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72-486: Skeptics such as Robert T. Carroll , Claus Larsen, and others have questioned the methodology of the Global Consciousness Project, particularly how the data are selected and interpreted, saying the data anomalies reported by the project are the result of "pattern matching" and selection bias which ultimately fail to support a belief in psi or global consciousness. Other critics have stated that

144-676: A portmanteau of electroencephalogram and Gaia . Supporters and skeptics have referred to the aim of the GCP as being analogous to detecting "a great disturbance in the Force ." The GCP has suggested that changes in the level of randomness may have occurred during the September 11, 2001 attacks when the planes first impacted, as well as in the two days following the attacks. Independent scientists Edwin May and James Spottiswoode conducted an analysis of

216-501: A posterior probability in the light of new, relevant data (evidence). The Bayesian interpretation provides a standard set of procedures and formulae to perform this calculation. The term Bayesian derives from the 18th-century mathematician and theologian Thomas Bayes , who provided the first mathematical treatment of a non-trivial problem of statistical data analysis using what is now known as Bayesian inference . Mathematician Pierre-Simon Laplace pioneered and popularized what

288-475: A bad or unhealthy form of radical skepticism. On this view, the "good" skeptic is a critically-minded person who seeks strong evidence before accepting a position. The "bad" skeptic, on the other hand, wants to "suspend judgment indefinitely... even in the face of demonstrable truth". Another categorization focuses on the motivation for the skeptical attitude. Some skeptics have ideological motives: they want to replace inferior beliefs with better ones. Others have

360-521: A doubting attitude toward knowledge claims that are rejected by many. Almost everyone shows some form of ordinary skepticism, for example, by doubting the knowledge claims made by flat earthers or astrologers . Philosophical skepticism, on the other hand, is a much more radical and rare position. It includes the rejection of knowledge claims that seem certain from the perspective of common sense . Some forms of it even deny that one knows that "I have two hands" or that "the sun will come out tomorrow". It

432-423: A general version of the theorem and used it to approach problems in celestial mechanics , medical statistics, reliability , and jurisprudence . Early Bayesian inference, which used uniform priors following Laplace's principle of insufficient reason , was called " inverse probability " (because it infers backwards from observations to parameters, or from effects to causes). After the 1920s, "inverse probability"

504-409: A given event for the GCP to say they have found a correlation. Wolcotte Smith said "A couple of additional statistical adjustments would have to be made to determine if there really was a spike in the numbers," referencing the data related to September 11, 2001. Similarly, Jeffrey D. Scargle believes unless both Bayesian and classical p-value analysis agree and both show the same anomalous effects,

576-419: A more practical outlook in that they see problematic beliefs as the cause of harmful customs they wish to stop. Some skeptics have very particular goals in mind, such as bringing down a certain institution associated with the spread of claims they reject. Philosophical skepticism is a prominent form of skepticism and can be contrasted with non-philosophical or ordinary skepticism. Ordinary skepticism involves

648-523: A number of Sophists . Gorgias , for example, reputedly argued that nothing exists, that even if there were something we could not know it, and that even if we could know it we could not communicate it. The Heraclitean philosopher Cratylus refused to discuss anything and would merely wriggle his finger, claiming that communication is impossible since meanings are constantly changing. Socrates also had skeptical tendencies, claiming to know nothing worthwhile. There were two major schools of skepticism in

720-481: A number of important responses. Hume's Scottish contemporary, Thomas Reid (1710–1796), challenged Hume's strict empiricism and argued that it is rational to accept "common-sense" beliefs such as the basic reliability of our senses, our reason, our memories, and inductive reasoning, even though none of these things can be proved. In Reid's view, such common-sense beliefs are foundational and require no proof in order to be rationally justified. Not long after Hume's death,

792-499: A permanent network of continuously-running REGs. This became the EGG project or Global Consciousness Project. Comparing the GCP to PEAR, Nelson, referring to the "field" studies with REGs done by PEAR, said the GCP used "exactly the same procedure... applied on a broader scale." The GCP's methodology is based on the hypothesis that events which elicit widespread emotion or draw the simultaneous attention of large numbers of people may affect

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864-467: A person and differ from person to person, for example, because they follow different cognitive norms. The opposite of skepticism is dogmatism , which implies an attitude of certainty in the form of an unquestioning belief. A similar contrast is often drawn in relation to blind faith and credulity. Various types of skepticism have been discussed in the academic literature. Skepticism is usually restricted to knowledge claims on one particular subject, which

936-405: A person is skeptical about claims made by their government about an ongoing war then the person doubts that these claims are accurate. In such cases, skeptics normally recommend not disbelief but suspension of belief, i.e. maintaining a neutral attitude that neither affirms nor denies the claim. This attitude is often motivated by the impression that the available evidence is insufficient to support

1008-633: A position, from "bad" or radical skepticism, which wants to suspend judgment indefinitely. Philosophical skepticism is one important form of skepticism. It rejects knowledge claims that seem certain from the perspective of common sense . Radical forms of philosophical skepticism deny that "knowledge or rational belief is possible" and urge us to suspend judgment on many or all controversial matters. More moderate forms claim only that nothing can be known with certainty, or that we can know little or nothing about nonempirical matters, such as whether God exists, whether human beings have free will, or whether there

1080-411: A religious skeptic might believe that Jesus existed (see historicity of Jesus ) while questioning claims that he was the messiah or performed miracles. Historically, religious skepticism can be traced back to Xenophanes , who doubted many religious claims of his time, although he recognized that " God is one, supreme among gods and men, and not like mortals in body or in mind." He maintained that there

1152-554: A result, a number of ostensibly scientific claims are considered to be " pseudoscience " if they are found to improperly apply or to ignore the fundamental aspects of the scientific method. Professional skepticism is an important concept in auditing . It requires an auditor to have a "questioning mind", to make a critical assessment of evidence, and to consider the sufficiency of the evidence. Bayesian probability Bayesian probability ( / ˈ b eɪ z i ə n / BAY -zee-ən or / ˈ b eɪ ʒ ən / BAY -zhən )

1224-454: A task left uncompleted by von Neumann and Oskar Morgenstern : their original theory supposed that all the agents had the same probability distribution, as a convenience. Pfanzagl's axiomatization was endorsed by Oskar Morgenstern: "Von Neumann and I have anticipated ... [the question whether probabilities] might, perhaps more typically, be subjective and have stated specifically that in the latter case axioms could be found from which could derive

1296-496: A thesis: the thesis that knowledge does not exist. Skepticism is related to various terms. It is sometimes equated with agnosticism and relativism . However, there are slight differences in meaning. Agnosticism is often understood more narrowly as skepticism about religious questions, in particular, about the Christian doctrine . Relativism does not deny the existence of knowledge or truth but holds that they are relative to

1368-405: A way of life. This is based on the idea that maintaining the skeptical attitude of doubt toward most concerns in life is superior to living in dogmatic certainty, for example because such a skeptic has more happiness and peace of mind or because it is morally better. In contemporary philosophy , on the other hand, skepticism is often understood neither as an attitude nor as a way of life but as

1440-448: Is an interpretation of the concept of probability , in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses ; that is, with propositions whose truth or falsity

1512-529: Is an afterlife. In ancient philosophy, skepticism was understood as a way of life associated with inner peace . Skepticism has been responsible for many important developments in science and philosophy. It has also inspired several contemporary social movements. Religious skepticism advocates for doubt concerning basic religious principles, such as immortality, providence , and revelation . Scientific skepticism advocates for testing beliefs for reliability, by subjecting them to systematic investigation using

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1584-510: Is controversial; Halpern found a counterexample based on his observation that the Boolean algebra of statements may be finite. Other axiomatizations have been suggested by various authors with the purpose of making the theory more rigorous. Bruno de Finetti proposed the Dutch book argument based on betting. A clever bookmaker makes a Dutch book by setting the odds and bets to ensure that

1656-507: Is either a Bayesian procedure or a limit of Bayesian procedures. Conversely, every Bayesian procedure is admissible . Following the work on expected utility theory of Ramsey and von Neumann , decision-theorists have accounted for rational behavior using a probability distribution for the agent . Johann Pfanzagl completed the Theory of Games and Economic Behavior by providing an axiomatization of subjective probability and utility,

1728-412: Is implementable in theory, and has kept experimental psychologists occupied for a half century. This work demonstrates that Bayesian-probability propositions can be falsified , and so meet an empirical criterion of Charles S. Peirce , whose work inspired Ramsey. (This falsifiability -criterion was popularized by Karl Popper . ) Modern work on the experimental evaluation of personal probabilities uses

1800-411: Is not possible, for example, to look at the data and predict with any accuracy what (if anything) the eggs may be responding to." Robert Matthews said that while it was "the most sophisticated attempt yet" to prove psychokinesis existed, the unreliability of significant events to cause statistically significant spikes meant that "the only conclusion to emerge from the Global Consciousness Project so far

1872-405: Is now called Bayesian probability. Bayesian methods are characterized by concepts and procedures as follows: Broadly speaking, there are two interpretations of Bayesian probability. For objectivists, who interpret probability as an extension of logic , probability quantifies the reasonable expectation that everyone (even a "robot") who shares the same knowledge should share in accordance with

1944-412: Is possible ( acatalepsy ). The Academic Skeptics claimed that some beliefs are more reasonable or probable than others, whereas Pyrrhonian skeptics argue that equally compelling arguments can be given for or against any disputed view. Nearly all the writings of the ancient skeptics are now lost. Most of what we know about ancient skepticism is from Sextus Empiricus , a Pyrrhonian skeptic who lived in

2016-414: Is run as a replication experiment, essentially combining the results of many distinct tests of the hypothesis. The hypothesis is tested by calculating the extent of data fluctuations at the time of events. The procedure is specified by a three-step experimental protocol. In the first step, the event duration and the calculation algorithm are pre-specified and entered into a formal registry. In the second step,

2088-511: Is taken seriously in philosophy nonetheless because it has proven very hard to conclusively refute philosophical skepticism. Skepticism has been responsible for important developments in various fields, such as science , medicine , and philosophy . In science, the skeptical attitude toward traditional opinions was a key factor in the development of the scientific method . It emphasizes the need to scrutinize knowledge claims by testing them through experimentation and precise measurement . In

2160-561: Is that data without a theory is as meaningless as words without a narrative". Petter Bancel reviews the data in a 2017 article and "finds that the data do not support the global consciousness proposal" and rather "All of the tests favor the interpretation of a goal-oriented effect." Skepticism Skepticism , also spelled scepticism in British English , is a questioning attitude or doubt toward knowledge claims that are seen as mere belief or dogma . For example, if

2232-455: Is unknown. In the Bayesian view, a probability is assigned to a hypothesis, whereas under frequentist inference , a hypothesis is typically tested without being assigned a probability. Bayesian probability belongs to the category of evidential probabilities; to evaluate the probability of a hypothesis, the Bayesian probabilist specifies a prior probability . This, in turn, is then updated to

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2304-429: Is why its different forms can be distinguished based on the subject. For example, religious skeptics distrust religious doctrines and moral skeptics raise doubts about accepting various moral requirements and customs. Skepticism can also be applied to knowledge in general. However, this attitude is usually only found in some forms of philosophical skepticism. A closely related classification distinguishes based on

2376-705: The Football World Cup , and television broadcasts such as the Academy Awards . FieldREG was extended to global dimensions in studies looking at data from 12 independent REGs in the US and Europe during a web-promoted "Gaiamind Meditation" in January 1997, and then again in September 1997 after the death of Diana, Princess of Wales . The project claimed the results suggested it would be worthwhile to build

2448-498: The scientific method , to discover empirical evidence for them. Skepticism , also spelled scepticism (from the Greek σκέπτομαι skeptomai , to search, to think about or look for), refers to a doubting attitude toward knowledge claims. So if a person is skeptical of their government's claims about an ongoing war then the person has doubts that these claims are true. Or being skeptical that one's favorite hockey team will win

2520-425: The source of knowledge , such as skepticism about perception , memory , or intuition . A further distinction is based on the degree of the skeptical attitude. The strongest forms assert that there is no knowledge at all or that knowledge is impossible. Weaker forms merely state that one can never be absolutely certain. Some theorists distinguish between a good or healthy form of moderate skepticism in contrast to

2592-462: The 1950s; the derived Bayesianism , neo-Bayesianism is of 1960s coinage. In the objectivist stream, the statistical analysis depends on only the model assumed and the data analysed. No subjective decisions need to be involved. In contrast, "subjectivist" statisticians deny the possibility of fully objective analysis for the general case. In the 1980s, there was a dramatic growth in research and applications of Bayesian methods, mostly attributed to

2664-848: The Ajñana philosopher Sanjaya Belatthiputta . A strong element of skepticism is found in Early Buddhism , most particularly in the Aṭṭhakavagga sutra. However the total effect these philosophies had on each other is difficult to discern. Since skepticism is a philosophical attitude and a style of philosophizing rather than a position, the Ajñanins may have influenced other skeptical thinkers of India such as Nagarjuna , Jayarāśi Bhaṭṭa , and Shriharsha . In Greece, philosophers as early as Xenophanes ( c.  570 – c.  475   BCE ) expressed skeptical views, as did Democritus and

2736-460: The Dutch book argument, nor any other in the personalist arsenal of proofs of the probability axioms, entails the dynamic assumption. Not one entails Bayesianism. So the personalist requires the dynamic assumption to be Bayesian. It is true that in consistency a personalist could abandon the Bayesian model of learning from experience. Salt could lose its savour." In fact, there are non-Bayesian updating rules that also avoid Dutch books (as discussed in

2808-683: The German philosopher Immanuel Kant (1724–1804) argued that human empirical experience has possibility conditions which could not have been realized unless Hume's skeptical conclusions about causal synthetic a priori judgements were false. Today, skepticism continues to be a topic of lively debate among philosophers. British philosopher Julian Baggini posits that reason is perceived as "an enemy of mystery and ambiguity," but, if used properly, can be an effective tool for solving many larger societal issues. Religious skepticism generally refers to doubting particular religious beliefs or claims. For example,

2880-669: The Renaissance and Reformation, particularly after the complete writings of Sextus Empiricus were translated into Latin in 1569 and after Martin Luther 's skepticism of holy orders. A number of Catholic writers, including Francisco Sanches ( c.  1550–1623 ), Michel de Montaigne (1533–1592), Pierre Gassendi (1592–1655), and Marin Mersenne (1588–1648) deployed ancient skeptical arguments to defend moderate forms of skepticism and to argue that faith, rather than reason, must be

2952-593: The ancient Greek and Roman world. The first was Pyrrhonism , founded by Pyrrho of Elis ( c.  360–270  BCE ). The second was Academic Skepticism , so-called because its two leading defenders, Arcesilaus ( c.  315–240  BCE ) who initiated the philosophy, and Carneades ( c.  217–128  BCE ), the philosophy's most famous proponent, were heads of Plato's Academy . Pyrrhonism's aims are psychological. It urges suspension of judgment ( epoche ) to achieve mental tranquility ( ataraxia ). The Academic Skeptics denied that knowledge

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3024-450: The basis of Bayesian inference has been supported by several arguments, such as Cox axioms , the Dutch book argument , arguments based on decision theory and de Finetti's theorem . Richard T. Cox showed that Bayesian updating follows from several axioms, including two functional equations and a hypothesis of differentiability. The assumption of differentiability or even continuity

3096-402: The basis of scientific understanding and empirical evidence. Scientific skepticism may discard beliefs pertaining to purported phenomena not subject to reliable observation and thus not systematic or empirically testable . Most scientists, being scientific skeptics, test the reliability of certain kinds of claims by subjecting them to systematic investigation via the scientific method . As

3168-464: The bookmaker profits—at the expense of the gamblers—regardless of the outcome of the event (a horse race, for example) on which the gamblers bet. It is associated with probabilities implied by the odds not being coherent . However, Ian Hacking noted that traditional Dutch book arguments did not specify Bayesian updating: they left open the possibility that non-Bayesian updating rules could avoid Dutch books. For example, Hacking writes "And neither

3240-566: The case for skepticism as powerfully as possible. Descartes argued that no matter what radical skeptical possibilities we imagine there are certain truths (e.g., that thinking is occurring, or that I exist) that are absolutely certain. Thus, the ancient skeptics were wrong to claim that knowledge is impossible. Descartes also attempted to refute skeptical doubts about the reliability of our senses, our memory, and other cognitive faculties. To do this, Descartes tried to prove that God exists and that God would not allow us to be systematically deceived about

3312-424: The championship means that one is uncertain about the strength of their performance. Skepticism about a claim implies that one does not believe the claim to be true. But it does not automatically follow that one should believe that the claim is false either. Instead, skeptics usually recommend a neutral attitude: beliefs about this matter should be suspended. In this regard, skepticism about a claim can be defined as

3384-512: The claim. Formally, skepticism is a topic of interest in philosophy , particularly epistemology . More informally, skepticism as an expression of questioning or doubt can be applied to any topic, such as politics, religion, or pseudoscience. It is often applied within restricted domains, such as morality ( moral skepticism ), atheism (skepticism about the existence of God ), or the supernatural . Some theorists distinguish "good" or moderate skepticism, which seeks strong evidence before accepting

3456-410: The data around the September 11 attacks and concluded there was no statistically significant change in the randomness of the GCP data during the attacks and the apparent significant deviation reported by Nelson and Radin existed only in their chosen time window. Spikes and fluctuations are to be expected in any random distribution of data, and there is no set time frame for how close a spike has to be to

3528-716: The desired numerical utility together with a number for the probabilities (cf. p. 19 of The Theory of Games and Economic Behavior). We did not carry this out; it was demonstrated by Pfanzagl ... with all the necessary rigor". Ramsey and Savage noted that the individual agent's probability distribution could be objectively studied in experiments. Procedures for testing hypotheses about probabilities (using finite samples) are due to Ramsey (1931) and de Finetti (1931, 1937, 1964, 1970). Both Bruno de Finetti and Frank P. Ramsey acknowledge their debts to pragmatic philosophy , particularly (for Ramsey) to Charles S. Peirce . The "Ramsey test" for evaluating probability distributions

3600-503: The discovery of Markov chain Monte Carlo methods and the consequent removal of many of the computational problems, and to an increasing interest in nonstandard, complex applications. While frequentist statistics remains strong (as demonstrated by the fact that much of undergraduate teaching is based on it ), Bayesian methods are widely accepted and used, e.g., in the field of machine learning . The use of Bayesian probabilities as

3672-476: The event data are extracted from the database and a Z score , which indicates the degree of deviation from the null hypothesis, is calculated from the pre-specified algorithm. In the third step, the event Z-score is combined with the Z-scores from previous events to yield an overall result for the experiment. The remote devices have been dubbed Princeton Eggs , a reference to the coinage electrogaiagram (EGG),

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3744-547: The field of medicine, skepticism has helped establish more advanced forms of treatment by putting into doubt traditional forms that were based on intuitive appeal rather than empirical evidence . In the history of philosophy, skepticism has often played a productive role not just for skeptics but also for non-skeptical philosophers. This is due to its critical attitude that challenges the epistemological foundations of philosophical theories. This can help to keep speculation in check and may provoke creative responses, transforming

3816-527: The history of philosophy and is still widely discussed today. As a philosophical school or movement, skepticism arose both in ancient Greece and India. In India the Ajñana school of philosophy espoused skepticism. It was a major early rival of Buddhism and Jainism , and possibly a major influence on Buddhism. Two of the foremost disciples of the Buddha , Sariputta and Moggallāna , were initially students of

3888-401: The kind of result GCP proposes will not be generally accepted. In 2003, a New York Times article concluded "All things considered at this point, the stock market seems a more reliable gauge of the national—if not the global—emotional resonance." In 2007, The Age reported that "[Nelson] concedes the data, so far, is not solid enough for global consciousness to be said to exist at all. It

3960-476: The literature on " probability kinematics " following the publication of Richard C. Jeffrey 's rule, which is itself regarded as Bayesian ). The additional hypotheses sufficient to (uniquely) specify Bayesian updating are substantial and not universally seen as satisfactory. A decision-theoretic justification of the use of Bayesian inference (and hence of Bayesian probabilities) was given by Abraham Wald , who proved that every admissible statistical procedure

4032-831: The nature of reality. Many contemporary philosophers question whether this second stage of Descartes's critique of skepticism is successful. In the eighteenth century a new case for skepticism was offered by the Scottish philosopher David Hume (1711–1776). Hume was an empiricist, claiming that all genuine ideas can be traced back to original impressions of sensation or introspective consciousness. Hume argued that on empiricist grounds there are no sound reasons for belief in God, an enduring self or soul, an external world, causal necessity, objective morality, or inductive reasoning. In fact, he argued that "Philosophy would render us entirely Pyrrhonian, were not Nature too strong for it." As Hume saw it,

4104-444: The needs of science and of human limitations, Bayesian statisticians have developed "objective" methods for specifying prior probabilities. Indeed, some Bayesians have argued the prior state of knowledge defines the (unique) prior probability-distribution for "regular" statistical problems; cf. well-posed problems . Finding the right method for constructing such "objective" priors (for appropriate classes of regular problems) has been

4176-430: The open access to the test data "is a testimony to the integrity and curiosity of those involved". But in analyzing the data for 11 September 2001, May et al. concluded that the statistically significant result given by the published GCP hypothesis was fortuitous, and found that as far as this particular event was concerned an alternative method of analysis gave only chance deviations throughout. Roger D. Nelson developed

4248-525: The output of hardware random number generators in a statistically significant way. The GCP maintains a network of hardware random number generators which are interfaced to computers at 70 locations around the world. Custom software reads the output of the random number generators and records a trial (sum of 200 bits) once every second. The data are sent to a server in Princeton, creating a database of synchronized parallel sequences of random numbers. The GCP

4320-658: The primary guide to truth. Similar arguments were offered later (perhaps ironically) by the Protestant thinker Pierre Bayle in his influential Historical and Critical Dictionary (1697–1702). The growing popularity of skeptical views created an intellectual crisis in seventeenth-century Europe. An influential response was offered by the French philosopher and mathematician René Descartes (1596–1650). In his classic work, Meditations of First Philosophy (1641), Descartes sought to refute skepticism, but only after he had formulated

4392-478: The prior probability. The term Bayesian derives from Thomas Bayes (1702–1761), who proved a special case of what is now called Bayes' theorem in a paper titled " An Essay Towards Solving a Problem in the Doctrine of Chances ". In that special case, the prior and posterior distributions were beta distributions and the data came from Bernoulli trials . It was Pierre-Simon Laplace (1749–1827) who introduced

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4464-502: The project as an extrapolation of two decades of experiments from the controversial Princeton Engineering Anomalies Research Lab (PEAR). In an extension of the laboratory research utilizing hardware Random Event Generators (REG) called FieldREG, investigators examined the outputs of REGs in the field before, during and after highly focused or coherent group events. The group events studied included psychotherapy sessions, theater presentations, religious rituals, sports competitions such as

4536-1130: The quest of statistical theorists from Laplace to John Maynard Keynes , Harold Jeffreys , and Edwin Thompson Jaynes . These theorists and their successors have suggested several methods for constructing "objective" priors (Unfortunately, it is not always clear how to assess the relative "objectivity" of the priors proposed under these methods): Each of these methods contributes useful priors for "regular" one-parameter problems, and each prior can handle some challenging statistical models (with "irregularity" or several parameters). Each of these methods has been useful in Bayesian practice. Indeed, methods for constructing "objective" (alternatively, "default" or "ignorance") priors have been developed by avowed subjective (or "personal") Bayesians like James Berger ( Duke University ) and José-Miguel Bernardo ( Universitat de València ), simply because such priors are needed for Bayesian practice, particularly in science. The quest for "the universal method for constructing priors" continues to attract statistical theorists. Thus,

4608-528: The randomization, blinding , and Boolean-decision procedures of the Peirce-Jastrow experiment. Since individuals act according to different probability judgments, these agents' probabilities are "personal" (but amenable to objective study). Personal probabilities are problematic for science and for some applications where decision-makers lack the knowledge or time to specify an informed probability-distribution (on which they are prepared to act). To meet

4680-434: The real basis of human belief is not reason, but custom or habit. We are hard-wired by nature to trust, say, our memories or inductive reasoning, and no skeptical arguments, however powerful, can dislodge those beliefs. In this way, Hume embraced what he called a "mitigated" skepticism, while rejecting an "excessive" Pyrrhonian skepticism that he saw as both impractical and psychologically impossible. Hume's skepticism provoked

4752-470: The rules of Bayesian statistics, which can be justified by Cox's theorem . For subjectivists, probability corresponds to a personal belief. Rationality and coherence allow for substantial variation within the constraints they pose; the constraints are justified by the Dutch book argument or by decision theory and de Finetti's theorem . The objective and subjective variants of Bayesian probability differ mainly in their interpretation and construction of

4824-607: The second or third century  CE . His works contain a lucid summary of stock skeptical arguments. Ancient skepticism faded out during the late Roman Empire, particularly after Augustine (354–430  CE ) attacked the skeptics in his work Against the Academics (386  CE ). There was little knowledge of, or interest in, ancient skepticism in Christian Europe during the Middle Ages. Interest revived during

4896-438: The theory in question in order to overcome the problems posed by skepticism. According to Richard H. Popkin, "the history of philosophy can be seen, in part, as a struggle with skepticism". This struggle has led many contemporary philosophers to abandon the quest for absolutely certain or indubitable first principles of philosophy, which was still prevalent in many earlier periods. Skepticism has been an important topic throughout

4968-622: The thesis that "the only justified attitude with respect to [this claim] is suspension of judgment". It is often motivated by the impression that one cannot be certain about it. This is especially relevant when there is significant expert disagreement. Skepticism is usually restricted to a claim or a field of inquiry. So religious and moral skeptics have a doubtful attitude about religious and moral doctrines. But some forms of philosophical skepticism, are wider in that they reject any form of knowledge. Some definitions, often inspired by ancient philosophy , see skepticism not just as an attitude but as

5040-402: The two denominations conflict concerning some belief. Additionally, they may also be skeptical of the claims made by atheists. The historian Will Durant writes that Plato was "as skeptical of atheism as of any other dogma". The Baháʼí Faith encourages skepticism that is mainly centered around self-investigation of truth. A scientific or empirical skeptic is one who questions beliefs on

5112-509: Was largely supplanted by a collection of methods that came to be called frequentist statistics . In the 20th century, the ideas of Laplace developed in two directions, giving rise to objective and subjective currents in Bayesian practice. Harold Jeffreys ' Theory of Probability (first published in 1939) played an important role in the revival of the Bayesian view of probability, followed by works by Abraham Wald (1950) and Leonard J. Savage (1954). The adjective Bayesian itself dates to

5184-552: Was one greatest God. God is one eternal being, spherical in form, comprehending all things within himself, is the absolute mind and thought, therefore is intelligent, and moves all things, but bears no resemblance to human nature either in body or mind." Religious skepticism is not the same as atheism or agnosticism , though these often do involve skeptical attitudes toward religion and philosophical theology (for example, towards divine omnipotence ). Religious people are generally skeptical about claims of other religions, at least when

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