-From the point of view of a formal science, it plays an important role in mathematics, philosophy, computer science and statistics. The Organon was Aristotle`s work on logic, the first analyses being the first explicit work of formal logic and introducing syllogistics. [40] The parts of syllogistic logic, also called conceptual logic, are the analysis of judgments in sentences consisting of two terms connected by a fixed number of relationships, and the expression of conclusions by syllogisms, which consist of two sentences that share a common concept as a premise. and a conclusion that is a thesis that concerns the two unrelated concepts of premises. Similarly, this type of formal logic is also©responsible for studying the philosophical and structural aspects of arguments. A proposition or logic calculus (also known as sentential calculus) is a formal system in which formulas representing statements can be formed by combining atomic sets (usually represented by p, q, etc.) using logical connectors (A n d, →, ∨, ≡, ∼, {displaystyle And,rightarrow,lor,equiv, sim,}, etc.); These proposals and connectors are the only elements of a standard instruction calculation. [41] Unlike predicate logic or syllogistic logic, where individual subjects and predicates (who do not have truth values) are the smallest unit, proposition logic takes complete statements with truth values as the most elementary component. [41] Quantifiers (e.B. p a r a t o d o s {displaystyle paratodos} or e x i s t e {displaystyle exists}) are included in the calculation of the extended statement, but quantify only on complete statements, and not on individual topics or predicates.
[41] A given proposition logic is a formal system of proof with rules that determine which well-formed formulas of a given language are “theorems” by proving them from supposed axioms without proof. [42] In this sense, it is said that in formal logic, thought is examined from the structured point, its validity or its invalidity. Science that examines forms of thought – concepts, judgments, explanations, demonstrations – from the point of view of their logical structure, that is, abstract from the concrete content of ideas, thus separating©only the general nature of the connection of the parts of that content. The main task of formal law is to formulate laws and principles©whose observance is necessary to reach authentic conclusions in the process of obtaining deductive knowledge. He began the formal logic of Aristotle, who created syllogistics. Later, the first Stoics contributed to the development of formal logic; in the Middle Ages, the Scholasten (Duns Scotus, Ockham and others); in the new era, especially Leibniz. A new stage of development of formal logic begins in the demarcation of the 19th and 20th centuries, when advances in mathematical (symbolic) linguistics gained in intensity. The latter, through the development of theological theories of mathematical thought and demonstrations, enriched formal logic with new methods©and means of linguistic research. The fact that an argument is misleading does not mean that its premises or conclusions are false or true.
An argument can have real premises and conclusions while being misleading. What makes an argument misleading is the invalidity of the argument itself. In fact, the conclusion that a statement is false because the argument it contains by inference is misleading is itself an error known as the Ad Logicam argument. [18] -Applies methods so effective©that©formal logic can distinguish evil from law. The origins of logic date back to antiquity, with independent eruptions in China, India and Greece. Since then, logic has traditionally been considered a branch of philosophy, but in the twentieth century logic became mainly mathematical logic and is therefore now also considered part of mathematics and even independent formal science. Through formal logic, it©is possible to add a value of truth or falsehood to a particular reasoning. Throughout history, several philosophers, mathematicians and scientists have defended formal logic.
Among them we can name the mathematician and lã³gico Alonzo Church; the philosopher, mathematician and logic Gottlob Frege; and the©mathematician and philosopher Alfred North Whitehead. Intuitionistic logic was proposed by L.E.J. Brouwer as the correct logic for arguing about mathematics, based on his rejection of the principle of the excluded third as part of his intuitionism. Brouwer rejected formalization in mathematics, but his student Arend Heyting formally studied intuitionistic logic, as did Gerhard Gentzen. Intuitionistic logic is of great interest to computer scientists because it is intuitionistic logic and sees many applications, such as extracting verified programs from tests and influencing the design of programming languages through formula matching as types. Well, this definition, like many others found in texts, makes us think that logic concerns only one thought or specialized knowledge, such as scientific or philosophical; However, this is not the case, because in addition to the fact that logic is an “instrument” for science, it is also for our daily life, since the practice of thought and thought is not reduced to the scientific field, because it is something that we often perform in conversations, discussions and decisions that life itself presents to us. For this reason, there is even currently talk of an informal logic, which, according to the Mexican philosopher Alejandro Herrera, proposes to examine the structure of thought in the questions of everyday life and has a double analytical and evaluative aspect. It attempts to overcome the mechanical aspect of the study of logic, as well as to understand and evaluate arguments with their natural fields, for example, legal, aesthetic and ethical.2 Science, which examines forms of thought – concepts, judgments, argumentation, demonstrations, etc. – from the point of view of their logical structure and the concrete content they express, ignored©. For example: in the judgments: “All students are schoolchildren”, “All whales are mammals”, “All humans are mortal”, there is another content; However, from a formal point of view, these judgments are of the same linguistic nature and, in this sense, there are no differences between them.
Formal logic is concerned only with the nature of the relationship that exists between the subject and the predicate, with the character of the generality of the subject (whether or not the subject reflects all the objects of a particular class), the conditions under which judgments are true, &c.; finally, its fundamental task is to establish permissible closure rules for the procedures in question. .