A postulate can be an expression that is transmitted as truth despite the lack of evidence and demonstrations.
Postulated is that expression that presents a truth without demonstrations or evidence, but that is admitted even despite the lack of evidence. The acceptance of the postulate is given by the lack of other expressions to which it can refer and by the need to use it in subsequent reasoning.
The postulates, therefore, are propositions that allow logical judgments to be developed. For philosophy , they are expressions that cannot be demonstrated from theory , but that must be admitted to understand something. In this sense, the notion of freedom can be understood as a philosophical postulate.
Another use of the concept of postulate is associated with the principles that certain groups or individuals defend and promote. For example: "The deputy's statements are contrary to the historical postulates of socialism" , "As a coach, my main postulate is respect for my rival" , "I work for this company because I have no other option, but I do not agree with its postulates." "I think they convey a message that is not healthy for society."
Postulates in science
At a general level, it can be said that science speaks of postulates to refer to those expressions that compile experience regarding an idea. They are propositions that allow us to substantiate what is seen and that, until now, have not been proven false. Therefore, scientific propositions can constitute the starting point of reasoning.
Geometry , for its part, accepts propositions as assumptions that are taken to prove something, while mathematics in a broader sense understands postulates as theoretical formulas accepted only by convention.
Tautologies and axioms
In this framework we must provide a brief definition of two concepts to explain the postulates in the field of mathematics: tautology and axiom . Regarding the first, propositional logic defines it as a formula that is true no matter what values are assigned to its atomic formulas. An axiom, on the other hand, is a proposition whose clarity is such that it is not necessary to provide a demonstration for it to be accepted.
Returning to mathematics, we could say that if we take two structures, such as integers and natural numbers, it would be correct that they comprise the same axioms . Despite this, the postulates serve to express what is fundamental about one or more structures, so that they are not tautologies, as logical axioms are.
Euclid made important mathematical postulates.
Euclid's Postulates
The mathematical theories that are part of modernity are based on several postulates. In the past, it was believed that any theory could be converted into a series of axioms and formulas, but over time scientists realized that this would not be possible. Among the most celebrated mathematical postulates are those of Euclid, which are detailed in the classical geometry treatise entitled The Elements , published around the year 300 BC. c.
These postulates are five, and the Greek mathematician Euclid conceived them with the intention of exposing the geometric knowledge of classical Greece. Let's see the complete list below:
* a line segment can be determined from any pair of different points;
* it is possible to extend a line segment in a line indefinitely;
* taking any center and radius it is possible to create a circle;
* There are no two different right angles, but they are all equal;
* when cutting two straight lines with a third so that when adding the two interior angles of one side the result is less than the sum of two straight lines, if the two remaining straight lines were extended they would be cut on the side of the smaller angles.
It is worth mentioning that the last postulate was questioned centuries later, and is currently replaced by the following: it is possible to draw only one parallel to a line starting from an exterior point .