This page was last updated on September 20, 1998.

accommodation: When a model succeeds in fitting, or conforming, to a phenomenon without predicting it.

adjustable parameters: Parameters, like the radius of circles, or the period of their motion, whose values are estimated from the observed data. A statement of their values is not referred to as an auxiliary assumption.

Almagest: A comprehensive treatise on astronomy, geography, and mathematics compiled by Ptolemy about A.D. 150.

ampliative argument: Any argument that is not deductively valid. The term refers to the fact that the conclusion of such argument goes beyond, or amplifies upon, the premises.

argument: A list of statements, one of which is the conclusion and the rest of which are the premises.

auxiliary assumptions: The assumptions made about particular systems, like the number of planets, the number of epicycles in Ptolemaic or Copernican astronomy, the absence of frictional forces in Newtonian mechanics, or in Einsteinian cosmology, the assumption that the mass in the universe is spread evenly in all directions. These are different from the values of adjustable parameters, which are inferred from the observational data. When combined with the respective theory, auxiliary assumptions lead to a model. The assumptions are often known to be false, in which case the model is called an idealization.

Bayesian Learning: A procedure whereby old probabilities, called prior probabilities, are updated in light of observational evidence, to new values, called posterior probabilities. The posterior probability is equal to prior probability conditional on the evidence. Let H be a hypothesis, and let Pr(H) be the prior probability of H. Let E be the new evidence. Then the posterior probability of H is equal to Pr(H/E).

Bayesianism: A form of probabilism. Its comes in a number of varieties. Objective Bayesianism assumes that probabilities can be assigned objectively, as inductive probabilities. Subjective Bayesianism assumes that all probabilities are epistemic or personal. See also Simple Bayesianism.

Bayesianism, Simple: A possible form of Bayesianism that is a combination of inductive logic and eliminative induction. It is subjective in the sense that it recognizes that the list of hypotheses from which the elimination takes place will vary from person to person, but it is objective in its idea of assigning an equal initial probability, or prior probability, to those hypotheses. When combined with the standard theory of Bayesian learning, it runs into difficulties, although this does not prove that all forms of Bayesianism run into the same difficulties.

begging the question: An argument is said to beg the question when it assumes what it purports to prove. For example: God exists because the bible says so and it is the word of God. The premise "The bible is the word of God" assumes that God exists, but that it is what is to be proved. The argument is circular in other words. Why is this bad when in any deductively valid argument, there is a sense in which the conclusion is contained in the premises? Why is it not the case that every deductive argument begs the question. The answer is that in a good deductive argument, the conclusion of an argument is at issue or in dispute, but the premises are not. In an argument that begs the question, there is at least one premise that is at issue or in dispute, so the argument is ineffective.

bleen: Object x is bleen at time t if and only if x is blue at time t and t < 2100, or x is green at time t and t 2100. See also, grue.

content: The content of a theory refers to what the theory says, or deductively entails. E.g., the predictive content of a theory is the set of predictions that it deductively entails.

commutation: A substitution, an exchange, or an interchange.

commutative: Independent of order. Used of a logical or mathematical operation that combines objects or sets of objects two at a time. If a + b = b + a, the operation indicated by + is commutative.

conditional probability: The probability that an event will occur, given that one or more other events have occurred.

conjunction: The position of a celestial body when it is on the same side of the sun from Earth.

Copernicus, Nicolaus: (1473-1543) Polish astronomer who advanced the theory that the earth and other planets revolve around the sun, disrupting the Ptolemaic system of astronomy. His major work was De Revolutionabus, published in 1543.

cosmic coincidence: A coincidence of events of the same kind, repeated many times, that has improbably arisen by chance. It is widely considered a basic principle of science that one should believe in as few cosmic coincidences as possible.

deduction: Logic. The process of reasoning in which a conclusion follows necessarily from the stated premises.

deductively valid: An argument is deductively valid if and only if it is impossible that its conclusion is false while its premises are true.

deferent circle: In Ptolemaic or Copernican cosmology, the main circle along which a planet, or an epicycle, travels around the center.

discovery: See invention.

eliminative induction: A deductively valid argument that states that one of a finite list of theories, models, or hypotheses, is true, then states that all but one of them is false, and then concludes that the remaining one is true.

epicycle: In Ptolemaic or Copernican cosmology, a small circle, the center of which moves on the circumference of the deferent circle, or on the circumference of another epicycle.

falsification: The process of proving a hypothesis false.

falsificationism: A form of hypothetico-deductivism in which progress arises through the falsification of theories. Our best theories are those that survive the severest tests. Falsificationism, in its na´ve form, runs conflicts with the Quine-Duhem thesis.

general: Not limited in scope, area, or application: as a general rule. Indefinite or unspecific.

grolor: A collective terms referring to properties grue or bleen, just as 'color' is a collective term for properties like green and blue.

grue: Object x is grue at time t if and only if either (x is green at time t and t < 2100) or (x is blue at time t and t 2100). Because the present time is before the year 2100 A. D., all emeralds are green at the present time and all emeralds are grue at the present time. Both of true descriptions of the state of emeralds at the present time. But if we project these facts into the future, they make different predictions about the state of emeralds after the year 2100.

hypothetico-deductivism: Any view of science in which theories are hypothesized, and then tested by deduction. The hypothesizing stage of the process (the context of discovery, or invention) is viewed as a question of psychology. The deductive stage of the process (the context of justification) is when predictions are made from the theory and compared to experience. This is the main subject of the philosophy of science. It is controversial whether the two contexts can be neatly separated in this way.

idealization: A model obtained from a theory using auxiliary assumptions that are known to be false, such as "there is no friction." Another example is the assumption that the mass of the universe is spread evenly in all directions in space originally used in 'big-bang' models of how the universe evolved.

induction, inductive reasoning: The process of deriving general principles from particular facts or instances.

induction, logical problem: See logical problem of induction.

induction, psychological problem: See psychological problem of induction.

induction, simple enumerative: See simple enumerative induction.

inductive logic: The view that the strength of an inductive argument is measured by the probability of the conditional on the premises. The probability may be inductive (logical) or epistemic (personal).

inductive strength: An argument is inductively strong if and only if it is improbable that its conclusion is false while its premises are true.

inductivism, na´ve: Na´ve inductivism attempts to solve the psychological problem of induction, the problem of how predictive expectations form. It says that our predictive expectations arise from the method of simple enumerative induction applied to observation statements, where the first step of collecting observation statements is prior to and independent of the subsequent inference.

inferior planets: Refers to planets moving faster in their orbits than earth; Mercury and Venus. Since, Copernicus, we know that the inferior planets are exactly those that are closer to the Sun from us.

invention, context of: Also, context of discovery. The context in which hypotheses are invented, or constructed. According to hypothetico-deductivism, the context of invention is quite separate and independent of the context of testing or justification.

joint probability: The probability that two or more specific outcomes will occur in an event.

justified, rationally: See rationally justified.

logically equivalent models: Also, equivalent models. Two models that make all the same assertions, including theoretical assertions.

logical problem of induction: Are we rationally justified in reasoning to general conclusions from repeated instances?

model: A theoretical statement, usually in the form of an equation, usually deduced from a theory with the aid a auxiliary assumptions.

modus tollens: Any pattern of deductive inference of the form: "If T then O. Not-O. Therefore, not-T." It is a deductively valid argument form.

necessary condition: E.g., being enrolled in this course is a necessary condition for you getting an A for the course. That is, you will not get an A if you are not registered. Or equivalently, if you do get an A, then you are registered. In general: A necessary condition for an event or state of affairs X is one that has to hold for X to be true. A necessary condition is contrasted with a sufficient condition. See also necessary and sufficient condition.

necessary and sufficient condition: A condition is necessary and sufficient for an event or state of affairs X if and only if it is necessary for X and sufficient for X. It is often expressed by the phrase ‘if and only if’ or the abbreviation ‘iff’. E.g., a necessary and sufficient condition for passing this course is to receive a passing grade while being registered for the course.

observed quantity: A quantity whose value is determined, at least approximately, by past observations alone, without the use of theoretical assumptions. E. g., the position of a planet against the fixed stars at a particular time.

opposition: a. The position of two celestial bodies when their longitude differs by 180░, especially a configuration in which the earth lies on a straight line between the sun and a superior planet or the moon. b. The position of the superior planet or the moon in this configuration.

paradigm: What Kuhn later termed the disciplinary matrix consisting of the background theory, or theories, methods, values, and exemplars used by a particular scientific community.

parameter: See adjustable parameters.

period of motion: The time it takes for one revolution around a circle.

phenonemon: A straightforward generalization of an observed regularity—usually accepted uncontroversially. For example: "Retrograde motion of a superior planet occurs when and only when the planet is in opposition to the Sun."

prediction: A statement deduced from a theory or a model stating the value, or approximate value, of an quantity, and which can be checked by observation. For example, Einstein's theory of gravitation predicted that the precession of the perihelion of Mercury is 574 seconds of arc per century, which is what is observed. Newton's theory predicted on 531 seconds of arc per century, a discrepancy of 43 seconds of arc per century. I note that this prediction was made with the aid of auxiliary assumptions; that is, via a simplified model. It was never proven that there is no Newtonian model that could make the correct prediction. Predictions need not always be of the future. For example, the assertion that there was a lunar eclipse of the sun in 350 B.C. counts as a prediction in our sense.

predictively equivalent models: Also, observationally equivalent models. Two models that, when combined with the same observed data, make the same predictions.

psychological problem of induction: Why do we have expectations about the future in which we have great confidence?

Popper, Sir Karl Raimund: (1902-1994) British philosopher of science known for his doctrine of falsificationism. His works include The Logic of Scientific Discovery (1931).

probabilism: The doctrine that probability is a sufficient basis for belief and action, since certainty in knowledge is unattainable. See also, Bayesianism.

probability, epistemic: Also called personal probability. Any probability of assignment that depends on the personal belief and knowledge of a particular person.

probability, inductive: Also called logical probability. The probability of the conclusion of an inductive argument conditional on the premises thought to be objective. In recent times, it is widely agreed that there is no such thing.

probability, conditional: See conditional probability.

probability, joint: See joint probability.

Ptolemy, Claudius: Second century A.D. Alexandrian astronomer, mathematician, and geographer who based his astronomy on the belief that all heavenly bodies revolve around the earth. His major work was the Almagest.

Quine-Duhem thesis: States that any seemingly disconfirming observational evidence can always be accommodated by any theory.

rationally justified: A form of inductive reasoning is rationally justified if it can be shown to be reliable. It is not enough that it is reliable. It must be shown to be reliable. Hume argued that there is no rationally justified form of inductive reasoning.

reliable: A rule, or form, of inductive reasoning is reliable if it yields approximately true conclusions most of the time.

retrograde: a. Of or relating to the orbital revolution or axial rotation of a planetary or other celestial body that moves clockwise from east to west, in the direction opposite to most celestial bodies. b. Of or relating to the brief, regularly occurring, apparently backward movement of a planetary body in its orbit as viewed against the fixed stars, caused by the differing orbital velocities of Earth and the body observed.

sound argument: An argument that is deductively valid and has all its premises true.

simple enumerative induction: A pattern of inference that begins with a list of observation statements of the form "this A is a B" and concludes that all A's are B's.

simplicity: Is usually considered to have many aspects. The simplicity of a model is usually taken to be the paucity of adjustable parameters, or fewness of adjustable parameters. It is not clear how one should define the simplicity of a theory.

specific: Limited in scope, area, and application. As in a specific statement that refers to a limited set of things, or particulars.

sufficient condition: E.g., getting an A in this course is a sufficient condition for passing this course. That is, it you get an A then you will pass. In general: a sufficient condition for an event or state of affairs X is one that enough to makes X true. A sufficient condition is contrasted with a necessary condition. See also, necessary and sufficient condition.

superior planet: Refers to planets moving slower in their orbits than earth; Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. Since Copernicus, we know that the superior planets are exactly those that are further from the Sun from us.

theory: A general set of laws and principles of broad scope, from which different models and idealizations are derived from various auxiliary assumptions.