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

(See also: Inductive Method, Induction, Mysticism, Mysticism Dictionary, Occultism, Occultism Dictionary)

See also:

History of the scientific method, History of the scientific method - Early empiricism and philosophy, History of the scientific method - The emergence of an inductive method, History of the scientific method - A schematic scientific method, History of the scientific method - Method called to question, History of the scientific method - Current issues

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These attempts to systematize a scientific method were faced with the problem of induction, which argues that inductive reasoning, in the context of scientific research, is not justified. David Hume set the difficulty out in detail. Briefly stated, he argued that there is no logical necessity that the future should resemble the past, thus we are unable to justify inductive reasoning itself by appealing to its past success. Karl Popper, following others, argued that a hypothesis must be falsifiable and that science would best progress using a deductive ...

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History of the scientific method, History of the scientific method - Early empiricism and philosophy, History of the scientific method - The emergence of an inductive method, History of the scientific method - A schematic scientific method, History of the scientific method - Method called to question, History of the scientific method - Current issues

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The Baconian method is the investigative method developed by Francis Bacon. It is an early forerunner of the scientific method. The method was put forward in Bacon's book Novum Organum, which means New Organ, and was supposed to replace the methods put forward in Aristotle's Organum. Baconian method - Baconian Method. The Baconian method consists of procedures for isolating the cause of a phenomenon, including the method of agreement, method of difference, and method of concomitant variation. ...

Including:

• Baconian method - Baconian Method
• Baconian method - Idols of The Mind
• Baconian method - Followers

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There are several meanings for the word deduction: Natural deduction Deductive reasoning Deductions in terms of taxation, such as Itemized deductions Standard deduction See also: Logic Venn diagram Inductive reasoning Both statistics and the scientific method rely on both induction and deduction. Other related archivesDeductive reasoning, Inductive reasoning, Itemiz

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A System of Logic is an 1843 book by English philosopher John Stuart Mill. In this work, he formulated the five principles of inductive reasoning that are known as Mill's methods. A System of Logic - External link. Excerpts from A System of Logic ...

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• A System of Logic - External link

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Victor Cousin (November 28, 1792 - January 13, 1867) was a French philosopher. Victor Cousin - Observational Method. The observational method applied to consciousness gives us the science of psychology. This is the basis and the only proper basis of ontology or metaphysics--the science of being--and of the philosophy of history. To the observation of consciousness Cousin adds induction as the complement of his method, by which he means inference as to reality necessitated by the data of consciousness, and r ...

Including:

• Victor Cousin - Observational Method
• Victor Cousin - Three Results of psychological observation
• Victor Cousin - Doctrine of the Reason
• Victor Cousin - Comparison to Kant Schelling and Hegel
• Victor Cousin - The absolute or infinite
• Victor Cousin - The self

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Confirmation bias is a type of statistical bias describing the tendency to search for or interpret information in a way that confirms one's preconceptions. In inductive inference, confirmation bias is a type of cognitive bias toward confirmation of the hypothesis under study. To compensate for this observed human tendency, the scientific method is constructed so that we must try to disprove our hypotheses. See falsifiability. Confirmation bias is a phenomenon wherein decision makers have been shown to actively seek out a ...

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Baconian Methods The Baconian method corresponds roughly to what is known in logic as the inductive method of reasoning, of which Francis Bacon (1561-1626) was a great advocate, as contrasted with the deductive method.

Considered to be the method of modern science, it consists in inferring general laws from the observation of particular instances; whereas in the deductive method, general laws are assumed because of the natural harmony of the universe, and particular instances or consequences are deduced as flowing forth from them.

In the Baconian method particular phenomena are examined with the view of finding out what is essential and excluding what is nonessential, and thus establishing a general law; but the weakness of this method is that the number of particular phenomena or details to be examined in order to arrive at truth must be virtually coextensive with infinity; for in any instance a body of particular phenomena may be encountered which demands immediate readjustment or radical shiftings in opinions in process of crystallization. Actually the scientific method is a combination of both methods: we cannot interpret phenomena without having at the outset some principle in mind; moreover, no sooner have we established a general law than we begin to apply it for the discovery of other phenomena, thus using the deductive method.

A more important objection to the inductive method as used by modern science is that it limits the basis of reasoning to the relative paucity of data furnished by our physical senses, which data we must first learn to understand beyond doubt; otherwise our reasoning is vicious. Blavatsky states that the secrets of invisible nature cannot be thus inferred, but that we must call in the aid of higher senses in order to obtain the necessary foundation for reasoning and to insure the adequate understanding of discoverable data.

See also INDUCTIVE METHOD

(See also: Baconian Methods, Mysticism, Mysticism Dictionary, Occultism, Occultism Dictionary)

In 1619, René Descartes began writing his first major treatise on proper scientific and philosophical thinking, the unfinished Rules for the Direction of the Mind. With this document, Descartes established the framework for a scientific method's guiding principles. The following quote from his 1637 treatise, Discourse on Method presents the four precepts that characterize a scientific method: "The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to a ...

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History of the scientific method, History of the scientific method - Early empiricism and philosophy, History of the scientific method - The emergence of an inductive method, History of the scientific method - A schematic scientific method, History of the scientific method - Method called to question, History of the scientific method - Current issues

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The Edwin Smith Papyrus (circa 1600 BC), an ancient surgical textbook, details the examination, diagnosis, treatment, and prognosis of numerous ailments. [1] Although the Ebers papyrus (ca 1550 BC) contains incantations and foul applications created to cast out diseased demons and other superstition, there is evidence of traditional empiricism. In Ancient Greece, towards the middle of the 5th century BC, some of the elements of a scientific tradition were already well established. In Protagoras (318d-f), Plato mentio ...

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History of the scientific method, History of the scientific method - Early empiricism and philosophy, History of the scientific method - The emergence of an inductive method, History of the scientific method - A schematic scientific method, History of the scientific method - Method called to question, History of the scientific method - Current issues

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Polyomino - Inductive exhaustive search. The most obvious method of enumerating the polyominoes, and also one of the slowest, is inductive exhaustive search. Given a list of polyominoes of area n, take each polyomino in turn, embed it in an n×n square, surround that square with a collar of cells to create an (n+2)×(n+2) square. For each vacant cell in that square that is adjacent to at least one occupied cell, fill the cell and strike out a bounding row of vacant cells and a bounding ...

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Polyomino, Polyomino - Free one-sided and fixed polyominoes, Polyomino - Number of polyominoes, Polyomino - Algorithms for enumeration of fixed polyominoes, Polyomino - Inductive exhaustive search, Polyomino - Growth method, Polyomino - Conway's method and Jensen's method, Polyomino - Asymptotic growth of the number of polyominoes, Polyomino - Fixed polyominoes, Polyomino - Free polyominoes, Polyomino - Special classes of polyominoes, Polyomino - Uses of polyominos, Polyomino - Etymology

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There are three common ways of defining distinct polyominoes: free polyominoes must be different under translation, rotation, and reflection one-sided polyominoes must be different under translation and rotation within in the plane fixed polyominoes must be different only under translation. The dihedral group D4 is the group of symmetries (symmetry group) of a square. This group contains four rotations and four reflections. It is ...

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Polyomino, Polyomino - Free one-sided and fixed polyominoes, Polyomino - Number of polyominoes, Polyomino - Algorithms for enumeration of fixed polyominoes, Polyomino - Inductive exhaustive search, Polyomino - Growth method, Polyomino - Conway's method and Jensen's method, Polyomino - Asymptotic growth of the number of polyominoes, Polyomino - Fixed polyominoes, Polyomino - Free polyominoes, Polyomino - Special classes of polyominoes, Polyomino - Uses of polyominos, Polyomino - Etymology

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Polyomino - Fixed polyominoes. Theoretical arguments and numerical calculations support the estimate where λ = 4.0626 and c = 0.3024. However, it should be emphasized that this result is not proven and the values of λ and c are only estimates. The known theoretical results are not nearl ...

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Polyomino, Polyomino - Free one-sided and fixed polyominoes, Polyomino - Number of polyominoes, Polyomino - Algorithms for enumeration of fixed polyominoes, Polyomino - Inductive exhaustive search, Polyomino - Growth method, Polyomino - Conway's method and Jensen's method, Polyomino - Asymptotic growth of the number of polyominoes, Polyomino - Fixed polyominoes, Polyomino - Free polyominoes, Polyomino - Special classes of polyominoes, Polyomino - Uses of polyominos, Polyomino - Etymology

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We call n the number of squares, and An the number of fixed polyominoes with n squares (possibly with holes). An enumeration gives the following table: The number of free polyominoes without holes is given by A000104; the number of one-sided polyominoes is given by A000988. As of 2004, Iwan Jensen has enumerated the fixed polyominoes up to n=56: A56 is approximately 6.915×1031. Free polyominoes have been enumerated up to n=28. See the exte ...

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Polyomino, Polyomino - Free one-sided and fixed polyominoes, Polyomino - Number of polyominoes, Polyomino - Algorithms for enumeration of fixed polyominoes, Polyomino - Inductive exhaustive search, Polyomino - Growth method, Polyomino - Conway's method and Jensen's method, Polyomino - Asymptotic growth of the number of polyominoes, Polyomino - Fixed polyominoes, Polyomino - Free polyominoes, Polyomino - Special classes of polyominoes, Polyomino - Uses of polyominos, Polyomino - Etymology

Read more here: » Polyomino: Encyclopedia II - Polyomino - Number of polyominoes

Baconian Methods The Baconian method corresponds roughly to what is known in logic as the inductive method of reasoning, of which Francis Bacon (1561-1626) was a great advocate, as contrasted with the deductive method.

Considered to be the method of modern science, it consists in inferring general laws from the observation of particular instances; whereas in the deductive method, general laws are assumed because of the natural harmony of the universe, and particular instances or consequences are deduced as flowing forth from them.

In the Baconian method particular phenomena are examined with the view of finding out what is essential and excluding what is nonessential, and thus establishing a general law; but the weakness of this method is that the number of particular phenomena or details to be examined in order to arrive at truth must be virtually coextensive with infinity; for in any instance a body of particular phenomena may be encountered which demands immediate readjustment or radical shiftings in opinions in process of crystallization. Actually the scientific method is a combination of both methods: we cannot interpret phenomena without having at the outset some principle in mind; moreover, no sooner have we established a general law than we begin to apply it for the discovery of other phenomena, thus using the deductive method.

A more important objection to the inductive method as used by modern science is that it limits the basis of reasoning to the relative paucity of data furnished by our physical senses, which data we must first learn to understand beyond doubt; otherwise our reasoning is vicious. Blavatsky states that the secrets of invisible nature cannot be thus inferred, but that we must call in the aid of higher senses in order to obtain the necessary foundation for reasoning and to insure the adequate understanding of discoverable data.

See also INDUCTIVE METHOD

(See also: Baconian Methods, Mysticism, Mysticism Dictionary, Occultism, Occultism Dictionary)

Exact formulas are known for enumerating polyominoes of special classes, such as the class of convex polyominoes and the class of directed polyominoes. The definition of a convex polyomino is different from the usual definition of convexity. A polyomino is said to be column convex if its intersection with any vertical line is convex (in other words, each column has no holes). Similarly, a polyomino is said to be row convex if its intersection with any horizontal line is convex. A polyomino ...

See also:

Polyomino, Polyomino - Free one-sided and fixed polyominoes, Polyomino - Number of polyominoes, Polyomino - Algorithms for enumeration of fixed polyominoes, Polyomino - Inductive exhaustive search, Polyomino - Growth method, Polyomino - Conway's method and Jensen's method, Polyomino - Asymptotic growth of the number of polyominoes, Polyomino - Fixed polyominoes, Polyomino - Free polyominoes, Polyomino - Special classes of polyominoes, Polyomino - Uses of polyominos, Polyomino - Etymology

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The Baconian method consists of procedures for isolating the cause of a phenomenon, including the method of agreement, method of difference, and method of concomitant variation. Bacon suggests that you draw up a list of all things in which the phenomenon you are trying to explain occurs, as well as a list of things in which it does not occur. Then you rank your lists according to the degree in which the phenomenon occurs in each one. Then you should be able to deduce what factors match the occurrence of the phenomenon in one list and ...

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Baconian method, Baconian method - Baconian Method, Baconian method - Idols of The Mind, Baconian method - Followers

Read more here: » Baconian method: Encyclopedia II - Baconian method - Baconian Method

Transfinite recursion is a notion closely related to transfinite induction, but whereas the latter is a method of proof, the former is a method of definition or construction. In the simple form, indexed by ordinals, one defines a sequence of sets--say, Aα for every ordinal α, or perhaps every α less than some bound γ--by specifying three things: What A0 is How to determine Aα+1 from Aα (or possibly from the entire s ...

See also:

Transfinite induction, Transfinite induction - Transfinite recursion, Transfinite induction - Relationship to AC

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Prolog was an early programming language that was billed by its designers as being based on mathematical logic. The basis for the claim that Prolog was that it used backward chaining from goal to subgoal (as in Planner). Schematically, the process is: goal :- subgoal1, ..., subgoaln. which states that in order to prove goal, it is sufficient to prove subgoal1See also:

Logic programming, Logic programming - Basis in mathematical logic, Logic programming - Prolog, Logic programming - Limitations of Prolog as logic programming, Logic programming - Inductive logic, Logic programming - Application domains, Logic programming - History

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