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  • Belief In God
  • Belief In God
  • Moral Knowledge
  • Moral Knowledge

Articles published on True Belief

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  • Research Article
  • 10.1007/s44204-026-00406-y
Virtue, value, and true beliefs: solving Wrenn’s problem of truth
  • Apr 21, 2026
  • Asian Journal of Philosophy
  • Timothy Perrine

Abstract Wrenn introduces a Problem of Truth. The problem is that two natural views about truth are at odds. The first is that truth confers value on beliefs; the second is that insofar as truth has an essence it is just saying things are as they are. But saying things are as they are does not appear to be a normative property; so how could it be a property that confers value on beliefs? Wrenn’s solution is to abandon the idea that truth confers value on beliefs. Nonetheless, he accepts that true beliefs are valuable. He argues that their value derives from a virtue, namely, the virtue of Truthfulness. My aim here is to investigate Wrenn’s Problem of Truth and his proposed solution. I argue that his solution fails because it runs afoul of the “wrong-reason” problem. I provide my own solution to the Problem of Truth on which conferring value is an essential property of truth, but not part of its essence. And lastly, I explore Wrenn’s implicit views about virtue and value, suggesting that they are at odds with a traditional view.

  • Research Article
  • 10.3389/fdpys.2026.1727052
False belief attribution in toddlers: an exploratory study with a novel unexpected-identity task
  • Mar 3, 2026
  • Frontiers in Developmental Psychology
  • Ilaria Grazzani + 2 more

Introduction Several studies, in the context of the debate on early implicit theory of mind, have investigated whether infants and toddlers are able to attribute false beliefs concerning the identity of an object. As a result, there is a lack of consensus regarding whether young children are able to understand others' belief about an object's identity when it can be represented in different ways. In the present study, we address this issue by using for the first time a close adaptation of a test originally devised by Butterfill and Apperly to advance the theoretical debate on early theory of mind. Given that this novel identity task could not be completed based on a minimal theory of mind, its use can play a significant role in such a debate. Method Employing an eye tracking system and based on the violation-of-expectation-paradigm, we explored how the participants (50 toddlers aged 20–24 months) performed in the true belief condition and in the false belief condition on a new identity task with a dual-identity object. Results Statistical analyses showed that the looking times and number of visits were not significantly higher in the TB condition than in the FB condition, supporting the claim that toddlers of this age don't demonstrate an implicit understanding of false belief. Discussion We discuss these outcomes in relation to the need for new studies operationalizing Butterfill and Apperly's test in order to advance the theoretical debate on one-system vs. two-system accounts of early theory of mind.

  • Research Article
  • 10.1093/chidev/aacaf001
Three-year-old children understand the false beliefs oftheir partner in collaborative decision making.
  • Feb 27, 2026
  • Child development
  • Bahar Köymen + 3 more

Classic false-belief tasks may be confusing because children converse with someone who knows that a situation has changed about a third person who does not know this. Two studies used a collaborative false-belief task in which US- and UK-based 3-year-olds (N = 84, 48 girls, data collection: 2023) and a partner had to jointly decide in which box a toy was hidden. Children informed their partner and provided reasons about the location of the toy more when their partner had a false belief than when they had a true belief. We discuss the hypothesis that collaborative decision making pushes children to understand how their partner's perspective relates to their own and, when they differ, to assess how each corresponds to reality.

  • Research Article
  • 10.1111/nous.70041
Virtuous Deferral
  • Feb 21, 2026
  • Noûs
  • J Adam Carter + 1 more

ABSTRACT Virtue epistemology has long struggled with the “Creditability Dilemma”: how can knowledge gained through deference be creditable to the knower if it primarily depends on others’ cognitive work? We propose a novel solution by developing a telic account of doxastic deference as a distinctive kind of social‐epistemic performance. On our view, such deference succeeds when a deferrer forms a true belief that p in domain d , which answers their query, on the basis of the fact that a deferee states that p because of their epistemically superior competence in d . Drawing on Sosa's framework of performance assessment, we identify a metaphysical hierarchy of increasingly creditable achievements in deferential belief‐formation, from mere accurate doxastic deferral through to fully apt doxastic deferral. This hierarchy reveals that the apparent tension between individual credit and epistemic dependence rests on an “inverse creditability” thesis which fails to apply in cases of deferential belief. Instead, the highest forms of deferential achievement often align with and track the cognitive achievements of those deferred to. This framework also illuminates expert identification and epistemic trespassing as problems of exercising deferential skill under suitably normal conditions.

  • Research Article
  • 10.1007/s11229-026-05453-9
Tracking the truth by selecting good data: coherence measures and data selection
  • Feb 17, 2026
  • Synthese
  • Edoardo Baccini + 3 more

Abstract In formal epistemology, a variety of probability-based coherence measures have been proposed that provide a quantitative formal representation of the coherence of a set of information pieces. While research has long focused on whether coherence measures are truth-conducive, the truth-conduciveness of coherence measures has so far been evaluated in static settings only: Coherence provides assessments about the truth of incoming information, but does not actively guide decisions to believe or discard pieces of information. In this paper, we propose to assess the truth-conduciveness of coherence measures with respect to their ability to lead agents to select true information and form correct beliefs in a dynamic iterative setting. At every time step, an agent receives a number of noisy signals about the actual truth values of a finite set of atomic propositional variables. The agent uses a coherence measure to decide which signals to trust and which to discard. By repeatedly picking signals that maximise the coherence of the propositions they currently believe to be true, the agent tries to select truthful signals and learn the correct truth-value assignment for the atomic variables. The contribution of this paper is three-fold. First, we propose a computational model to assess the truth-tracking abilities of different coherence measures. Second, using computational simulations, we compare a number of widely discussed coherence measures from the novel standpoint of our iterated data-collection setting: We show that, when signals are not too noisy, agents who employ the Glass-Olsson relative overlap measure outperform agents employing all other tested measures, and that all measures become progressively worse at leading agents towards the truth as signals degrade. Finally, we discuss how coherence affects the emergence of different dynamics and attitudes in belief revision.

  • Research Article
  • 10.36948/ijfmr.2026.v08i01.68082
Nyāya Logic and Western Epistemology: Towards a Comparative Theory of Knowledge
  • Feb 4, 2026
  • International Journal For Multidisciplinary Research
  • Mukul Bala

This study explores the epistemological dialogue between Nyāya logic of classical Indian philosophy and Western epistemology, aiming to develop a comparative theory of knowledge. Nyāya epistemology, codified in the Nyāya Sūtras of Gautama, presents a pluralistic framework of four pramāṇas—perception (pratyakṣa), inference (anumāna), comparison (upamāna), and verbal testimony (śabda). It situates valid cognition (pramā) not only as a theoretical achievement but also as an instrumental means for the attainment of liberation (mokṣa). Western epistemology, from Plato’s concept of knowledge as justified true belief to the analytic refinements of Russell, Quine, and Williamson, has traditionally emphasized perception and inference, often underestimating the role of testimony in knowledge formation. By placing these two traditions in dialogue, this paper identifies points of convergence in rational inquiry and logical methodology, as well as divergences in the treatment of epistemic sources, the role of metaphysics, and the ultimate purpose of knowledge. It proposes a comparative theory of knowledge that integrates the analytical precision of Western philosophy with the pluralistic inclusivity of Nyāya, offering insights for contemporary debates in cognitive science, artificial intelligence, and cross-cultural philosophy.

  • Research Article
  • 10.12775/setf.2026.004
The Epistemological AI Turn: From JTB to KnowledgeS
  • Jan 23, 2026
  • Scientia et Fides
  • Roman Krzanowski + 1 more

In this paper, we examine whether large language models (LLMs) can be said to possess knowledge in the sense defined by the Justified True Belief (JTB) framework, and if not, whether any alternative form of knowledge can meaningfully be attributed to them. While LLMs perform impressively across various cognitive tasks—such as summarization, translation, and content generation—they lack belief, justification, and truth-evaluation, which are essential components of the JTB model. We argue that attributing human-like knowledge (in the JTB sense or its variants) to LLMs constitutes a category mistake. Accordingly, LLMs should not be regarded as epistemic agents with human-like capacities, but rather as machine tools that simulate certain functions of human cognition. We acknowledge, however, that when used critically and ethically, these tools can enhance human cognitive performance. To distinguish the capacities of LLMs from human cognitive agency, we introduce the term knowledgeS to denote the structured linguistic outputs produced by LLMs in response to complex cognitive tasks. We refer to the emergence of knowledgeS as marking an “epistemological AI turn.” Finally, we explore the theological implications of AI-generated knowledge. Because LLMs lack conscience and moral sense, they risk detaching knowledge from ethical grounding. Within normative traditions such as Christianity, knowledge is inseparable from moral responsibility rooted in the faith of a religious community. If AI-generated religious texts are mistaken for genuine spiritual insight, they may promote a form of “algorithmic gnosis”—content that mimics sacred language while remaining spiritually hollow. Such developments could erode the moral and spiritual depth of religious expression. As AI systems assume increasingly authoritative roles, society must guard against confusing knowledgeS with genuine, embodied, and ethically accountable knowing, which remains unique to human agency.

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  • Research Article
  • 10.1007/s11023-026-09759-y
Responsible Assessment of Beliefs Based on Computational Results: Expanding on Computational Reliabilism
  • Jan 21, 2026
  • Minds and Machines
  • Michael W Schmidt + 1 more

In order for advanced computational systems, such as AI systems, to be successfully integrated in liberal democracies, the people who design, use or are affected by these systems in many cases must be adequately disposed to hold the results of these systems to be true. How is such belief in these results justified, given the opaque nature of advanced computational systems and the possibility of error? The theory of “computational reliabilism” (CR) outlines how such belief can be justified and lead to a genuine advancement in human knowledge. The basic idea of CR is that the belief in the results of computational systems, despite their opacity, can be justified by their positive rate of producing true beliefs. In this paper, we show that CR needs to be expanded by focusing more on the human agents who are interacting with these systems epistemically and the consequences of the human-computer interaction. The reliability of a belief-forming process based on a computational system can only be assessed by taking into account both these agents and the ethical stakes involved. Moreover, if CR is intended to guide action, a responsible assessment of reliability must rely on an internal type of justification that is relative to the respective epistemic agent and typically necessitates an institutionalized division of epistemic labor.

  • Research Article
  • 10.59865/prajn.2026.2
AN ACTION-ORIENTED ACCOUNT OF KNOWLEDGE: AN ALTERNATIVE APPROACH TO THE GETTIER PROBLEM BASED UPON WANG YANGMING’S PHILOSOPHY
  • Jan 14, 2026
  • Prajñā Vihāra
  • Caiqin Liu

The Gettier problem for the classical analysis of knowledge (also known as the JTB theory) arises from scenarios where a justified true belief is true by chance, and as a result is not plausibly taken to be an instance of knowledge. Epistemologists often address the Gettier problem by positing extra conditions to construct a stable connection between the subject and truth. However, they tend to overlook the dynamic and practical aspects of knowledge, focusing instead on providing a ‘static’ reductive analysis that captures the fixed essence of the concept of knowledge. I critique such limitations and argue that knowledge resists static and fixed definitions, requiring a more dynamic and practice-oriented perspective. In this essay, I provide an alternative approach to understand knowledge with respect to the Chinese philosopher Wang Yangming’s theory of the unity of knowledge and action (zhi xing he yi 知行合一). Submitted: 19 November 2025 Accepted: 27 December 2025

  • Research Article
  • 10.62461/cql181026
A Critique on the Solution of Zakzewoski’s Virtue Responsibilism to the Gettier Problem
  • Jan 1, 2026
  • Religion and Social Communication
  • Caiqin Liu

Edmund Gettier demonstrated that the traditional analysis of knowledge (as a justified true belief) is insufficient. Some philosophers have proposed that virtue epistemology holds the key to solving the Gettier problem. Among them, Zagzebski’s virtue responsibilism has gained significant popularity. This solution posits that knowledge is a belief state originating from acts of intellectual virtue, where these acts are driven by intellectually virtuous motivations, the cognizer successfully achieves the ultimate goal of motivation (truth and understanding) through these acts. In other words, knowledge (truth) is attained because of the operation of one’s intellectual virtues. This revision of the traditional analysis of knowledge purportedly escapes the problems identified in the Gettier cases. In this paper, I argue that Zagzebski’s definition of knowledge is problematic as it cannot be proven that intellectual virtue is a necessary condition for knowledge. Furthermore, in the metaphysical context of mind–things dualism, it is unrealistic to attempt to establish a stable and reliable connection between intellectual virtue (the mind) and truth (the external world). In short, the intellectual virtue of epistemic agent cannot guarantee the acquisition of knowledge. It is not the key to solving the Gettier problem.

  • Research Article
  • 10.52834/jmr.2025.214203
The Worst Types of Sins and Their Effects on Human Thought in Belief and Behavior
  • Dec 31, 2025
  • Journal of Misan Researches
  • حامد هادي بدن

The divine will was for the Islamic community to be a harmonious, loving society, blessed with the pure servitude of Allah Almighty, free from any blemish that might divide its members and undermine its unity. Division in Islam is tantamount to disobeying Allah, His Messenger, and the guiding Imams. Sins often occur as a result of following the whims of the soul, which commands evil. The most prominent effects of these sins include disobeying parents, consuming usury, drinking alcohol, and speaking ill of one's parents, which leads to weakness and debility. One of the motives that lead to the sins committed by man and which have afflicted the Islamic nation yesterday and today is distancing oneself from the religion of Allah Almighty and not adhering to the rope represented by the Prophet Muhammad (peace be upon him and his family) and the family of the Prophet (peace be upon them). Today, we are working to solve this according to the Qur’anic approach represented by correct thought and true Islamic belief, so that the culture of the Holy Qur’an may prevail among young people, especially in the educational environment, to build the family, on correct Islamic foundations to ensure a righteous society that fights negative phenomena with degrading content, with a sound intellectual weapon, deriving its components from belief, jurisprudence and logic, according to the approach of Sharia in Islam

  • Research Article
  • 10.17990/rpf/2025_81_4_1173
Towards a Pure Causal-historical Theory of Reference Borrowing
  • Dec 31, 2025
  • Revista Portuguesa de Filosofia
  • Jaakko Reinikainen

This paper develops and defends a pure causal-historical theory of reference borrowing, understood as a theory that explains successful reference transmission without appeal to independently specified conceptual or descriptive content. Starting from Kripke’s insight that speakers can refer to historically distant individuals via chains of transmission, the paper distinguishes sharply between the epistemic individuation of reference—relevant to interpretation, communication, and cognitive access—and its metaphysical individuation, grounded in causal-historical relations. Against hybrid theories of reference borrowing, particularly those that posit minimal true or approximately true categorical beliefs as necessary conditions for successful borrowing, the paper advances a three-step objection based on arguments from ignorance, error, and theoretical incompleteness. Drawing on the mental files framework, it argues that descriptive information plays an explanatory role on the epistemic side of reference, but not on the metaphysical side. Through discussion of canonical cases involving historical names, fictional misunderstandings, and runic inscriptions, the paper concludes that reference borrowing can succeed in the absence of associated true descriptions, provided that the appropriate causal-historical connections are in place. The result is a programmatic defense of reference as a substantive causal relation, open in principle to empirical investigation, and irreducible to descriptive or hybrid accounts.

  • Research Article
  • 10.33423/jop.v25i4.8033
Knowledge Is Not What It Used to Be: Organizational Research Implications of Critical Theory and Postmodern Thought
  • Dec 29, 2025
  • Journal of Organizational Psychology
  • Robert Donmoyer

Critical theory and postmodern/poststructuralist thought continue to be influential in academia and, increasingly, even in some parts of popular culture. Both movements, in somewhat different ways, challenge the traditional conception of knowledge as “justified true belief,” as well as claims that empirical research can provide such knowledge. Because academia tends to be siloed (One university in Australia, for example, even established two different departments in the same academic discipline, one for critical theorists, the other for more traditional academics.), social scientists who study organizations empirically often have ignored or, possibly, may not even be aware of critical theory and/or postmodernist thought. This paper explores a range of exceptions to this statement. Some of the exceptions discussed here are quite problematic; others appear to represent more defensible ways to inquire into organizations and organizational life from a critical theory or postmodernist perspective.

  • Research Article
  • 10.1007/s11229-025-05382-z
How moral philosophers can help society
  • Dec 8, 2025
  • Synthese
  • Kian Mintz-Woo

Abstract This paper argues that moral philosophers can have a special role in helping members of society come to choose which moral theories to believe. Importantly, the argument does not depend on the idea that moral philosophers (more) reliably have true moral beliefs (or are “Strong Moral Experts”). Instead, the argument is that moral philosophers are well-placed to develop understanding of moral theories by drawing out valid implications (they are “Weak Moral Experts”). By developing valid moral arguments, and by making the relevant implications accessible to society, moral philosophers can help people understand the costs and benefits of various moral theories, allowing them to make more informed choices. This does not imply that everyone will agree; there is room for disagreement about the weight to put on various theoretical costs and benefits. But it does give a metaphilosophical picture of the role of moral philosophers, justify certain kinds of public philosophy, and explain the value that moral philosophers can add to society at the philosophy-public interface.

  • Research Article
  • 10.1007/s11245-025-10284-3
Charity in Radical Interpretation
  • Dec 1, 2025
  • Topoi
  • Kirk Ludwig

Abstract In later work, Davidson distinguished two strands in the Principle of Charity which he called the Principle of Coherence and the Principle of Correspondence (“Three Varieties of Knowledge” 1991). The Principle of Coherence tells us to find another to be rational and intelligible. The Principle of Correspondence deals with the connection between another’s hold true attitudes and her environment. I focus on the Principle of Correspondence. I consider three interpretations suggested in Davidson’s work. The first is the Principle of Sentential Truth, which requires the interpreter to find the speaker’s hold true attitudes to be true. The second is the Principle of Agreement in Belief, which requires the interpreter to find the speaker to be largely in agreement with the interpreter about her environment. The third is the Principle of True Belief, which requires the speaker to be largely right about her environment. I argue none of these is adequate to the task Davidson sets himself. I consider a fourth principle, the Principle of Salience, which requires the interpreter to find the speaker to be speaking truly about things that the interpreter would find salient in the speaker’s position. The last of these is connected with the intuitive idea of triangulation in Davidson’s later work. I argue that the interpreter needs to employ the Principle of Salience, but this requires the interpreter to justify an a posteriori assumption about targets of interpretation. I assess the implications of this for Davidson’s anti-Cartesian epistemology and philosophy of mind.

  • Research Article
  • Cite Count Icon 1
  • 10.1007/s10071-025-02028-y
Is dogs' tendency to follow human misleading communicative cues influenced by humans' auditory perspective?
  • Nov 23, 2025
  • Animal cognition
  • Lucrezia Lonardo + 3 more

Studying Theory of Mind in non-verbal populations requires designing tasks that address the distinction between responding based on directly perceivable cues and additionally inferring others' mental states. We designed and pre-registered an auditory version of a non-verbal change-of-location task, to investigate whether dogs are sensitive to a human communicator's mental states about the location of food. With control conditions we ruled out alternative cognitive processes such as associative learning. Dogs (N = 240) could witness that food was hidden first in one opaque bucket (A) and then relocated to a second opaque bucket (B) by an experimenter. Before being allowed to retrieve the food from one of the buckets, dogs received a misleading suggestion (A) from the communicator, who could not see the scene. In all conditions, the communicator could hear food being hidden in A, due to the presence of bells on the lid of this bucket. We manipulated whether she could also hear that food was removed from A and relocated to B (true belief) or not (silent bells on B, leading to her false belief). Importantly, in both conditions the communicator behaved identically (present in the room, suggesting A). Dogs' responses were not statistically different from those of a previous study using a similar change-of-location task in the visual domain (Lonardo et al.288(1955),2021, https://doi.org/10.1098/rspb.2021.0906 ). Dogs' choices in the present study, however, did not differ significantly across conditions, suggesting that any auditory perspective-taking ability they might possess did not have a sufficiently large effect to be detected in this study.

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  • Research Article
  • 10.1162/opmi.a.258
Agenda Setting and The Emperor’s New Clothes: People Diagnose Information Cascades During Sequential Testimony by Reasoning About Informants’ Speaking Order and Social Status
  • Nov 22, 2025
  • Open Mind : Discoveries in Cognitive Science
  • Emory Richardson + 2 more

Consensus-based social learning strategies often outcompete other strategies in evolutionary models. But while formal proofs suggest that consensus’ reliability is compromised when individual judgments are not independent, this makes for a notoriously implausible assumption in the biological world: the people we learn from are constantly learning from each other as well. How do we avoid being misled by consensus? We present three experiments and a computational model examining commonsense reasoning about how people’s public and private judgments are influenced by the consensus and social status of those around them. Results suggest that while people realize that these two factors can cause others’ public and private judgments to diverge, their own trust in public consensus depends on how accurately they believe it reflects their informants’ true beliefs.

  • Research Article
  • 10.3390/philosophies10060126
Justified True Belief + Diachronic Justification: A Contemporary Defence
  • Nov 18, 2025
  • Philosophies
  • Ahmet Küçükuncular

I defend a diachronic constraint on justification as a necessary condition for knowledge. In my view (JTB + D), a belief is knowledge-apt only if its justification is maintainable over a context-sensitive interval Δ under ordinary avenues of evidence-accrual, including reliable memory, testimony, and communal inquiry, with no accessible undefeated defeaters arising within that interval. This temporal, process-sensitive requirement mitigates Gettier-style luck by targeting “snapshot” justification that would easily collapse under minimal further scrutiny (as in Fake Barn County), while avoiding infallibilism and over-intellectualism. I calibrate Δ by stakes and domain volatility to avoid vagueness and moving goalposts, distinguish responsive stability from mere habituation, and show how the account handles no-new-evidence scenarios without undermining ordinary memorial and testimonial knowledge. Conceptually, the proposal integrates internalist and externalist insights as it preserves reason-responsiveness over time and serves as an actual-world temporal analogue of safety, not a standalone fourth ‘dimension’. I engage canonical cases and acknowledge Zagzebski’s challenge: the view does not promise full Gettier immunity, but it raises the bar for counterexamples in ordinary environments. The result is a principled, parameterised refinement of the justification condition that better captures knowledge as an enduring, responsibly supported true belief.

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  • Research Article
  • 10.1007/s44163-025-00534-z
A JTB based study of epistemic attribution to robots as “Knowledge”
  • Nov 17, 2025
  • Discover Artificial Intelligence
  • Tetsuya Matsui

Abstract This study investigated how users perceive the concept of “knowledge” in robots and how this perception differs from their views on human knowledge. Based on the Justified True Belief (JTB) framework for knowledge, I conducted three experiments to verify whether users apply the same standards to a robot’s knowledge as they do to human knowledge. In Experiment 1, I demonstrated that the conditions under which users attribute knowledge differ between humans and robots through an experiment where participants read a Gettier-type scenario and answered questions. Experiment 2 examined the threshold at which information is perceived as “knowledge,” revealing that users tend to demand more direct verification from robots than from humans. Experiment 3 examined the impact of beliefs about the robot’s knowledge, identified in Experiments 1 and 2, on users’ moral judgments. The results showed that users attributed less responsibility to the robot as an accomplice to the crime than to a human accomplice. These results suggest that users perceive robots’ knowledge as inflexible, requiring direct perception, and fundamentally different from human knowledge and reasoning. These findings provide important insights for the design of human–robot interaction (HRI) systems. Understanding users’ perceptions of robot knowledge may be essential for building trust in future human–robot collaboration.

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  • Research Article
  • Cite Count Icon 1
  • 10.1007/s10462-025-11383-8
Philosophical proposition optimizer (ΦPO): an epistemology-inspired algorithm for numerical optimization
  • Nov 4, 2025
  • Artificial Intelligence Review
  • Siamak Talatahari + 2 more

Abstract The development of intelligent optimization methods has become a highly active research area in recent decades. This paper introduces a philosophy-inspired optimization algorithm called the Philosophical Proposition Optimizer (ΦPO), which models knowledge acquisition based on philosophical propositions in epistemology. In the proposed philosophical model, three developmental states for philosophical propositions, Justified True Belief (JTB), Possibly False Belief (PFB), and Unjustified True Belief (UTB), are iteratively refined using three specialized operators: Providing Justification (PJ), Raising Metaphysical Skepticism (RMS), and Raising Epistemic Skepticism (RES). To evaluate the performance of ΦPO on challenging optimization problems, it is applied to the single-objective bound-constrained benchmark problems of the IEEE Congress on Evolutionary Computation 2014 and 2024 (CEC 2014 and 2024), as well as to benchmark engineering problems. The performance of ΦPO is compared against five categories of algorithms: (1) widely used classical methods, (2) established post-2019 methods, (3) advanced PSO- and DE-based methods, (4) winners of CEC competitions, and (5) well-studied methods for solving engineering design problems. Two established non-parametric statistical methods, the Friedman test and the Wilcoxon signed-rank test, are used to analyze performance. The findings highlight the advantages of ΦPO across a range of numerical optimization problems, underscoring its competitiveness and potential in the field. Importantly, ΦPO was intentionally designed to be simple, interpretable, and parameter-free, avoiding complex adaptive strategies and extensive parameter tuning. It consistently delivers stable, high-quality solutions and exhibits fast convergence in many cases. The results demonstrate that ΦPO performs competitively across multiple benchmark suites, often ranking among the top-performing algorithms and outperforming several state-of-the-art methods, including recent CEC competition winners and engineering-specific optimizers. Its unique epistemic approach to solution refinement further enhances robustness, distinguishing it in both numerical and engineering optimization tasks.

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