Because the study of randomness and divine providence involves terminology that lacks standardized meanings, we have included a lexicon of some key terms. Please read through them before submitting your proposal. You may use them in other ways if you choose, but if you do, be sure to call our attention to the meaning you are using. Also, for some of the terms, we have included more than one possible definition. If you use one of these terms, tell us which definition you are using.

Randomness lexicon

Agent (agency)
One who performs a voluntary action.
Algorithmic information theory
A subfield of information theory and computer science that concerns itself with the relationship between computation and information…Informally, from the point of view of algorithmic information theory, the information content of a string is equivalent to the length of the shortest possible self-contained representation of that string... Unlike classical information theory, algorithmic information theory gives formal, rigorous definitions of an infinite random string and a random infinite sequence that do not depend on physical or philosophical intuitions about nondeterminism or likelihood. (WP)
Anthropic principle
See weak anthropic principle and strong anthropic principle.
The belief that deities do not exist; see theism.
Beam splitter
A mirror that partially reflects light and transmits the remainder.
Bell's theorem
A result proven by John S. Bell in 1964 establishing that any hidden variables that would account for quantum indeterminacy must be non-local without violating relativity theory ("peaceful co-existence") in the sense that joint events occur randomly when observed individually and spatially separated, yet their joint events have a higher or lower coincidence rate than could be expected classically.
Biological concept of randomness
The notion that mutations in an organism occur independently of the organism's environment and are not a response to opportunities or needs.
Bohmian mechanics
…a deterministic version of quantum theory articulated by Louis de Broglie in 1927 in which the evolution of the wave function is "guided" by "pilot waves" that are not detectable by the observer. A similar principle was introduced by David Bohm in 1952. It is the simplest example of what is often called a hidden variables interpretation of quantum mechanics. In Bohmian mechanics a system of particles is described in part by its wave function, evolving, as usual, according to Schrödinger's equation. However, the wave function provides only a partial description of the system. This description is completed by the specification of the actual positions and momenta of the particles. The latter evolve according to the "guiding equation," which expresses the velocities of the particles in terms of the wave function. (SEP) Most contemporary physicists do not affirm the Bohmian interpretation.
Brownian motion
…the presumably random drifting of particles suspended in a fluid (a liquid or a gas) or the mathematical model used to describe such random movements…Brownian motion is among the simplest of the continuous-time stochastic (or probabilistic) processes. (WP)
The relationship between an event (the efficient cause) and a second event (the effect), where the second event is understood as a consequence of the first. (WP)
Causally closed universe
A universe in which there is no causal input from outside that universe. Many theists affirm a causally open universe.
Causally open universe
A universe that is not causally closed. Thus, in a causally open universe, it is possible for a physical event not to be fully accounted for by earlier physical events.
Central Limit Theorem
A key result in statistics which, in its most common form, asserts that the mean of n independent, identically distributed, random variables will approach a normal distribution as n gets large. There are several variants of the common form.
A common word that has no standardized definition. In ordinary usage it often refers to events that have no assignable cause. In technical settings in which the word random is reserved for numbers, it is sometimes used to refer to events that in other contexts would be called random.
Chaos theory
A mathematical theory describing dynamical systems by a set of coupled non-linear differential equations that represent the interaction of several physical parameters. The solution of these equations describes the deterministic evolution of the dynamical system but is highly sensitive to the values of the initial conditions. Owing to the fact that these initial conditions cannot be specified with sufficient precision the outcome of the evolution is not predictable. Small differences in the initial conditions are amplified by the nonlinear coupling (feedback) so that highly divergent results may arise from apparently equal initial states. Therefore, although the systems evolve deterministically the future states are not predictable.
The merging of genetic lineages backwards to a most recent common ancestor. (WP)
Collapse of the wave function
The phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer or with any sufficient macroscopic entity (including a simple molecule), as long as the interaction is irreversible. (WP)
Copenhagen interpretation of QM
The idea that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta, entities which fit neither the classical idea of particles nor the classical idea of waves. According to the interpretation, the act of measurement causes the set of probabilities to immediately and randomly assume only one of the possible values. (WP)
Counterfactual conditional
A conditional (or "if-then") statement indicating what would be the case if its antecedent were true (although it is not true). (WP)
The religious belief that humanity, life, the earth, and the universe are the creation of a supernatural being, most often the Abrahamic God. There are several varieties of creationism including young earth creationism, old earth creationism, gap creationism, dayage creationism, progressive creationism, intelligent design, and theistic evolution. (WP) Some scholars distinguish the creatio ex nihilo doctrine from "creationism." In this perspective God ultimately sustains everything in being (existence) and order, but does not act at a level accessible to the natural sciences.
A philosophical position stating that the state of the universe at time T fully determines the state of the universe at any earlier or later time.
One of several transport phenomena that occur in nature. From the atomistic point of view, diffusion is considered as a result of the random walk of the diffusing particles. (WP) The random walk of a particle is usually defined as a trajectory involving collisions with other particles that change the direction of motion such that after each collision the particle retains no memory of its previous direction and all directions after the collision are equally probable.
Divine Action project
A joint undertaking of the Vatican Observatory and the Center for Theology and the Natural Sciences in Berkeley. Over the period from 1993-2002, it produced a series of five volumes of scholarly papers exploring scientific perspectives on the nature of God's actions in the physical universe along with many other topics.
Divine concurrence
The doctrine that for any causal transaction that occurs in the universe, God has to approve of it. While Christian theological traditions have generally affirmed this doctrine, they vary in their understanding of how much independence of action this allows creatures.
The arising of novel structures, patterns and properties in complex systems. These emergent structures, patterns, processes and properties cannot be reduced without remainder to the underlying structures, patterns, processes and properties. An example is the wetness of water which, as an emergent property, does not occur because of a property of "wetness" attributed to the H2O molecules that make up water. C.f. reductionism.
Entropy (Thermodynamical concept)
A thermodynamic property that can be used to determine the energy not available for work in a thermodynamic process, such as in energy conversion devices, engines, or machines… These processes reduce the state of order of the initial systems, and therefore entropy is an expression of disorder or randomness. (WP)
Entropy (Statistical mechanics concept)
A measure of the number of ways in which a system may be arranged, often taken to be a measure of "disorder" (the higher the entropy, the higher the disorder). This definition describes the entropy as being proportional to the natural logarithm of the number of possible microscopic configurations of the individual atoms and molecules of the system (microstates) which could give rise to the observed macroscopic state (macrostate) of the system. (WP)
Epistemic randomness
Suppose an event has more than one possible outcome. If the indeterminacy can (at least in principle) be removed by the addition of further knowledge, the randomness is epistemic.
A word that has a large number of meanings many of which incorporate philosophical and/or theological assumptions. In this lexicon, it will simply refer to any change across successive generations in the inherited characteristics of biological populations. (WP)
Evolutionary game theory
The application of game theory to evolving populations of life forms in biology. EGT is useful in this context by defining a framework of contests, strategies, and analytics into which Darwinian competition can be modeled. (WP)
Fine-tuning argument
The proposition that the conditions that allow life in the universe can only occur when certain universal fundamental physical constants lie within a very narrow range, so that if any of several fundamental constants were only slightly different, the universe would be unlikely to be conducive to the establishment and development of matter, astronomical structures, elemental diversity, or life as it is presently understood. (WP) "One reaction to these apparent enormous coincidences is to see them as substantiating the theistic claim that the universe has been created by a personal God and as offering the material for a properly restrained theistic argument—hence the fine-tuning argument. It's as if there are a large number of dials that have to be tuned to within extremely narrow limits for life to be possible in our universe. It is extremely unlikely that this should happen by chance, but much more likely that this should happen, if there is such a person as God." (Alvin Plantinga)
First law of thermodynamics
A version of the law of conservation of energy, specialized for thermodynamical systems. It is usually formulated by stating that the change in the internal energy of a closed system is equal to the amount of heat supplied to the system, minus the amount of work performed by the system on its surroundings. The law of conservation of energy can be stated: The energy of an isolated system is constant. (WP) (See causally closed universe)
Future contingent
Contingent statements about the future—such as future events, actions, states etc. To qualify as contingent the predicted event, state, action or whatever is at stake must neither be impossible nor inevitable…the problem of future contingents concerns how to ascribe truth-values to such statements…The theological issue of how to reconcile the assumption of God's foreknowledge with the freedom and moral accountability of human beings has been a main impetus to the discussion and a major inspiration to the development of various logical models of time and future contingents. This theological issue is connected with the general philosophical question of determinism versus indeterminism. (SEP)
Guided evolution
The notion of guided evolution affirms the typical underlying principles of evolution: an old earth, progression of life from simple to relatively complex forms, descent with modification, common ancestry of all living things on earth, and the existence of a naturalistic mechanism (typically random genetic mutations and natural selection) driving the process. However, it denies that the process of evolution proceeds solely by means of naturalistic mechanisms; rather it affirms the special creative activity of God in the process although it does not specify where that activity has occurred. (Alvin Plantinga)
The view that a scientific theory is a useful instrument for doing things in the world but not for explaining or understanding the world. In this lexicon, its importance is that an instrumental approach does not consider the matter of whether randomness is ontological.
Kochen-Specker theorem
A formal constructive result proving that certain finite collections of quantum observables (even of single quanta) cannot classically exist simultaneously.
Kolmogorov complexity
The complexity of a string is the length of the string's shortest description in some fixed universal description language. A binary string can be said to be random if the Kolmogorov complexity of the string is at least the length of the string. (WP)
Law of large numbers
A theorem in probability theory that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed. (WP)
Laws of nature
Within metaphysics, there are two competing theories of laws of nature. On one account, the regularity theory, laws of nature are statements of the uniformities or regularities in the world; they are mere descriptions of the way the world is. On the other account, the necessitarian theory, laws of nature are the "principles" which govern the natural phenomena of the world. That is, the natural world "obeys" the laws of nature. This seemingly innocuous difference marks one of the most profound gulfs within contemporary philosophy, and has quite unexpected, and wide-ranging, implications. (IEP)
Martin-Löf randomness
Let K(w) denote the minimum length of a computer program (written in some fixed programming language) that takes no input and will output a specified string w (of characters or bits). Given a natural number c, we say that w is c-incompressible if K(w)>|w|-c. An infinite sequence S is Martin-Löf random if and only if there is a constant c such that all of S's finite prefixes are c-incompressible.
The theory that the only thing that exists is matter; that all things are composed of material and all phenomena (including consciousness) are the result of material interactions. (WP)
A difficult term to define. Someone being raised from the dead or water being turned into wine are examples of events typically thought of as miracles. To qualify as a miracle, an event has to be unusual and have a spiritual significance.
A religious doctrine which attempts to reconcile the providence of God with human free will. Molinists hold that in addition to knowing everything that does or will happen, God also knows what his creatures would (not just could) freely choose if placed in any circumstance. By employing this "middle knowledge" in his creative decisions, God perfectly accomplishes His will in the lives of genuinely free creatures. (WP)
Changes in a genomic sequence: the DNA sequence of a cell's genome or the DNA or RNA sequence of a virus. (WP)
Natural law
See laws of nature.
The viewpoint that laws of nature (as opposed to supernatural ones) operate in the universe, and that nothing exists beyond the natural universe or, if it does, it does not affect the natural universe. Followers of naturalism (naturalists) assert that natural laws are the rules that govern the structure and behavior of the natural universe, that the universe is a product of these laws. (WP)
A metaphysical view according to which general or abstract terms and predicates exist, while universals or abstract objects, which are sometimes thought to correspond to these terms, do not exist. Thus, there are at least two main versions of nominalism. One version denies the existence of universals—things that can be instantiated or exemplified by many particular things (e.g. strength, humanity). The other version specifically denies the existence of abstract objects—objects that do not exist in space and time. (WP)
The negation of determinism. That is, the philosophical position that the state of the universe at time T does not fully determine the state of the universe at all earlier and later times.
Objective probability
One of two common interpretations of probability: (1) An interpretation based on the observation that a given type of event (such as a die yielding a six) tends to occur at a persistent rate, or "relative frequency", in a long run of trials. (WP) (2) A "logical" interpretation in which probability is viewed as a property of the possible outcomes. See subjective probability.
A divine attribute. God's "perfect ability to do all things that are consistent with the divine character." (Thomas Oden) "He has absolute power over all things so that nothing can resist him." (Herman Bavinck) While this doctrine affirms that God has all the power it is possible for a being to possess, for most theologians this means that God cannot do that which is logically impossible – e.g., make 7 + 5 ≠ 12 with the usual meanings of 7, +, 5, =, and 12.
Another divine attribute. "…God's mode of being present to all aspects of both space and time. Although God is present in all space and time, God is not locally limited to any particular time or space." (Thomas Oden) "God is in all things by his presence, insofar as everything is naked and open to his eyes." (Thomas Aquinas)
Another divine attribute. "God's complete knowledge of the world and time." (Thomas Oden) God knows all that can be known. Some (proponents of Present Knowledge) believe God knows all that has occurred and is occurring, but not what humans will freely do in the future since there is nothing yet in those contexts to be known. Others (proponents of Simple Foreknowledge) believe that God knows all that has occurred, is occurring, and will actually occur. Still others (proponents of Middle Knowledge) believe that God knows all that has occurred, is occurring, will actually occur, and what would have occurred (would occur) in every possible situation, including those that will not actually occur.
Ontic randomness
See ontological randomness.
Ontological randomness
Randomness that is not epistemic. That is, the randomness is a fundamental property of the nature of the event or the process that produced it and not merely a result of human limitations.
Open theology
While important differences of opinion exist among open theologians, the following statements comprise core themes that the majority, if not all, would affirm: Creatures – at least humans – are genuinely free to make choices pertaining to their earthly lives and eternal destiny; God experiences others in some way analogous to how creatures experience others; both creatures and God are relational beings, which means that both God and creatures are affected by others in give-and-take relationships; God experiences changes, yet God's nature or essence is unchanging; God takes calculated risks, because God is not all-controlling; creatures are called to act in loving ways that please God and make the world a better place; the future is open – it is not predetermined or fully known by God as it is affected by human decision-making; God's expectations about the future are often partly dependent upon creaturely actions; although everlasting, God experiences time in a way analogous to how creatures experience time. (Open Theology and Science web site)
Poisson law of small numbers
Suppose the likelihood of an event is constant over certain time periods of specified duration and occurrences of the event are independent of each other. Then the frequencies of occurrences in a single period will follow a precise mathematical pattern known as a Poisson distribution. The fact that this distribution is followed even when frequencies are relatively small is sometimes called the Poisson law of small numbers.
Principle of least action
As formulated by the 17th century physicist Pierre Louis Maupertuis, "Nature is thrifty in all its actions." Alternatively, it could be stated as "Nature always finds the most efficient path between two points." Some scholars have used the principle to argue that nature has a teleological quality although this assertion has been controversial.
Principle of sufficient reason
Anything that happens does so for a reason or cause.
Probabilistic causation
Designates a group of theories that aim to characterize the relationship between cause and effect using the tools of probability theory. The central idea behind these theories is that causes change the probabilities of their effects rather than determining their effects. (SEP)
That preservation, care and government which God exercises over all things He has created, in order that they may accomplish the ends for which they were created. (International Standard Bible Encyclopedia.)
A key word in this lexicon, but not one that enjoys a widely accepted univocal definition. Popular definitions typically use notions such as without aim, pattern, or purpose. Physical scientists often use it to refer to the absence of discernible cause. Mathematical and statistical definitions typically refer to unpredictability of events and the absence of pattern in sequences. For some more formal treatments see biological concept of randomness, Kolmogorov complexity, and Martin-Löf randomness in this lexicon. Also c.f. chance.
Reductionism encompasses a set of ontological, epistemological, and methodological claims about the relations between different scientific domains. The basic question of reduction is whether the properties, concepts, explanations, or methods from one scientific domain (typically at higher levels of organization) can be deduced from or entirely explained by the properties, concepts, explanations, or methods from another domain of science (typically one about lower levels of organization). (SEP) The term is sometimes used pejoratively by religious thinkers when critiquing certain scientific speculations, for example, that human consciousness can be explained by molecular biology.
Second law of thermodynamics
The principle that the total entropy of any system will not decrease other than by increasing the entropy of some other system in which it is embedded. Hence, in a system isolated from its environment, the entropy of that system will not decrease. (WP)
Strong anthropic principle
Based on the observation that conscious observers – a life form – exist in the observable universe, the assertion that the universe must have those properties which allow life to develop within it at some stage in its history. (John D. Barrow and Frank J.Tipler)
Subjective probability
An interpretation of probability in which it is seen as subjective plausibility, that is, as the amount of confidence an individual has in an assertion. An individual's subjective probabilities are regarded as rational if they satisfy the axioms of probability.
A philosophical account which holds that final causes exist in nature, meaning that design and purpose analogous to that found in human actions are inherent also in the rest of nature. (WP)
In the Abrahamic religions, this has traditionally been the belief that there is an all-powerful, all-knowing perfectly good immaterial person who has created the world, has created human beings 'in his own image,' and to whom we owe worship, obedience and allegiance. (Alvin Plantinga). Theism also includes less traditional beliefs such as the view that God is the "ground of being" or "ultimate reality" and that God is not a "person" but is more than that, God is "suprapersonal"; a recent example is the theology of Paul Tillich. The term includes belief in one god (monotheism) and many gods (polytheism). See atheism.
The term has no universally agreed upon definition, but usually refers to an attempt to justify God's ways to man by giving reasons God might have for allowing a particular evil.
Weak Anthropic principle
Based on the observation that conscious life forms self-evidently exist in the universe, the principle that observed values of all physical and cosmological quantities are not equally probable but they take on values restricted by the requirement that there exist sites where carbon-based life can evolve and by the requirements that the universe be old enough for it to have already done so. (John D. Barrow and Frank J.Tipler)


  • IEP – Internet Encyclopedia of Philosophy
  • SEP – Stanford Encyclopedia of Philosophy
  • WP – Wikipedia