Reasoning

The Raison nement is a cognitive process which makes it possible to obtain new results or to check a fact by calling upon different " lois" or Experiment S, it does not matter their scope of application: mathematical, legal system, Physical and Chemical (Experimental method), Pedagogy, etc

Objectives of the reasoning

One leads reasoning for objective S different, which can combine:

It is said that the individual carries out Inférence S and that the mechanism of development of these inférences is called reasoning.

The various reasoning

A reasoning being based more on rules formulated in mathematical language will be known as rather Rationaliste. This form of reasoning is dominating in France.

A reasoning being based more on lived experiments will be known as rather Empirique. This form of reasoning, which does not exclude the rigor, including in the Experimental method, is dominating in England.

Descartes affirmed: “There are not other ways which are offered to the men, to arrive at an unquestionable knowledge of the truth, which obvious intuition and the deduction necessary”. He admitted the importance of the intuition, which was confirmed by Spinoza and Bergson. However, all Intuition is not inevitably obvious as long as it is not divided.

The general Logique is based on the tradition of the Syllogisme S (see Logique).

In a Logical mathematics (logical of the proposals, logic of predicates, modal logic, etc), one agrees to consider three means of construction of reasoning:

  • the Deduction: Deductive reasoning
  • the Abduction: Reasoning by abduction
  • the induction: Reasoning by induction

They are presented schematically thus, while being based on the traditional notations of logic (→ for the implication): The rule of deduction is read as follows:

  • if has is true
  • and if if has is true then B is also is true
  • then B is true.

The rule of abduction is read as follows:

  • if B is true
  • and if if has is true then B is also is true
  • then has is true.

The process of construction of a simple reasoning consists in applying at least one of these three rules to an initial theory; it is thus a means of adding new proposals to it.

A reasoning is known as deductive if it is based only on the rule of deduction; it is known as hypothetical if it rests on at least one of the rules of abduction or induction.

Only the deduction preserves the coherence of a theory: if the initial theory is coherent, then any theory which is a deductive consequence remains coherent.

A deductive N-consequence D of an initial theory I is a theory obtained after application of a number unspecified but finished deductions on I.

The deductive fence D of an initial theory I is its deductive N-consequence, N being infinite.

A theory is known as maximalement coherent (or coherent within the meaning of Hilbert) if its deductive fence does not contain the proposal false .

In the majority of the systems of the calculation of the proposals, one finds the rules following

The modus tollens is regarded in general as a derived rule. The natural Déduction adds to it rules of introduction and elimination. The Calcul of the séquents considers only rules of introduction and in more the rule of cut.

Quotations

“ All our reasoning is reduced to yield to the feeling. But the imagination is similar and contrary with the Sentiment; so that one cannot distinguish between these opposites. One says that my feeling is imagination, the other that its imagination is feeling. It would be necessary to have a rule. The Raison is offered but it is pliable with all directions. And thus there is not. ” Blaise Pascal.

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