The concept of transitive self-reflection is deeply rooted in philosophical discourses, including Hegel’s notion of "recognition" [1] and Sartre’s "being-for-others" [2]. These ideas emphasize the necessity of external interaction for self-awareness. Modern cognitive science complements these perspectives, highlighting how transitive self-reflection engages both introspection and external feedback to refine one's sense of self [3]. This contrasts with intransitive self-reflection, which focuses solely on internal states, lacking the enriching influence of external engagement [4].

The concept of intelligence has been defined in various ways, with numerous tests designed to measure its presence. A common underlying assumption in these definitions is that human cognitive abilities serve as intelligence benchmarks. In this paper, we adopt the same perspective: for a system to be considered intelligent, its cognitive performance must be comparable to that of humans. A system lacking a fundamental aspect of human cognition cannot be deemed truly intelligent. Based on this premise, we explore a crucial prerequisite for intelligence.

Self-reflection—the ability to introspect and analyze one's thoughts, emotions, and actions—is often regarded as a hallmark of higher intelligence [5]. However, an even more sophisticated indicator is what we term "transitive self-reflection". This concept extends beyond mere self-awareness; it involves understanding not only oneself but also how one is perceived by others, as well as how others perceive each other's perceptions of oneself [6]. Such multi-layered awareness indicates a complex cognitive architecture capable of modeling intricate social dynamics and predicting the cascading effects of one's actions within a network of interacting minds [7].

Transitive self-reflection is not limited to social interactions but also extends to how one's image is mirrored in the environment—through reflections in mirrors, water, or other reflective surfaces. These external representations provide an additional perspective on self-awareness, reinforcing the ability to perceive oneself from an external viewpoint [8].

Evidence of transitive self-reflection is apparent in various aspects of human behavior. Social interactions require individuals to constantly monitor and adjust their behavior based on how they believe they are perceived [6]. Gossip exemplifies this process, as people attempt to infer how their actions are interpreted and relayed by others [5]. Strategic thinking in games like poker demands an advanced level of transitive self-reflection, where players must anticipate not only their opponents' strategies but also their opponents' understanding of their strategies. Even emotions such as embarrassment arise from transitive self-reflection, as individuals become aware of how they are perceived in a negative light [8].

This study examines transitive self-reflection as a fundamental criterion for intelligence, particularly in the context of artificial intelligence. We investigate its manifestation in humans, its potential presence (or absence) in other animals [9], and the feasibility of replicating it in machines. Ultimately, we argue that transitive self-reflection may be the key to advancing the next generation of intelligent systems. To explore this, we conduct a series of experiments with several popular artificial intelligence systems based on Large Language Models (LLMs), assessing the type of intelligence they currently exhibit.

These systems cannot independently produce genuinely new ideas. However, they serve as effective tools for trained specialists, who can iteratively refine their outputs to construct meaningful works.

The structure of this paper is as follows: Chapter 2 introduces the concept of transitive self-reflection, and Chapter 3 explores its connection to intelligence. The work concludes with a discussion of future directions.

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