LECTURE No. 2. Logic. The main stages in the development of science

The history of logic is long. As mentioned above, at all times man has strived for the truth, however, certain conditions were necessary for the emergence of the doctrine of the correctness of thinking. Here is the general mental development of a person, and the peculiarities of culture. And, of course, the presence of a spoken language is necessary. All the necessary factors were combined more than two thousand years ago in India, China, Greece. Initially, logic was born and developed as part of philosophy. Word "philosophy" comes from two Greek words "philo" and "sophos", "love" and "science" respectively. Thus, "philosophy" literally means "love of science". Philosophy is a science that combines all human knowledge about the world around us, the features of human consciousness and the laws of being.

In general, the process of development of logic can be divided into several stages: the logic of the Ancient World, ancient logic, the logic of the Middle Ages, the logic of the Renaissance, the New Age, and, finally, modern logic. Let's pass to consideration of each stage which is passed by logic in the development.

1. The logic of the ancient world

The logic of the ancient world owes its appearance to the philosophers of China, India and Greece. It is known that in the early stages of development, logical knowledge was of an ontological nature, i.e., the laws of thinking were equated with the laws of being. Much attention during this period was paid to inference, and the latter was practically identified with proof.

Rhetoric gave impetus to the development of logic. Oratory used the rudiments of logical knowledge to achieve the main goal of the speaker - to convince the listeners, and not to establish the truth, as is the case in later periods. The logical element here is subordinate in nature, it is, as it were, an integral part of oratory.

Philosophy as a body of scientific knowledge originated and developed simultaneously in ancient states that had different views on the world around them, with different approaches to its study and with a different body of accumulated knowledge. Therefore, the philosophical knowledge of the Ancient World can be divided into two depending on the state in which it originated. One of these movements arose in Ancient Greece, the other was fundamentally an Eastern approach to science, characteristic of philosophers in India and China. Modified under the influence of time, the Greek direction of philosophy is now represented in Russia, Western Europe and America, where it came through the Roman Empire and Byzantium along with the belief in one God. The Indo-Chinese direction of philosophy was adopted in Mongolia, Japan, Korea, Indonesia and other countries [1].

It is necessary to consider in more detail the logic of the ancient states.

2. Ancient India and Ancient China

Ancient india. Ancient India is a very original country. It is known for great thinkers and numerous philosophical movements. Ancient Indian philosophy to this day is considered a meaningful and well-developed system that accurately reflects many features of the surrounding world. The logical knowledge accumulated by ancient Indian scientists also has a fairly clear structure and, what is especially important, contains logical concepts, approaches and methods that became known in the system of Western logic only several centuries later.

Philosophical ideas in ancient India were developed by representatives of 16 schools, the main of which were the Charvaka, Lokayata (founded by Brihaspati and his student Charvaka), Vaisheshika (the founder of Canada), Nyaya (Gautama) and Jainism (Vardhamana Mahavira) schools. These schools belonged to the materialistic direction of philosophy, i.e., their representatives believed that the material world exists objectively, and matter is primary in relation to consciousness and exists forever. They were opposed by representatives of philosophical schools preaching an idealistic approach to the study of the world. They considered the spiritual principle, consciousness and thinking to be primary, and pushed the material world into the background. Yoga and Buddhism, as well as Mimamsa and Vedanta, adhered to such ideas.

It is necessary to mention the school that adheres to an intermediate position, i.e., assigns equal positions to the material and spiritual (ideal) principles. In connection with such a variety of philosophical approaches, disputes between representatives of different philosophical schools were of considerable, or rather, even decisive importance in the development of the logic of ancient India.

Today, the Vedas are considered the main and oldest literary monument of ancient Indian philosophy. It is a collection of philosophical ideas and thoughts. However, the Vedas are of a general nature, which led to the creation of the Upanishads by the Brahmins, which interpret and interpret the provisions contained in the Vedas. Logical knowledge, on the other hand, did not have a systematic consolidation for a long time, but was written down in the form of brief aphorisms and systematized only in the XNUMXth century. BC e., starting from Dinang.

The development of the logic of ancient India has about two millennia, and partly because it has not yet been fully studied. This is also seen in the works devoted to the logic and philosophy of Ancient India. Despite the considerable number of such publications, they do not contain a unified approach to the issue under consideration. However, this does not prevent the recognition of the fact that ancient Indian logic has an original character and features that distinguish it from the logic of ancient Greece. So, the syllogism here is divided not into ten, but into five members (thesis, basis, example, application, conclusion); deduction and induction are considered inseparable; mental and verbal speech are distinguished; the basis of perception is the acquired experience, and the judgment is considered part of the inference.

Despite a long period and a special approach to the development of logic, in ancient India there is only one complete system of it - navya-nyaya, translated as "new logic". Here, logic is seen as a new science, contributing to a more complete and objective knowledge of oneself and the world around, as well as obtaining truthful information. However, the traditional approach to categories makes the original Navya-nyaya logical teaching somewhat awkward. Also, as its disadvantage, one can point out the lack of differences between the abstract conclusion and a specific example.

All approaches to the study of logic can be divided into two branches: classical and non-classical. The first is characterized by the presence of two truth values, that is, judgments can be either true or false. The second implies an infinite set of truth values, constructiveness of methods of proof and modality of judgments. Sometimes negations contained in classical logic can be excluded.

It should be mentioned that modern, mathematical logic contains elements of both classical and non-classical logic.

Late Navya-nyaya, according to some scholars, in many ways surpassed the achievements of Aristotle's logic. However, despite the high level of development and an enviable understanding of the laws of logic, the philosophers of ancient India did not use symbols. They were replaced by a complex system of cliches, using which many different expressions could be obtained.

Ancient China. In Ancient China, much attention was paid to ethical, philosophical and political issues, which were enshrined in a large number of treatises. This is how the science of names (theory of names) developed, the laws of thinking and the specifics of reasoning and statements were revealed.

The origin of the logic of Ancient China, according to modern historians, took place in the periods of Chuncu and Zhangguo, which are known for the emergence of a new concept of "philosophical discussion". Also, this period (722-221 BC) is characterized by the emergence and development of a process called "the rivalry of a hundred schools." Among the well-known representatives of philosophical teachings, who also develop the ideas of logic, are the names of Confucius and Mozi.

The philosophical schools that existed in China at that time include mingjia (school of names), fajia (school of laws), zhujia (developing Confucian ideas) and mojia (school of Mohists). As a result of the activities of these schools, a more or less harmonious system of logic gradually began to take shape. However, since logical knowledge was fragmented, fixed not in one source, but in many treatises, they required systematization. A school was needed that would unite all knowledge about logic in a single act, which would greatly simplify the use of logical achievements. The Mojia school became such a school. Later Mohists, using the philosophy of Mozi, wrote the first treatise on logic in China called "Mobian".

Logic in ancient China dealt with a number of problems specific to Chinese society of that period. Among them are theories of names, statements, reasoning and disputes. As can be seen, the logical science of ancient China was closely connected with writing and especially the spoken language, and was, as it were, hampered by it. Thus, the main efforts of philosophers were concentrated around the concepts of "min" and "tsy", i.e., the theory of names and statements, but no differences were made in the meaning of these concepts.

China has always been a very distinctive country with a rich culture, a developed social system and a strong sense of submission. The younger in age must obey the elder, the latter obeyed the elder in position, etc. Wise men and elders always enjoyed certain privileges. This situation could not but be reflected in the logic of ancient China. Political and ethical doctrines had a strong influence on logical theories here, and logic itself was applied in nature and was used to achieve rhetorical goals. Therefore, there was practically no clear system of knowledge about inferences. Preference was given to the content of thinking over form. As a result, although logic in Ancient China arose in time earlier than ancient Greek, its structure was never built and remained in its infancy.

3. Ancient Greece

It was here that the problems of logic were considered and developed most thoroughly. Logical questions are considered here by such philosophers as Parmenides and Zeno (representatives of the Elean philosophical school), Heraclid, the sophists Protagoras, Gorgias and others, Democritus and Aristotle. The activities of these philosophers directly or indirectly touched upon questions of logic. The ideas of the representatives of the Eleatic direction and the adherents of the logic of Heraclid came into conflict due to their opposite. The Eleatic school preached metaphysical theories, that is, a way of studying phenomena in which they are considered separately from each other and in an unchanged state. Heraclitus philosophy adhered to the ideas of dialectics (phenomena are studied in development and interaction).

The main feature that characterizes the philosophical approach of the sophists is that they human beings were proposed as a research object, and not the surrounding world, as it was before. The Sophists viewed logic not as a science that allows one to establish the truth, but as a means of achieving victory in an argument. To do this, they deliberately violated the laws of logic.

First opposed the sophists Democritus (460-370 BC), who belonged to the materialistic philosophical school. The philosophical system created by Democritus contains the doctrine of being, the theory of knowledge, ethics and aesthetics, cosmology, physics, biology, politics and logic. He also developed and consolidated in his Treatise "On Logic" ("Canons") the first system of logic. Democritus is considered one of the founders of inductive logic, since his treatise is based on empirical principles. Considering judgments, Democritus distinguishes subject and predicate in them.

Problems of logic were also dealt with Socrates (469-399 BC) and Plato (428-347 BC). In the teachings of Socrates, the method was considered the main one, which made it possible to obtain the truth, and also contained the idea that knowledge of any subject becomes possible only if it is reduced to a general concept and on this basis this concept is judged. To achieve the truth, Socrates suggested that his students give a definition to any phenomenon, feature or characteristic feature inherent in the surrounding world or a person. Then, if such a definition turned out, in his opinion, to be insufficiently complete or correct, he, using examples from life, pointed out the mistakes made by the interlocutor, and then changed and supplemented it.

Socrates considered the achievement of knowledge to be the discovery of patterns and the definition of a concept for a number of things. In the process of achieving knowledge, the common features of objects and the differences between them were taken into account.

Ancient Greek philosopher Plato was a student of Socrates and developed theories of knowledge and logicbased on the teacher's ideas. Using his theories, Plato first received new concepts, and then tried to break them down into types and systematize them.

To do this, he used his favorite technique called "dichotomy", that is, the division of the concept of A into B and not B (for example, crimes can be intentional and unintentional, and animals can be vertebrates or invertebrates). As in the school of Socrates, the students of Plato's Academy were busy getting new definitions. In modern philosophical science there is a mention of a curious case connected precisely with definitions. Plato, describing man, said that man "is a two-legged animal without feathers." Having learned about this definition, the famous philosopher Diogenes plucked a chicken and brought it to Plato's Academy during a lecture with the words: "Here is Plato's man." Plato was forced to admit the insufficiency of his definition and made changes according to which "man is a two-legged animal without feathers and with flat nails."

Plato created a system of objective idealism, according to which the spiritual principle (as opposed to subjective idealism) exists independently of human consciousness. In this theory, Plato used the division of the world into material and ideal (spiritual) and made the first dependent on the second. In other words, the material world, according to Plato, is unstable and changeable, in contrast to the ideal world, which exists independently of matter and human consciousness. He considered ideas to be eternal and unchanging, and the material world, as it were, a projection of the ideal. In other words, a thing is only a reflection of an idea.

Plato developed the theory of judgment, created two rules for the division of concepts, and also distinguished the relationship of difference from the relationship of opposites.

Thus, many philosophers of ancient Greece worked on questions of logic, but its founder is considered to be Aristotle Stagirsky (Aristotle was born in the city of Stagir - this is where his nickname came from). He devoted himself to the study of many sciences, such as philosophy, logic, physics, astronomy, psychology, rhetoric, etc. Many of his works are devoted to these subjects. It was Aristotle who formalized the knowledge of logic into a clear system and discovered that knowledge, no matter where it comes from, always has a linguistic expression. From this he concluded that scientific knowledge is a sequence of statements united by logical connections and deduced from one another.

Aristotle's logic is called formal or traditional. It includes such sections as concept, judgment, laws of correct thinking, inferences, argumentation and hypothesis. Aristotle's important achievement is that he first formulated laws of correct thinking: the law of identity, the law of non-contradiction and the law of excluded middle, and also began to study human thinking in order to derive its logical forms. These laws were formulated in the most important work of Aristotle "Metaphysics".

Aristotle created syllogism theory, reviewed theory of definition and division of concepts and theory of proof. The main works in this area are treatises "First Analytics" и "Second Analytics", which subsequently, along with other works, were combined into "Organon" - a method, means or instrument of cognition of reality.

This work contains the opinion that the laws of logic are inextricably linked with the surrounding world and with man and cannot exist in isolation from them. This conclusion also confirms that the logic corresponds to the culture of a particular society and reflects the features that characterize this culture. For example, in Indian logic there is no law of the excluded middle, which is characteristic of Aristotle's logic. According to scientists, this trend can be traced in the cultures of these countries as a whole. Thus, the population of countries in which the logic of Aristotle has become widespread tends more towards straight lines, which is clearly seen in judgments about good and evil, which are characterized by uncompromisingness, as well as in architecture (ancient columns) and weapons (a straight sword). Eastern countries are closer to the curve line (Muslim crescent, crooked swords, greater freedom of judgment).

Aristotle considers a statement to be true if it corresponds to the situation of the surrounding world, i.e., reflects the real state of things. False, therefore, were considered judgments that are used not to reflect objective reality, but to consciously or accidentally change this reality, i.e., "fitting" the phenomena of the surrounding world to the required answer. In other words, what is false is that which breaks existing connections between things or creates new ones that exist only in words. Starting from this concept of truth, Aristotle creates his own logic.

In conclusion, it is necessary to mention Stoic logic - a system of knowledge developed by adherents of the megaro-stoic school, the Stoics Zeno and Chrysippus and megarics Diodorus, Stilpo, Philo and Eubulides. As a result of the activities of this school, modern logic received an analysis of logical concepts negation, conjunction, disjunction and implication. They saw the task of logic as getting rid of errors and creating the opportunity to correctly judge things. Logic must study not only verbal signs, but also the thoughts expressed in them. Going beyond formal logic, representatives of the Megaro-Stoic school divided logic into dialectics and rhetoric.

Unfortunately, the ideas of this philosophical school in the field of logic have only partially survived to our time.

4. Medieval logic

Medieval logic is, for the most part, an interpretation and analysis of ancient philosophical theories. Mainly studied questions modal logic, the theory of logical implication, the theory of semantic paradoxes, and also an analysis of selecting and excluding judgments was carried out. The main directions considering questions of logic were the direction of realists and nominalists. The first believed that general concepts exist independently of individual things. Nominalists took opposite positions and believed that general concepts only name individual things that are real. It should be noted that both of these approaches are incorrect.

The most famous scientists who worked on questions of logic in the Mediterranean are William of Ockham, Duns Scotus, Raymond Lull, Jean Buridan, Albert of Saxony. Special mention should be made of William Occam, who is famous for creating a logical tool called "Occam's blade".

The science developed in Syria served as a conductor between ancient and Arabic logic. Questions of logic in the Arab world were dealt with by such scholars as al-Farabi, considered the founder of Syriac logic, Ibn Sina (Avicenna), Ibn Rushd (Averroes).

Al-Farabi was an ideological follower of Aristotle. He commented Aristotle's main work "Organon". Al-Farabi's logic is aimed at studying scientific thinking and examines questions of truth, based on the concept of truth developed by Aristotle. The structure of his logic consists of two parts, one considers representations and concepts, and the other studies the theory of judgments, inferences and evidence. Al-Farabi paid special attention to issues of the theory of knowledge and grammar.

The interpretation of the works of Aristotle was continued by Ibn-Sina. He used translations and commentaries of ancient works created by al-Farabi. Avicenna studied Aristotelian syllogistics, traced the dependencies and connections between categorical and conditional propositions, as well as the expression of implication through disjunction and negation. The scientist consolidated his ideas in the textbook "Logic".

The most famous and used work on logic is treatise "Summulae logicales", containing a number of new ideas in the field of propositional logic. This work was written by Peter of Spain.

Author: Shadrin D.A.

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