As we all known, with the founding of Euclidean geometry in ancient Greece, with the development of analytic geometry and other kinds of geometries, with F.Kline" s Erlanger program in 1872 and the new developments of geometry in 20th century such as topology and so on, man has developed their understand of geometry. On the other hand, Euclid formed geometry as a deductive system by using axiomatic theory for the first time. The content and method of geometry have dramatically changed, but the geometry curriculum has not changed correspondingly until the first strike from Kline and Perry" s appealing.

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These are (1) denying the relationship between sense and existence,(2) doing not accord with the law of causality,(3) imaging the universe using deductive method of mathematics,(4) propagating the super distance effect which do not need time,(5) using wrong philosophy and physics concepts,(6) studying the origin of the universe,(7) departing from axiomatic system,(8) denying the definitions of basic physical quantities.

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The chapter 5, The Deductive Axiomatics of Theory of Evolution andSelf-organization Theory, proposes that the description which transfer thefunctional statements about phenomena of life into causal statements eventuallyinvolves theories about evolution.

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The economics methodology has formed a whole battery of analytical framework and tool under the influence of scientific philosophy, which is characterized by logic positivism, negativism and historical materialism. The fundamental characteristics of the economics methodology are based on the axiomatization positive logic deductive method, which assumes the rational human being as its hypothetic premise. The most remarkable characteristic of the economics methodology is the general application of mathematics in economics and it is developing forward to the more accurate and magnificent system.

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Stark and Bainbridge, then, follow the form of theorizing that, according to Ernest Nagel (1961) and certain other philosophers, consitutes the deductive mode of science.

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Legal syllogism is the basic model which is used by the accuser, the defender and the trier in criminal trial. What is its logical foundation? There are mainly three kinds of viewpoints up to now. According to traditional theory, it is categorical syllogism and deductivists think it is whole deductive logic, while anti-deductivists deny that logic plays an important role in a trial.

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Legal syllogism is the basic model which is used by the accuser,the defender and the judge in criminal trial.What is its logical foundation? There are mainly three kinds of viewpoints up to now.According to traditional theory,it is categorical syllogism,and deductivists think it is whole deductive logic,while anti-deductivists deny that logic plays an important role in a trial.

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In the area of adjudication, by contrast to the experience approach of the parties and others, the cognitional approach of the fact-finder is deductive cognition.

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In this paper a combinational theory of compilers is described and a formal deductive system is given.

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