agent should produce a new output (whose
content is deterministic) in response to receiving D knowledge of Type 2. This hypothetical
situation would generate a derivative version of D knowledge (namely, D’). Then,
the agent should produce another output in response to receiving D’, thereby
generating another derivative version of D knowledge (namely, D’’). To aid in
understanding this somewhat complex scenario, let us go back to the Millie story.
With regard to the Millie of the original world, D’ knowledge might state as
follows:
“Millie responds
to D knowledge. She speaks, “Am I living in a Matrix?”
D’’
knowledge might state:
“Millie responds
to D’ knowledge. She speaks, ‘I might need to take some medication to calm my
caffeine-induced paranoia. Or maybe this world that I’m living in was
monstrously rigged, and I must somehow survive by figuring out how I first
reacted to… I don’t know, but it seems like this situation that I’m in happened
already once before, and I must figure out whatever this evil gadget had said
in the first place. Let me think… Whatever action I take right now, was that
also predetermined?’”
See the
following formal mappings:
I = {x1,
x2, …, xn, (xn+1), (xn+2), … }
O = {y1,
y2, …, yn, (yn+1), (yn+2), …}
xD
= xn+1 yD
= yn+1
xD’
= xn+2 yD’ = yn+2
… …
The above mappings
may develop indefinitely.[8]
All these potentially infinite counterfactual cases are included in Type 3.[9]
Further, it can be said that this type of knowledge is generated by an inherent configuration of the world.[10]
For instance, Tegmark (2008) argues that it is “plausible that our universe
could be simulated by quite a short computer program” (p. 18). Based on the idea
that “our universe is mathematics”
(p. 1), he maintains that its realization only requires storage of “all the
4-dimensional data” (i.e., all the “[encoded] properties of the mathematical
structure that is our universe”) (p. 18). He states that a “complete
description” of a mathematical structure is “a specification of the relations
between the elements” of the mathematical structure (p. 18). As such, the
4-dimensional data primarily relate to the abstract realm of mathematics. If
his argument is true, we would not need any type of D knowledge (consisting of
verbal descriptions in atomic-sentential form) in order to simulate a universe.
Rather, D knowledge would be a byproduct of the mathematical structure and its
specification.
3. The
Vantage Point Problem
This
section explores how the “vantage point problem” stated in this paper’s
introduction can be addressed by relying on the concept of D knowledge. Let us
first look into two philosophical cases where this problem has not been
properly addressed.
(1)
Tegmark[11]
(2008) asserts that “[t]here exists an external physical reality completely
independent of us humans” and that “[o]ur external physical reality is a
mathematical structure (p. 1). However, despite his convincing arguments, he
still fails to address the vantage point problem. In footnote 3 on p. 5, he
notices the problem of how a mathematician should derive, through (i) a
mathematical structure alone, (ii) an empirical domain and (iii) “a set of
correspondence rules which link parts of the mathematical structure with parts
of the empirical domain.” He hints at a possibility of achieving this by
introducing a “car” analogy. Specifically, “given an abstract but complete
description of a car (essentially the locations of its atoms),” “someone” that
wants “practical use of this car” might “be able to figure out how the car
works and write her own manual” by “carefully examining the original
description.” Put simply:
“Someone” → Mathematician
Description
of the car →
Mathematical structure of the universe
Practical
use of the car → Empirical domain of the universe
Knowledge
of how the car works → Correspondence rules linking the mathematical structure
with the empirical domain
While the
mathematician is part of the universe, that “someone” is not part of the car.
Therefore, the car analogy fails. In fact, the above analogy well illustrates a
common mistake made by scientists as well as philosophers – namely, the
confusion that arises from the vantage point problem.
(2) Dennett
(2003) notes that "confusion [over determinism] arises when one tries to
maintain two perspectives on the universe at once" (p. 93). One
perspective is the "God's eye" perspective, and the other is the
"engaged perspective of an agent within the universe" (p. 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'" (p. 93). Dennett appears to give equal
weights to both perspectives but cautions against assuming them at the same
time. He does not provide a philosophical scheme where both perspectives can
coexist.
The two
cases illustrate the ongoing struggle of scientists and philosophers to
reconcile the discrepancy between a human agent making a declarative statement
(i.e., a deterministic worldview) about the universe at large and the universe
where the agent belongs. It is believed that this paper has resolved this issue
to a certain extent. Unlike machines, human intelligence is capable of emergently
processing -- to use a bit of an oxymoron -- even “otherworldly but comprehensible” knowledge
(i.e., D knowledge). By definition, D knowledge is an entirety of verbal
descriptions encompassing the whole universe. This type of knowledge is
inaccessible in principle; therefore, it can be considered to exist in an “otherworldly”
realm. Nevertheless, it is deemed “comprehensible” from the human agent’s
perspective, as evidenced by its capacity to provide a non-trivial response to
D knowledge. This has a metaphysical implication that the human agent could
potentially view the universe from a vantage point situated in a realm beyond
the universe despite actually being part of the universe. However, for machine
intelligence, D knowledge is neither “otherworldly” nor “comprehensible.” In fact,
there is no type of information at all that can be genuinely comprehended by
machine intelligence. This is demonstrated through the triviality of responses
it might generate with regard to D knowledge in Section 2.1.
Further, the
same level of triviality could be said to be exhibited by a hypothetical agent whose
declaration of determinism should be assumed to be qualitatively inseparable --
in a pancomputational[12]
sense, for instance -- from all the other events of the universe. If no
distinction is made between such an act of declaration and the events of the
universe that are yet to include the act of declaration, no scholarly
discussion on determinism would have any meaning. Therefore, the declaration of
determinism should by necessity stand out by acquiring a particular
metaphysical meaning in the midst of all the events of the universe. This is
achieved by granting a privileged status to a determinist regardless of the
truthfulness of her argument. The grant of such a status can be justified by her
inherent capacity to comprehend D knowledge. Finally, note that this peculiar
dynamics between the determinist and the universe can be best described through
a dialectic circle in Maybee (2020, Section 1). This circle grows as the
determinist and the objects/events of the universe continue to encircle each
other in an alternating manner. It is this dialectic circle that provides Wittgenstein’s
(1922) “metaphysical subject” (p. 75) with a holistic scheme for investigation
of the universe.
4. Summary
The major
ideas of this paper can be outlined as follows.
(1)
Deterministic knowledge
l Type
1
n Dictates the
world.
n Includes
finite counterfactual cases.
l Type
2
n Reflects the
world.
n Includes
no counterfactual cases.
l Type
3
n Is
generated by the world.
n Includes
infinite counterfactual cases.
(2)
Metaphysically open deterministic worlds
l Trivially
deterministic world
n Its
agent executes rigid processing.
l Non-trivially
deterministic world
n Its
agent executes emergent processing.
Based on the above conceptual scheme, this
paper has sought to distinguish human from machine intelligence by allowing for
hard determinism. In accordance with this scheme, it attempted to answer the
question of how to establish a qualitative distinction between a human agent as
an investigator of the universe and the universe that the agent belongs to.
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[1] Wittgenstein (1922)
notes that “the philosophical I” is a “metaphysical subject” that is “not a
part of the world” (p. 75). Determinism is a philosophical judgment imposed
upon the world by the determinists. Thus, the determinists’ reasoning mind
should not belong in the world.
[2] Vihvelin
(2023) proposes “[leaving] open the metaphysical possibility of time travel to
the past and backwards causation” (Abstract). These concepts are philosophically
worth considering even though they unlikely to materialize in reality.
Similarly, although an agent can never know the future with certainty, we can
at least consider the possibility.
[3] We
assume that the cognitive agent receives only a “small breadth” of D knowledge
that is associated with the agent. The entirety of D knowledge would be too
immense to be processed by any agent.
[4]
Müller (2014) validly distinguishes between two different physical
processes P1 and P2, which perform the same computation C
(p. 9). Similarly, the original and simulated worlds are computationally the
same but ultimately different.
[5] A representation-bearer is a means
through which an object being represented is thought/perceived by an agent. See
Frankish & Ramsey (2012, p. 9).
[6] Connectionism
suggests that “individual neurons do not transmit large amounts of symbolic
information” and that “they compute by being appropriately connected to large
numbers of similar units” (Feldman & Ballard, 1982, p. 208). Testing
whether a connectionist-based AI could think like humans may require a
different approach (e.g., Schneider’s (2019) ACT test (p. 54)).
[7]
The Millie scenario to be
discussed in Section 2.1 includes stochastic outcomes in response to a
counterfactual input event.
[8] Similarly, Sterelny (1990) notes that the “ability to
think about the world as it is and as it might be, to think indefinitely many
and indefinitely complex thoughts” may be a “necessary condition on having
intentional states” (p. 29).
[9] When considering the infinite counterfactual cases, we
see that there can be no predefined type of D knowledge (i.e., Type 1)
that dictates a
non-trivial world.
[10]
This configuration may be unidentifiable as demonstrated in the Kantian
antinomies (Kant, 1998, pp. 470-495).
[11]
Tegmark is a determinist. He supports Einstein’s dictum that “God does not play
dice” (p. 10).
[12] According to
pancomputationalism, “everything is a computing system” and “minds are
computing systems too” (Piccinini, 2007, p. 95).
