Kıyas Şekillerinin Geometrik Yöntemle İrcâ‘ı
Reduction of Syllogism Figures by Geometric Method

Summary/Abstract: This study suggests a method for establishing a correct syllogism which regulates principles of logic and for reduction of syllogisms to first figure. This geometric method depends on the correspondence of four figures of syllogism with four straight triangles formed by a second square drawn in a main square. The middle term is on the right angled corners of the triangles. The minor term and the minor premise of syllogism are on the vertical edge, the major term and the major premise are on the horizontal edge. The conclusion has drawn diagonally from the minor term to the major term. In this method, the syllogism can be shown quickly. In addition, the reduction of syllogisms can be done easily and accurately without requiring any knowledge other than knowing the general rules of syllogism and the two specific rules of first figure and geometrical appearance of this figure’s four valid modes. Summary: There is a distinct importance for syllogism among the types of reasoning in terms of logic which it is main goal is protect the mind from falling into the wrong during thinking. The type of syllogism that most emphasized by logicians is categorical syllogism and when mentioned the term of syllogism usually meant this. A valid categorical syllogism contains three categorical propositions. Two of them premises and one conclusion. The middle term must be distributed in at least one of the premises but cannot be distributed in conclusion.In comparison with this the categorical syllogism was expressed in four figures. These figures are; the first figure which the middle term becomes attribute in minor premise and subject in major term, the second figure which the middle term becomes attribute in both premises, the third figure which the middle term becomes subject in both premises and finally the fourth figure which the middle term becomes subject in minor premise and attribute in major term. According to quantity and quality of premises and conclusion, every figures involve another sub-figures named mods. When considered this rules there is nineteen valid syllogism mods among the sixty-four total mods. Four of this mods for first figure; four ones for second figure, six ones for third figure and five ones for fourth figure.The first figure has been regarded as the perfect figure because it is the closest match to the human mind and nature. For the control of validity, the other figures have done by reduction. The process of reduction is a method used not only to show validity of a valid syllogism but also to show the invalidity of incorrect ones. Generally accepted three ways for reduction. Converting of premises, transposing of premises and indirect reduction that also called reduction per impossible. In order to do the process of reduction, it is necessary to know the name of each mode, the meaning of the mnemonic letters on it that show how the reduction process is done. This is the case when the valid syllogism mods are reduced. However, there is neither a name and nor mnemonic letters for invalid syllogisms as like as valid ones. For this reason, although there are some methods, but no certain method guided by mnemonic letters for reduction of invalid syllogism to first figure some methods.The geometric reduction method that proposed in this article removes this difficulty and makes possible to reduction of invalid syllogisms as easily as valid ones. Geometrical representation of syllogisms is a very effective and easy method for identify the terms and premise in syllogism, understanding of invalidity in a syllogism which resulted from lacking attention to general and specific rules of syllogism. In addition, by this method the process of reduction can be done easily a correctly for demonstration of syllogism’s validity. Although there have been previous studies on the syllogism figures by venn diagrams, these are mostly confined to a geometric representation of the reasoning in syllogism. The method suggested in this article is new method offering far more opportunities than a mere demonstration for checking the syllogisms and reduction of them to first figure.This geometric method depends on the correspondence of four figures of syllogism with four straight triangles formed by a second square drawn in a main square. The middle term is on the right angled corners of the triangles. The minor term and the minor premise of syllogism are on the vertical edge, the major term and the major premise are on the horizontal edge. The conclusion has drawn diagonally from the minor term to the major term. On arrows indicating propositions, there are one notch for positive, two for universal negative, and three notches for particular negative propositions. When reduced the syllogism valid or invalid to first figure’s geometrical shape, if there is an event of a contradictory for the specific and general rules of syllogism, this can be shown automatically. For example, if the three notched arrow of geometric shape when converted, this means converting of particular-negative which cannot be done and thus can be shown invalidity of syllogism. In this method, the syllogism can be shown quickly and reduction of syllogisms can be done easily and accurately without requiring any knowledge other than knowing the general rules of syllogism and the geometrical appearance of the first figure’s four valid modes. The syllogisms in other three figures when drawn according to the first figure’s geometric shape the conversions and transpositions has done spontaneously.

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