The development of logic is connected with the constant advancing of the process of world cognition. Therefore, it is necessary to stress that logic is a part of every contemporary science. Logic is a crucial attribute of semantics, mathematics, psychology, and other bodies of knowledge, which emerged in the 5th century BC. The evolution of logic is shaped by the three major approaches to explaining the causal relations between matters and substances: Chinese, Indian, and Greek cognitions. Beyond doubt, these domains intersected in certain areas and, thus, modern logic is based on all three approaches. Aristotle devised European (Greek) system of world cognition, from which the profound knowledge about logic can be retrieved. In addition, the Islamic philosophers, such as Avicenna, contributed to the European postulates of logic. This paper investigates the history of logic from Aristotelian teachings to the Arabic, Chinese, Indian doctrines and defines principles underlying current approaches to the perception of the world.
Irrespective of Aristotle’s invaluable contribution to the formation of logic, the philosopher’s interest in the causal relations originates from Plato’s views. Apart from being Aristotle’s teacher, Plato is known for his dialectic approach to world cognition, which suggested the implementation of the deductive reasoning. Aristotle employed his teacher’s methods and continued working with the deductive reasoning. In particular, he was the first to conclude that to create a chain of reasoning, it is necessary to connect subjects and predicates. This assertion declares that every argument consists of certain subjects, predicates, and conclusion (s) derived from a developed rationale.
The fruitful work of Plato and Aristotle presents three possible fallacies: false subjects, erroneous predicates, or irrational conclusions. Aristotle was the first to propose not only the system of reasoning but also the anticipated fallacies. Apart from argument-related fallacies, the philosopher also detected the irrational persuasive strategies such as “as argumentum ad hominem (appeal to a person) and argumentum ad populum (appeal to the crowd). For instance, argumentum ad hominem implies that if a person is wrong about something, the idea(s) he or she advocates is altogether erroneous. To explain the fallacy of this premise, Aristotle applies a negative categorical proposition: “Some ? is not an ?.” In other words, even if a person is wrong about something, or something is considered to be wrong with the person, it does not necessarily mean that the claim of this individual is false.
The fallacy of reasoning may also occur when the subjects are wrong or not reliable. Specifically, all matters are considered to belong to three planes of existence: possible, impossible, and necessary. In case the notions of possible existence are taken for granted (as the matters of the necessary existence), the conclusions may be erroneous.
The Islamic philosopher Avicenna developed a similar system of possible, impossible, and necessary existence. In the Medieval times, the development of logic relocated from Europe to the Arabic world where the local thinkers shaped, corrected, and completed the works of Aristotle and his followers. For instance, Avicenna believed that the matters of the necessary existence existed for their own sake and the sake of other matters. In this regard, the matters that exist cannot be impossible, and the matters that are impossible cannot be possible because if they could have been possible, they would have existed in the plane of necessary existence. A Persian philosopher Algazel utilized Avicenna’s “theory of definition and classification” along with other philosophic insights in theology. The Arabic philosophers believed that only God existed for His own sake. Another Islamic philosopher Averroes applied the discussed classification to other spheres of human life. Consequently, the above-described determinism was successfully deployed in theology and sciences.
The developed insights came back to Europe later and were implemented in the process of world cognition. For example, the scepticism of Descartes states that to define the true matters from the false ones, people should detect what remains unchanged in both realities: human life and dreams. This rationale is rather important for the development of the exact sciences since only the subjects of these sciences (arithmetic, geometry, etc.) remain unchanged regardless the activity. Starting with the 17th century, the evolution of logic in Europe resulted in the expression of the causal relations with the help of symbols as it was done in Egypt and China. Given that mathematics heavily relies on the principles of logic, the European scholars worked at developing the relations and appropriate symbols that later would be used in equations.
Having scrutinized the role of logic in the modern mathematics, it is possible to track the development of this science starting with Aristotelian logic. For instance, the scholars Bertrand Russell and Alfred North Whitehead decided to simplify mathematics to logic a century ago, which was revealed in their work, Principia Mathematica. Therefore, Aristotelian teachings about subjects and predicates are manifested in all mathematic premises. For instance, there is an axiom of extensionality, which states that “if two sets have the same members, they are identical. The subjects and predicates in this example are easily identifiable, which affirms the incorporation of Aristotle’s approach.
The European and Islamic philosophers asserted that mathematic axioms are the subjects of the necessary existence. Consequently, the use of axioms for proving theorems implies that the subjects of the constructed rationale are free from fallacy. Due to the fact that modern mathematics is based on the principles of logic, most relations of the mathematic subjects can be simplified and explained with the help of the logical insights that were evolving since the times of Aristotle.
The research of the history of logic regarding the Chinese traditions indicates that Chinese philosophy is not aimed at establishing the causal links between the matters. Instead, the Chinese philosophers developed a semantic theory to explain the function of matters. Consequently, the distinction approach towards world cognition differs from building the relations between the matters, which is typical for the European school of logic. It is necessary to mention that Chinese philosophy predefines disputes and, respectfully, the need for persuasion by the diverse ways of distinctions. Moreover, it is believed that there is only one true semantic approach and, thus, there are always the wrong and right sides in every dispute. These Chinese ‘dialecticians’ share Plato’s dialectics who claimed that there is always one truth, and it can be revealed through disputes and scrutiny.
The Indian tradition of logic resembled the Chinese distinction school. Indian philosophy transformed into Buddhism teachings, which stipulate that the main approach to world cognition lies in the differentiation of the matters in accordance with the properties they possess. The corresponding doctrine known as apoha presumes inclusion and exclusion of defining properties. This statement demonstrates the substantial level of the similarity between Indian and Chinese philosophy of logic. Simultaneously, the arguments based on the properties of subjects are constructed in resemblance to Aristotelian logic, particularly in developing arguments that apply to affirmations and denials. These similarities and diversities in the approaches to world cognition originate from the complex relations between people’s rational and irrational (emotional, cultural) sides. Estimating the connection between logic and psychology, it should be emphasized that logic is a subset of psychology. Due to the well-known assertion that “a man is a rational animal,” it is possible to presume that a human being remains rational even after having been raised outside the society. In this case, the applied system of logic is probably the same, for instance, some a is b, or some a is not b. However, the choice of predicates and conclusions might differ depending on an individual’s background and experience. Apart from logic, human’s psyche comprises various emotions, attitudes, psychological states that shape the rationale processes. The existence without rationale is possible regardless the fact that the process of world cognition is impossible without establishing causal relations between the observed or abstracted matters. Consequently, unlike mathematics, psychology cannot be simplified to logic in a proper manner.
In conclusion, the analysis of the history of logic indicates that modern European school of logic originates from the Aristotelian logic. Moreover, the views of Aristotle were developed under the influence of the philosophic insights dating back to the 5th century BC. Apart from Greek philosophy, the history of logic was affected and shaped by the Arabic, Chinese, and Indian approaches to world cognition. In the modern world, logic can be observed in all sciences, but above all, the rationale thinking can be observed in the exact sciences. In particular, theorems and hypotheses consist of subjects and predicates that are framed with a conclusion. The properties of subjects are derived from the doctrine about the possible, impossible, and necessary existence. According to Indian and Chinese logic, the credibility of subjects is defined by detecting and assessing their properties, which is a recognized approach in modern mathematics. Due to the fact that logic is a subset of human’s psyche, this science is being shaped by the prime essays and other aspects of people’s mentality. For this reason, there are different approaches to world cognition and, respectfully, different traditions of logic such as the Greek, Arabic, Indian, and Chinese.