Induction

In mathematics, ∈-induction is a variant of transfinite induction, which can be used in set theory to prove that all sets satisfy a given property P(x). The induction hypothesis is for every set x, if ∀y (y∈x → P(y)), then P(x), from which we can infer that P(x) holds for all sets x. The ...

Induction: Encyclopedia II - Inductance - Properties of inductance The above equation can be rearranged as follows: Taking the time derivative of both sides of the equation yields: In most physical cases, the inductance is constant with time and so By Faraday's Law of Induction we have: where is the Electromotive force (emf) and v is the induced voltage. Note that the emf is opposite to the induced voltage. Th ...

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Induction: Encyclopedia - Abscisic acid

Abscisic acid (ABA), also known as abscissin, is a plant hormone. Abscisic acid - Location Characteristics and Occasions for Synthesis Induction. Released during desiccation (of vegetative tissues) Has been found to peak at night Synthesized in green fruit and seeds at the beginning of the wintering period As well as moving within the leaf it can be transferred to the leaf from the roots by the transpiration stream Rapidly translocated Produc ...

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Induction: Encyclopedia - Cogency

An argument is cogent if and only if the truth of the argument's premises would render the truth of the conclusion probable (i.e., the argument is strong) and the premises are, in fact, true. Cogency can be considered inductive logic's analogue to deductive logic's "validity." As an example, consider the following. Without looking, Jill pulled out 100 marbles from a bag; 95 of the marbles Jill pulled out were red. Therefore, the next marble Jill ...

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Induction: Encyclopedia - CYP3A4

Cytochrome P450 3A4 (abbreviated CYP3A4) (EC 1.14.14.1), a member of the cytochrome P450 mixed-function oxidase system, is arguably the most important enzyme involved in the metabolism of xenobiotics in the body. CYP3A4 is involved in the oxidation of the largest range of substrates of all the CYPs. CYP3A4 is also, correspondingly, present in the largest quantity of all the CYPs in the liver. It should be noted that foetuses do not express CYP3A4 in their liver/tissues; but rather CYP3A7 which acts on a similar range of ...

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Induction: Encyclopedia - Binomial theorem

In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. Its simplest version reads whenever n is any non-negative integer, the numbers are the binomial coefficients, and n! denotes the factorial of n. This formula, and the triangular arrangement of the binomial coefficients, are often attributed to Blaise Pascal who described them in the 17th century. It was, however, known to Chinese mathematician Yang Hui in the 13th century. The Persian mathematicia ...

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Induction: Encyclopedia - Capacitance

Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. The capacitance is usually defined as the total electric charge placed on the object divided by the potential of the object: or, according to Gauss's law, the capacitance can be expressed as the electric flux per volt where C is the capacitance in farads Q is the charge in coulombs ...

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Induction: Encyclopedia - CW complex

In topology, a CW complex is a type of topological space introduced by J.H.C. Whitehead to meet the needs of homotopy theory. The idea was to have a class of spaces that was broader than simplicial complexes (we could say now, had better categorical properties); but still retained a combinatorial nature, so that computational considerations were not ignored. The name itself is unrevealing: C ...

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Induction: Encyclopedia - David Stove

David Charles Stove (1927–1994), was a conservative Australian philosopher of science, and essayist in the popular press. His contributions to the philosophy of science include detailed criticisms of David Hume's inductive skepticism, as well as the alleged irrationalism of his disciplinary contemporaries Karl Popper, Thomas Kuhn, Imre Lakatos, and Paul Feyerabend. He also marshalled a positive defense of inductivism in his 1986 work, The Rationality of Induction. Stove was also a staunch critic of sociobiology, going as far as describing the field as a new ...

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Induction: Encyclopedia - Andre Reed

Andre Reed (born January 29, 1964 in Allentown, Pennsylvania) is a former professional American football player who played wide receiver in the NFL for 16 seasons, 15 with the Buffalo Bills (1985-1999) and one with the Washington Redskins (2000). He is widely considered one of the best wide receivers to ever play the game. Andre Reed - NFL records. Reed ranks highly in many career NFL receiving categories. He is fourth in receptions with 951 (behind only Jerry Rice, Cris Carter and Tim Brown), sixth in rece ...

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Induction: Encyclopedia - Analogy

Analogy is either the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), or a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from a particular to another particular, as opposed to deduction, induction and abduction, where at least one of the premises or the conclusion is general. The word analogy can also refer to the relation between the source and the target themselves, which is often, though not necessarily, a simil ...

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Analogy - Models and theories of analogy

Analogy - Applications and types of analogy

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Induction: Encyclopedia - Inference

Inference is the act or process of drawing a conclusion based solely on what one already knows. Suppose you see rain on your window - you can infer from that, quite trivially, that the sky is grey. Looking out the window would have yielded the same fact, but through a process of perception, not inference (note however that perception itself can be viewed as an inferential process). Inference is studied within several different fields. Human inference (i.e. how humans draw conclusions) is traditionally studied within the field o ...

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Inference - An example: the classic syllogism

Inference - Automatic logical inference

Inference - An example: inference using Prolog

Inference - Inference and uncertainty

Induction: Spiritual - Theosophy Dictionary on Inductive Method, Induction

Inductive Method, Induction In logic, the process of reasoning from the parts to the whole, from the particular to the general, or from the individual to the universal; contrasted with the deductive method, which reasons from the whole to the parts, from the general to the particular from the universal to the individual.

It is associated with Aristotle as contrasted with Plato, also with Francis Bacon and modern science in general. Science endeavors to establish general laws by reasoning from particular observations; but it is necessary to assume that what is true in an individual case will be true in the general case of which it is only an instance. The hypotheses thus framed are necessarily and naturally regarded as provisional, subject to modification in the light of subsequent, more extended observations of nature.

This method endeavors to come to an understanding of nature by a continued process of trial and error, the formulation of its laws becoming ever wider. But an essential part of this method itself is deductive, since we continually reason back from the provisional hypotheses we have laid down to the new facts which we seek to discover in support or in refutation of them. For this reason, the method of science has often been called a deductive-inductive method. Indeed, pure induction is probably inconceivable, since we cannot enter upon a mental process unless we first entertain some general ideas. Induction and deduction are interdependent functions of the ratiocinative mind.

Further, the data of scientific induction are sensory percepts; and no amount of such data will enable us to ascertain the truth about the causal worlds which underlie phenomena. If we admit, with Plato, the existence of intuition or direct perception of essential truths, or if we accept his doctrine of the existence of soul memories latent in the mind, we have a resource which will free us from complete reliance on this synthetic method of reaching general truths.

See also BACONIAN METHODS

Induction: Encyclopedia II - Inductance - Usage

The flux through the ith circuit in a set is given by: so that the induced emf, , of a specific circuit, i, in any given set can be given directly by: ...

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