Logic, Philosophy of Mathematics, Philosophy of Logic, Philosophy of Computation, Philosophy of Science
I view logic not merely as a technical toolkit but as a powerful methodology for philosophical inquiry, fundamentally reshaping our understanding of core concepts such as proof, truth, computation, and infinity. This philosophical commitment prompted a strategic shift in my focus from 2017 onward, leading to a systematic exploration of the incompleteness phenomenon revealed by Gödel's theorems and its profound implications for the philosophy of mathematics, logic and computation. The incompleteness phenomenon highlights the inherent limits of formal systems, prompting exploration of the differences between human and machine intelligence, as well as the boundless and non-mechanical nature of human reason.
My early work (pre-2017) established my technical rigor through foundational research in pure set theory, focusing on concrete incompleteness in higher-order arithmetic and large cardinals research.
Since 2017, my research has focused on exploring the landscape of incompleteness from integrated logical, foundational, and philosophical perspectives, structured around three interconnected themes, with findings published in leading international journals and a research monograph by Springer:
· Theme 1: The Limits of Gödel's Incompleteness Theorems. I investigate the applicability limits of Gödel's Theorems. We demonstrate that the First Incompleteness Theorem is, in a sense, limitless. Additionally, I examine the intensionality of the Second Incompleteness Theorem, clarifying how its validity depends on various factors.
· Theme 2: Meta-Mathematical Properties Related to Incompleteness. This theme involves a systematic study of the meta-mathematical properties of arithmetical theories that lead to incompleteness and undecidability. A central result of this research is the proof that no minimal effective inseparable theory exists with respect to interpretability.
· Theme 3: Philosophical Questions Related to Incompleteness. I explore the philosophical implications of Gödel's theorems, the depth of Gödel's theorems, the anti-mechanist argument, and the nature of arithmetical truth and pluralism.