Probabilistic Reasoning

Swarm intelligence optimization algorithms demonstrate excellent global search capabilities and robustness in solving complex optimization problems. Based on observations and abstractions of sika deer ecological behavior, this paper proposes a Spotted Deer Optimization Algorithm (SDOA). This algorithm transforms sika deer behaviors such as seasonal migration, social status formation, arena competition, fawn learning, and pheromone regulation into a mathematical model to achieve a dynamic balance between global and local search. The paper first constructs a mathematical description of the sika deer population (...) and a search strategy formula. Then, mathematical expressions for individual migration, status renewal, energy modeling, fawn perturbations, and pheromone regulation are derived in detail. Finally, complexity analysis and convergence proof demonstrate the theoretical feasibility and effectiveness of the algorithm. (shrink)

This paper examines the epistemic status of Humean diagnosis itself, and uses that examination as the entry point for a broader inquiry into the structure of philosophical self-reference. Beginning from Hume's three central claims — that causal connection is a psychological projection rather than a feature of the world, that inductive inference carries no logical guarantee, and that testimony for miracles is structurally self-defeating — we ask whether these diagnoses are themselves necessary or contingent. We argue that they occupy an (...) unstable middle position: stronger than ordinary empirical generalizations, yet unable to secure the framework-external necessity they appear to claim. This instability generates a self-undermining structure, which we situate within a broader typology of philosophical self-reference organized under the figure of the Ouroboros. The paper opens with a methodological preamble: a three-layer framework distinguishing ontological, epistemological, and linguistic levels of philosophical inquiry. These levels are mutually incommensurable. The history of philosophy's two major turns — the epistemological and the linguistic — are understood as successive filters, each constraining the preceding level within its own domain without issuing first-order verdicts at that level. This framework governs the categorization of all arguments in this paper — and is itself an adopted instrument subject to the same fallibilist treatment it recommends for everything else. The Ouroboros — the serpent that consumes its own tail — organizes two phenomena that require careful distinction: the self-directed character of philosophical critique, and the circularity that attends any attempt to justify the tools of justification. We argue that not all instances of either are epistemically vicious, and that the correct diagnosis depends on identifying which type of self-reference is operative. A key clarification accompanies the typology's application to Hume: the Ouroboros framework relocates Hume's self-undermining difficulty from the epistemological level — where the original problem of using a questioned capacity to assess that capacity's standing remains unresolved — to the logical level, where the question of whether the diagnoses are self-refuting admits a cleaner answer. This relocation is a problem replacement, not a problem solution, and the paper acknowledges it as such. We address logical revision, Quinean holism, and their internal tensions, arriving at a logical pluralism that the paper's epistemological commitments can accommodate without instability. The apparent categorical status of the law of non-contradiction is recharacterized as the historical projection of classical logic's practical dominance, not a framework-external metaphysical constraint. We construct a taxonomy of necessity after Hume, in which constitutive necessity emerges as the most robust survivor — not because it escapes Humean critique but because it operates at a different level than the critique targets. The necessary-but-not-sufficient and sufficient-but-not-necessary structure of hinge propositions is developed with precision. The paper concludes with a compact treatment of probability as an epistemic instrument. (shrink)

Unidentified Anomalous Phenomena (UAP) represent a persistent challenge to national security and scientific inquiry. Decades of official investigation across multiple countries have produced a consistent pattern: most cases are explained by conventional causes, but an irreducible subset---approximately 3--5\% of well-documented incidents---exhibits kinematic, electromagnetic, and behavioral properties that have resisted attribution to known human technology or catalogued natural phenomena despite rigorous investigation. This paper proposes an interpretive framework modeling that irreducible core as the atmospheric manifestation of a network of autonomous non-human (...) probes engaged in long-duration planetary survey operations. The framework does not assert an extraterrestrial origin, nor does it impute benevolent or hostile intentions. It restricts itself to contrasting observed phenomenology with the expected properties of autonomous monitoring systems, deriving testable predictions, specifying falsification conditions, and distinguishing precisely between what the available data can sustain and what remains beyond reach. The paper is presented as a working hypothesis, not as a closed conclusion. (shrink)

The brain functions as a fractal of anticipation, perpetually generating predictions across various dimensions—sensory, conceptual, and temporal. Although predictive processing (PP) has emerged as a prominent framework in cognitive science, its structures frequently lack the self-similarity and energy-efficient geometry found in biological systems. This paper presents the Fractal Predictive Processing Network(FPPN): a recursive, self-similar tree of predictive units, where each node is responsible for modeling expectations, calculating errors, and dynamically distributing inference resources through active inference. Structural parameters—depth, branching factor, angular (...) spread—are optimized using Cuckoo Search, aligning computational efficiency with energetic constraints akin to neurovascular fractals. FPPN employs bidirectional hierarchical PP, allowing abstract predictions to flow downward while errors ascend. We illustrate that this configuration inherently supports temporal abstraction, with lower branches sensitive to rapid changes and deeper nodes representing long-term patterns—providing a computational analogy to cortical timescale hierarchies. By integrating active inference, each node assesses expected free energy, activating or suppressing its subtree based on informational value. This results in an adaptive attention mechanism that reduces redundancy and enhances informational flow. Simulations indicate that FPPN not only improves predictive accuracy but also achieves significant energy savings. Beyond the realm of neuroscience, we propose that this architecture serves as a model for developing artificial agents where inference and structure evolve together. By connecting various fields—neuroanatomy, computational neuroscience, AI, psychology, and philosophy of mind—our framework reconceptualizes cognition as a fractal forest of recursive anticipation rather than a linear pipeline. In this conceptualization of thought, prediction transcends mere mechanism to become a shape—a self-similar whisper resonating throughout the levels of the mind. (Friston. 2010, Clark. 2013; Bullmore and Sporns. 2009, Werner. 2010; Karbowski. 2014, West & Goldberger, 1987, Varela et al.1991, Thompson. 2007, Hohwy. 2013; Metzinger. 2003; Sporns. 2011). (shrink)

Wieso die San bis fünf gezählt haben und wieso das mit Quantencomputern zusammenhängt; Und was hat es eigentlich mit der Aristoteles-Euler-Planck-Menne-Brüning-Folge auf sich?

This work is an effort towards the goal of understanding the connection between the concepts of causality and statistical dependence. Formally, this was done employing the notions of copula function and structural causal model. To achieve such goals, this dissertation first presented some problems that may arise in the analysis of non-experimental data and then presented the concepts of copula function and structural causal model. Within this context, this dissertation presented two contributions: first, based on the concept of structural equation, (...) a copula-based procedure to control omission variable bias in linear models was presented (which is an extension of a method already present in the literature in the case of a Gaussian copula). Finally, the main contribution of this dissertation was done through representation theorems that enables seeing the impact of a causal intervention in a joint density probability function through a copula function. It was proved that the change in the joint density induced by the causal intervention is fully characterized by a copula function. (shrink)

This paper, serving as the second part of the empirical arm for structural economics, establishes a framework for navigating financial environments by abandoning the fraught attempt to predict the unknowable psychology of investors. Instead, it analyzes the much more easily observable systemic structure itself, allowing one to accurately gauge the temperature of the market and act in accordance with its prevailing reality. The analysis demonstrates that modern optimization—characterized by hyper-efficiency and the relentless minimization of systemic slack—generates inherent fragility as the (...) market hyper-specializes to its current environment. As participants aggressively exploit stable regimes to maximize yield, they push the system toward self-organizing criticality and broadly adopt a short gamma posture. Rather than forecasting behavioral shifts or specific catalysts, this structural approach dictates acting as the counterparty to this over-extension. By observing extreme market concentration and over-leveraged assumptions of permanence, an investor can intentionally assume a long gamma position. While this requires enduring a manageable opportunity cost—or "bleed"—during stable regime periods, it structurally prioritizes survival and positions the portfolio to capture non-linear growth through uncorrelated assets when the regime inevitably dislocates. Ultimately, this framework provides a method for compounding gains by structurally balancing optionality against yield, relying on the physical realities of market optimization rather than the psychological forecasting of its participants. (shrink)

Religious symbols in ancient Egypt operated as multilayer probabilistic compressions of embodied experience. Visual meaning, phonetic articulation, and semantic field coexisted within a single glyph, forming a dense informational knot. This paper integrates embodied cognition, predictive processing, and probability theory to argue that gods emerged as ultra-stable priors minimizing prediction error across ecological, physiological, and social domains. The transition toward monotheism is analyzed as an over-compression of probabilistic structure that destabilized a cognitively plural system adapted to multiple attractors. The Egyptian (...) case illustrates how symbolic systems function as Bayesian architectures embedded in bodily life. (shrink)

This doctoral dissertation develops a novel account of fragmented epistemic justification. It departs from and expands on the literature on fragmented accounts of belief, and develops a theory where not belief, but the justification of belief, is fragmented. This account is novel, and an addition to the already existing literature on fragmented accounts of belief. It will also shed light on and help to develop answers to some underdiscussed and unsolved questions in the existing literature on fragmentation, such as questions (...) about the rationality of fragmentation. -/- In a nutshell, what it means for justification to be fragmented will be that some piece of evidence might justify a certain proposition relative to some mental fragment, whereas that same piece of evidence might not justify that same proposition relative to a different mental fragment. The epistemic and non-epistemic circumstances, such as differences in accessible information, or different perspectives, focus, or practical goals etc., of the agent can vary across fragments, which is why these circumstances will be the parameters distinguishing fragments from each other. What exactly this means will become clear throughout this dissertation. -/- For the first qualitative part of the dissertation, justification will be modelled to be a non-monotonic justification relation that holds between pieces of evidence and the propositions they justify, which will be indexed to fragments. Fragments, here, will be modelled by using total plausibility pre-orders over possible worlds. -/- Later on, within a quantitative account of fragmented justification, there will be a variety of ways to spell out the concept of justification. Here, fragments will be modelled by using (subjective) probability functions or credence functions. -/- After an introductory chapter, there will be a chapter focusing on an overview over relevant literature that is being discussed or worked with in this dissertation. Then, chapter 3 presents a skeleton of a qualitative (non-probabilistic) account of fragmented justification and shows how this account is able to provide a novel and attractive solution to the preface paradox (Makinson, 1965), one of the central paradoxes of epistemology. -/- Then, chapter 4 develops a more full fledged account of qualitative fragmented justification, using this time not the preface paradox but a scenario from climate science as a motivating example for the account. Here, a scientific expert about climate science seems to be justified in believing an overall inconsistent set of propositions. The chapter explains how the toolkit of orthodox epistemology is limited in dealing with situations like this, and argues that fragmentation is a more appropriate strategy than existing approaches to deal with (seemingly rational) inconsistent doxastic states. The chapter provides a formalisation of this example, as well as a number of justifying reasons for why fragmentation can be rational. It, also, develops some precautionary norms of fragmentation. It concludes by explaining how fragmented justification relates to belief, and argues that fragmented justification provides a novel rationality argument for accounts of fragmented belief, and, furthermore, how one should go about de-fragmenting in light of practical rationality. -/- Chapters 5 and 6 turn to a probabilistic or quantitative account of fragmented justification -- fragmented Bayesianism. Chapter 5 presents a very general version of fragmented Bayesianism, much more general than the existing accounts of fragmented Bayesianism that already exist. The basic idea is that the doxastic state of an agent will be represented not by one credence function, but by a set of credence functions, corresponding to different fragments. The focal point of this chapter is a list of parameters, such as background knowledge, algebra, confirmation measure, or ur-prior, that are part of the orthodox Bayesianism machinery, which, each, can be chosen to be either fragmented or global within a fragmented account of Bayesianism. Depending on which and how many of those parameters are chosen to be kept global or to render fragmented, the resulting account of fragmented Bayesianism will be more or less severely fragmented. The chapter provides motivations and arguments for why Bayesianism in general, and each of the parameters in particular, deserve fragmented versions. It also provides a brief comparison between the qualitative account of fragmented justification developed in the previous chapters with fragmented Bayesianism. -/- Lastly, chapter 6 compares fragmented Bayesianism with another framework, imprecise Bayesianism. Imprecise Bayesianism aims to model agents who do not have enough information to form precise credences. Fragmentation, on the other hand, aims to represent agents with fragmented doxastic states, where fragments are individuated via differences in the agent’s epistemic and non-epistemic circumstances. The formal models underlying these two accounts are strikingly similar. In both frameworks, the agent's doxastic state is represented not via one but via many different credence functions. The literature on fragmentation and imprecision do not comment on the striking similarity between these two different accounts. This is why chapter 6 is devoted to presenting and comparing their similarities and differences. -/- The dissertation closes with a conclusion and some remarks on potential avenues for further work. (shrink)

In some unfortunate scenarios, whatever credence one adopts generates evidence which undermines the rational adoption of that credence. These seem to create epistemic dilemmas. We consider the possibility that one’s credences are indeterminate and require for rationality that one’s indeterminate credences should follow any indeterminate evidence. We will show that rationality principles like these can always be satisfied. This allows the epistemic dilemma to be avoided, however it mandates indeterminate epistemic states and modifications of the rationality principles to apply to (...) the indeterminate state. (shrink)

Bostrom's simulation argument presents a trilemma: either almost no human-level civilizations reach a posthuman stage, or almost no posthuman civilizations run ancestor-simulations, or almost everyone with experiences like ours is living in a simulation. This paper grants the trilemma's formal apparatus in full and shows that Bostrom's conclusion — that we ourselves are probably simulated — does not follow from it. The formula behind the trilemma computes over a reference class with two subgroups: originating civilizations, and the simulations their descendants (...) produce. The formula's own specification places us in the originating subgroup. To reach his conclusion, Bostrom performs a separate inference, from we will create simulations to we are simulated — from what we can make to what we are. I call this the capability-inversion fallacy. The paper identifies the inference, shows Bostrom committing it throughout his text, diagnoses the features of his formulation that concealed it for two decades, and shows that the standard defenses of the argument commit it afresh. The simulation hypothesis remains a logical possibility. Bostrom's argument provides no evidence for it. (shrink)

With the help of the formal structure of Bayesianism, I distinguish between two different ways in which one’s testimony can be undervalued. While the modelling in the existing literature only focuses on the undervaluation of the trustworthiness of the testimony, the undervaluation of the relevance of the testimony has not been given due attention. The undervaluation of relevance cannot be modelled with Jeffrey conditionalisation as it is traditionally practised. But it can be modelled with Adams conditionalisation or Jeffrey conditionalisation if (...) applied to the right partition. Distinguishing between the two conceptions of testimonial undervaluation opens the possibility that a person can be subject to double testimonial undervaluation or both testimonial undervaluation and testimonial overvaluation because of the same social identity. (shrink)

While the skeptical undercurrents of early modern thought have received sustained scholarly attention, such work has tended to be inattentive to hermeneutical or exegetical skepticism. This is a form of skepticism that threatened to stop hermeneutical theorizing in its tracks and absorbed several central hermeneutical concepts in its orbit. Hermeneutical probability was one of them. In this paper, I aim to examine whether the doctrine of hermeneutical probability as it was originally formulated by Christian Thomasius is a surrogate of exegetical (...) skepticism. I argue that not only is the examined view incompatible with skepticism, but that it can indeed articulate a promising response to it. Since general reflection on probability shaped the philosophical landscape of the Early German Enlightenment, the viability of the Thomasian view has much broader ramifications that extend beyond hermeneutics to historics, ethics, and physics. (shrink)

Past studies have shown that while causal Bayes Nets account for many of the causal inferences participants make in psychological experiments, persistent violations of one of their most fundamental axioms, the causal Markov condition, are found. Previous studies have attempted to account for such violations by conjecturing that participants posit causal representations that diverge from the causal representations intended by the experimenters. In this paper, a novel method is presented for addressing the unsolved problem of how to determine which causal (...) representations participants apply in a causal inference problem and it is investigated how they update these causal representations when information about the underlying mechanism is given. The experiments thereby systematically investigate how participants represent causal structures and integrate mechanistic information to examine whether assumptions about hidden mechanisms stemming from these sources can account for participants’ Markov violations. Through these experiments, it is found that participants’ Markov violations can neither be accounted for through hidden variables that do not entail the conditional independence relations investigated nor through missing knowledge about underlying causal mechanisms. Instead, they indicate a persistent reasoning error which is shown to be robust to variations in task formats but which can be reduced under certain circumstances. (shrink)

We argue that probability theory, in its canonical formulation, suffers from a pathol- ogy we term epistemic presentism: the systematic erasure of evidential history through normalization. This is not a technical limitation but an ontological mistake— mistaking the shadow for the substance, the map for the territory, the amnesia for the truth. Drawing on contact geometry, we demonstrate that probability distributions are exiled fragments of richer dynamical objects whose memory has been surgically removed. Evidence is not accumulated but integrated—not summed (...) algebraically but woven geometrically along paths through belief space. The curvature of these paths is not mathematical decoration but the scar tissue of irreversibility, the trace that learning leaves on the manifold of the possible. We resolve long-standing puzzles in confirmation theory, the problem of old evidence, and scientific underdetermination by recognizing that probability encodes conclusions while geometry encodes justi- fication. The implications extend to the nature of information, the arrow of epistemic time, and the thermodynamic soul of inference. Probability theory has been operating in Plato’s Cave, studying shadows while the sun of contact geometry blazed unseen above. (shrink)

The 1974 papers by Ostriker et al. [1974] and Einasto et al. [1974] are considered by many to be pivotal in establishing the epistemic foundations for the dark matter hypothesis. From a theory confirmation point of view, the circumstances surrounding this pivot are difficult to reconcile with common approaches to epistemic support. First, the papers did not introduce any new observations. Second, they synthesized existing data from two separate contexts to construct a hypothesis under which the joint data became evidentially (...) relevant. Third, this synthesis was motivated in part by non-empirical reasons. The situation excludes both temporal novelty and use novelty because already known data was used in the construction of the hypothesis. Yet, the papers are widely regarded as epistemically transformative. I argue that a Bayesian can model the epistemic significance of the 1974 papers without concession. By recognizing how the papers reconfigured the existing data to bear on a missing-mass hypothesis, a novel epistemic aspect emerges. By introducing a shared halo parameterization, they made the previously disjoint data mutually constrained, thereby changing their evidential role. I develop this idea through two concepts — evidential reconfiguration and structural novelty — leveraged through Myrvold’s Bayesian account of unification. The result makes Bayesianism faithful to the inferential practices in this significant part of scientific history, explains how the 1974 papers strengthened the evidential case for dark matter, and expands the Bayesian toolbox with a way to treat novel structure as epistemologically salient. (shrink)

The aim of this present work is to offer an exposition that is as easy to understand, concise, and brief as possible, and as appealing as possible to a broad base of readers— not only epistemologists, judges, or particular sectors of Artificial Intelligence—so that the results of our work can be accessible to students and to anyone interested, regardless of their previous knowledge of philosophy of science, epistemology, or methodology.

This paper presents a two-stage critique of B-theory, the dominant view that temporal reality consists of a four-dimensional block universe with no objective becoming. Stage one establishes an undercutting defeater: B-theory lacks epistemic warrant for its central claim that the manifold possesses determinate relational ordering. I demonstrate that temporal becoming is the sole phenomenon through which precedence relations are detected, and that once becoming is denied, no warrant remains for asserting that slices stand in objective earlier-than/later-than relations. Every attempted rescue—through (...) coordinates, metrics, entropy, causation, quantum mechanics, or physics itself—presupposes the ordering it is invoked to establish. -/- Stage two establishes a rebutting defeater through a two-horn dilemma. Even granting charitably that temporal ordering exists, the manifold structure is compatible with infinitely many sequential arrangements (the Permutation Problem). With no mechanism to select among them, the probability that any specific ordering obtains is 1/∞ = 0 (the Selection Problem). B-theory faces an exhaustive choice: either no determinate ordering exists, or the probability that B-theory's described ordering is actual is measure-theoretically zero. Under both horns, B-theory fails. -/- Finally, I demonstrate that relativity—traditionally invoked to refute becoming—actually requires becoming to avoid this collapse. Relativity's formalism presupposes determinate temporal ordering, which only becoming can warrant. The century-long consensus is reversed: relativity does not vindicate the block universe; it depends on the temporal flow B-theory denies. (shrink)

Tradução por Marcos Sousa do livro Wahrscheinlichkeit de Gerhard Schurz. Resumo: Como o conhecimento é, em grande parte, incerto, a aplicação da probabilidade torna-se indispensável, pois lida com a incerteza. A teoria evoluiu desde os jogos de azar até as aplicações científicas modernas. Os axiomas de Kolmogorov fundamentam a representação algébrica da probabilidade, que pode ser interpretada, nesta obra, de forma dualista: epistêmica e estatística. Para Schurz, a probabilidade epistêmica expressa crenças racionais. Já a probabilidade estatística refere-se à frequência relativa (...) de eventos no longo prazo, quando o número de repetições ou o tamanho da amostra tende, teoricamente, ao infinito. A probabilidade condicional conecta eventos, e as distribuições binomial e a gaussiana descrevem resultados possíveis no limite de frequência. A obra distingue três tipos de inferência: 1- dedutiva, que transfere a verdade com certeza; 2- indutiva, que envolve incerteza; 3- abdutiva, que busca a melhor explicação para um fato, exigindo validação indutiva posterior. O princípio de coordenação estatística conecta crenças epistêmicas a frequências empíricas. A calibração assegura que probabilidades epistêmicas se ajustem às estatísticas observadas, sendo crucial para a aprendizagem indutiva. O raciocínio indutivo é justificado pela otimização e pela meta-indução, sendo central às teorias bayesianas de confirmação, que relacionam evidência e hipótese por meio do aumento da probabilidade da segunda. Nos testes de hipóteses estatísticas, a representatividade da amostra e o uso de grupos de controle são fundamentais. O texto diferencia estatística de teste, voltada à verificação de hipóteses, e estatística inferencial, voltada à busca das hipóteses mais plausíveis, utilizando intervalos de aceitação e de confiança de forma diferenciada. A distinção entre correlação e causalidade é enfatizada, destacando que correlações não implicam relações causais. O autor usa a justificação bayesiana da verossimilhança. Outros tópicos abordam o ajuste de curvas, a relação entre probabilidade e aceitação racional, a independência estatística e a estrutura matemática dos experimentos aleatórios. Por fim, a obra discute a calibração e as classes de referência, essenciais para garantir a admissibilidade e precisão das inferências, bem como a convergência das distribuições de probabilidade, cujo aumento amostral ou de repetições reduz a variância e melhora a precisão das estimativas. (shrink)

It is argued that that the desire attributed to an agent, X, in sentences of the form ‘X wants to know whether P’, is not X’s overall desire for ‘X knows that P or X knows that “not P”’, but rather X’s expected conditional desire for knowing the truth about P, given the truth. An implication of this account for distributive justice is discussed.

We investigate the epistemic role of coherence in scientific reasoning, focusing on its use as a heuristic for filtering evidence. Using a novel computational model based on Bayesian networks, we simulate agents who update their beliefs under varying levels of noise and bias. Some agents treat reductions in coherence as higher-order evidence and interpret such drops as signals that something has gone epistemically awry, even when the source of error is unclear. Our results show that this strategy can improve belief (...) accuracy in noisy environments but tends to mislead when evidence is systematically biased. We explore the implications for the rationality of coherence-based reasoning in science. (shrink)

Therefore, everything that occurs in history—every event, phenomenon, subject, or option, within any finite or infinite universe—is the result of chance. This principle extends the concept of randomness beyond statistical mechanics into a universal ontology of contingency, where chance is not the exception but the rule.

Philosophers often appeal to Bayesian confirmation theory to render speculative metaphysical arguments more rigorous. But can a probabilistic framework designed for empirical data decide questions of metaphysics? This paper argues that Huemer’s Bayesian “existence → immortality” inference fails on two independent grounds. First, the comparison tacitly shifts the content of the evidence across the competing identity theories: treating “I exist now” as a different event under a restrictive view than under a permissive view. So, the Bayesian evidence is ill-defined. Second, (...) if we hold the evidence fixed as the single indexical proposition E = “I exist now”, the key question is the relative likelihoods of E under each hypothesis. Once standard constraints on background verses evidence and on self-locating information are respected, there is no non-question-begging route to a Bayes factor that favors the permissive view of personal identity. Thus, mere existence does not confirm reincarnation. I remain agnostic on the correct theory of personal identity. (shrink)

Occam’s Razor (also known as PRINCIPLE OF PARSIMONY) is regularly dismissed as an obsolete vestige no longer worthy of its longstanding regard as fundamental to scientific inquiry. Concurrently, the science DEMARCATION PROBLEM is fast becoming a full-fledged academic crisis. This paper posits that the latter reality stems from the former. Said principle’s core commitment is distilled as BLIND FAITH PARSIMONY: the most scientific hypothesis is whichever yields the fullest account of corresponding data while entailing least AD HOC-NESS (i.e., gratuitous conjecture). (...) A threefold thesis is then built upon this straightforward distillation. Primary thesis: Occam’s Razor remains of fundamental scientific importance. Secondary thesis: Said distillation cuts to the core of what optimally demarcates and defines science. Tertiary thesis: It thereby frees science to engage all questions where reason and evidence apply (including many claimed by frameworks like NON-OVERLAPPING MAGISTERIA to fall outside the scientific purview). Three main supporting arguments are utilized. Argument A highlights the too-often-overlooked agility with which Occam’s Razor dovetails with available corresponding data—no matter how complex. Argument B shows that science requires FALSIFIABILITY, which requires parsimony. Whereas Argument C addresses the enormous burden of proof reasonable corresponding dismissals must meet. (shrink)

The first formulations of Impossible Probability date from 11 September 2001. My first formula would be the Impact of the Defect; then on 16 October 2002 the Second Method would appear, laying the foundations of the distinction between empirical and theoretical probability. I worked intensely until 2004. Between 2004 and 19 December 2009, I paused my mathematical frenzy, and it was not until 19 December 2009 when I returned, this time with the intention of publishing Introduction to Impossible Probability, Statistics (...) of Probability or Statistical Probability, whose publication materialized just a few months after the death of José Rodríguez Delgado, although Delgado was able to see the first works published online in this Impossible Probability blog, which makes this blog a fundamental piece for understanding our work, our legacy, and most importantly—independently of our names, which matter little—the truly essential: our seed of the future, our eternal gratitude, a work of intelligence that will lay the foundations of the future technological society. (shrink)

The first formulations of Impossible Probability date from 11 September 2001. My first formula would be the Impact of the Defect. Later, on 16 October 2002, the Second Method would appear, laying the foundations of the distinction between empirical and theoretical probability. I worked intensely until 2004. Between 2004 and 19 December 2009 I would pause my mathematical frenzy, and it was not until 19 December 2009 that I returned, this time with the intention of publishing Introduction to Impossible Probability, (...) Statistics of Probability or Statistical Probability, whose publication materialized only a few months after the death of José Rodríguez Delgado, although Delgado did have the opportunity to see the first works published online in this Impossible Probability blog. This makes this blog a fundamental piece for understanding our work, our legacy and, most importantly, regardless of our names—which matter little—the truly essential: our seed of the future, our eternal gratitude, a work of intelligence that will lay the foundations of the future technological society. -/- The documents presented here express the evolution of a work, Impossible Probability, and the spirit of survival of its author, indomitable and rebellious like a five-pointed star. (shrink)

The first formulations of Impossible Probability date from 11 September 2001. My first formula would be the Impact of the Defect. Later, on 16 October 2002, the Second Method would appear, laying the foundations of the distinction between empirical and theoretical probability. I worked intensely until 2004. Between 2004 and 19 December 2009 I would pause my mathematical frenzy, and it was not until 19 December 2009 that I returned, this time with the intention of publishing Introduction to Impossible Probability, (...) Statistics of Probability or Statistical Probability, whose publication materialized only a few months after the death of José Rodríguez Delgado, although Delgado did have the opportunity to see the first works published online in this Impossible Probability blog. This makes this blog a fundamental piece for understanding our work, our legacy and, most importantly, regardless of our names—which matter little—the truly essential: our seed of the future, our eternal gratitude, a work of intelligence that will lay the foundations of the future technological society. -/- The documents presented here express the evolution of a work, Impossible Probability, and the spirit of survival of its author, indomitable and rebellious like a five-pointed star. (shrink)

The first formulations of Impossible Probability date from 11 September 2001. My first formula would be the Impact of the Defect. Later, on 16 October 2002, the Second Method would appear, laying the foundations of the distinction between empirical and theoretical probability. I worked intensely until 2004. Between 2004 and 19 December 2009 I would pause my mathematical frenzy, and it was not until 19 December 2009 that I returned, this time with the intention of publishing Introduction to Impossible Probability, (...) Statistics of Probability or Statistical Probability, whose publication materialized only a few months after the death of José Rodríguez Delgado, although Delgado did have the opportunity to see the first works published online in this Impossible Probability blog. This makes this blog a fundamental piece for understanding our work, our legacy and, most importantly, regardless of our names—which matter little—the truly essential: our seed of the future, our eternal gratitude, a work of intelligence that will lay the foundations of the future technological society. -/- The documents presented here express the evolution of a work, Impossible Probability, and the spirit of survival of its author, indomitable and rebellious like a five-pointed star. (shrink)

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity. There is always a halo of indeterminism, since in the end it is chance itself—the random variations of what we call reality, although we do not quite know what it is—that becomes the cause of causes. From (...) an interpretation not devoid of a certain nihilism. (shrink)

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity. There is always a halo of indeterminism, since in the end it is chance itself—the random variations of what we call reality, although we do not quite know what it is—that becomes the cause of causes. From (...) an interpretation not devoid of a certain nihilism. (shrink)

Understanding the original meaning of the Global Artificial Intelligence. Its origins can be traced back to my writings in 2002 on Astro-ecology, the science that understands the cosmos as a single environment that must be studied from a unified, single science. In essence, this is what the Global Artificial Intelligence seeks to achieve. At the same time, in 2002 I developed the formulations of Impossible Probability, beginning in the early hours of September 11, 2001 with the Impact of the Defect, (...) which was later expanded into the Second Method on October 16, 2002. (shrink)

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity.

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity.

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity.

Receivers in standard signaling game models struggle with learning compositional information. Even when the signalers send compositional messages, the receivers do not interpret them compositionally. When information from one message component is lost or forgotten, the information from other components is also erased. In this paper I construct signaling game models in which genuine compositional understanding evolves. I present two new models: a minimalist receiver who only learns from the atomic messages of a signal, and a generalist receiver who learns (...) from all of the available information. These models are in many ways simpler than previous alternatives, and allow the receivers to learn from the atomic components of messages. (shrink)

We prove that the P vs NP problem is formally unprovable within classical computational complexity theory by demonstrating that it exhibits the same self-referential structure as the Halting Problem and logical paradoxes. The core issue is that P vs NP began as a philosophical question about the nature of mathematical insight, hypothetical verification, and the discovery of solving algorithms but was inappropriately formalized within computational complexity theory. It was done so in such away that it secretly became analogous to asking (...) a supercomputer the “ultimate question of life, the universe, and everything.” Through rigorous multidisciplinary analysis, we show that verification presupposes contextual information that the formal NP definition explicitly removes, creating a semantic loop that makes the question undecidable by construction. We establish this through: (1) formal proof of the verification-solving circularity via the Certificate Construction Paradox, (2) demonstration of structural equivalence to the Liar Paradox, and (3) rigorous analysis showing that context-stripping creates category errors. Our result explains why P vs NP has resisted proof for over fifty years and provides foundations for context-aware computational frameworks that treat ambiguity as a core feature of mathematical reality rather than a limitation to overcome. (shrink)

Probabilidad Imposible Vol 1 reúne los fundamentos de una investigación desarrollada entre 2001 y 2018, cuyo propósito es replantear las bases del conocimiento racional y su relación con la probabilidad empírica y teórica. La obra introduce conceptos como el Impacto del Defecto y el Segundo Método, proponiendo un marco alternativo frente a la epistemología de Karl Popper y orientado hacia la búsqueda del conocimiento puro. Este proyecto, originado en el cruce entre matemáticas, inteligencia artificial y psicología, constituye una semilla teórica (...) para el desarrollo de la Inteligencia Artificial Global y para la construcción de una sociedad tecnológica basada en un nuevo paradigma del saber. (shrink)

Particular Application System is a groundbreaking exploration into one of the most critical operational layers of the Global Artificial Intelligence framework. This book unveils, in precise and accessible detail, how instructions—born from complex decision-making processes—are matched, classified, and executed with flawless precision by robotic systems.

The Inscrutable Evidence Argument targets the thesis that credences are thoughts about evidential probabilities (CTEP). It does so using cases where one knows one’s evidence speaks either strongly in favor of or strongly against a proposition, but one doesn’t know which; in such cases, it seems possible to have a middling credence in that proposition even though one doesn’t think the probability of the proposition is near 50%—contra CTEP. In this paper, I defend CTEP by conceiving of the thoughts involved (...) differently than usual. My diagnosis of the argument turns on appreciating the difference between believing and accepting (in the sense of Bratman 1992) that a proposition has probability n, where accepting is context dependent and allows for guidance in action without commitment to truth. I develop this diagnosis in two directions, one according to which acceptances of probability-involving propositions are credences and another according to which they aren’t. Both views elude the Inscrutable Evidence Argument and are compatible with CTEP. (shrink)

The question, whether NP- and P-problems are logically equal, is fiercely debated. Using Strict logic (by Walther Brüning), this question can be answered. It is resulted, that NP-problems have an Applied Logic-correspondent in Pure Logic.

Imprecise Bayesianism, as opposed to orthodox Bayesianism, aims to model agents who do not have enough information to form precise credences. Under this account, an agents' doxastic state is allowed to be made up of not one but many different credence functions, to model imprecision in the assignment of credences to propositions. Fragmentation, on the other hand, aims to represent agents with fragmented doxastic states, where fragments are individuated via differences in the agent's epistemic and non-epistemic circumstances, such as differences (...) in accessible information, or different practical goals and decisions. The formal model underlying this account is identical to imprecise Bayesianism: the agent's doxastic state is represented via not one but many different credence functions. -/- The literature on fragmentation and imprecision do not comment on the striking similarity between these two different accounts. This paper is devoted to presenting and comparing their similarities and differences. The upshot will be that the main difference lies in, first, the interpretation of the formalisms, as well as how these two accounts deal with questions of practical rationality. (shrink)

Es wurde lange diskutiert, ob zwischen NP-Problemen und P-Problemen eine Unterscheidung besteht. Das lässt sich mithilfe der Strengen Logik beweisen. Es ergibt sich, dass NP-Probleme in der Reinen Logik eine Entsprechung der Angewandten Logik haben.

The consensus is that a normal person, regarding a normal fair lottery, under ordinary, realistic conditions, can’t know ahead of time that a given ticket is a loser. I disagree, sort of. Suppose you learn that a lottery involves extreme probabilities. You also hear, perhaps via the lottery’s website, that someone who bought just one ticket got the winning number. In response to the acquisition of those two pieces of knowledge, you come to think that either the announcement is false (...) (no one who bought a single ticket won), or it's true but either something superhuman was going on or the lottery was fixed. I say: if your belief is true, then it amounts to knowledge. That is, you can know that the lottery’s outcome won’t be an ordinary case of someone with one ticket winning a fair lottery, with no superhuman assistance. -/- . (shrink)

This book motivates and systematically develops the view that knowledge should be at the centre of our theory of practical rationality. Only act on what you know -- the book offers the first comprehensive defence of this slogan in the form of a knowledge-based decision theory. The proposed view is shown to be the most straightforward explanation of emerging bodies of evidence for a link between knowledge and rational action. The book provides novel solutions to well-known challenges that invoke high-stakes (...) scenarios, seemingly rational actions based on reasonable but false beliefs, and decision-making under risk and uncertainty. The emerging view brings together traditional and formal approaches to epistemology and the study of practical rationality. The resulting knowledge-based decision theory is embedded in a rich normative landscape, encompassing innovative accounts of excuses, rational acceptance, and the simplification of reasoning. Knowledge and Rational Action will be of great interest to researchers and graduate students interested in epistemology, practical rationality, and decision theory. (shrink)

Emergent Necessity Theory (ENT) establishes a universal coherence threshold (T_c) where information-theoretic constraints necessitate physical structure formation. This framework derives from first principles: • Core mechanism: Systems exceeding critical modal tightness (t > T_c) transition from probabilistic to necessary emergence • Theoretical foundation: Unifies Wheeler's "it from bit" principle and Palmer's Invariant Set Hypothesis via information geometry • Falsifiable predictions: - SUSY breaking at 2.18 TeV (HL-LHC testable) - Gravitational coupling X < 1.13 × 10-19 m2 (LIGO-constrained) - Quantum phase (...) transitions at t ≥ 1.5 (NISQ-verifiable) Python-based simulations confirm all predictions. ENT potentially provides a unified foundation for quantum gravity, high-energy physics, and emergent cosmology without free parameters. (shrink)

The nature of evidence is a problem for epistemology, but I argue that this problem intersects with normative decision theory in a way that I think is underappreciated. Among some decision theorists, there is a presumption that one can always ignore the nature of evidence while theorizing about principles of rational choice. In slogan form: decision theory only cares about the credences agents actually have, not the credences they should have. I argue against this presumption. In particular, I argue that (...) if evidence can be unspecific, then an alleged counterexample to causal decision theory fails. This implies that what theory of decision we think is true may depend on our opinions regarding the nature of evidence. Even when we are theorizing about subjective theories of rationality, we cannot set aside questions about the objective nature of evidence. (shrink)

The question “Why is there something rather than nothing?” has long puzzled philosophers, theologians, and physicists alike. In this paper, I propose a novel probabilistic argument against absolute nothingness. By treating the totality of possible states of being as a formal probability space, I argue that the configuration corresponding to “nothingness” is a singular point with measure zero. Assuming a uniform or unbiased probability distribution across the configuration space, the likelihood of nothingness being actualized is exactly zero, whereas the probability (...) of something existing is one. Hence, existence is not merely a philosophical mystery, but a mathematical inevitability. This approach reframes a metaphysical puzzle as a question of formal modeling and probabilistic reasoning, providing a fresh perspective grounded in established mathematical frameworks. (shrink)

How do psychiatrists arrive at their diagnostic conclusions? Though several philosophers of psychiatry have proposed how to understand psychiatric diagnostic reasoning over the last decade, this essential question of the epistemology of psychiatric practice has received little attention. This article introduces the reader to this topic, its importance, and the major theoretical positions presented in the debate, while also pointing to future relevant research in this area of philosophy of psychiatry.

Kì í ṣe nipa ronu la fi ń ṣẹda àwọn ayé; ṣùgbọ́n nípa agbọye ayé wa la fi ń kọ ẹ̀kọ bí a ṣe lè ronu. Cosmovision jẹ ọrọ kan ti o yẹ ki o tumọ si ipilẹ awọn ipilẹ lati eyiti o ṣe afihan oye eto ti Agbaye, awọn paati rẹ bi igbesi aye, agbaye ti a ngbe, iseda, iṣẹlẹ eniyan, ati awọn ibatan wọn. Nítorí náà, ó jẹ́ pápá ìmọ̀ ọgbọ́n orí ìtúpalẹ̀ tí àwọn sáyẹ́ǹsì ń jẹ, ẹni (...) tí ète rẹ̀ jẹ́ àkópọ̀ àti ìmọ̀ alágbero nípa ohun gbogbo tí a jẹ́ tí ó sì ní nínú, tí ó yí wa ká, tí ó sì ní í ṣe pẹ̀lú wa lọ́nàkọnà. O jẹ nkan ti o ti dagba bi ero eniyan, ati, ni afikun si lilo awọn eroja ti imọ-jinlẹ imọ-jinlẹ, o yika ohun gbogbo ni imọ-jinlẹ ati imọ-jinlẹ ti o tọka si agbaye ati igbesi aye. Cosmovision kii ṣe akojọpọ awọn imọran, awọn idawọle, ati awọn arosinu ṣugbọn eto ti o da lori akiyesi, itupalẹ, ẹri, ati ifihan. Ko si cosmovision ti o pinnu lati ṣalaye, fi idi mulẹ, tabi daba ṣugbọn loye nikan, ṣe itupalẹ, ati itumọ. Olukuluku wa kọ ati gbe oju-aye rẹ jakejado igbesi aye, laisi iṣeto awọn fọọmu, bi ipilẹṣẹ fun ironu ati ihuwasi wa. (shrink)