Understanding Logic: Formal, Material, and Historical Perspectives
Introduction to Logic
The term ‘logic’ is derived from the Greek word ‘logos,’ which in ancient Greek meant ‘thought,’ ‘reason,’ ‘word,’ or ‘knowledge.’ Logiké referred to ‘on the logos.’ Ultimately, logic studies the human ability to think and reason.
Logic can be defined as the set of skills aimed at enunciating the laws governing human thought processes, as well as the methods applied to reasoning and reflection to achieve a system of reasoning that leads to results considered accurate or true.
Logic is often divided into formal and material logic:
Formal Logic
Formal logic, also called pure logic, is the study of the correct and valid forms of reasoning. It focuses on the structure of reasoning itself, regardless of the specific content. It treats the content as abstract logical entities, ensuring the laws apply universally.
Reasoning is a human process of thinking that moves from a set of known facts (premises) to new knowledge (conclusion). This conclusion does not rely on new observations but is derived from the premises.
The truth in formal logic is a formal truth. It is true as long as the premises are true, indicating a consistency within the reasoning itself. Even if the premises and conclusion are false, the reasoning can still be considered correct or valid as an argument.
Material Logic
Material logic, also called applied logic, examines the content of the premises and whether the conclusion is consistent with reality. It aims to reach a conclusion that is materially true.
While the premises in pure logic are abstract entities, material logic deals with concepts of empirical origin. It acknowledges that it is difficult to find real-world concepts that perfectly match the abstract objects of logic.
For concepts of empirical origin, it is often impossible to state with absolute certainty whether they match or do not match these concepts. Therefore, the laws of formal logic should be applied with caution when dealing with such concepts. Formal logic is most applicable in exact and abstract sciences like mathematics, logic, and mechanics, as well as in abstract disciplines like legal interpretation.
Therefore, for logical propositions using those concepts, the laws of formal logic will be applicable only with special caution. Thus, the laws of formal logic only apply to tight range in the field of exact and purely abstract sciences such as mathematics, logic, mechanics, and only those rules and abstract disciplines such as legal interpretation .
Brief History of Logic
Aristotle’s contributions to abstract knowledge, particularly formal logic, are significant. He is considered the creator of formal logic and his work has had a lasting impact.
Aristotle’s main contribution was the syllogistic, the study of reasoning through syllogisms. This is also known as the logic of propositions or classical logic. Later philosophers, especially those of the Stoic school and pre-Christian and Aristotelian scholasticism, developed modal logics.
Significant new contributions to logic emerged in the nineteenth century with the development of mathematical logic, influenced by Leibniz, Boole, and Frege.
Gottfried Wilhelm Leibniz
Gottfried Wilhelm Leibniz (1646-1716), a German mathematician and philosopher, is considered a key figure in mathematical logic. He developed the idea of a calculus ratiocinator, a set of rules applicable to general concepts that would allow philosophical questions to be addressed with mathematical reasoning. This concept, though initially forgotten, aimed to apply the precision of exact sciences to philosophical issues.
George Boole
Mathematical logic, also called symbolic logic, developed in the nineteenth century, particularly after George Boole (1815-1864). His book, “An Investigation of the Laws of Thought,” introduced Boolean algebra, which formalized logical calculations and allowed mathematical procedures to be applied to logical problems. This laid the foundation for modern computer technology, further developed by Emil Post and Alan Mathison Turing (1912-1954), the creator of the Automatic Digital Machine.
Bertrand Russell and Alfred North Whitehead
The culmination of symbolic logic is “Principia Mathematica” by Bertrand Russell (1872-1970) and Alfred North Whitehead (1861-1947), published between 1910 and 1913. This work argues that pure mathematics is derived from purely logical premises. The importance of transcendental logic is evident in all spheres of human knowledge, demonstrating the link between its philosophical origins, its connection to the foundations of mathematics, and its impact on computing.
The influence of logic extends to various aspects of daily life, including industry, communications, and consumer goods. Understanding the intellectual effort of Aristotle and the rules of logic is crucial for making informed decisions in personal, political, economic, and legal contexts.