Complexity

From Wikipedia, the free encyclopedia

Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, meaning there is no reasonable higher instruction to define the various possible interactions.

The term is generally used to characterize something with many parts where those parts interact with each other in multiple ways, culminating in a higher order of emergence greater than the sum of its parts. The study of these complex linkages at various scales is the main goal of complex systems theory.

Science as of 2010 takes a number of approaches to characterizing complexity; Zayed et al. reflect many of these. Neil Johnson states that "even among scientists, there is no unique definition of complexity – and the scientific notion has traditionally been conveyed using particular examples..." Ultimately Johnson adopts the definition of "complexity science" as "the study of the phenomena which emerge from a collection of interacting objects".

Overview

Definitions of complexity often depend on the concept of a confidential "system" – a set of parts or elements that have relationships among them differentiated from relationships with other elements outside the relational regime. Many definitions tend to postulate or assume that complexity expresses a condition of numerous elements in a system and numerous forms of relationships among the elements. However, what one sees as complex and what one sees as simple is relative and changes with time. 

Warren Weaver posited in 1948 two forms of complexity: disorganized complexity, and organized complexity. Phenomena of 'disorganized complexity' are treated using probability theory and statistical mechanics, while 'organized complexity' deals with phenomena that escape such approaches and confront "dealing simultaneously with a sizable number of factors which are interrelated into an organic whole". Weaver's 1948 paper has influenced subsequent thinking about complexity.

The approaches that embody concepts of systems, multiple elements, multiple relational regimes, and state spaces might be summarized as implying that complexity arises from the number of distinguishable relational regimes (and their associated state spaces) in a defined system. 

Some definitions relate to the algorithmic basis for the expression of a complex phenomenon or model or mathematical expression, as later set out herein.

Disorganized vs. organized

One of the problems in addressing complexity issues has been formalizing the intuitive conceptual distinction between the large number of variances in relationships extant in random collections, and the sometimes large, but smaller, number of relationships between elements in systems where constraints (related to correlation of otherwise independent elements) simultaneously reduce the variations from element independence and create distinguishable regimes of more-uniform, or correlated, relationships, or interactions. 

Weaver perceived and addressed this problem, in at least a preliminary way, in drawing a distinction between "disorganized complexity" and "organized complexity". 

In Weaver's view, disorganized complexity results from the particular system having a very large number of parts, say millions of parts, or many more. Though the interactions of the parts in a "disorganized complexity" situation can be seen as largely random, the properties of the system as a whole can be understood by using probability and statistical methods. 

A prime example of disorganized complexity is a gas in a container, with the gas molecules as the parts. Some would suggest that a system of disorganized complexity may be compared with the (relative) simplicity of planetary orbits – the latter can be predicted by applying Newton's laws of motion. Of course, most real-world systems, including planetary orbits, eventually become theoretically unpredictable even using Newtonian dynamics; as discovered by modern chaos theory.

Organized complexity, in Weaver's view, resides in nothing else than the non-random, or correlated, interaction between the parts. These correlated relationships create a differentiated structure that can, as a system, interact with other systems. The coordinated system manifests properties not carried or dictated by individual parts. The organized aspect of this form of complexity vis-a-vis to other systems than the subject system can be said to "emerge," without any "guiding hand". 

The number of parts does not have to be very large for a particular system to have emergent properties. A system of organized complexity may be understood in its properties (behavior among the properties) through modeling and simulation, particularly modeling and simulation with computers. An example of organized complexity is a city neighborhood as a living mechanism, with the neighborhood people among the system's parts.

Sources and factors

There are generally rules which can be invoked to explain the origin of complexity in a given system.

The source of disorganized complexity is the large number of parts in the system of interest, and the lack of correlation between elements in the system. 

In the case of self-organizing living systems, usefully organized complexity comes from beneficially mutated organisms being selected to survive by their environment for their differential reproductive ability or at least success over inanimate matter or less organized complex organisms.

Complexity of an object or system is a relative property. For instance, for many functions (problems), such a computational complexity as time of computation is smaller when multitape Turing machines are used than when Turing machines with one tape are used. Random Access Machines allow one to even more decrease time complexity (Greenlaw and Hoover 1998: 226), while inductive Turing machines can decrease even the complexity class of a function, language or set (Burgin 2005). This shows that tools of activity can be an important factor of complexity.

Varied meanings

In several scientific fields, "complexity" has a precise meaning:

• In computational complexity theory, the amounts of resources required for the execution of algorithms is studied. The most popular types of computational complexity are the time complexity of a problem equal to the number of steps that it takes to solve an instance of the problem as a function of the size of the input (usually measured in bits), using the most efficient algorithm, and the space complexity of a problem equal to the volume of the memory used by the algorithm (e.g., cells of the tape) that it takes to solve an instance of the problem as a function of the size of the input (usually measured in bits), using the most efficient algorithm. This allows classification of computational problems by complexity class (such as P, NP, etc.). An axiomatic approach to computational complexity was developed by Manuel Blum. It allows one to deduce many properties of concrete computational complexity measures, such as time complexity or space complexity, from properties of axiomatically defined measures.
• In algorithmic information theory, the Kolmogorov complexity (also called descriptive complexity, algorithmic complexity or algorithmic entropy) of a string is the length of the shortest binary program that outputs that string. Minimum message length is a practical application of this approach. Different kinds of Kolmogorov complexity are studied: the uniform complexity, prefix complexity, monotone complexity, time-bounded Kolmogorov complexity, and space-bounded Kolmogorov complexity. An axiomatic approach to Kolmogorov complexity based on Blum axioms (Blum 1967) was introduced by Mark Burgin in the paper presented for publication by Andrey Kolmogorov. The axiomatic approach encompasses other approaches to Kolmogorov complexity. It is possible to treat different kinds of Kolmogorov complexity as particular cases of axiomatically defined generalized Kolmogorov complexity. Instead of proving similar theorems, such as the basic invariance theorem, for each particular measure, it is possible to easily deduce all such results from one corresponding theorem proved in the axiomatic setting. This is a general advantage of the axiomatic approach in mathematics. The axiomatic approach to Kolmogorov complexity was further developed in the book (Burgin 2005) and applied to software metrics (Burgin and Debnath, 2003; Debnath and Burgin, 2003).
• In information processing, complexity is a measure of the total number of properties transmitted by an object and detected by an observer. Such a collection of properties is often referred to as a state.
• In physical systems, complexity is a measure of the probability of the state vector of the system. This should not be confused with entropy; it is a distinct mathematical measure, one in which two distinct states are never conflated and considered equal, as is done for the notion of entropy in statistical mechanics.
• In mathematics, Krohn–Rhodes complexity is an important topic in the study of finite semigroups and automata.
• In Network theory complexity is the product of richness in the connections between components of a system, and defined by a very unequal distribution of certain measures (some elements being highly connected and some very few, see complex network).
• In software engineering, programming complexity is a measure of the interactions of the various elements of the software. This differs from the computational complexity described above in that it is a measure of the design of the software.
• In abstract sense – Abstract Complexity, is based on visual structures perception  It is complexity of binary string defined as a square of features number divided by number of elements (0's and 1's). Features comprise here all distinctive arrangements of 0's and 1's. Though the features number have to be always approximated the definition is precise and meet intuitive criterion.

Other fields introduce less precisely defined notions of complexity:

• A complex adaptive system has some or all of the following attributes:
  • The number of parts (and types of parts) in the system and the number of relations between the parts is non-trivial – however, there is no general rule to separate "trivial" from "non-trivial";
  • The system has memory or includes feedback;
  • The system can adapt itself according to its history or feedback;
  • The relations between the system and its environment are non-trivial or non-linear;
  • The system can be influenced by, or can adapt itself to, its environment;
  • The system is highly sensitive to initial conditions.

Study

Complexity has always been a part of our environment, and therefore many scientific fields have dealt with complex systems and phenomena. From one perspective, that which is somehow complex – displaying variation without being random – is most worthy of interest given the rewards found in the depths of exploration. 

The use of the term complex is often confused with the term complicated. In today's systems, this is the difference between myriad connecting "stovepipes" and effective "integrated" solutions. This means that complex is the opposite of independent, while complicated is the opposite of simple.

While this has led some fields to come up with specific definitions of complexity, there is a more recent movement to regroup observations from different fields to study complexity in itself, whether it appears in anthills, human brains, or stock markets, social systems. One such interdisciplinary group of fields is relational order theories.

Topics

Behaviour

The behavior of a complex system is often said to be due to emergence and self-organization. Chaos theory has investigated the sensitivity of systems to variations in initial conditions as one cause of complex behaviour.

Mechanisms

Recent developments around artificial life, evolutionary computation and genetic algorithms have led to an increasing emphasis on complexity and complex adaptive systems.

Simulations

In social science, the study on the emergence of macro-properties from the micro-properties, also known as macro-micro view in sociology. The topic is commonly recognized as social complexity that is often related to the use of computer simulation in social science, i.e.: computational sociology.

Systems

Systems theory has long been concerned with the study of complex systems (in recent times, complexity theory and complex systems have also been used as names of the field). These systems are present in the research of a variety disciplines, including biology, economics, social studies and technology. Recently, complexity has become a natural domain of interest of real world socio-cognitive systems and emerging systemics research. Complex systems tend to be high-dimensional, non-linear, and difficult to model. In specific circumstances, they may exhibit low-dimensional behaviour.

Data

In information theory, algorithmic information theory is concerned with the complexity of strings of data. 

Complex strings are harder to compress. While intuition tells us that this may depend on the codec used to compress a string (a codec could be theoretically created in any arbitrary language, including one in which the very small command "X" could cause the computer to output a very complicated string like "18995316"), any two Turing-complete languages can be implemented in each other, meaning that the length of two encodings in different languages will vary by at most the length of the "translation" language – which will end up being negligible for sufficiently large data strings. 

These algorithmic measures of complexity tend to assign high values to random noise. However, those studying complex systems would not consider randomness as complexity. 

Information entropy is also sometimes used in information theory as indicative of complexity.

Recent work in machine learning has examined the complexity of the data as it affects the performance of supervised classification algorithms. Ho and Basu present a set of complexity measures for binary classification problems.

The complexity measures broadly cover:

• the overlaps in feature values from differing classes.
• the separability of the classes.
• measures of geometry, topology, and density of manifolds. Instance hardness is another approach seeks to characterize the data complexity with the goal of determining how hard a data set is to classify correctly and is not limited to binary problems.

Instance hardness is a bottom-up approach that first seeks to identify instances that are likely to be misclassified (or, in other words, which instances are the most complex). The characteristics of the instances that are likely to be misclassified are then measured based on the output from a set of hardness measures. The hardness measures are based on several supervised learning techniques such as measuring the number of disagreeing neighbors or the likelihood of the assigned class label given the input features. The information provided by the complexity measures has been examined for use in meta learning to determine for which data sets filtering (or removing suspected noisy instances from the training set) is the most beneficial and could be expanded to other areas.

In molecular recognition

A recent study based on molecular simulations and compliance constants describes molecular recognition as a phenomenon of organisation. Even for small molecules like carbohydrates, the recognition process can not be predicted or designed even assuming that each individual hydrogen bond's strength is exactly known.

Applications

Computational complexity theory is the study of the complexity of problems – that is, the difficulty of solving them. Problems can be classified by complexity class according to the time it takes for an algorithm – usually a computer program – to solve them as a function of the problem size. Some problems are difficult to solve, while others are easy. For example, some difficult problems need algorithms that take an exponential amount of time in terms of the size of the problem to solve. Take the travelling salesman problem, for example. It can be solved in time ${\displaystyle O(n^{2}2^{n})}$ (where n is the size of the network to visit – the number of cities the travelling salesman must visit exactly once). As the size of the network of cities grows, the time needed to find the route grows (more than) exponentially.

Even though a problem may be computationally solvable in principle, in actual practice it may not be that simple. These problems might require large amounts of time or an inordinate amount of space. Computational complexity may be approached from many different aspects. Computational complexity can be investigated on the basis of time, memory or other resources used to solve the problem. Time and space are two of the most important and popular considerations when problems of complexity are analyzed.

There exist a certain class of problems that although they are solvable in principle they require so much time or space that it is not practical to attempt to solve them. These problems are called intractable. 

There is another form of complexity called hierarchical complexity. It is orthogonal to the forms of complexity discussed so far, which are called horizontal complexity.

Consequentialism

From Wikipedia, the free encyclopedia

Every advantage in the past is judged in the light of the final issue. —Demosthenes

Consequentialism is the class of normative ethical theories holding that the consequences of one's conduct are the ultimate basis for any judgment about the rightness or wrongness of that conduct. Thus, from a consequentialist standpoint, a morally right act (or omission from acting) is one that will produce a good outcome, or consequence. 

Consequentialism is primarily non-prescriptive, meaning the moral worth of an action is determined by its potential consequence, not by whether it follows a set of written edicts or laws. One example would entail lying under the threat of government punishment to save an innocent person's life, even though it is illegal to lie under oath. 

Consequentialism is usually contrasted with deontological ethics (or deontology), in that deontology, in which rules and moral duty are central, derives the rightness or wrongness of one's conduct from the character of the behaviour itself rather than the outcomes of the conduct. It is also contrasted with virtue ethics, which focuses on the character of the agent rather than on the nature or consequences of the act (or omission) itself, and pragmatic ethics which treats morality like science: advancing socially over the course of many lifetimes, such that any moral criterion is subject to revision. Consequentialist theories differ in how they define moral goods. 

Some argue that consequentialist and deontological theories are not necessarily mutually exclusive. For example, T. M. Scanlon advances the idea that human rights, which are commonly considered a "deontological" concept, can only be justified with reference to the consequences of having those rights. Similarly, Robert Nozick argues for a theory that is mostly consequentialist, but incorporates inviolable "side-constraints" which restrict the sort of actions agents are permitted to do.

Philosophies

State consequentialism

It is the business of the benevolent man to seek to promote what is beneficial to the world and to eliminate what is harmful, and to provide a model for the world. What benefits he will carry out; what does not benefit men he will leave alone.

— Mozi, Mozi (5th century BC) Part I

Mohist consequentialism, also known as state consequentialism, is an ethical theory which evaluates the moral worth of an action based on how much it contributes to the welfare of a state. According to the Stanford Encyclopedia of Philosophy, Mohist consequentialism, dating back to the 5th century BCE, is the "world's earliest form of consequentialism, a remarkably sophisticated version based on a plurality of intrinsic goods taken as constitutive of human welfare".

Unlike utilitarianism, which views utility as the sole moral good, "the basic goods in Mohist consequentialist thinking are... order, material wealth, and increase in population". During Mozi's era, war and famines were common, and population growth was seen as a moral necessity for a harmonious society. The "material wealth" of Mohist consequentialism refers to basic needs like shelter and clothing, and the "order" of Mohist consequentialism refers to Mozi's stance against warfare and violence, which he viewed as pointless and a threat to social stability. Stanford sinologist David Shepherd Nivison, in The Cambridge History of Ancient China, writes that the moral goods of Mohism "are interrelated: more basic wealth, then more reproduction; more people, then more production and wealth... if people have plenty, they would be good, filial, kind, and so on unproblematically".

The Mohists believed that morality is based on "promoting the benefit of all under heaven and eliminating harm to all under heaven". In contrast to Jeremy Bentham's views, state consequentialism is not utilitarian because it is not hedonistic or individualistic. The importance of outcomes that are good for the community outweigh the importance of individual pleasure and pain. The term state consequentialism has also been applied to the political philosophy of the Confucian philosopher Xunzi.

On the other hand, the "Legalist" Han Fei "is motivated almost totally from the ruler's point of view".

Utilitarianism

Jeremy Bentham, best known for his advocacy of utilitarianism

Nature has placed mankind under the governance of two sovereign masters, pain and pleasure. It is for them alone to point out what we ought to do, as well as to determine what we shall do. On the one hand the standard of right and wrong, on the other the chain of causes and effects, are fastened to their throne. They govern us in all we do, in all we say, in all we think...

— Jeremy Bentham, The Principles of Morals and Legislation (1789) Ch I, p 1

In summary, Jeremy Bentham states that people are driven by their interests and their fears, but their interests take precedence over their fears, and their interests are carried out in accordance with how people view the consequences that might be involved with their interests. "Happiness" on this account is defined as the maximization of pleasure and the minimization of pain. Historically, hedonistic utilitarianism is the paradigmatic example of a consequentialist moral theory. This form of utilitarianism holds that what matters is the aggregate happiness; the happiness of everyone and not the happiness of any particular person. John Stuart Mill, in his exposition of hedonistic utilitarianism, proposed a hierarchy of pleasures, meaning that the pursuit of certain kinds of pleasure is more highly valued than the pursuit of other pleasures. However, some contemporary utilitarians, such as Peter Singer, are concerned with maximizing the satisfaction of preferences, hence "preference utilitarianism". Other contemporary forms of utilitarianism mirror the forms of consequentialism outlined below.

Ethical egoism

Ethical egoism can be understood as a consequentialist theory according to which the consequences for the individual agent are taken to matter more than any other result. Thus, egoism will prescribe actions that may be beneficial, detrimental, or neutral to the welfare of others. Some, like Henry Sidgwick, argue that a certain degree of egoism promotes the general welfare of society for two reasons: because individuals know how to please themselves best, and because if everyone were an austere altruist then general welfare would inevitably decrease.

Ethical altruism

Ethical altruism can be seen as a consequentialist ethic which prescribes that an individual take actions that have the best consequences for everyone except for himself. This was advocated by Auguste Comte, who coined the term "altruism," and whose ethics can be summed up in the phrase "Live for others".

Rule consequentialism

In general, consequentialist theories focus on actions. However, this need not be the case. Rule consequentialism is a theory that is sometimes seen as an attempt to reconcile deontology and consequentialism—and in some cases, this is stated as a criticism of rule consequentialism. Like deontology, rule consequentialism holds that moral behavior involves following certain rules. However, rule consequentialism chooses rules based on the consequences that the selection of those rules has. Rule consequentialism exists in the forms of rule utilitarianism and rule egoism.

Various theorists are split as to whether the rules are the only determinant of moral behavior or not. For example, Robert Nozick holds that a certain set of minimal rules, which he calls "side-constraints", are necessary to ensure appropriate actions. There are also differences as to how absolute these moral rules are. Thus, while Nozick's side-constraints are absolute restrictions on behavior, Amartya Sen proposes a theory that recognizes the importance of certain rules, but these rules are not absolute. That is, they may be violated if strict adherence to the rule would lead to much more undesirable consequences.

One of the most common objections to rule-consequentialism is that it is incoherent, because it is based on the consequentialist principle that what we should be concerned with is maximizing the good, but then it tells us not to act to maximize the good, but to follow rules (even in cases where we know that breaking the rule could produce better results).

Brad Hooker avoided this objection by not basing his form of rule-consequentialism on the ideal of maximizing the good. He writes:

…the best argument for rule-consequentialism is not that it derives from an overarching commitment to maximise the good. The best argument for rule-consequentialism is that it does a better job than its rivals of matching and tying together our moral convictions, as well as offering us help with our moral disagreements and uncertainties.

Derek Parfit described Brad Hooker's book on rule-consequentialism Ideal Code, Real World as the "best statement and defence, so far, of one of the most important moral theories".

Rule-consequentialism may offer a means to reconcile pure consequentialism with deontological, or rules-based ethics.

Two-level consequentialism

The two-level approach involves engaging in critical reasoning and considering all the possible ramifications of one's actions before making an ethical decision, but reverting to generally reliable moral rules when one is not in a position to stand back and examine the dilemma as a whole. In practice, this equates to adhering to rule consequentialism when one can only reason on an intuitive level, and to act consequentialism when in a position to stand back and reason on a more critical level.

This position can be described as a reconciliation between act consequentialism – in which the morality of an action is determined by that action's effects – and rule consequentialism – in which moral behavior is derived from following rules that lead to positive outcomes.

The two-level approach to consequentialism is most often associated with R. M. Hare and Peter Singer.

Motive consequentialism

Another consequentialist version is motive consequentialism which looks at whether the state of affairs that results from the motive to choose an action is better or at least as good as each of the alternative state of affairs that would have resulted from alternative actions. This version gives relevance to the motive of an act and links it to its consequences. An act can therefore not be wrong if the decision to act was based on a right motive. A possible inference is, that one can not be blamed for mistaken judgments if the motivation was to do good.

Negative consequentialism

Most consequentialist theories focus on promoting some sort of good consequences. However, negative utilitarianism lays out a consequentialist theory that focuses solely on minimizing bad consequences. 

One major difference between these two approaches is the agent's responsibility. Positive consequentialism demands that we bring about good states of affairs, whereas negative consequentialism requires that we avoid bad ones. Stronger versions of negative consequentialism will require active intervention to prevent bad and ameliorate existing harm. In weaker versions, simple forbearance from acts tending to harm others is sufficient. An example of this is the Slippery Slope Argument, which encourages others to avoid a specified act on the grounds that it may ultimately lead to undesirable consequences.

Often "negative" consequentialist theories assert that reducing suffering is more important than increasing pleasure. Karl Popper, for example, claimed "…from the moral point of view, pain cannot be outweighed by pleasure...". (While Popper is not a consequentialist per se, this is taken as a classic statement of negative utilitarianism.) When considering a theory of justice, negative consequentialists may use a statewide or global-reaching principle: the reduction of suffering (for the disadvantaged) is more valuable than increased pleasure (for the affluent or luxurious).

Teleological ethics

Teleological ethics (Greek telos, "end"; logos, "science") is an ethical theory that holds that the ends or consequences of an act determine whether an act is good or evil. Teleological theories are often discussed in opposition to deontological ethical theories, which hold that acts themselves are inherently good or evil, regardless of the consequences of acts. The saying, "the end justifies the means", meaning that if a goal is morally important enough, any method of achieving it is acceptable.

Teleological theories differ on the nature of the end that actions ought to promote. Eudaemonist theories (Greek eudaimonia, "happiness") hold that the goal of ethics consists in some function or activity appropriate to man as a human being, and thus tend to emphasize the cultivation of virtue or excellence in the agent as the end of all action. These could be the classical virtues—courage, temperance, justice, and wisdom—that promoted the Greek ideal of man as the "rational animal", or the theological virtues—faith, hope, and love—that distinguished the Christian ideal of man as a being created in the image of God.

John Stuart Mill, an influential liberal thinker of the 19th century and a teacher of utilitarianism

 

Utilitarian-type theories hold that the end consists in an experience or feeling produced by the action. Hedonism, for example, teaches that this feeling is pleasure—either one's own, as in egoism (the 17th-century English philosopher Thomas Hobbes), or everyone's, as in universalistic hedonism, or utilitarianism (the 19th-century English philosophers Jeremy Bentham, John Stuart Mill, and Henry Sidgwick), with its formula of the "greatest pleasure of the greatest number".

Other utilitarian-type views include the claims that the end of action is survival and growth, as in evolutionary ethics (the 19th-century English philosopher Herbert Spencer); the experience of power, as in despotism; satisfaction and adjustment, as in pragmatism (20th-century American philosophers Ralph Barton Perry and John Dewey); and freedom, as in existentialism (the 20th-century French philosopher Jean-Paul Sartre).

The chief problem for eudaemonist theories is to show that leading a life of virtue will also be attended by happiness—by the winning of the goods regarded as the chief end of action. That Job should suffer and Socrates and Jesus die while the wicked prosper, then seems unjust. Eudaemonists generally reply that the universe is moral and that, in Socrates' words, "No evil can happen to a good man, either in life or after death," or, in Jesus' words, "But he who endures to the end will be saved." (Matt 10:22). 

Utilitarian theories, on the other hand, must answer the charge that ends do not justify the means. The problem arises in these theories because they tend to separate the achieved ends from the action by which these ends were produced. One implication of utilitarianism is that one's intention in performing an act may include all of its foreseen consequences. The goodness of the intention then reflects the balance of the good and evil of these consequences, with no limits imposed upon it by the nature of the act itself—even if it be, say, the breaking of a promise or the execution of an innocent man. Utilitarianism, in answering this charge, must show either that what is apparently immoral is not really so or that, if it really is so, then closer examination of the consequences will bring this fact to light. Ideal utilitarianism (G.E. Moore and Hastings Rashdall) tries to meet the difficulty by advocating a plurality of ends and including among them the attainment of virtue itself, which, as John Stuart Mill affirmed, "may be felt a good in itself, and desired as such with as great intensity as any other good".

Acts and omissions, and the "act and omissions doctrine"

Since pure consequentialism holds that an action is to be judged solely by its result, most consequentialist theories hold that a deliberate action is no different from a deliberate decision not to act. This contrasts with the "acts and omissions doctrine", which is upheld by some medical ethicists and some religions: it asserts there is a significant moral distinction between acts and deliberate non-actions which lead to the same outcome. This contrast is brought out in issues such as voluntary euthanasia.

Issues

Action guidance

One important characteristic of many normative moral theories such as consequentialism is the ability to produce practical moral judgements. At the very least, any moral theory needs to define the standpoint from which the goodness of the consequences are to be determined. What is primarily at stake here is the responsibility of the agent.

The ideal observer

One common tactic among consequentialists, particularly those committed to an altruistic (selfless) account of consequentialism, is to employ an ideal, neutral observer from which moral judgements can be made. John Rawls, a critic of utilitarianism, argues that utilitarianism, in common with other forms of consequentialism, relies on the perspective of such an ideal observer. The particular characteristics of this ideal observer can vary from an omniscient observer, who would grasp all the consequences of any action, to an ideally informed observer, who knows as much as could reasonably be expected, but not necessarily all the circumstances or all the possible consequences. Consequentialist theories that adopt this paradigm hold that right action is the action that will bring about the best consequences from this ideal observer's perspective.

The real observer

In practice, it is very difficult, and at times arguably impossible, to adopt the point of view of an ideal observer. Individual moral agents do not know everything about their particular situations, and thus do not know all the possible consequences of their potential actions. For this reason, some theorists have argued that consequentialist theories can only require agents to choose the best action in line with what they know about the situation. However, if this approach is naïvely adopted, then moral agents who, for example, recklessly fail to reflect on their situation, and act in a way that brings about terrible results, could be said to be acting in a morally justifiable way. Acting in a situation without first informing oneself of the circumstances of the situation can lead to even the most well-intended actions yielding miserable consequences. As a result, it could be argued that there is a moral imperative for an agent to inform himself as much as possible about a situation before judging the appropriate course of action. This imperative, of course, is derived from consequential thinking: a better-informed agent is able to bring about better consequences.

Consequences for whom

Surveyed consequences of whistleblowing

 

Moral action always has consequences for certain people or things. Varieties of consequentialism can be differentiated by the beneficiary of the good consequences. That is, one might ask "Consequences for whom?"

Agent-focused or agent-neutral

A fundamental distinction can be drawn between theories which require that agents act for ends perhaps disconnected from their own interests and drives, and theories which permit that agents act for ends in which they have some personal interest or motivation. These are called "agent-neutral" and "agent-focused" theories respectively. 

Agent-neutral consequentialism ignores the specific value a state of affairs has for any particular agent. Thus, in an agent-neutral theory, an actor's personal goals do not count any more than anyone else's goals in evaluating what action the actor should take. Agent-focused consequentialism, on the other hand, focuses on the particular needs of the moral agent. Thus, in an agent-focused account, such as one that Peter Railton outlines, the agent might be concerned with the general welfare, but the agent is more concerned with the immediate welfare of herself and her friends and family.

These two approaches could be reconciled by acknowledging the tension between an agent's interests as an individual and as a member of various groups, and seeking to somehow optimize among all of these interests. For example, it may be meaningful to speak of an action as being good for someone as an individual, but bad for them as a citizen of their town.

Human-centered?

Many consequentialist theories may seem primarily concerned with human beings and their relationships with other human beings. However, some philosophers argue that we should not limit our ethical consideration to the interests of human beings alone. Jeremy Bentham, who is regarded as the founder of utilitarianism, argues that animals can experience pleasure and pain, thus demanding that 'non-human animals' should be a serious object of moral concern. More recently, Peter Singer has argued that it is unreasonable that we do not give equal consideration to the interests of animals as to those of human beings when we choose the way we are to treat them. Such equal consideration does not necessarily imply identical treatment of humans and non-humans, any more than it necessarily implies identical treatment of all humans.

Value of consequences

One way to divide various consequentialisms is by the types of consequences that are taken to matter most, that is, which consequences count as good states of affairs. According to utilitarianism, a good action is one that results in an increase in pleasure, and the best action is one that results in the most pleasure for the greatest number. Closely related is eudaimonic consequentialism, according to which a full, flourishing life, which may or may not be the same as enjoying a great deal of pleasure, is the ultimate aim. Similarly, one might adopt an aesthetic consequentialism, in which the ultimate aim is to produce beauty. However, one might fix on non-psychological goods as the relevant effect. Thus, one might pursue an increase in material equality or political liberty instead of something like the more ephemeral "pleasure". Other theories adopt a package of several goods, all to be promoted equally.

Virtue ethics

Consequentialism can also be contrasted with aretaic moral theories such as virtue ethics. Whereas consequentialist theories posit that consequences of action should be the primary focus of our thinking about ethics, virtue ethics insists that it is the character rather than the consequences of actions that should be the focal point. Some virtue ethicists hold that consequentialist theories totally disregard the development and importance of moral character. For example, Philippa Foot argues that consequences in themselves have no ethical content, unless it has been provided by a virtue such as benevolence.

However, consequentialism and virtue ethics need not be entirely antagonistic. Iain King has developed an approach that reconciles the two schools. Other consequentialists consider effects on the character of people involved in an action when assessing consequence. Similarly, a consequentialist theory may aim at the maximization of a particular virtue or set of virtues. Finally, following Foot's lead, one might adopt a sort of consequentialism that argues that virtuous activity ultimately produces the best consequences.

Max Weber

Ultimate end

The ultimate end is a concept in the moral philosophy of Max Weber, in which individuals act in a faithful, rather than rational, manner.

We must be clear about the fact that all ethically oriented conduct may be guided by one of two fundamentally differing and irreconcilably opposed maxims: conduct can be oriented to an "ethic of ultimate ends" or to an "ethic of responsibility." This is not to say that an ethic of ultimate ends is identical with irresponsibility, or that an ethic of responsibility is identical with unprincipled opportunism. Naturally, nobody says that. However, there is an abysmal contrast between conduct that follows the maxim of an ethic of ultimate ends—that, is in religious terms, "the Christian does rightly and leaves the results with the Lord"—and conduct that follows the maxim of an ethic of responsibility, in which case one has to give an account of the foreseeable results of one's action.

— Max Weber, Politics as a Vocation, 1918

Etymology

The term "consequentialism" was coined by G. E. M. Anscombe in her essay "Modern Moral Philosophy" in 1958, to describe what she saw as the central error of certain moral theories, such as those propounded by Mill and Sidgwick.

The phrase and concept of "The end justifies the means" are at least as old as the first century BC. Ovid wrote in his Heroides that Exitus acta probat "The result justifies the deed".

Criticisms

G. E. M. Anscombe objects to consequentialism on the grounds that it does not provide ethical guidance in what one ought to do because there is no distinction between consequences that are foreseen and those that are intended.

Bernard Williams has argued that consequentialism is alienating because it requires moral agents to put too much distance between themselves and their own projects and commitments. Williams argues that consequentialism requires moral agents to take a strictly impersonal view of all actions, since it is only the consequences, and not who produces them, that are said to matter. Williams argues that this demands too much of moral agents—since (he claims) consequentialism demands that they be willing to sacrifice any and all personal projects and commitments in any given circumstance in order to pursue the most beneficent course of action possible. He argues further that consequentialism fails to make sense of intuitions that it can matter whether or not someone is personally the author of a particular consequence. For example, that participating in a crime can matter, even if the crime would have been committed anyway, or would even have been worse, without the agent's participation.

Some consequentialists—most notably Peter Railton—have attempted to develop a form of consequentialism that acknowledges and avoids the objections raised by Williams. Railton argues that Williams's criticisms can be avoided by adopting a form of consequentialism in which moral decisions are to be determined by the sort of life that they express. On his account, the agent should choose the sort of life that will, on the whole, produce the best overall effects.

Pascal's Wager

From Wikipedia, the free encyclopedia

Blaise Pascal

 

Pascal's Wager is an argument in philosophy presented by the seventeenth-century French philosopher, mathematician and physicist Blaise Pascal (1623–1662). It posits that humans bet with their lives that God either exists or does not. 

Pascal argues that a rational person should live as though God exists and seek to believe in God. If God does not actually exist, such a person will have only a finite loss (some pleasures, luxury, etc.), whereas he stands to receive infinite gains (as represented by eternity in Heaven) and avoid infinite losses (eternity in Hell).

Pascal's Wager was based on the idea of the Christian God, though similar arguments have occurred in other religious traditions. The original wager was set out in section 233 of Pascal's posthumously published Pensées ("Thoughts"). These previously unpublished notes were assembled to form an incomplete treatise on Christian apologetics. 

Historically, Pascal's Wager was groundbreaking because it charted new territory in probability theory, marked the first formal use of decision theory, and anticipated future philosophies such as existentialism, pragmatism and voluntarism.

The Wager

The Wager uses the following logic (excerpts from Pensées, part III, §233):

1. God is, or God is not. Reason cannot decide between the two alternatives.
2. A Game is being played... where heads or tails will turn up.
3. You must wager (it is not optional).
4. Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing.
5. Wager, then, without hesitation that He is. (...) There is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite. And so our proposition is of infinite force, when there is the finite to stake in a game where there are equal risks of gain and of loss, and the infinite to gain.
6. But some cannot believe. They should then 'at least learn your inability to believe...' and 'Endeavour then to convince' themselves.

Pascal asks the reader to analyze humankind's position, where our actions can be enormously consequential but our understanding of those consequences is flawed. While we can discern a great deal through reason, we are ultimately forced to gamble. Pascal cites a number of distinct areas of uncertainty in human life: 

Category	Quotation(s)
Uncertainty in all	This is what I see, and what troubles me. I look on all sides, and everywhere I see nothing but obscurity. Nature offers me nothing that is not a matter of doubt and disquiet.
Uncertainty in Man's purpose	For after all what is man in nature? A nothing in relation to infinity, all in relation to nothing, a central point between nothing and all and infinitely far from understanding either.
Uncertainty in reason	There is nothing so conformable to reason as this disavowal of reason.
Uncertainty in science	There no doubt exist natural laws, but once this fine reason of ours was corrupted, it corrupted everything.
Uncertainty in religion	If I saw no signs of a divinity, I would fix myself in denial. If I saw everywhere the marks of a Creator, I would repose peacefully in faith. But seeing too much to deny Him, and too little to assure me, I am in a pitiful state, and I would wish a hundred times that if a god sustains nature it would reveal Him without ambiguity. We understand nothing of the works of God unless we take it as a principle that He wishes to blind some and to enlighten others.
Uncertainty in skepticism	It is not certain that everything is uncertain.

Pascal describes humanity as a finite being trapped within an incomprehensible infinity, briefly thrust into being from non-being, with no explanation of "Why?" or "What?" or "How?" On Pascal's view, human finitude constrains our ability to reliably achieve truth. 

Given that reason alone cannot determine whether God exists, Pascal concludes that this question functions like a coin toss. However, even if we do not know the outcome of this coin toss, we must base our actions on some expectation about the outcome. We must decide whether to live as though God exists, or whether to live as though God does not exist, even though we may be mistaken in either case. 

In Pascal's assessment, participation in this wager is not optional. Merely by existing in a state of uncertainty, we are forced to choose between the available courses of action for practical purposes.

Explanation

The Pensées passage on Pascal's Wager is as follows:

If there is a God, He is infinitely incomprehensible, since, having neither parts nor limits, He has no affinity to us. We are then incapable of knowing either what He is or if He is....
..."God is, or He is not." But to which side shall we incline? Reason can decide nothing here. There is an infinite chaos which separated us. A game is being played at the extremity of this infinite distance where heads or tails will turn up. What will you wager? According to reason, you can do neither the one thing nor the other; according to reason, you can defend neither of the propositions.
Do not, then, reprove for error those who have made a choice; for you know nothing about it. "No, but I blame them for having made, not this choice, but a choice; for again both he who chooses heads and he who chooses tails are equally at fault, they are both in the wrong. The true course is not to wager at all."
Yes; but you must wager. It is not optional. You are embarked. Which will you choose then? Let us see. Since you must choose, let us see which interests you least. You have two things to lose, the true and the good; and two things to stake, your reason and your will, your knowledge and your happiness; and your nature has two things to shun, error and misery. Your reason is no more shocked in choosing one rather than the other, since you must of necessity choose. This is one point settled. But your happiness? Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.
"That is very fine. Yes, I must wager; but I may perhaps wager too much." Let us see. Since there is an equal risk of gain and of loss, if you had only to gain two lives, instead of one, you might still wager. But if there were three lives to gain, you would have to play (since you are under the necessity of playing), and you would be imprudent, when you are forced to play, not to chance your life to gain three at a game where there is an equal risk of loss and gain. But there is an eternity of life and happiness. And this being so, if there were an infinity of chances, of which one only would be for you, you would still be right in wagering one to win two, and you would act stupidly, being obliged to play, by refusing to stake one life against three at a game in which out of an infinity of chances there is one for you, if there were an infinity of an infinitely happy life to gain. But there is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite.

Pascal begins by painting a situation where both the existence and non-existence of God are impossible to prove by human reason. So, supposing that reason cannot determine the truth between the two options, one must "wager" by weighing the possible consequences. Pascal's assumption is that, when it comes to making the decision, no one can refuse to participate; withholding assent is impossible because we are already "embarked", effectively living out the choice. 

We only have two things to stake, our "reason" and our "happiness". Pascal considers that if there is "equal risk of loss and gain" (i.e. a coin toss), then human reason is powerless to address the question of whether God exists. That being the case, then human reason can only decide the question according to possible resulting happiness of the decision, weighing the gain and loss in believing that God exists and likewise in believing that God does not exist. 

He points out that if a wager was between the equal chance of gaining two lifetimes of happiness and gaining nothing, then a person would be a fool to bet on the latter. The same would go if it was three lifetimes of happiness versus nothing. He then argues that it is simply unconscionable by comparison to bet against an eternal life of happiness for the possibility of gaining nothing. The wise decision is to wager that God exists, since "If you gain, you gain all; if you lose, you lose nothing", meaning one can gain eternal life if God exists, but if not, one will be no worse off in death than if one had not believed. On the other hand, if you bet against God, win or lose, you either gain nothing or lose everything. You are either unavoidably annihilated (in which case, nothing matters one way or the other) or lose the opportunity of eternal happiness. In note 194, speaking about those who live apathetically betting against God, he sums up by remarking, "It is to the glory of religion to have for enemies men so unreasonable..."

Inability to believe

Pascal addressed the difficulty that 'reason' and 'rationality' pose to genuine belief by proposing that "acting as if [one] believed" could "cure [one] of unbelief":

But at least learn your inability to believe, since reason brings you to this, and yet you cannot believe. Endeavour then to convince yourself, not by increase of proofs of God, but by the abatement of your passions. You would like to attain faith, and do not know the way; you would like to cure yourself of unbelief, and ask the remedy for it. Learn of those who have been bound like you, and who now stake all their possessions. These are people who know the way which you would follow, and who are cured of an ill of which you would be cured. Follow the way by which they began; by acting as if they believed, taking the holy water, having masses said, etc. Even this will naturally make you believe, and deaden your acuteness.

Analysis with decision theory

The possibilities defined by Pascal's Wager can be thought of as a decision under uncertainty with the values of the following decision matrix. 

	God exists (G)	God does not exist (¬G)
Belief (B)	+∞ (infinite gain)	−1 (finite loss)
Disbelief (¬B)	−∞ (infinite loss)	+1 (finite gain)

Given these values, the option of living as if God exists (B) dominates the option of living as if God does not exist (¬B), as long as one assumes a positive probability that God exists. In other words, the expected value gained by choosing B is greater than or equal to that of choosing ¬B. 

In fact, according to decision theory, the only value that matters in the above matrix is the +∞ (infinitely positive). Any matrix of the following type (where f₁, f₂, and f₃ are all negative or finite positive numbers) results in (B) as being the only rational decision.

	God exists (G)	God does not exist (¬G)
Belief (B)	+∞	f1
Disbelief (¬B)	f2	f3

Misunderstanding of the wager

Many criticisms have explained that the wager has been used as a supposed theory of the necessity to believe, although that was never Pascal's intention. As Laurent Thirouin writes:

The celebrity of fragment 418 has been established at the price of a mutilation. By titling this text "the wager", readers have been fixated only on one part of Pascal's reasoning. It doesn't conclude with a QED at the end of the mathematical part. The unbeliever who had provoked this long analysis to counter his previous objection ("Maybe I bet too much") is still not ready to join the apologist on the side of faith. He put forward two new objections, undermining the foundations of the wager: the impossibility to know, and the obligation of playing.

To be put at the beginning of Pascal's planned book, the wager was meant to show that logical reasoning cannot support faith or lack thereof,

We have to accept reality and accept the reaction of the libertine when he rejects arguments he is unable to counter. The conclusion is evident: if men believe or refuse to believe, it is not how some believers sometimes say and most unbelievers claim, because their own reason justifies the position they have adopted. Belief in God doesn't depend upon rational evidence, no matter which position.

Pascal's intended book was precisely to find other ways to establish the value of faith, an apology for the Christian faith.

Criticism

Criticism of Pascal's Wager began in his own day, and came from both atheists, who questioned the 'benefits' of a deity whose 'realm' is beyond reason, and the religiously orthodox, who primarily took issue with the wager's deistic and agnostic language. It is criticized for not proving God's existence, the encouragement of false belief, and the problem of which religion and which God should be worshipped.

Nature as not a proof of the existence of God

Voltaire (another prominent French writer of the Enlightenment), a generation after Pascal, rejected the idea that the wager was "proof of God" as "indecent and childish", adding, "the interest I have to believe a thing is no proof that such a thing exists". Pascal, however, did not advance the wager as a proof of God's existence but rather as a necessary pragmatic decision which is "impossible to avoid" for any living person. He argued that abstaining from making a wager is not an option and that "reason is incapable of divining the truth"; thus, a decision of whether to believe in the existence of God must be made by "considering the consequences of each possibility". 

Voltaire's critique concerns not the nature of the Pascalian wager as proof of God's existence, but the contention that the very belief Pascal tried to promote is not convincing. Voltaire hints at the fact that Pascal, as a Jansenist, believed that only a small, and already predestined, portion of humanity would eventually be saved by God. 

Voltaire explained that no matter how far someone is tempted with rewards to believe in Christian salvation, the result will be at best a faint belief. Pascal, in his Pensees, agrees with this, not stating that people can choose to believe (and therefore make a safe wager), but rather that some cannot believe. 

As Étienne Souriau explained, in order to accept Pascal's argument, the bettor needs to be certain that God seriously intends to honour the bet; he says that the Wager assumes that God also accepts the bet, which is not proved; Pascal's bettor is here like the fool who seeing a leaf floating on a river's waters and quivering at some point, for a few seconds, between the two sides of a stone, says: "I bet a million with Rothschild that it takes finally the left path." And, effectively, the leaf passed on the left side of the stone, but unfortunately for the fool Rothschild never said "I [will take that] bet".

Argument from inconsistent revelations

Since there have been many religions throughout history, and therefore many conceptions of God (or gods), some assert that all of them need to be factored into the Wager, in an argument known as the argument from inconsistent revelations. This, its proponents argue, would lead to a high probability of believing in "the wrong god", which, they claim, eliminates the mathematical advantage Pascal claimed with his Wager. Denis Diderot, a contemporary of Voltaire, concisely expressed this opinion when asked about the Wager, saying "an Imam could reason the same way". J. L. Mackie notes that "the church within which alone salvation is to be found is not necessarily the Church of Rome, but perhaps that of the Anabaptists or members of The Church of Jesus Christ of Latter-day Saints or the Muslim Sunnis or the worshipers of Kali or of Odin."

Another version of this objection argues that for every religion that promulgates rules, there exists another religion that has rules of the opposite kind. If a certain action leads one closer to salvation in the former religion, it leads one further away from it in the latter. Therefore, the expected value of following a certain religion could be negative. Or, one could also argue that there are an infinite number of mutually exclusive religions (which is a subset of the set of all possible religions), and that the probability of any one of them being true is zero; therefore, the expected value of following a certain religion is zero. 

Pascal considers this type of objection briefly in the notes compiled into the Pensées, and dismisses it as obviously wrong and disingenuous:

What say [the unbelievers] then? "Do we not see," say they, "that the brutes live and die like men, and Turks like Christians? They have their ceremonies, their prophets, their doctors, their saints, their monks, like us," etc. If you care but little to know the truth, that is enough to leave you in repose. But if you desire with all your heart to know it, it is not enough; look at it in detail. That would be sufficient for a question in philosophy; but not here, where everything is at stake. And yet, after a superficial reflection of this kind, we go to amuse ourselves, etc. Let us inquire of this same religion whether it does not give a reason for this obscurity; perhaps it will teach it to us.

 

This short but densely packed passage, which alludes to numerous themes discussed elsewhere in the Pensées, has given rise to many pages of scholarly analysis. 

Pascal says that unbelievers who rest content with the many-religions objection are people whose scepticism has seduced them into a fatal "repose". If they were really bent on knowing the truth, they would be persuaded to examine "in detail" whether Christianity is like any other religion, but they just cannot be bothered. Their objection might be sufficient were the subject concerned merely some "question in philosophy", but not "here, where everything is at stake". In "a matter where they themselves, their eternity, their all are concerned", they can manage no better than "a superficial reflection" ("une reflexion légère") and, thinking they have scored a point by asking a leading question, they go off to amuse themselves.

As Pascal scholars observe, Pascal regarded the many-religions objection as a rhetorical ploy, a "trap" that he had no intention of falling into. If, however, any who raised it were sincere, they would want to examine the matter "in detail". In that case, they could get some pointers by turning to his chapter on "other religions". 

As David Wetsel notes, Pascal's treatment of the pagan religions is brisk: "As far as Pascal is concerned, the demise of the pagan religions of antiquity speaks for itself. Those pagan religions which still exist in the New World, in India, and in Africa are not even worth a second glance. They are obviously the work of superstition and ignorance and have nothing in them which might interest 'les gens habiles' ('clever men')". Islam warrants more attention, being distinguished from paganism (which for Pascal presumably includes all the other non-Christian religions) by its claim to be a revealed religion. Nevertheless, Pascal concludes that the religion founded by Mohammed can on several counts be shown to be devoid of divine authority, and that therefore, as a path to the knowledge of God, it is as much a dead end as paganism. Judaism, in view of its close links to Christianity, he deals with elsewhere.

The many-religions objection is taken more seriously by some later apologists of the Wager, who argue that, of the rival options, only those awarding infinite happiness affect the Wager's dominance. In the opinion of these apologists "finite, semi-blissful promises such as Kali's or Odin's" therefore drop out of consideration. Also, the infinite bliss that the rival conception of God offers has to be mutually exclusive. If Christ's promise of bliss can be attained concurrently with Jehovah's and Allah's (all three being identified as the God of Abraham), there is no conflict in the decision matrix in the case where the cost of believing in the wrong conception of God is neutral (limbo/purgatory/spiritual death), although this would be countered with an infinite cost in the case where not believing in the correct conception of God results in punishment (hell).

Furthermore, ecumenical interpretations of the Wager argue that it could even be suggested that believing in a generic God, or a god by the wrong name, is acceptable so long as that conception of God has similar essential characteristics of the conception of God considered in Pascal's Wager (perhaps the God of Aristotle). Proponents of this line of reasoning suggest that either all of the conceptions of God or gods throughout history truly boil down to just a small set of "genuine options", or that if Pascal's Wager can simply bring a person to believe in "generic theism" it has done its job.

Pascal argues implicitly for the uniqueness of Christianity in the Wager itself, writing: "If there is a God, He is infinitely incomprehensible...Who then can blame the Christians for not being able to give reasons for their beliefs, professing as they do a religion which they cannot explain by reason?"

Argument from inauthentic belief

Some critics argue that Pascal's Wager, for those who cannot believe, suggests feigning belief to gain eternal reward. This would be dishonest and immoral. In addition, it is absurd to think that God, being just and omniscient, would not see through this deceptive strategy on the part of the "believer", thus nullifying the benefits of the Wager.

Since these criticisms are concerned not with the validity of the Wager itself, but with its possible aftermath—namely that a person who has been convinced of the overwhelming odds in favor of belief might still find himself unable to sincerely believe—they are tangential to the thrust of the Wager. What such critics are objecting to is Pascal's subsequent advice to an unbeliever who, having concluded that the only rational way to wager is in favor of God's existence, points out, reasonably enough, that this by no means makes him a believer. This hypothetical unbeliever complains, "I am so made that I cannot believe. What would you have me do?" Pascal, far from suggesting that God can be deceived by outward show, says that God does not regard it at all: "God looks only at what is inward." For a person who is already convinced of the odds of the Wager but cannot seem to put his heart into the belief, he offers practical advice. 

Explicitly addressing the question of inability to believe, Pascal argues that if the Wager is valid, the inability to believe is irrational, and therefore must be caused by feelings: "your inability to believe, because reason compels you to [believe] and yet you cannot, [comes] from your passions." This inability, therefore, can be overcome by diminishing these irrational sentiments: "Learn from those who were bound like you. . . . Follow the way by which they began; by acting as if they believed, taking the holy water, having masses said, etc. Even this will naturally make you believe, and deaden your acuteness.—'But this is what I am afraid of.'—And why? What have you to lose?"

Some other critics have objected to Pascal's Wager on the grounds that he wrongly assumes what type of epistemic character God would likely value in his rational creatures if he existed.

Variations

• Muslim Imam Ja'far al-Sadiq is recorded to have postulated variations of the Wager on several occasions in different forms, including his famed 'Tradition of the Myrobalan Fruit.' In the Sh'i'i hadith book al-Kafi, al-Sadiq declares to an atheist "If what you say is correct – and it is not – then we will both succeed. But if what I say is correct – and it is – then I will succeed, and you will be destroyed."
• An instantiation of this argument, within the Islamic kalam tradition, was discussed by Imam al-Haramayn al-Juwayni (d. 478/1085) in his Kitab al-irshad ila-qawati al-adilla fi usul al-i'tiqad, or A Guide to the Conclusive Proofs for the Principles of Belief.
• The Sophist Protagoras had an agnostic position regarding the gods, but he nevertheless continued to worship the gods. This could be considered as an early version of the Wager.
• In the famous tragedy of Euripides Bacchae, Kadmos states an early version of Pascal's Wager. It is noteworthy that at the end of the tragedy Dionysos, the god to whom Kadmos referred, appears and punishes him for thinking in this way. Euripides, quite clearly, considered and dismissed the wager in this tragedy.
• The Christian apologist Arnobius of Sicca (d. 330) stated an early version of the argument in his book Against the Pagans.
• Pascal's Wager is often concluded (not by Pascal) by stating that people should 'choose the safer wager'. Pascal stated that people could not simply choose to believe, but that they might develop a faith through their actions.
• In the Sanskrit classic Sārasamuccaya, Vararuci makes a similar argument to Pascal's Wager.
• A 2008 philosophy book, How to Make Good Decisions and Be Right All the Time, presents a secular revision of Pascal’s wager: “What does it hurt to pursue value and virtue? If there is value, then we have everything to gain, but if there is none, then we haven’t lost anything.... Thus, we should seek value.”
• The stoic philosopher and Roman Emperor Marcus Aurelius expressed a similar sentiment in the second book of Meditations, saying "Since it is possible that thou mayest depart from life this very moment, regulate every act and thought accordingly. But to go away from among men, if there are gods, is not a thing to be afraid of, for the gods will not involve thee in evil; but if indeed they do not exist, or if they have no concern about human affairs, what is it to me to live in a universe devoid of gods or devoid of Providence?"