Rethinking Human and Machine Intelligence through Kant’s Incongruent Counterparts

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 the LH world. Also, the right hand is inconceivable in the LH world.

LH₂: A right hand can enter into the LH world, and if it does, it will be perceived no differently than the existing left hand.

RH₁: A left hand cannot enter into the RH world. Nevertheless, its attributes can be hypothesized in the RH world.

RH₂: A left hand can enter into the RH world. Also, the RH world can hypothesize the attributes of the left hand before such entry takes place.

These cases will be mentioned again for analogical reasoning in Section 2.1 and Section 2.2

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) Deterministic world: A world where events are deterministic. There is metaphysical significance in considering a case of providing D knowledge to a cognitive agent of this world.2

Definition (1) 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.

Definition (2) introduces a seemingly contradictory idea. If D knowledge were provided to the agent, it suggests that she could gain knowledge about her future. However, if she did attain such knowledge, the D knowledge would no longer be valid because it fails to describe one particular event: her attainment of the knowledge. To address this apparent contradiction, this paper will examine reception of D knowledge in a metaphysical sense only.3

Now let us define two deterministic worlds that are established as “ICs.”

(i) An 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

According to Schwartz (2012), determinism is 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 that the deterministic worlds (i) and (ii) are computationally identical up to a particular 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 becomes necessary to assume that such a divergence is possible.

For further discussion, this paper will use concepts of computationalism to investigate the characteristics of information processing exhibited by both agents. 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.

(a) 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.

(b) 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 highly stochastic nature.7 Such a feature might hinder accurate realization of a scripted scenario. 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, …, x_n}

O = {y₁, y₂, …, y_n}

Since this is a trivially deterministic world, only one of the input events from x₁ to x_n 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:

x_D = x_k (x_D is reduced to x_k.) 1 ≤ k ≤ n

x_D = Reception of D knowledge

y_D = y_k

y_D = A 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, …, x_n}

O = {y_1[1], …, y_1[s1]}, {y_2[1], …, y_2[s2]}, …, {y_n[1], …, y_n[sn]}

x_D = x_k (x_D is reduced to x_k.) 1 ≤ k ≤ n

y_D = One element from {y_k[1], …, y_k[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 (which means that the counterfactual cases are unknown). “x_n+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, …, x_n,(x_n+1)}

O = {y₁, y₂, …, y_n, (?)}

x_D = x_n+1  y_D = ?

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 her reception of D knowledge.

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, …, x_n, (x_n+1), (x_n+2), … }

O = {y₁, y₂, …, y_n, (y_n+1), (y_n+2), …}

x_D = x_n+1   y_D = y_n+1

x_D’ = x_n+2   y_D’ = y_n+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) Tegmark11 (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 presenting 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

Car → Universe

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. The analogy would have been more accurate if the “someone” had a complete description of both herself and the car.12 Tegmark’s case is one instance illustrating 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. He adds 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. Specifically, he does not reveal how it is possible for the agent within the universe to assert determinism from a provisional God’s-eye perspective.

The above 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 inherently inaccessible; 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 illustrated 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 pancomputational13 sense, from all the other events of the world. Specifically, in a world without any distinction between the two (i.e., espousal of determinism and the other physical phenomena), the agent (possibly a machine agent) would have no motivation in the first place to assume a higher “vantage point” from which to view the world. Roughly speaking, in such a world, no scholarly discussion on determinism would have any meaning. If our universe is to be depicted differently from that world, a determinist’s declaration of determinism should by necessity stand out by acquiring a particular metaphysical meaning amidst all the events of the universe. This is achieved by granting a privileged status to the determinist regardless of the truthfulness of her argument. She can be granted such a status because of her inherent capacity to comprehend D knowledge.

Finally, note that this peculiar dynamic between the determinist’s philosophical mind and the universe can be best described through a dialectic circle in Maybee (2020, Section 1). Before the determinist decides on the determinacy of the events of the universe, these events must first be placed within the determinist’s scope of thoughts. In other words, they should become the objects of the determinist’s speculative investigation. Then, as the determinist declares determinism, she realizes that the entire process (from her investigation up to the declaration) is also part of the deterministic scenario of the universe. Subsequently, she concludes from a transient God’s-eye perspective that every time she declares determinism, this would have also been predetermined. In hindsight, she realizes that her conclusion was also predetermined.

The above process continues, 14 thereby generating the dialectic circle. It expands as the determinist’s mind and the objects/events of the universe continue to encircle each other in an alternating manner. This type of circle provides a more nuanced illustration than the image of “eye” of the “metaphysical subject” encapsulated within “the field of sight” in Wittgenstein (1922, p. 75), as well as a different image that one may newly draw by placing the eye outside the field of sight.

4. Conclusion

The main ideas of this paper can be outlined as follows.

(1)

Deterministic knowledge

• Type 1

  ■

  Dictates the world.

  ■

  Includes finite counterfactual cases.

• Type 2

  ■

  Reflects the world.

  ■

  Includes no counterfactual cases.

• Type 3

  ■

  Is generated by the world.

  ■

  Includes infinite counterfactual cases.

(2)

Deterministic worlds

• Trivially deterministic world

  ■

  Its agent executes rigid processing.

• Non-trivially deterministic world

  ■

  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 justify a determinist’s assertion of determinism by placing the determinist within the universe.