Common knowledge (logic)

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https://en.wikipedia.org/wiki/Common_knowledge_(logic) 

Common knowledge is a special kind of knowledge for a group of agents. There is common knowledge of p in a group of agents G when all the agents in G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum.

The concept was first introduced in the philosophical literature by David Kellogg Lewis in his study Convention (1969). The sociologist Morris Friedell defined common knowledge in a 1969 paper. It was first given a mathematical formulation in a set-theoretical framework by Robert Aumann (1976). Computer scientists grew an interest in the subject of epistemic logic in general – and of common knowledge in particular – starting in the 1980s. There are numerous puzzles based upon the concept which have been extensively investigated by mathematicians such as John Conway.

The philosopher Stephen Schiffer, in his 1972 book Meaning, independently developed a notion he called "mutual knowledge" which functions quite similarly to Lewis's and Friedel's 1969 "common knowledge".

Example

Puzzle

The idea of common knowledge is often introduced by some variant of induction puzzles:

On an island, there are k people who have blue eyes, and the rest of the people have green eyes. At the start of the puzzle, no one on the island ever knows their own eye color. By rule, if a person on the island ever discovers they have blue eyes, that person must leave the island at dawn; anyone not making such a discovery always sleeps until after dawn. On the island, each person knows every other person's eye color, there are no reflective surfaces, and there is no communication of eye color.

At some point, an outsider comes to the island, calls together all the people on the island, and makes the following public announcement: "At least one of you has blue eyes". The outsider, furthermore, is known by all to be truthful, and all know that all know this, and so on: it is common knowledge that he is truthful, and thus it becomes common knowledge that there is at least one islander who has blue eyes. The problem: assuming all persons on the island are completely logical and that this too is common knowledge, what is the eventual outcome?

Solution

The answer is that, on the kth dawn after the announcement, all the blue-eyed people will leave the island.

Proof

The solution can be seen with an inductive argument. If k = 1 (that is, there is exactly one blue-eyed person), the person will recognize that he alone has blue eyes (by seeing only green eyes in the others) and leave at the first dawn. If k = 2, no one will leave at the first dawn. The two blue-eyed people, seeing only one person with blue eyes, and that no one left on the 1st dawn (and thus that k > 1), will leave on the second dawn. Inductively, it can be reasoned that no one will leave at the first k − 1 dawns if and only if there are at least k blue-eyed people. Those with blue eyes, seeing k − 1 blue-eyed people among the others and knowing there must be at least k, will reason that they must have blue eyes and leave.

What's most interesting about this scenario is that, for k > 1, the outsider is only telling the island citizens what they already know: that there are blue-eyed people among them. However, before this fact is announced, the fact is not common knowledge.

For k = 2, it is merely "first-order" knowledge. Each blue-eyed person knows that there is someone with blue eyes, but each blue eyed person does not know that the other blue-eyed person has this same knowledge.

For k = 3, it is "second order" knowledge. Each blue-eyed person knows that a second blue-eyed person knows that a third person has blue eyes, but no one knows that there is a third blue-eyed person with that knowledge, until the outsider makes his statement.

In general: For k > 1, it is "(k − 1)th order" knowledge. Each blue-eyed person knows that a second blue-eyed person knows that a third blue-eyed person knows that.... (repeat for a total of k − 1 levels) a kth person has blue eyes, but no one knows that there is a "kth" blue-eyed person with that knowledge, until the outsider makes his statement. The notion of common knowledge therefore has a palpable effect. Knowing that everyone knows does make a difference. When the outsider's public announcement (a fact already known to all, unless k=1 then the one person with blue eyes would not know until the announcement) becomes common knowledge, the blue-eyed people on this island eventually deduce their status, and leave.

Formalization

Modal logic (syntactic characterization)

Common knowledge can be given a logical definition in multi-modal logic systems in which the modal operators are interpreted epistemically. At the propositional level, such systems are extensions of propositional logic. The extension consists of the introduction of a group G of agents, and of n modal operators K_i (with i = 1, ..., n) with the intended meaning that "agent i knows." Thus K_i ${\displaystyle \varphi }$ (where ${\displaystyle \varphi }$ is a formula of the calculus) is read "agent i knows ${\displaystyle \varphi }$." We can define an operator E_G with the intended meaning of "everyone in group G knows" by defining it with the axiom

${\displaystyle E_{G}\varphi \Leftrightarrow \bigwedge _{i\in G}K_{i}\varphi ,}$

By abbreviating the expression ${\displaystyle E_{G}E_{G}^{n-1}\varphi }$ with ${\displaystyle E_{G}^{n}\varphi }$ and defining ${\displaystyle E_{G}^{0}\varphi =\varphi }$, we could then define common knowledge with the axiom

${\displaystyle C\varphi \Leftrightarrow \bigwedge _{i=0}^{\infty }E^{i}\varphi }$

There is however a complication. The languages of epistemic logic are usually finitary, whereas the axiom above defines common knowledge as an infinite conjunction of formulas, hence not a well-formed formula of the language. To overcome this difficulty, a fixed-point definition of common knowledge can be given. Intuitively, common knowledge is thought of as the fixed point of the "equation" ${\displaystyle C_{G}\varphi =\varphi \wedge E_{G}(C_{G}\varphi )}$. In this way, it is possible to find a formula ${\displaystyle \psi }$ implying ${\displaystyle E_{G}(\varphi \wedge C_{G}\varphi )}$ from which, in the limit, we can infer common knowledge of ${\displaystyle \varphi }$. 

This syntactic characterization is given semantic content through so-called Kripke structures. A Kripke structure is given by (i) a set of states (or possible worlds) S, (ii) n accessibility relations ${\displaystyle R_{1},\dots ,R_{n}}$, defined on ${\displaystyle S\times S}$, intuitively representing what states agent i considers possible from any given state, and (iii) a valuation function ${\displaystyle \pi }$ assigning a truth value, in each state, to each primitive proposition in the language. The semantics for the knowledge operator is given by stipulating that ${\displaystyle K_{i}\varphi }$ is true at state s iff ${\displaystyle \varphi }$ is true at all states t such that ${\displaystyle (s,t)\in R_{i}}$. The semantics for the common knowledge operator, then, is given by taking, for each group of agents G, the reflexive and transitive closure of the ${\displaystyle R_{i}}$, for all agents i in G, call such a relation ${\displaystyle R_{G}}$, and stipulating that ${\displaystyle C_{G}\varphi }$ is true at state s iff ${\displaystyle \varphi }$ is true at all states t such that ${\displaystyle (s,t)\in R_{G}}$.

Set theoretic (semantic characterization)

Alternatively (yet equivalently) common knowledge can be formalized using set theory (this was the path taken by the Nobel laureate Robert Aumann in his seminal 1976 paper). We will start with a set of states S. We can then define an event E as a subset of the set of states S. For each agent i, define a partition on S, P_i. This partition represents the state of knowledge of an agent in a state. In state s, agent i knows that one of the states in P_i(s) obtains, but not which one. (Here P_i(s) denotes the unique element of P_i containing s. Note that this model excludes cases in which agents know things that are not true.)

We can now define a knowledge function K in the following way:

${\displaystyle K_{i}(e)=\{s\in S\mid P_{i}(s)\subset e\}}$

That is, K_i(e) is the set of states where the agent will know that event e obtains. It is a subset of e.

Similar to the modal logic formulation above, we can define an operator for the idea that "everyone knows e".

${\displaystyle E(e)=\bigcap _{i}K_{i}(e)}$

As with the modal operator, we will iterate the E function, ${\displaystyle E^{1}(e)=E(e)}$ and ${\displaystyle E^{n+1}(e)=E(E^{n}(e))}$. Using this we can then define a common knowledge function,

${\displaystyle C(e)=\bigcap _{n=1}^{\infty }E^{n}(e).}$

The equivalence with the syntactic approach sketched above can easily be seen: consider an Aumann structure as the one just defined. We can define a correspondent Kripke structure by taking (i) the same space S, (ii) accessibility relations ${\displaystyle R_{i}}$ that define the equivalence classes corresponding to the partitions ${\displaystyle P_{i}}$, and (iii) a valuation function such that it yields value true to the primitive proposition p in all and only the states s such that ${\displaystyle s\in E^{p}}$, where ${\displaystyle E^{p}}$ is the event of the Aumann structure corresponding to the primitive proposition p. It is not difficult to see that the common knowledge accessibility function ${\displaystyle R_{G}}$ defined in the previous section corresponds to the finest common coarsening of the partitions ${\displaystyle P_{i}}$ for all ${\displaystyle i\in G}$, which is the finitary characterization of common knowledge also given by Aumann in the 1976 article.

Applications

Common knowledge was used by David Lewis in his pioneering game-theoretical account of convention. In this sense, common knowledge is a concept still central for linguists and philosophers of language (see Clark 1996) maintaining a Lewisian, conventionalist account of language.

Robert Aumann introduced a set theoretical formulation of common knowledge (theoretically equivalent to the one given above) and proved the so-called agreement theorem through which: if two agents have common prior probability over a certain event, and the posterior probabilities are common knowledge, then such posterior probabilities are equal. A result based on the agreement theorem and proven by Milgrom shows that, given certain conditions on market efficiency and information, speculative trade is impossible.

The concept of common knowledge is central in game theory. For several years it has been thought that the assumption of common knowledge of rationality for the players in the game was fundamental. It turns out (Aumann and Brandenburger 1995) that, in 2-player games, common knowledge of rationality is not needed as an epistemic condition for Nash equilibrium strategies.

Computer scientists use languages incorporating epistemic logics (and common knowledge) to reason about distributed systems. Such systems can be based on logics more complicated than simple propositional epistemic logic, see Wooldridge Reasoning about Artificial Agents, 2000 (in which he uses a first-order logic incorporating epistemic and temporal operators) or van der Hoek et al. "Alternating Time Epistemic Logic".

In his 2007 book, The Stuff of Thought: Language as a Window into Human Nature, Steven Pinker uses the notion of common knowledge to analyze the kind of indirect speech involved in innuendoes.

Belief

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https://en.wikipedia.org/wiki/Belief 

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A belief is an attitude that something is the case, or that some proposition about the world is true. In epistemology, philosophers use the term "belief" to refer to attitudes about the world which can be either true or false. To believe something is to take it to be true; for instance, to believe that snow is white is comparable to accepting the truth of the proposition "snow is white". However, holding a belief does not require active introspection. For example, few carefully consider whether or not the sun will rise tomorrow, simply assuming that it will. Moreover, beliefs need not be occurrent (e.g. a person actively thinking "snow is white"), but can instead be dispositional (e.g. a person who if asked about the color of snow would assert "snow is white").

There are various different ways that contemporary philosophers have tried to describe beliefs, including as representations of ways that the world could be (Jerry Fodor), as dispositions to act as if certain things are true (Roderick Chisholm), as interpretive schemes for making sense of someone's actions (Daniel Dennett and Donald Davidson), or as mental states that fill a particular function (Hilary Putnam). Some have also attempted to offer significant revisions to our notion of belief, including eliminativists about belief who argue that there is no phenomenon in the natural world which corresponds to our folk psychological concept of belief (Paul Churchland) and formal epistemologists who aim to replace our bivalent notion of belief ("either we have a belief or we don't have a belief") with the more permissive, probabilistic notion of credence ("there is an entire spectrum of degrees of belief, not a simple dichotomy between belief and non-belief").

Beliefs are the subject of various important philosophical debates. Notable examples include: "What is the rational way to revise one's beliefs when presented with various sorts of evidence?"; "Is the content of our beliefs entirely determined by our mental states, or do the relevant facts have any bearing on our beliefs (e.g. if I believe that I'm holding a glass of water, is the non-mental fact that water is H₂O part of the content of that belief)?"; "How fine-grained or coarse-grained are our beliefs?"; and "Must it be possible for a belief to be expressible in language, or are there non-linguistic beliefs?".

Psychology

Mainstream psychology and related disciplines have traditionally treated belief as if it were the simplest form of mental representation and therefore one of the building blocks of conscious thought. Philosophers have tended to be more abstract in their analysis, and much of the work examining the viability of the belief concept stems from philosophical analysis.

The concept of belief presumes a subject (the believer) and an object of belief (the proposition). So, like other propositional attitudes, belief implies the existence of mental states and intentionality, both of which are hotly debated topics in the philosophy of mind, whose foundations and relation to brain states are still controversial.

Beliefs are sometimes divided into core beliefs (that are actively thought about) and dispositional beliefs (that may be ascribed to someone who has not thought about the issue). For example, if asked "do you believe tigers wear pink pajamas?" a person might answer that they do not, despite the fact they may never have thought about this situation before.

This has important implications for understanding the neuropsychology and neuroscience of belief. If the concept of belief is incoherent, then any attempt to find the underlying neural processes that support it will fail.

Philosopher Lynne Rudder Baker has outlined four main contemporary approaches to belief in her book Saving Belief:

• Our common-sense understanding of belief is correct – Sometimes called the "mental sentence theory," in this conception, beliefs exist as coherent entities, and the way we talk about them in everyday life is a valid basis for scientific endeavour. Jerry Fodor was one of the principal defenders of this point of view.
• Our common-sense understanding of belief may not be entirely correct, but it is close enough to make some useful predictions – This view argues that we will eventually reject the idea of belief as we know it now, but that there may be a correlation between what we take to be a belief when someone says "I believe that snow is white" and how a future theory of psychology will explain this behaviour. Philosopher Stephen Stich has argued for this particular understanding of belief.
• Our common-sense understanding of belief is entirely wrong and will be completely superseded by a radically different theory that will have no use for the concept of belief as we know it – Known as eliminativism, this view (most notably proposed by Paul and Patricia Churchland) argues that the concept of belief is like obsolete theories of times past such as the four humours theory of medicine, or the phlogiston theory of combustion. In these cases science has not provided us with a more detailed account of these theories, but completely rejected them as valid scientific concepts to be replaced by entirely different accounts. The Churchlands argue that our common-sense concept of belief is similar in that as we discover more about neuroscience and the brain, the inevitable conclusion will be to reject the belief hypothesis in its entirety.
• Our common-sense understanding of belief is entirely wrong; however, treating people, animals, and even computers as if they had beliefs is often a successful strategy – The major proponents of this view, Daniel Dennett and Lynne Rudder Baker, are both eliminativists in that they hold that beliefs are not a scientifically valid concept, but they do not go as far as rejecting the concept of belief as a predictive device. Dennett gives the example of playing a computer at chess. While few people would agree that the computer held beliefs, treating the computer as if it did (e.g. that the computer believes that taking the opposition's queen will give it a considerable advantage) is likely to be a successful and predictive strategy. In this understanding of belief, named by Dennett the intentional stance, belief-based explanations of mind and behaviour are at a different level of explanation and are not reducible to those based on fundamental neuroscience, although both may be explanatory at their own level.

Strategic approaches make a distinction between rules, norms and beliefs as follows:

• Rules. Explicit regulative processes such as policies, laws, inspection routines, or incentives. Rules function as a coercive regulator of behavior and are dependent upon the imposing entity's ability to enforce them.
• Norms. Regulative mechanisms accepted by the social collective. Norms are enforced by normative mechanisms within the organization and are not strictly dependent upon law or regulation.
• Beliefs. The collective perception of fundamental truths governing behavior. The adherence to accepted and shared beliefs by members of a social system will likely persist and be difficult to change over time. Strong beliefs about determinant factors (i.e., security, survival, or honor) are likely to cause a social entity or group to accept rules and norms.

Historical conceptions of belief

In the context of Ancient Greek thought, three related concepts were identified regarding the concept of belief: pistis, doxa, and dogma. Simplified, pistis refers to "trust" and "confidence," doxa refers to "opinion" and "acceptance," and dogma refers to the positions of a philosopher or of a philosophical school such as Stoicism.

Emotion and beliefs

Research has indicated that emotion and cognition act in conjunction to produce beliefs, and more specifically emotion plays a vital role in the formation and maintenance of beliefs.

Formation

We are influenced by many factors that ripple through our minds as our beliefs form, evolve, and may eventually change

Psychologists study belief formation and the relationship between beliefs and actions. Three models of belief formation and change have been proposed:

Conditional inference process

When people are asked to estimate the likelihood that a statement is true, they search their memory for information that has implications for the validity of this statement. Once this information has been identified, they estimate the likelihood that the statement would be true if the information were true, and the likelihood that the statement would be true if the information were false. If their estimates for these two probabilities differ, people average them, weighting each by the likelihood that the information is true and false. Thus, information bears directly on beliefs of another, related statement.

Linear models

Unlike the previous model, this one takes into consideration the possibility of multiple factors influencing belief formation. Using regression procedures, this model predicts belief formation on the basis of several different pieces of information, with weights assigned to each piece on the basis of their relative importance.

Information processing models and change

These models address the fact that the responses people have to belief-relevant information is unlikely to be predicted from the objective basis of the information that they can recall at the time their beliefs are reported. Instead, these responses reflect the number and meaning of the thoughts that people have about the message at the time that they encounter it.

Some influences on people's belief formation include:

• Internalization of beliefs during childhood, which can form and shape our beliefs in different domains. Albert Einstein is often quoted as having said that "Common sense is the collection of prejudices acquired by age eighteen." Political beliefs depend most strongly on the political beliefs most common in the community where we live. Most individuals believe the religion they were taught in childhood.
• Charismatic leaders can form or modify beliefs (even if those beliefs fly in the face of all previous beliefs). Rational individuals need to reconcile their direct reality with any said belief; therefore, if belief is not present or possible, it reflects the fact that contradictions were necessarily overcome using cognitive dissonance.
• Advertising can form or change beliefs through repetition, shock, and association with images of sex, love, beauty, and other strong positive emotions. Contrary to intuition, a delay, known as the sleeper effect, instead of immediate succession may increase an advertisement's ability to persuade viewer's beliefs if a discounting cue is present.
• Physical trauma, especially to the head, can radically alter a person's beliefs.

However, even educated people, well aware of the process by which beliefs form, still strongly cling to their beliefs, and act on those beliefs even against their own self-interest. In Anna Rowley's book, Leadership Therapy, she states "You want your beliefs to change. It's proof that you are keeping your eyes open, living fully, and welcoming everything that the world and people around you can teach you." This means that peoples' beliefs should evolve as they gain new experiences.

Modification of beliefs

An extensive amount of scientific research and philosophical discussion exists around the modification of beliefs, which is commonly referred to as belief revision. Generally speaking, the process of belief revision entails the believer weighing the set of truths and/or evidence, and the dominance of a set of truths or evidence on an alternative to a held belief can lead to revision. One process of belief revision is Bayesian updating and is often referenced for its mathematical basis and conceptual simplicity. However, such a process may not be representative for individuals whose beliefs are not easily characterized as probabilistic.

There are several techniques for individuals or groups to change the beliefs of others; these methods generally fall under the umbrella of persuasion. Persuasion can take on more specific forms such as consciousness raising when considered in an activist or political context. Belief modification may also occur as a result of the experience of outcomes. Because goals are based, in part on beliefs, the success or failure at a particular goal may contribute to modification of beliefs that supported the original goal.

Whether or not belief modification actually occurs is dependent not only on the extent of truths or evidence for the alternative belief, but also characteristics outside the specific truths or evidence. This includes, but is not limited to: the source characteristics of the message, such as credibility; social pressures; the anticipated consequences of a modification; or the ability of the individual or group to act on the modification. Therefore, individuals seeking to achieve belief modification in themselves or others need to consider all possible forms of resistance to belief revision.

Prediction

Different psychological models have tried to predict people's beliefs and some of them try to estimate the exact probabilities of beliefs. For example, Robert Wyer developed a model of subjective probabilities. When people rate the likelihood of a certain statement (e.g., "It will rain tomorrow"), this rating can be seen as a subjective probability value. The subjective probability model posits that these subjective probabilities follow the same rules as objective probabilities. For example, the law of total probability might be applied to predict a subjective probability value. Wyer found that this model produces relatively accurate predictions for probabilities of single events and for changes in these probabilities, but that the probabilities of several beliefs linked by "and" or "or" do not follow the model as well.

Knowledge and epistemology

A Venn diagram illustrating the traditional definition of knowledge as justified true belief (represented by the yellow circle). The Gettier problem gives us reason to think that not all justified true beliefs constitute knowledge.

Epistemology is concerned with delineating the boundary between justified belief and opinion, and involved generally with a theoretical philosophical study of knowledge. The primary problem in epistemology is to understand exactly what is needed in order for us to have knowledge. In a notion derived from Plato's dialogue Theaetetus, where the epistemology of Socrates (Platon) most clearly departs from that of the sophists, who at the time of Plato seem to have defined knowledge as what is here expressed as "justified true belief". The tendency to translate from belief (here: doxa – common opinion) to knowledge (here: episteme), which Plato (e.g. Socrates of the dialogue) utterly dismisses, results from failing to distinguish a dispositive belief (gr. 'doxa', not 'pistis') from knowledge (episteme) when the opinion is regarded true (here: orthé), in terms of right, and juristically so (according to the premises of the dialogue), which was the task of the rhetors to prove. Plato dismisses this possibility of an affirmative relation between belief (i.e. opinion) and knowledge even when the one who opines grounds his belief on the rule, and is able to add justification (gr. logos: reasonable and necessarily plausible assertions/evidence/guidance) to it.

Plato has been credited for the "justified true belief" theory of knowledge, even though Plato in the Theaetetus (dialogue) elegantly dismisses it, and even posits this argument of Socrates as a cause for his death penalty. Among American epistemologists, Gettier (1963) and Goldman (1967), have questioned the "justified true belief" definition, and challenged the "sophists" of their time.

Justified true belief

Justified true belief is a definition of knowledge that gained approval during the Enlightenment, "justified" standing in contrast to "revealed". There have been attempts to trace it back to Plato and his dialogues. The concept of justified true belief states that in order to know that a given proposition is true, one must not only believe the relevant true proposition, but also have justification for doing so. In more formal terms, an agent ${\displaystyle S}$ knows that a proposition ${\displaystyle P}$ is true if and only if:

• ${\displaystyle P}$ is true
• ${\displaystyle S}$ believes that ${\displaystyle P}$ is true, and
• ${\displaystyle S}$ is justified in believing that ${\displaystyle P}$ is true

This theory of knowledge suffered a significant setback with the discovery of Gettier problems, situations in which the above conditions were seemingly met but where many philosophers deny that anything is known. Robert Nozick suggested a clarification of "justification" which he believed eliminates the problem: the justification has to be such that were the justification false, the knowledge would be false. Bernecker and Dretske (2000) argue that "no epistemologist since Gettier has seriously and successfully defended the traditional view." On the other hand, Paul Boghossian argues that the justified true belief account is the "standard, widely accepted" definition of knowledge.

Epistemology versus religion

Historically belief-in belonged in the realm of religious thought, belief-that instead belonged to epistemological considerations.

Belief-in

To "believe in" someone or something is a distinct concept from "believing-that." There are at least these types of belief-in:

• Commendatory / faith – we may make an expression of 'faith' in respect of some performance by an agent X, when without prejudice to the truth value of the factual outcome or even confidence in X otherwise, we expect that specific performance. In particular self-confidence or faith in one's self is this kind of belief.
• Existential claim – to claim belief in the existence of an entity or phenomenon in a general way with the implied need to justify its claim of existence. It is often used when the entity is not real, or its existence is in doubt. "He believes in witches and ghosts" or "many children believe in Santa Claus" or "I believe in a deity" are typical examples. The linguistic form is distinct from the assertion of the truth of a proposition since verification is either considered impossible or irrelevant or a counterfactual situation is assumed.

Belief-that

Economic belief

Economic beliefs are beliefs which are reasonably and necessarily contrary to the tenet of rational choice or instrumental rationality.

Studies of the Austrian tradition of the economic thought, in the context of analysis of the influence and subsequent degree of change resulting from existing economic knowledge and belief, has contributed the most to the subsequent holistic collective analysis.

Delusion

Insofar as the truth of belief is expressed in sentential and propositional form we are using the sense of belief-that rather than belief-in. Delusion arises when the truth value of the form is clearly nil.

Delusions are defined as beliefs in psychiatric diagnostic criteria (for example in the Diagnostic and Statistical Manual of Mental Disorders). Psychiatrist and historian G.E. Berrios has challenged the view that delusions are genuine beliefs and instead labels them as "empty speech acts," where affected persons are motivated to express false or bizarre belief statements due to an underlying psychological disturbance. However, the majority of mental health professionals and researchers treat delusions as if they were genuine beliefs.

Science

In scientific medical writing, the verb 'believe' can mean "actively accept as true" on the basis of external evidence (for example, a statement of the type, "we believe that x is a better treatment than y in this disease" can imply that "after examining the available evidence, we have concluded that x is...").

Religion

Religious belief refers to attitudes towards mythological, supernatural, or spiritual aspects of a religion. Religious belief is distinct from religious practice and from religious behaviours – with some believers not practicing religion and some practitioners not believing religion. Religious beliefs, deriving from ideas that are exclusive to religionoften relate to the existence, characteristics and worship of a deity or deities, to the idea of divine intervention in the universe and in human life, or to the deontological explanations for the values and practices centered on the teachings of a spiritual leader or community. In contrast to other belief systems, religious beliefs are usually codified.

Forms

A popular view holds that different religions each have identifiable and exclusive sets of beliefs or creeds, but surveys of religious belief have often found that the official doctrine and descriptions of the beliefs offered by religious authorities do not always agree with the privately held beliefs of those who identify as members of a particular religion. For a broad classification of the kinds of religious belief, see below.

Fundamentalism

First self-applied as a term to the conservative doctrine outlined by anti-modernist Protestants in the United States, "fundamentalism" in religious terms denotes strict adherence to an interpretation of scriptures that are generally associated with theologically conservative positions or traditional understandings of the text and are distrustful of innovative readings, new revelation, or alternative interpretations. Religious fundamentalism has been identified in the media as being associated with fanatical or zealous political movements around the world that have used a strict adherence to a particular religious doctrine as a means to establish political identity and to enforce societal norms.

Orthodoxy

First used in the context of Early Christianity, the term "orthodoxy" relates to religious belief that closely follows the edicts, apologies, and hermeneutics of a prevailing religious authority. In the case of Early Christianity, this authority was the communion of bishops, and is often referred to by the term "Magisterium". The term orthodox was applied almost as an epithet to a group of Jewish believers who held to pre-Enlightenment understanding of Judaism – now known as Orthodox Judaism. The Eastern Orthodox Church of Christianity and the Catholic Church each consider themselves to be the true heir to Early Christian belief and practice. The antonym of "orthodox" is "heterodox", and those adhering to orthodoxy often accuse the heterodox of apostasy, schism, or heresy.

Modernism/reform

The Renaissance and later the Enlightenment in Europe exhibited varying degrees of religious tolerance and intolerance towards new and old religious ideas. The philosophes took particular exception to many of the more fantastical claims of religions and directly challenged religious authority and the prevailing beliefs associated with the established churches. In response to the liberalizing political and social movements, some religious groups attempted to integrate Enlightenment ideals of rationality, equality, and individual liberty into their belief systems, especially in the nineteenth and twentieth centuries. Reform Judaism and Liberal Christianity offer two examples of such religious associations.

Approaches to others

Adherents of particular religions deal with the differing doctrines and practices espoused by other religions or by other religious denominations in a variety of ways.

Exclusivism

People with exclusivist beliefs typically explain other beliefs either as in error, or as corruptions or counterfeits of the true faith. This approach is a fairly consistent feature among smaller new religious movements that often rely on doctrine that claims a unique revelation by the founders or leaders, and considers it a matter of faith that the "correct" religion has a monopoly on truth. All three major Abrahamic monotheistic religions have passages in their holy scriptures that attest to the primacy of the scriptural testimony, and indeed monotheism itself is often vouched as an innovation characterized specifically by its explicit rejection of earlier polytheistic faiths.

Some exclusivist faiths incorporate a specific element of proselytization. This is a strongly-held belief in the Christian tradition which follows the doctrine of the Great Commission, and is less emphasized by the Islamic faith where the Quranic edict "There shall be no compulsion in religion" (2:256) is often quoted as a justification for toleration of alternative beliefs. The Jewish tradition does not actively seek out converts.

Exclusivism correlates with conservative, fundamentalist, and orthodox approaches of many religions, while pluralistic and syncretist approaches either explicitly downplay or reject the exclusivist tendencies within a religion.

Inclusivism

People with inclusivist beliefs recognize some truth in all faith systems, highlighting agreements and minimizing differences. This attitude is sometimes associated with Interfaith dialogue or with the Christian Ecumenical movement, though in principle such attempts at pluralism are not necessarily inclusivist and many actors in such interactions (for example, the Roman Catholic Church) still hold to exclusivist dogma while participating in inter-religious organizations.

Explicitly inclusivist religions include many that are associated with the New Age movement, as well as modern reinterpretations of Hinduism and Buddhism. The Bahá'í Faith considers it doctrine that there is truth in all faith-systems.

Pluralism

People with pluralist beliefs make no distinction between faith systems, viewing each one as valid within a particular culture.

Syncretism

People with syncretic views blend the views of a variety of different religions or traditional beliefs into a unique fusion which suits their particular experiences and contexts (see eclecticism). Unitarian Universalism exemplifies a syncretic faith.

Adherence

Typical reasons for adherence to religion include the following:

• Some see belief in a deity as necessary for moral behavior.
• Some regard religious practices as serene, beautiful, and conducive to religious experiences, which in turn support religious beliefs.
• Organized religions promote a sense of community among their followers, and the moral and cultural common ground of these communities makes them attractive to people with similar values. Indeed, while religious beliefs and practices are usually connected, some individuals with substantially secular beliefs still participate in religious practices for cultural reasons.
• Each religion asserts that it is a means by which its adherents may come into closer contact with the Divine, with Truth, and with spiritual power. They all promise to free adherents from spiritual bondage, and to bring them into spiritual freedom. It naturally follows that a religion which can free its adherents from deception, sin, and spiritual death will have significant mental-health benefits. Abraham Maslow's research after World War II showed that Holocaust survivors tended to be those who held strong religious beliefs (not necessarily temple attendance, etc.), suggesting that belief helped people cope in extreme circumstances. Humanistic psychology went on to investigate how religious or spiritual identity may have correlations with longer lifespan and better health. The study found that humans may particularly need religious ideas to serve various emotional needs such as the need to feel loved, the need to belong to homogeneous groups, the need for understandable explanations and the need for a guarantee of ultimate justice. Other factors may involve sense of purpose, sense of identity, or a sense of contact with the divine. See also Man's Search for Meaning, by Viktor Frankl, detailing his experience with the importance of religion in surviving the Holocaust. Critics assert that the very fact that religion was the primary selector for research subjects may have introduced a bias, and that the fact that all subjects were Holocaust survivors may also have had an effect. According to Larson et al. (2000), "[m]ore longitudinal research with better multidimensional measures will help further clarify the roles of these [religious] factors and whether they are beneficial or harmful."

Psychologist James Alcock also summarizes a number of apparent benefits which reinforce religious belief. These include prayer appearing to account for successful resolution of problems, "a bulwark against existential anxiety and fear of annihilation," an increased sense of control, companionship with one's deity, a source of self-significance, and group identity.

Apostasy

Typical reasons for rejection of religion include:

• Some people regard certain fundamental doctrines of some religions as illogical, contrary to experience, or unsupported by sufficient evidence; such people may reject one or more religions for those reasons. Even some believers may have difficulty accepting particular religious assertions or doctrines. Some people believe the body of evidence available to humans to be insufficient to justify certain religious beliefs. They may thus disagree with religious interpretations of ethics and human purpose, or with various creation myths. This reason has perhaps been aggravated by the protestations and emphases of some fundamentalist Christians.
• Some religions include beliefs that certain groups of people are inferior or sinful and deserve contempt, persecution, or even death, and that non-believers will be punished for their unbelief in an after-life. Adherents to a religion may feel antipathy to unbelievers. Numerous examples exist of people of one religion or sect using religion as an excuse to murder people with different religious beliefs. To mention just a few examples:
  • the slaughter of the Huguenots by French Catholics in the sixteenth century
  • Hindus and Muslims killing each other when Pakistan separated from India in 1947
  • the persecution and killing of Shiite Muslims by Sunni Muslims in Iraq
  • the murder of Protestants by Catholics and vice versa in Ireland (both of these examples in the late twentieth century)
  • the Israeli–Palestinian conflict that continues as of 2018 – According to some critics of religion, such beliefs can encourage completely unnecessary conflicts and in some cases even wars. Many atheists believe that, because of this, religion is incompatible with world peace, freedom, civil rights, equality, and good government. On the other hand, most religions perceive atheism as a threat and will vigorously and even violently defend themselves against religious sterilization, making the attempt to remove public religious practices a source of strife.
• Some people may be unable to accept the values that a specific religion promotes and will therefore not join that religion. They may also be unable to accept the proposition that those who do not believe will go to hell or be damned, especially if said nonbelievers are close to the person.
• The maintenance of life and the achievement of self-esteem require of a person the fullest exercise of reason—but morality (people are taught) rests on and requires faith.

Collective belief

A world view comprises a set of mutually supportive beliefs. The beliefs of any such system can be religious, philosophical, political, ideological, or a combination of these. Philosopher Jonathan Glover says that beliefs are always part of a belief system, and that tenanted belief systems are difficult for the tenants to completely revise or reject. This insight has relevance for inquisitors, missionaries, agitprop groups and thought-police.

Perspectives

A collective belief is referred to when people speak of what "we" believe when this is not simply elliptical for what "we all" believe.

Sociologist Émile Durkheim wrote of collective beliefs and proposed that they, like all "social facts", "inhered in" social groups as opposed to individual persons. Jonathan Dancy states that "Durkheim's discussion of collective belief, though suggestive, is relatively obscure".

Philosopher Margaret Gilbert (1942- ) has offered a related account in terms of the joint commitment of a number of persons as a body to accept a certain belief. According to this account, individuals who together collectively believe something need not personally believe it individually. Gilbert's work on the topic has stimulated a developing literature among philosophers. One question that has arisen is whether and how philosophical accounts of belief in general need to be sensitive to the possibility of collective belief.

Philosopher Jonathan Glover warns that belief systems are like whole boats in the water; it is extremely difficult to alter them all at once (for example, it may be too stressful, or people may maintain their biases without realizing it).

 

Jonathan Glover (1941- ) believes that he and other philosophers ought to play some role in starting dialogues between people with deeply-held, opposing beliefs, especially if there is risk of violence. Glover also believes that philosophy can offer insights about beliefs that would be relevant to such dialogue.

Glover suggests that beliefs have to be considered holistically, and that no belief exists in isolation in the mind of the believer. Each belief always implicates and relates to other beliefs. Glover provides the example of a patient with an illness who returns to a doctor, but the doctor says that the prescribed medicine is not working. At that point, the patient has a great deal of flexibility in choosing what beliefs to keep or reject: the patient could believe that the doctor is incompetent, that the doctor's assistants made a mistake, that the patient's own body is unique in some unexpected way, that Western medicine is ineffective, or even that Western science is entirely unable to discover truths about ailments.

Glover maintains that any person can continue to hold any belief if they would really like to (for example, with help from ad hoc hypotheses). One belief can be held fixed, and other beliefs will be altered around it. Glover warns that some beliefs may not be entirely explicitly believed (for example, some people may not realize they have racist belief-systems adopted from their environment as a child). Glover believes that people tend to first realize that beliefs can change, and may be contingent on their upbringing, around age 12 or 15.

Glover emphasizes that beliefs are difficult to change. He says that one may try to rebuild one's beliefs on more secure foundations (axioms), like building a new house, but warns that this may not be possible. Glover offers the example of René Descartes, saying: "[Descartes] starts off with the characteristic beliefs of a 17th-century Frenchman; he then junks the lot, he rebuilds the system, and somehow it looks a lot like the beliefs of a 17th-century Frenchman." To Glover, belief systems are not like houses but are instead like boats. As Glover puts it: "Maybe the whole thing needs rebuilding, but inevitably at any point you have to keep enough of it intact to keep floating."

Glover's final message is that if people talk about their beliefs, they may find more deep, relevant, philosophical ways in which they disagree (e.g., less obvious beliefs, or more-deeply-held beliefs). Glover thinks that people often manage to find agreements and consensus through philosophy. He says that at the very least, if people do not convert each other, they will hold their own beliefs more openmindedly and will be less likely to go to war over conflicting beliefs.

The British philosopher Stephen Law (1960-) has described some belief systems (including belief in homeopathy, psychic powers, and alien abduction) as "claptrap" and says that such belief-systems can "draw people in and hold them captive so they become willing slaves of claptrap [...] if you get sucked in, it can be extremely difficult to think your way clear again".