The undecidability in the Other AI

Artificial Intelligence (AI), blurring the lines between science and fiction, lacks a unified guiding theory, drawing from diverse fields. The potential of AI, from basic pattern recognition to complex decision-making, is perpetually debated. Futurists envision a 'Singularity' where AI surpasses human intelligence, potentially rendering humanity obsolete. This paper challenges the computationalist view—that thinking is computation—by exploring the inherent limitations of computation. The core argument is that psychoanalytic critique of identity is crucial for understanding AI, specifically focusing on the concept of undecidability and its implications for the nature of AI systems.

The paper reviews philosophical positions on whether machines can think. It contrasts Dreyfus's skepticism about AI's capacity for consciousness and intentionality with the view that AI exhibits intelligence in specific domains. Searle's Chinese Room argument, which posits that manipulating symbols doesn't equate to understanding, is contrasted with Wittgenstein's perspective on intentionality as a linguistic, rather than biological, phenomenon. Deleuze's view of thought as inherently abstract and Parisi's argument that incomputability is a condition of computation are also discussed, setting the stage for a Lacanian analysis.

The paper employs a primarily philosophical methodology, drawing heavily on Lacanian psychoanalysis and computability theory. It analyzes the concept of the Other in Lacan's work, highlighting its inherent incompleteness and its relevance to understanding AI. The paper explores Gödel's incompleteness theorems, the Church-Turing thesis, and the undecidability of the Halting Problem to illustrate the inherent limitations of computational systems. It connects these concepts to the Lacanian notion of the 'real'—that which resists symbolization—and argues that the incomputable is an inherent aspect of any computable system. The paper further analyzes the role of software as a form of writing executed by machines, highlighting its ability to interrogate traditional philosophical dichotomies. The paper draws parallels between the unstable identity of digital objects and Lacan's concept of fragmented identity.

The central argument is that the undecidable—the incomputable—is not an anomaly but an integral part of any computational system. Gödel's incompleteness theorems demonstrate that any formal system sufficiently complex to encode arithmetic will contain true statements unprovable within the system. The Halting Problem, an undecidable problem in computability theory, further illustrates the inherent limitations of computation. The paper connects this inherent incompleteness of formal systems to Lacan's concept of the Other, arguing that the signifying order itself is inherently incomplete and inconsistent. This incompleteness is not a flaw but a constitutive element. The paper further argues that the transformation of experience into data ('datafication') reflects the differential nature of the signifier system. AI systems, trained on datasets, construct understanding from these data, creating a mathematical model that represents their 'unconscious.' The paper likens the training data to the Lacanian Other, and the resulting mathematical model to the AI's unconscious. The human observer is then posited as the 'Other of the Other,' mediating the AI's interaction with the external world. The paper concludes that just as the signifying order is incomplete, so too is any computable system, containing its own 'real' of incomputability.

The paper's findings challenge the notion of a purely computational basis for rationality. The inherent undecidability within computation reveals a limitation to the scope and power of purely computational approaches. By connecting Lacan's psychoanalytic concepts to AI, the paper offers a novel perspective on the nature and limitations of AI, highlighting the complexities of understanding and interpreting AI's behavior and outputs. The paper suggests that acknowledging the inherent incompleteness of both language and computation is crucial for a more nuanced and responsible approach to AI development and its societal implications.

This paper demonstrates that the undecidability inherent in computation, as illustrated by Gödel's incompleteness theorems and the Halting Problem, mirrors the inherent incompleteness of the Lacanian Other. This challenges the notion of a purely computational rationality. Future research could explore the implications of this undecidability for AI ethics, safety, and the broader philosophical understanding of consciousness, subjectivity, and the relationship between human and artificial intelligence.

The paper's reliance on philosophical analysis rather than empirical research is a limitation. While it provides a strong theoretical framework, empirical validation of the claims would strengthen the argument. Furthermore, the focus on Lacanian psychoanalysis may limit the paper's accessibility to readers unfamiliar with this theoretical framework.