Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce)

Explaining the undecidability of first-order logic

Timm Lampert — 2024-12-31

Turing proved the unsolvability of the decision problem for first-order logic (Entscheidungsproblem) in his famous paper On Computable Numbers, with an Application to the Entscheidungsproblem. From this proof it follows that attempts to specify a solution for the Entscheidungsproblem through pattern detection in automated theorem proving (ATP) must fail. Turing’s proof, however, merely predicts the non-existence of such solutions; it does not construct concrete examples that explain why specific attempts to solve the decision problem by pattern detection fail. ATP-search often runs in infinite loops in the case of unprovable, i.e. not refutable, formulas and one can ask why finite patterns of repeated inference steps cannot serve as criteria for unprovability. We answer this question by constructing pairs of formulas (ϕ,ϕ′) such that ϕ is provable (refutable) and ϕ′ is unprovable (satisfiable in an infinite domain) but all but the last proof step of the ATP-search for ϕ is a proper part of the endless ATP-search for ϕ′. We generate such pairs of formulas by mimicking computable sequences for a certain kind of universal Turing machine, namely, splitting Turing machines (STMs), via sequences of inference steps in ATP. In contrast to Turing’s and the textbooks’ method to formalize Turing machines, our method does not rely on further axioms and allows us to transfer the straightforward insight that the halting problem cannot be solved through pattern detection to the case of the Entscheidungsproblem. Our method is a constructive alternative to general undecidability proofs that explains why a scientific problem, namely the Entscheidungsproblem, is unsolvable in a specific way. This explanation provides a better understanding of the failure of pattern detection, which is of interest to: (i) the programmer, who is concerned with prospects and limits of pattern detection, (ii) the logician, who is interested in identifying logical properties by properties of an ideal notation, and (iii) the philosopher, who is interested in proof methods.

Upholding human dignity in AI: Advocating moral reasoning over consensus ethics for value alignment

Octavian-Mihai Machidon — 2024-12-31

Artificial intelligence (AI) offers transformative advancements across sectors such as healthcare, agriculture, and environmental sustainability. However, a pressing ethical challenge remains: aligning AI systems with human values in a manner that is stable, coherent, and universally applicable. As AI increasingly mediates human perception, shapes social interactions, and influences decision-making, it raises profound ethical concerns about its impact on human dignity and social well-being. The prevailing consensus-based approach, advocated by figures such as Google DeepMind’s Iason Gabriel, suggests that AI ethics should reflect majority societal or political viewpoints. While this model offers flexibility, it also risks moral relativism and ethical instability as social norms fluctuate.
This paper argues that consensus-based ethics are inadequate for safeguarding fundamental values—especially human dignity—which should not be subject to shifting public opinion. Instead, it advocates for a moral framework that transcends cultural and political trends, providing a stable foundation for AI ethics. Through case studies like social media recommendation algorithms that exploit users’ vulnerabilities, particularly those of children and teenagers, the paper highlights the risks of AI systems driven by profit-oriented metrics without ethical oversight. Drawing on insights from moral philosophy and theology, particularly the works of Joseph Ratzinger, it contends that aligning AI with moral reasoning is essential to uphold human dignity, prevent texploitation, and promote the common good.

Homeostasis as a foundation for adaptive and emotional artificial intelligence

Anna Sarosiek — 2024-12-31

Homeostasis, a fundamental biological mechanism, enables living organisms to maintain internal balance despite changing environmental conditions. Inspired by these adaptive processes, research into artificial intelligence (AI) seeks to develop systems capable of dynamic adaptation, introspection, and empathetic interactions with users. This article explores the potential of implementing homeostatic mechanisms in AI as a foundation for emotional intelligence and self-regulation. Key questions include the distinction between simulation and actual experience, the role of machine introspection, and the emergence of qualitative states akin to phenomenal experiences. Drawing on Antonio Damasio’s theory and classical concepts from cybernetics, the article investigates how homeostatic principles might inspire the development of AI, paving the way for more flexible and context-aware technologies.

Philosophy in the context of physics and cosmology: Leszek M. Sokołowski’s philosophical views

Kamil Piotr Trombik — 2024-12-31

The article attempts to reconstruct and analyze selected philosophical views of Leszek Sokołowski—a Krakow physicist and cosmologist who published many works dealing with issues on the border of science and philosophy (including metaphysics). An important aim of the article is also to place Sokołowski’s views in the context of the concept of “philosophy in science” (by M. Heller) and the phenomenon of the Kraków School of Philosophy in Science. In this paper, I suggest that Sokołowski’s views fit into the philosophy initiated by Michał Heller, and Sokołowski himself can be considered a member of the Kraków School of Philosophy in Science.

Orientation in the environment like perceiving affordances? Andrzej Lewicki’s account of cognition

Michał Piekarski — 2024-12-31

The purpose of this article is to present Andrzej Lewicki’s account of cognition as orientation in the environment, comparing it with James J. Gibson’s ecological psychology. To do so, we conduct a comparative analysis of the former’s theory of indicators and the latter’s theory of affordance. The theoretical frame for our study is cognitive ecology, a research tradition characteristic of various studies of cognition, including contemporary ones. This allows us to show that, despite differences in the backgrounds and methodologies of these researchers, Lewicki can be considered one of the pioneers of contemporary ecological trends in cognitive science, although his influence has not been as widespread as that of Gibson. Our analysis proceeds in several steps. We begin with an overview of the biographies, backgrounds, and interests of the two researchers, as well as a brief introduction to cognitive ecology and related terms. Next, we discuss action/value indicators theory and affordances theory. We then compare Lewicki’s and Gibson’s approaches in more detail in terms of their use of similar research heuristics. The article ends with conclusions that go beyond historical issues.