Philosophy of Being and Knowledge

Epistemology (Philosophy of Knowledge)

Theory of Proof

Knowledge is not only a true belief but also a proven belief. To know something, it is insufficient merely to be confident; one must also be able to demonstrate it. Hence, understanding the nature of knowledge is impossible without analyzing the problem of proof. A proposition can be considered proven only when its truth is beyond doubt. There are several models of proof, all closely linked to logic. The only way to prove new knowledge is to show unequivocally that it follows from existing knowledge. The process of deriving new knowledge from previously known facts is known in logic as deduction. Just as there are three forms of deduction in logic, epistemology identifies three types of proof: deriving specific knowledge from general principles, deriving general principles from individual cases, and proving one individual case based on others whose truth is indisputable.

• Deduction: This is a form of reasoning where more specific conclusions are derived from more general premises. A traditional and well-known example of deductive reasoning is: "All men are mortal. Socrates is a man. Therefore, Socrates is mortal." In this deduction, specific knowledge (Socrates is mortal) is derived from a general principle (All men are mortal). Deductive reasoning is considered the most rigorous form of proof, as there is no better way to demonstrate a belief than to show that it is merely an expression of a general law. If the general law is undisputed, then everything derived from it is also evident. To perform a deductive proof, one must:

✵ Have a principle or general proposition whose truth is beyond doubt, from which new knowledge follows. In the deduction, this principle serves as the major premise (All men are mortal).

✵ Show that the new knowledge derived from the deductive reasoning is related to the general principle. In the deduction, this role is filled by the minor premise (Socrates is a man).

✵ Construct the deduction correctly. Logic has developed a set of rules to build a valid deductive argument. Without adhering to these rules, proof is impossible.

• Induction: This form of reasoning involves deriving a general statement from multiple or a few specific observations. For example: "Iron conducts electricity. Tungsten conducts electricity. Silver conducts electricity. Iron, tungsten, and silver are metals. Therefore, metals conduct electricity." Although induction helps in establishing general beliefs, it is not as precise as deduction. The primary problem with induction is the impossibility of including all possible individual cases. The conclusion that all metals conduct electricity is only reliable if one can test every piece of metal that has ever existed or will ever exist; however, this is impossible. No one can test all metals. Methods to increase the reliability of inductive conclusions exist, but none can achieve absolute certainty through induction alone. The reliability is enhanced by incorporating as much and as varied data as possible. For instance, to assert that all metals conduct electricity, it is insufficient to test a hundred pieces of iron in one laboratory. Physicists must test as many types of metals as possible, in different natural and artificial conditions, in various laboratories, and using diverse technologies. Induction based on the use of the most varied data is called scientific induction.
• Deduction and Induction are the two main types of reasoning. Aristotle, who analyzed and described these forms of reasoning, showed that human intellect employs a third form of proof, which is not an independent type of reasoning but a combination of the two. Aristotle called this form of reasoning paradigm, while modern logicians commonly refer to it as analogical reasoning. A paradigm is the derivation of new specific knowledge from old specific knowledge. It consists of two parts, the first being an inductive reasoning and the second being a deductive reasoning, with the conclusion of the inductive syllogism serving as the major premise, i.e., the general principle, of the deductive epicyclism. For example: "Iron conducts electricity. Tungsten conducts electricity. Silver conducts electricity. Iron, tungsten, and silver are metals. Therefore, metals conduct electricity. Gold is a metal. Therefore, gold conducts electricity." The first part of this reasoning is induction, and its conclusion serves as the major premise for the second part, which is deduction. Unlike a paradigm, which proves specific knowledge based on general principles, and induction, which proves general principles based on specific knowledge, a paradigm proves the truth of a proposition based on another proposition related to an analogous situation. If iron conducts electricity, then gold must also conduct electricity, as both iron and gold are metals. The scientific community's focus on paradigms as a method of scientific inquiry intensified in the 1970s, when Thomas Kuhn demonstrated that paradigms are the primary method of scientific proof.