The complexity of syllogistics gives rise to false conclusions
The Greek word syllogistikós derived from the Latin syllogistĭcus , which is the closest etymological antecedent of syllogistic . This adjective allows you to qualify what is linked to the syllogism .
Syllogism
The notion of syllogism refers to an argument composed of three propositions . Of these propositions, the third necessarily arises by deduction from the first two.
The syllogistic argument , in this framework, follows this method . This structure is known as the syllogistic form .
It can be said, therefore, that the syllogistic form contemplates three propositions: two premises and a conclusion , which is deduced from the others. This is the basis of Aristotelian logic , developed by the Greek Aristotle (384 BC – 322 BC) and considered the backbone of scientific thought .
The truthfulness
It is important to keep in mind that, although the syllogistic form may be correct from a logical point of view, the veracity of the conclusion is not guaranteed if certain rules of the premises and their terms are not respected. Suppose that an argument is based on this premise: “All Argentines are South Americans.” Then it continues with another premise: “There are South Americans who are Brazilians.” Following logic , one could reach the conclusion: “Therefore, there are Brazilians who are Argentinian.” In this case, the syllogistic form is fulfilled at a general level, but the conclusion is not true (discounting the possibility that a Brazilian also has Argentine nationality).
Let us now look at a syllogistic argument whose conclusion is true:
Premise No. 1: “Human beings cannot fly”
Premise No. 2: “Eagles fly”
Conclusion: “Therefore, eagles are not human beings”
Elements and structure
So far we have seen the general characteristics of syllogistic and the relationship that exists between the premises. Let's see its elements in greater detail below. First we have three terms: the subject , the predicate and the middle , which are represented by the letters S , P and M , respectively. Then comes the antecedent , which is made up of two judgments called premises . Finally there is the consequent , which is the conclusion as a judgment of all of the above.
From the point of view of structure, we can group these elements into the following three parts:
* major premise : it is the judgment that contains the predicate of the conclusion, which is compared with the middle term;
* minor premise : here we have the minor term of the conclusion, which is also compared to the middle;
* consequent : also called conclusion , it is the judgment that derives from affirming or denying (uniting or separating) the relationship between the subject and the predicate.
There are several key concepts, which are repeated throughout the definition: the judgments , from which the premises arise; the terms , which after being related constitute the argument .
«Eagles are not human beings»
Properties of the terms
When talking about the terms we must consider their extension , which refers to a quantity . Both the subject and the predicate and the middle term can be taken in their universal extension as well as in their particular extension . Syllogistic understands this in the following way: the first covers all the individuals to whom the concept can refer; the second, on the other hand, covers a limited group.
On the other hand we have the relationship or quality that exists between the terms. This can be affirmative (union) or negative (separation), depending on whether it can be stated that S is P or the opposite, respectively. Returning to extension, we must point out that the predicate of an affirmation has a particular extension in all cases, while that of a negation has a universal one.