The work provides comprehensively definitive, unconditional proofs of Riemann's hypothesis, Goldbach's conjecture, the 'twin primes' conjecture, the Collatz conjecture, the Newcomb-Benford theorem, and the Quine-Putnam Indispensability thesis. The proofs validate holonomic metamathematics, meta-ontology, new number theory, new proof theory, new philosophy of logic, and unconditional disproof of the P/NP problem. The proofs, metatheory, and definitions are also confirmed and verified with graphic proof of intrinsic enabling and sustaining principles of reality.

The Riemann zeta function ζ(s) is a central object in number theory and complex analysis, defined for complex variables and intimately connected to the distribution of prime numbers through its zeros. The famous Riemann Hypothesis conjectures that all non-trivial zeros of the zeta function lie on the critical line Re(s) = 1 2 . In this paper, we explore the Riemann zeta function through the lens of set-theoretic and sweeping net methods, leveraging creative comparisons of specific (...) sets to gain deeper insight into the distribution of its zeros. By rewording and analyzing the Riemann Hypothesis using set-theoretic arguments, applying sweeping net techniques, and integrating modal logic interpretations, we aim to provide new perspectives and support for this profound conjecture. Our objectives are: • Define the zeta function and its properties relevant to the zeros. • Reword the Riemann Hypothesis using set-theoretic language and establish logical equivalence. • Introduce and compare specific sets related to the zeros of ζ(s). • Apply set-theoretic and sweeping net methods to analyze the distribution of zeros. • Provide rigorous proofs about the absence of zeros in certain regions, including mechanical justifi- cations with all steps. • Incorporate modal logic interpretations into the proof. • Discuss implications for the Riemann Hypothesis. (shrink)

This paper is trying to show the significance for science history studies of the internet´s access to rare books each time more easier; it was choiced the work of one of the most important and influent mathematicians, Georg Friedrich Bernhard Riemann (1826-1866), “Oeuvres Mathématiques”, composed with published memories during Riemann´s life, and posthumously published memories and fragments. It was been analised and commented the posthumous memory about the hypothesis which serve to geometry basis, fundamental on modern sciences, (...) as Riemann´s space conception, and without it, it couldn´t be possible the exact formulation of Relativity Theory or fundamental advances on mathematics like the solving of some differential equations. It was been trying to show how the reading of an original text of the important mathematician can be rich and full of teaching through the return to his thinking origin. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure (...) mathematics and for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

Look! Up in the bookshelf! Is it science? Is it science-fiction? No, it's Super Science: strange visitor from the future who can be everywhere in the universe and everywhen in time, can change the world in a single bound and who - disguised as a mild mannered author - fights for truth, justice and the super-scientific way. -/- Though I put a lot of hard work into this book, I can't take all the credit. I believe that the whole universe (...) - everything on Earth and in space plus everything in the past, present, and future - is entangled and unified. Everybody is part of this unity, so anybody could have written the ideas in this book. It turned out to be me simply because I've got intense curiosity about the book's contents, enough persistence and imagination to combine science with topics like religion and philosophy, and enough spare time to assemble all the pre-existing pieces in space and time (my contribution to the book is like putting together the pieces of a big jigsaw puzzle). -/- This book, with its vast collection of scientific fact and study results, presents some fascinating theories and is an expansive journey through my research. The topic will appeal to the science-minded reader who is open to speculating on how conditions may evolve in the future, perhaps questioning the very foundations of our place in the universe. This book is not written as a single story but is a collection of 9 articles written in the first half of 2022. Each chapter of this book is presented as a research paper. There's the abstract, the introduction, the keywords, the body of the work divided into sections, and a reference section. Though this might turn some readers off, I'm a member of ResearchGate, a community of researchers. So it isn't surprising that I've presented this book this way. Each article is meant to be self-contained and well explained in plain English. As a result, some explanations appear in several of the articles. -/- Please be patient when you encounter jargon and mathematics - I've tried to keep these to a minimum but they're bound to put in an appearance in a book that's largely about science (and I have compiled an enormous amount of intricate research for this project, hopefully impressing with the organization). Quotes from a range of scientists and icons in the industry should add further fascination to the descriptions, inspiring the reader into more of an openness to speculating on the distant future. There's a lot to absorb here but understanding the future . . . It Don't Come Easy (just ask Ringo Starr who once dreamed he was an alien living on another planet in the future. -/- Contents -/- Special Relativity's Consequences For General Relativity, Quantum Mechanics And Quantum Gravity (Can Science And The Paranormal Coexist?) -/- Intergalactic Travel and Riemann Hypothesis - featuring Dark Matter, Dark Energy, Higgs Boson, Higgs Field, Electroweak Interaction, No Big Bang, Other Dimensions, Plus Other Physics and Mathematics -/- New Perspectives On Life, Death, Cancer and Covid-19 Arising From An Artificially Intelligent, Non-probabilistic Universe -/- Unipositional Interpretation Of Quantum Mechanics Means Entanglement Occurring Simultaneously With Gravitational Slingshots Reduces Problems Associated With Spaceflight -/- Unipositional Interpretation Of Quantum Mechanics Explains Time Dilation, Updates Cosmology -/- WHERE DID EVERYTHING COME FROM – Combining Science, Mathematics, Computers, Religion, Philosophy, Relativity, Quantum Physics, Darwinism, and a Podcast to Reach One Person’s Plausible Ideas -/- Thoughts on Artificial Intelligence and the Origin of Life Resulting from General Relativity, with Neo-Darwinist Reference to Human Evolution and Mathematical Reference to Cosmology -/- Planet 9 and Black Hole Versus Relativity’s Precession and Dark Matter -/- THE WORLD’S REAL-LIFE EXPERIMENTS WITH COVID-19 AND PHYSICS ALTER SOCIETY AND GLOBAL ECONOMICS . (shrink)

The year in the title comes from “2001: A Space Odyssey”. The article was inspired by reading about the Vera C. Rubin Telescope, due to begin operations in Chile next year. The article I read talked about the telescope photographing the entire Southern Hemisphere sky but the heading spoke of watching the whole universe. Reconciling the Southern Hemisphere with the entire cosmos quickly became the challenge I chose to accept. The Unimaginable Telescope uses multi-messenger (combined neutrino / gravitational / electromagnetic) (...) astronomy, quantum (and macroscopic) entanglement, as well as Unipositional Quantum Mechanics to not only observe the entire universe but also to instantly transmit messages to every possible coordinate in time as well as space and, from “reflections” of those signals which arrive back on Earth of 4 001 instantaneously, pinpoint the locations of extraterrestrial civilizations. The telescope’s functions include the potential to form a spaceship and crew that could be transported to the Voyager and Pioneer probes that exited the solar system way back in the early 2000s. They’d visit the spaceprobes in order to service and repair them, collect them and bring them back to a museum, or whatever … Other topics covered by this article include dark matter and modified dark matter, human/AI partnership, electric dipole moment, quantum/macroscopic entanglement, hidden electromagnetism in cosmological constant, time dilation, Wick rotation, Vector-Tensor-Scalar (and elliptical VTS) geometry, quantum spin, precession related to Mercury and Planet 9, Riemann hypothesis, solar system and intergalactic and time travel, infinite and eternal universe with a beginning, ETs the Extraterrestrials, model universe, origin of life, heaven on earth, Weyl and Majorana fermions, topological insulators and topological superconductors, topological propulsion and topological manufacturing, consciousness, Higgs boson and Higgs field, plus ocean tides and Saturn’s moon Enceladus with A Brief History of Gravity. (shrink)

Euclid's classic proof about the infinitude of prime numbers has been a standard model of reasoning in student textbooks and books of elementary number theory. It has withstood scrutiny for over 2000 years but we shall prove that despite the deceptive appearance of its analytical reasoning it is tautological in nature. We shall argue that the proof is more of an observation about the general property of a prime numbers than an expository style of natural deduction of the proof of (...) their infinitude. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or (...) objective Bayesianism or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

Revista Cunoașterea Științifică este o publicație trimestrială din domeniile științei și filosofiei, și domenii conexe de studiu și practică. -/- Cuprins: -/- EDITORIAL / EDITORIAL -/- Nicolae SFETCU Defense Against Advanced Cyber Attacks Apărarea împotriva atacurilor cibernetice avansate -/- ȘTIINȚE NATURALE / NATURAL SCIENCE -/- Nicolae SFETCU Cosmological Tests Based on General Relativity for Gravity Teste cosmologice bazate pe relativitatea generală pentru gravitație -/- Ștefan-Daniel FLOREA Integrating modern technology into seismic risk management Integrarea tehnologiei moderne în gestionarea riscului seismic -/- (...) ȘTIINȚE SOCIALE / SOCIAL SCIENCE -/- Dan D. FARCAȘ Some opinions regarding the ethnogenesis of the Romanians (2) Câteva opinii privind etnogeneza românilor (2) -/- Aliona ROZOVEL UTA Gagauzia, de jure an integral and inalienable part of the Republic of Moldova, de facto tends towards separatism UTA Găgăuzia de jure parte integrantă și inalienabilă a Republicii Moldova, de facto tinde spre separatism -/- ȘTIINȚE FORMALE / FORMAL SCIENCE -/- Constantin POMPARĂU What is the Riemann hypothesis and why it cannot be proved Ce este ipoteza Riemann și de ce nu poate fi demonstrată -/- Ana Denisa CUTEAN și Iulia Denisa MOGA Accounting for infrastructure assets Contabilitatea activelor de infrastructură -/- Iulia Denisa MOGA The technique of the cost approach: construction evaluation Tehnica abordării prin cost: evaluarea construcțiilor -/- FILOSOFIE / PHILOSOPHY -/- Nicolae SFETCU The Republic of Plato: A Philosophical Odyssey Republica lui Platon: o odisee filosofică -/- ISSN 2821-8086 ISSN-L 2821-8086, DOI: 10.58679/CS26154. (shrink)

These involved theorems on sweeping nets, saddle maps and complex analysis are a thorough examination of the method an its fundamental mechanics. The basic foundation of this analytical method is useful to any artificer of mechanical programs or development of software applications that involve computer vision or graphics. These methods will have application to further theories and methods in string theory and cosmology or even approximation of environmental factors for machine learning. -/- .

A look at the dynamical concept of space and space-generating processes to be found in Kant, J.F. Herbart and the mathematician Bernhard Riemann's philosophical writings.

According to one theory, the brain is a sophisticated hypothesis tester: perception is Bayesian unconscious inference where the brain actively uses predictions to test, and then refine, models about what the causes of its sensory input might be. The brain’s task is simply continually to minimise prediction error. This theory, which is getting increasingly popular, holds great explanatory promise for a number of central areas of research at the intersection of philosophy and cognitive neuroscience. I show how the theory (...) can help us understand striking phenomena at three cognitive levels: vision, sensory integration, and belief. First, I illustrate central aspects of the theory by showing how it provides a nice explanation of why binocular rivalry occurs. Then I suggest how the theory may explain the role of the unified sense of self in rubber hand and full body illusions driven by visuotactile conflict. Finally, I show how it provides an approach to delusion formation that is consistent with one-deficit accounts of monothematic delusions. (shrink)

Preregistration has been proposed as a useful method for making a publicly verifiable distinction between confirmatory hypothesis tests, which involve planned tests of ante hoc hypotheses, and exploratory hypothesis tests, which involve unplanned tests of post hoc hypotheses. This distinction is thought to be important because it has been proposed that confirmatory hypothesis tests provide more compelling results (less uncertain, less tentative, less open to bias) than exploratory hypothesis tests. In this article, we challenge this proposition (...) and argue that there are several advantages of exploratory hypothesis tests that can make their results more compelling than those of confirmatory hypothesis tests. We also consider some potential disadvantages of exploratory hypothesis tests and conclude that their advantages can outweigh the disadvantages. We conclude that exploratory hypothesis tests avoid researcher commitment and researcher prophecy biases, reduce the probability of data fraud, are more appropriate in the context of unplanned deviations, facilitate inference to the best explanation, and allow peer reviewers to make additional contributions at the data analysis stage. In contrast, confirmatory hypothesis tests may lead to an inappropriate level of confidence in research conclusions, less appropriate analyses in the context of unplanned deviations, and greater bias and errors in theoretical inferences. (shrink)

According to the conventionalist doctrine of space elaborated by the French philosopher-scientist Henri Poincaré in the 1890s, the geometry of physical space is a matter of definition, not of fact. Poincaré's Hertz-inspired view of the role of hypothesis in science guided his interpretation of the theory of relativity (1905), which he found to be in violation of the axiom of free mobility of invariable solids. In a quixotic effort to save the Euclidean geometry that relied on this axiom, Poincaré (...) extended the purview of his doctrine of space to cover both space and time. The centerpiece of this new doctrine is what he called the "principle of physical relativity," which holds the laws of mechanics to be covariant with respect to a certain group of transformations. For Poincaré, the invariance group of classical mechanics defined physical space and time (Galilei spacetime), but he admitted that one could also define physical space and time in virtue of the invariance group of relativistic mechanics (Minkowski spacetime). Either way, physical space and time are the result of a convention. (shrink)

It is generally accepted among philosophers of science that hypothesis testing is a key methodological feature of science. As far as philosophical theories of confirmation are con...

There are scenarios in which letting one’s own views on the question whether p direct one’s inquiry into that question brings about individual and collective epistemic benefits. However, these scenarios are also such that one’s evidence doesn’t support believing one’s own views. So, how to vindicate the epistemic benefits of directing one’s inquiry in such an asymmetric way, without asking one to hold a seemingly irrational doxastic attitude? To answer this question, the paper understands asymmetric inquiry direction in terms of (...) having one’s inquiry be guided by a doxastic attitude, which I call hypothesis, that’s governed by the following norm: One’s hypothesis that p is rational just in case it is a manifestation of the best feasible way to form a doxastic attitude regarding p that promotes the best feasible ways to advance towards settling the question of p’s (or of any other suitably related proposition’s) truth-value. (shrink)

The singularity hypothesis is a radical hypothesis about the future of artificial intelligence on which self-improving artificial agents will quickly become orders of magnitude more intelligent than the average human. Despite the ambitiousness of its claims, the singularity hypothesis has been defended at length by leading philosophers and artificial intelligence researchers. In this paper, I argue that the singularity hypothesis rests on scientifically implausible growth assumptions. I show how leading philosophical defenses of the singularity hypothesis (...) (Chalmers 2010, Bostrom 2014) fail to overcome the case for skepticism. I conclude by drawing out philosophical implications of this discussion for our understanding of consciousness, personal identity, digital minds, existential risk, and ethical longtermism. GPI Working Paper No . 19-2022. (shrink)

This paper examines the second geometrical problem in the Meno. Its purpose is to explore the implication of Cook Wilson’s interpretation, which has been most widely accepted by scholars, in relation to the nature of hypothesis. I argue that (a) the geometrical hypothesis in question is a tentative answer to a more basic problem, which could not be solved by available methods at that time, and that (b) despite the temporary nature of a hypothesis, there is a (...) rational process for formulating it. The paper also contains discussion of the method of analysis, problem reduction and a diorism, which have often been ambiguously explained in relation to the geometrical problem in question. (shrink)

If the Past Hypothesis underlies the arrows of time, what is the status of the Past Hypothesis? In this paper, I examine the role of the Past Hypothesis in the Boltzmannian account and defend the view that the Past Hypothesis is a candidate fundamental law of nature. Such a view is known to be compatible with Humeanism about laws, but as I argue it is also supported by a minimal non-Humean "governing'' view. Some worries arise from (...) the non-dynamical and time-dependent character of the Past Hypothesis as a boundary condition, the intrinsic vagueness in its specification, and the nature of the initial probability distribution. I show that these worries do not have much force, and in any case they become less relevant in a new quantum framework for analyzing time's arrows---the Wentaculus. Hence, the view that the Past Hypothesis is a candidate fundamental law should be more widely accepted than it is now. (shrink)

This paper -distinguishes between the Hypothesis of Extended Cognition and the Hypothesis of Embedded Cognition, characterizing them as competitors (both motivated by situated, interactive cognitive processing, with the latter being the more conservative of the two interpretations of the data) -clarifies the relation between content externalism and extended cognition -introduces the problem of cognitive bloat, as part of a critical discussion of Clark and Chalmers's "past-endorsement criterion" (if the criterion is embraced, we privilege the internal, endorsing process -- (...) which looks more like an embedded view -- and if the criterion is rejected, bloat follows) and as a problem for extended views more generally -develops a dilemma critical of Clark and Chalmers's "explanatory kinds" argument for extended mind and cognition (arguing that their reasoning faces serious problems regardless of whether one individuates the kinds in question in a fine-grained or a coarse-grained way) -argues that an appeal to functionalism doesn't resolve the issue -argues for the priority, in debates about extended cognition, of the identification of cognitive systems (e.g., because a functionalist approach can't be applied unless we already know what count as inputs and outputs, which requires having already identified the boundaries of the cognitive system). (shrink)

Epistemic contextualism is one of the most hotly debated topics in contemporary epistemology. Contextualists claim that ‘know’ is a context-sensitive verb associated with different evidential standards in different contexts. Contextualists motivate their view based on a set of behavioural claims. In this paper, I show that several of these behavioural claims are false. I also show that contextualist test cases suffer from a critical confound, which derives from people's tendency to defer to speakers’ statements about their own mental states. My (...) evidence consists in results from several behavioural experiments. I conclude that contextualism is an idle hypothesis and I propose some general methodological lessons. (shrink)

This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly (...) pick out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum. (shrink)

The primary sense of the word ‘hypothesis’ in modern colloquial English includes “proposition not yet settled” or “open question”. Its opposite is ‘fact’ in the sense of “proposition widely known to be true”. People are amazed that Plato [1, p. 1684] and Aristotle [Post. An. I.2 72a14–24, quoted below] used the Greek form of the word for indemonstrable first principles [sc. axioms] in general or for certain kinds of axioms. These two facts create the paradoxical situation that in many (...) cases it is impossible to translate the Greek form of the word using the English form: the primary sense of the word ‘hypothesis’ in modern colloquial English is diametrically opposed to one sense used by Plato and by his most accomplished student Given current colloquial English usage it is impossible to get the word hypothesis to carry the connotation of “settled truth” much less “axiomatic truth”. The ‘hypo-’ [under] in the Plato-Aristotle use of ‘hypothesis’ might carry the sense of “basis” or “foundational” as opposed to “less than usual or normal”. This paradox parallels the one pointed out by Robin Smith: it is impossible for the English word ‘syllogism’ to carry the meaning of its Greek form Aristotle intended. There are other cases as well: it is impossible for the English biological term ‘genus’ to carry the meaning of its Greek form the Greek genos refers to family as in our ‘genealogy’, not to “higher species” as in our ‘generic’. (shrink)

Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for these modalities (...) to be logically consistent. Prisms composed of hexagons of oppositions show how the credal modalities obtained from two agnostic tests vary according to their threshold values. Nested hexagons of oppositions summarize logical relations between the credal modalities in these tests and prove new relations. (shrink)

Extant literature on Goodman’s ‘New Riddle of Induction’ deals mainly with two versions. I consider both of them, starting from the (‘epistemic’) version of Goodman’s classic of 1954. It turns out that it belongs to the realm of applications of inductive logic, and that it can be resolved by admitting only significant evidence (as I call it) for confirmations of hypotheses. Sect. 1 prepares some ground for the argument. As much of it depends on the notion of evidential significance, this (...) concept is defined and its introduction motivated. Further, I introduce and explain the distinction between support and confirmation: put in a slogan, ‘confirmation is support by significant evidence’. The second section deals with the Riddle itself. I demonstrate that, given the provisions of the first section, not ‘anything confirms anything’: significant green-evidence confirms only green-hypotheses (and no grue-hypotheses), and significant grue-evidence confirms only grue-hypotheses (and no green-hypotheses), whichever terms we use for expressing these evidences or hypotheses. The third section rounds off my treatment. First I show that Frank Jackson’s use of his counterfactual condition is unsuccessful. Further, I argue that no unwanted consequences result, if one starts from the other, ‘objective’, definition of ‘grue’, as it constitutes no more than a mere fact of logic that cannot do any harm. Finally, I present a grue-case involving both kinds of definition, where the exclusive confirmation of either the green- or the grue-hypothesis is shown. (shrink)

A computational methodology called Grossone Infinity Computing introduced with the intention to allow one to work with infinities and infinitesimals numerically has been applied recently to a number of problems in numerical mathematics (optimization, numerical differentiation, numerical algorithms for solving ODEs, etc.). The possibility to use a specially developed computational device called the Infinity Computer (patented in USA and EU) for working with infinite and infinitesimal numbers numerically gives an additional advantage to this approach in comparison with traditional methodologies studying (...) infinities and infinitesimals only symbolically. The grossone methodology uses the Euclid’s Common Notion no. 5 ‘The whole is greater than the part’ and applies it to finite, infinite, and infinitesimal quantities and to finite and infinite sets and processes. It does not contradict Cantor’s and non-standard analysis views on infinity and can be considered as an applied development of their ideas. In this paper we consider infinite series and a particular attention is dedicated to divergent series with alternate signs. The Riemann series theorem states that conditionally convergent series can be rearranged in such a way that they either diverge or converge to an arbitrary real number. It is shown here that Riemann’s result is a consequence of the fact that symbol ∞ used traditionally does not allow us to express quantitatively the number of addends in the series, in other words, it just shows that the number of summands is infinite and does not allows us to count them. The usage of the grossone methodology allows us to see that (as it happens in the case where the number of addends is finite) rearrangements do not change the result for any sum with a fixed infinite number of summands. There are considered some traditional summation techniques such as Ramanujan summation producing results where to divergent series containing infinitely many positive integers negative results are assigned. It is shown that the careful counting of the number of addends in infinite series allows us to avoid this kind of results if grossone-based numerals are used. (shrink)

Pierre-Sylvain Régis’s Cartesianism is quite singular in seventeenth-century French philosophy. Though, can we speak of a form of experimental science in Régis’s work? After exploring his notions of ‘system’ and ‘hypothesis’, I will define his position in relation to Claude Perrault, Jacques Rohault, and the Royal Society. I argue, first, that the contrasts which traverse French science are not so much about the use of experiments but about whether or not observational data can be traced back to hypotheses and (...) to a coherent system. Secondly, that we can detect a significant similarity between Boyle’s positions and the views expressed by Perrault and also by Régis. Lastly, that French science, even in its Cartesian version, is much more probabilistic than English experimental philosophy. (shrink)

“Dutch Book” arguments and references to gambling theorems are typical in the debate between Bayesians and scientists committed to “classical” statistical methods. These arguments have rarely convinced non-Bayesian scientists to abandon certain conventional practices, partially because many scientists feel that gambling theorems have little relevance to their research activities. In other words, scientists “don’t bet.” This article examines one attempt, by Schervish, Seidenfeld, and Kadane, to progress beyond such apparent stalemates by connecting “Dutch Book”–type mathematical results with principles actually endorsed (...) by practicing experimentalists. (shrink)

Two main cognitive theories predict that people find refuting evidence that falsifies their theorising difficult, if not impossible to consider, even though such reasoning may be pivotal to grounding their everyday thoughts in reality (i.e., Poletiek, 1996; Klayman & Ha, 1987). In the classic 2-4-6 number sequence task devised by psychologists to test such reasoning skills in a simulated environment – people fail the test more often than not. In the 2-4-6 task participants try to discover what rule the number (...) triple 2-4-6 conforms to. The rule is ‘ascending numbers’, but it is tricky to discover this rule. Participants tend to generate hypotheses with the properties of the 2-4-6 triple, for example, ‘even numbers ascending in twos’. They must search for evidence to test whether their hypothesis is the rule. But experimental evidence has shown that they tend to generate confirming triples that they expect to be consistent with their hypothesis rather than inconsistent falsifying triples. Counter to the two main hypothesis testing theories this paper demonstrates that falsification is possible in five 2-4-6 task experiments when participants consider an Imaginary Participant’s hypothesis. Experiment 1 and 2 show that competition with an opponent hypothesis tester facilitates falsification. Experiments 3 to 5 show that the consideration of an alternative hypothesis helps this falsification of hypotheses lead to rule discovery. The implications of the results for theories of hypothesis testing and reasoning are discussed. (shrink)

Developments that suggest the universe is full of life make the Fermi paradox increasingly pressing, but our search for an extraterrestrial technological civilization (“ETC”) is handicapped by our ignorance of its probable nature and behavior. This paper offers a way around this problem by drawing on information theoretical concepts, including game theory and Bayesian probability. It argues that, whatever its ultimate goals, an ETC would have the same instrumental goals as other intelligent agents. Generically, these are self-preservation and the acquisition (...) of resources. For an advanced ETC, these generic goals imply the objectives of removing existential threats and acquiring strategic and non-strategic information. Since the most problematic existential threats for any ETC would be from other civilizations and planets hosting such civilizations would also be copious sources of information, these objectives would lead it to gather information from these locations and to protect itself against them. This dual-goals hypothesis resolves the Fermi paradox, redirects the search for extraterrestrial intelligence and makes testable predictions regarding ETC’s behavior on Earth if it is here. (shrink)

This paper examines how accepting the simulation hypothesis as a serious philosophical proposition forces a fundamental reconsideration of epistemological certainty. While previous work has focused on the probability of living in a simulation or the nature of consciousness within simulations, we demonstrate that the mere possibility of simulated reality creates a unique crisis for knowledge hierarchies that differs fundamentally from traditional sceptical arguments. Unlike Cartesian doubt, which preserves the notion of an objective reality while questioning our access to it, (...) the simulation hypothesis suggests reality itself might be programmatically mutable. We argue this undermines traditional distinctions between scientific and religious epistemology, creates an insoluble verification paradox for scientific methodology, and requires a radical reimagining of knowledge and truth. While we suggest that complete epistemological scepticism might be avoided through appeal to necessary logical primitives, we conclude that accepting the possibility of simulated reality requires a fundamental reconstruction of how we understand knowledge, scientific practice, and the relationship between competing explanatory frameworks. (shrink)

The hypothesis that God supernaturally raised Jesus from the dead is argued by William Lane Craig to be the best explanation for the empty tomb and postmortem appearances of Jesus because it satisfies seven criteria of adequacy better than rival naturalistic hypotheses. We identify problems with Craig’s criteria-based approach and show, most significantly, that the Resurrection hypothesis fails to fulfill any but the first of his criteria—especially explanatory scope and plausibility.

Each day people are presented with circumstances that may require speculation. Scientists may ponder questions such as why a star is born or how rainbows are made, psychologists may ask social questions such as why people are prejudiced, and military strategists may imagine what the consequences of their actions might be. Speculations may lead to the generation of putative explanations called hypotheses. But it is by checking if hypotheses accurately reflect the encountered facts that lead to sensible behaviour demonstrating a (...) true understanding. If evidence shows a hypothesis to be false, then people should rationally abandon it, especially if there are negative consequences. The aim of this thesis is to examine how effectively people search for evidence in their hypothesis testing to test whether or not their hypotheses are true or false in competitive games. -/- Research findings from six studies of hypothesis testing behaviour in competitive deductive tasks are explored. Chapter by chapter the thesis tests how everyday people, and master chess players, tackle hypothesis testing in mathematical tasks, such as how to solve sequential number sequence puzzles when thinking about an opponent, or how to solve chess problems in a variety of contexts. The implications of the results are discussed in light of aspects of general cognition: such as reasoning, social hypothesis testing and planning. (shrink)

David. J. Chalmers examines eleven possible solutions to the meta-problem of consciousness, ‘the problem of explaining why we think that there is a problem of consciousness.’ The present paper argues that Chalmers overlooks an explanation that he has otherwise taken seriously, and which a number of philosophers, physicists, and computer scientists have taken seriously as well: the hypothesis that we are living in a computer simulation. This paper argues that a particular version of the simulation hypothesis is at (...) least as good of a solution to the meta-problem of consciousness as many explanations Chalmers considers, and may even be a better one—as it may be the best solution to a much broader meta-philosophical problem: the ‘meta-problem of everything’, the problem of explaining why our world has the quantum-mechanical, relativistic, and philosophical features it does. (shrink)

Complex constraints like conditionals ('If A, then B') and probabilistic constraints ('The probability that A is p') pose problems for Bayesian theories of learning. Since these propositions do not express constraints on outcomes, agents cannot simply conditionalize on the new information. Furthermore, a natural extension of conditionalization, relative information minimization, leads to many counterintuitive predictions, evidenced by the sundowners problem and the Judy Benjamin problem. Building on the notion of a `paradigm shift' and empirical research in psychology and economics, I (...) argue that the model of hypothesis testing can explain how people learn complex, theory-laden propositions like conditionals and probability constraints. Theories are formalized as probability distributions over a set of possible outcomes and theory change is triggered by a constraint which is incompatible with the initial theory. This leads agents to consult a higher order probability function, or a 'prior over priors,' to choose the most likely alternative theory which satisfies the constraint. The hypothesis testing model is applied to three examples: learning a simple probabilistic constraint involving coin bias, the sundowners problem for conditional learning, and the Judy Benjamin problem for learning conditional probability constraints. (shrink)

Smarandache Hypothesis states that there is no speed limit of anything, including light and particles. While the idea is quite simple and based on known hypothesis of quantum mechanics, called Einstein-Podolski-Rosen paradox, in reality such a superluminal physics seems still hard to accept by majority of physicists. Here we review some experiments to support superluminal physics and also findings to explain Smarandache Quantum Paradoxes and Quantum Sorites Paradox. We also touch briefly on new experiment on magneton, supporting SubQuantum (...) Kinetic Model of Electron. (shrink)

What is wrong with ad hoc hypotheses? Ever since Popper’s falsificationist account of adhocness, there has been a lively philosophical discussion about what constitutes adhocness in scientific explanation, and what, if anything, distinguishes legitimate auxiliary hypotheses from illicit ad hoc ones. This paper draws upon distinct examples from pseudoscience to provide us with a clearer view as to what is troubling about ad hoc hypotheses. In contrast with other philosophical proposals, our approach retains the colloquial, derogative meaning of adhocness, and (...) calls attention to the way in which the context of a theoretical move bears on the charge of adhocness. We also discuss the role of motivations implicit in the concept of adhocness, and the way ad hoc moves draw on theory-internal rationalizations. (shrink)

According to the knowledge argument, physicalism fails because when physically omniscient Mary first sees red, her gain in phenomenal knowledge involves a gain in factual knowledge. Thus not all facts are physical facts. According to the ability hypothesis, the knowledge argument fails because Mary only acquires abilities to imagine, remember and recognise redness, and not new factual knowledge. I argue that reducing Mary’s new knowledge to abilities does not affect the issue of whether she also learns factually: I show (...) that gaining specific new phenomenal knowledge is required for acquiring abilities of the relevant kind. Phenomenal knowledge being basic to abilities, and not vice versa, it is left an open question whether someone who acquires such abilities also learns something factual. The answer depends on whether the new phenomenal knowledge involved is factual. But this is the same question we wanted to settle when first considering the knowledge argument. The ability hypothesis, therefore, has offered us no dialectical progress with the knowledge argument, and is best forgotten. (shrink)

In his [1937, 1938], Paul Dirac proposed his “Large Number Hypothesis” (LNH), as a speculative law, based upon what we will call the “Large Number Coincidences” (LNC’s), which are essentially “coincidences” in the ratios of about six large dimensionless numbers in physics. Dirac’s LNH postulates that these numerical coincidences reflect a deeper set of law-like relations, pointing to a revolutionary theory of cosmology. This led to substantial work, including the development of Dirac’s later [1969/74] cosmology, and other alternative cosmologies, (...) such as the Brans-Dicke modification of GTR, and to extensive empirical tests. We may refer to the generic hypothesis of “Large Number Relations” (LNR’s), as the proposal that there are lawlike relations of some kind between the dimensionless numbers, not necessarily those proposed in Dirac’s early LNH. Such relations would have a profound effect on our concepts of physics, but they remain shrouded in mystery. Although Dirac’s specific proposals for LNR theories have been largely rejected, the subject retains interest, especially among cosmologists seeking to test possible variations in fundamental constants, and to explain dark energy or the cosmological constant. In the first two sections here we briefly summarize the basic concepts of LNR’s. We then introduce an alternative LNR theory, using a systematic formalism to express variable transformations between conventional measurement variables and the true variables of the theory. We demonstrate some consistency results and review the evidence for changes in the gravitational constant G. The theory adopted in the strongest tests of Ġ/G, by the Lunar Laser Ranging (LLR) experiments, assumes: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m, as a fundamental relationship. Experimental measurements show the RHS to be close to zero, so it is inferred that significant changes in G are ruled out. However when the relation is derived in our alternative theory it gives: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m – (dR/dt)/R. The extra final term (which is the Hubble constant) is not taken into account in conventional derivations. This means the LLR experiments are consistent with our LNR theory (and others), and they do not really test for a changing value of G at all. This failure to transform predictions of LNR theories correctly is a serious conceptual flaw in current experiment and theory. (shrink)

A comprehensive introduction to the Language of Though Hypothesis (LOTH) accessible to general audiences. LOTH is an empirical thesis about thought and thinking. For their explication, it postulates a physically realized system of representations that have a combinatorial syntax (and semantics) such that operations on representations are causally sensitive only to the syntactic properties of representations. According to LOTH, thought is, roughly, the tokening of a representation that has a syntactic (constituent) structure with an appropriate semantics. Thinking thus consists (...) in syntactic operations defined over representations. Most of the arguments for LOTH derive their strength from their ability to explain certain empirical phenomena like productivity, systematicity of thought and thinking. (shrink)

A traditional problem with the performative hypothesis is that it cannot assign proper truth-conditions to a declarative sentence. This paper shows that the problem is solved by adopting a multidimensional semantics on which sentences have more than just truth-conditions. This is good news for those who want to at least partially revive the hypothesis. The solution also brings into focus a lesson about what issues to consider when drawing the semantics/pragmatics boundary.

The simulation hypothesis is a view of the nature of reality, suggesting that our world is likely a computer simulation created by an advanced civilization. In contrast, illusionism is a theory about the nature of phenomenal consciousness, arguing that phenomenal consciousness is an illusion and can be fully explained in physical terms. I argue that if our world is a simulated construct, illusionism could be incorrect. Specifically, even if our phenomenal experiences can be explained as illusionism suggests, advanced civilizations (...) could still create subjectively indistinguishable experiences by constructing a psychological system external to our world. Since we cannot determine which scenario we belong to, the illusionist explanation is not universally valid. Furthermore, I argue that even if the simulation hypothesis is impossible, illusionism remains flawed. Consequently, while the simulation hypothesis may function as a mere assumption, it exposes the inherent limitations of both illusionism and physicalism. (shrink)

According to the AI ensoulment hypothesis, some future AI systems will be endowed with immaterial souls. I argue that we should have at least a middling credence in the AI ensoulment hypothesis, conditional on our eventual creation of AGI and the truth of substance dualism in the human case. I offer two arguments. The first relies on an analogy between aliens and AI. The second rests on the conjecture that ensoulment occurs whenever a physical system is “fit to (...) possess” a soul, where very roughly this amounts to being physically structured in such a way that the system can meaningfully cooperate with the operations of the soul. (shrink)

Cognitive modules are internal mental structures. Some theorists and empirical researchers hypothesise that the human mind is either partially or massively comprised of structures that are modular in nature. Is the massive modularity of mind hypothesis a cogent view about the ontological nature of human mind or is it, rather, an effective/ineffective adaptationist discovery heuristic for generating predictively successful hypotheses about both heretofore unknown psychological traits and unknown properties of already identified psychological traits? Considering the inadequacies of the case (...) in favour of massive modularity as an ontological hypothesis, I suggest approaching and valuing massive modularity as an adaptationist discovery heuristic. (shrink)

According to the Donohue-Levitt hypothesis, the legalization of abor- tion in the United States in the 1970s explains some of the decrease in crime in the 1990s. In this paper, I challenge this hypothesis. First, I argue against the intermediate mechanisms whereby abortion in the 1970s is supposed to cause a decrease in crime in the 1990s. Second, I argue against the correlations that sup- port this causal relationship.

I reflect on the commentaries on my ‘skill hypothesis’ from Andrews/westra, Tomasello, Sterelny, and Railton. I discuss the difference between normative cognition and the broader category of action-guiding representation, and I reflect on the relationship between joint intentionality and normative cognition. I then consider Sterelny and Railton’s variants on the skill hypothesis, which highlight some important areas where future evidence could help us refine the account: the relative importance of on-the-fly skill execution vs. longer-term strategizing, the relative importance (...) of toolmaking vs. collaborative foraging, and the question of whether norms are encoded in control models themselves or in the goals and ideals that our control models help us pursue. (shrink)

In this paper, I propose that, in addition to the multiverse hypothesis, which is commonly taken to be an alternative explanation for fine-tuning, other than the design hypothesis, the simulation hypothesis is another explanation for fine-tuning. I then argue that the simulation hypothesis undercuts the alleged evidential connection between ‘designer’ and ‘supernatural designer of immense power and knowledge’ in much the same way that the multiverse hypothesis undercuts the alleged evidential connection between ‘fine-tuning’ and ‘fine-tuner’ (...) (or ‘designer’). If this is correct, then the fine-tuning argument is a weak argument for the existence of God. (shrink)

We respond to Stephen T. Davis’ criticism of our earlier essay, “Assessing the Resurrection Hypothesis.” We argue that the Standard Model of physics is relevant and decisive in establishing the implausibility and low explanatory power of the Resurrection hypothesis. We also argue that the laws of physics have entailments regarding God and the supernatural and, against Alvin Plantinga, that these same laws lack the proviso “no agent supernaturally interferes.” Finally, we offer Bayesian arguments for the Legend hypothesis (...) and against the Resurrection hypothesis. (shrink)

The Whorfian hypothesis has received support from recent findings in psychology, linguistics, and anthropology. This evidence has been interpreted as supporting the view that language modulates all stages of perception and cognition, in accordance with Whorf’s original proposal. In light of a much broader body of evidence on time perception, I propose to evaluate these findings with respect to their scope. When assessed collectively, the entire body of evidence on time perception shows that the Whorfian hypothesis has a (...) limited scope and that it does not affect early stages of time perception. In particular, all the available evidence shows that the scope of language modulation is limited in the case of time perception, and that the most important mechanisms for time perception are cognitive clocks and simultaneity windows, which we use to perceive the temporal properties of events. Language modulation has distorting effects, but only at later stages of processing or with respect to specific categorization tasks. The paper explains what is the role of these effects in the context of all the available evidence on time cognition and perception. (shrink)

(Draft of Feb 2023, see upcoming issue for Chalmers' reply) In Reality+: Virtual Worlds and the Problems of Philosophy, David Chalmers argues, among other things, that: if we are living in a full-scale simulation, we would still enjoy broad swathes of knowledge about non-psychological entities, such as atoms and shrubs; and, our lives might still be deeply meaningful. Chalmers views these claims as at least weakly connected: The former claim helps forestall a concern that if objects in the simulation are (...) not genuine (and so not knowable), then life in the simulation is illusory and therefore, not as valuable as a non-simulated life. Taking up these questions, I argue that in general, the value of social knowledge for a meaningful life dramatically swamps the value of non-social knowledge for a meaningful life. Along the way, I propose a non-additive model of the meaningfulness of life, according to which the overall effect of some potential contributor of value to a life depends in part on what is already in a life. One upshot is that the vindication of non-social knowledge, absent a correlative vindication of social knowledge, contributes either not at all or scarcely at all to the claim that our lives in the simulation might be deeply meaningful. This is so even though the vindication of non-social knowledge does forestall the concern that in the simulation, our lives might be wholly meaningless. (shrink)