Arguments of the deductive or inductive type are arguments made up of apodictic propositions. This means that they are affirmed and/or denied in an absolute way, caring for themselves to be true or false. However, there are other forms of arguments that are based on hypothetical or disjunctive propositions. Hypothetical propositions are those that establish a conditional statement, aiming at a consequence according to what was established before. Disjunctive propositions involve alternatives that depend on the facts.
Conditional arguments are a way of establishing the validity of the argument, according to the relationship between two poles: one is the antecedent, and the other the consequent, data in form If p, then q. There are four basic models, two valid and two invalid. Follow below:
- The first is called ACKNOWLEDGMENT OF THE BACKGROUND. It has to be a conditional statement If p then q, if what was said before is affirmed (background = P), the conclusion is valid (consequent = q). It is noticed that although the model is established, the adopted signals must be taken into account. Therefore, what is valid is the confirmation of the antecedent of the hypothesis.
- The second valid conditional argument mode is the DENIAL OF THE CONSEQUENTIAL. I mean that if a statement if p then q we have the denial of what is said later (consequent = non-q), the conclusion must also be the denial of what was said before (antecedent = non-p). Here, the “signs” adopted for the calculation of predicates should also be observed.
- The third mode is the STATEMENT OF THE CONSEQUENTIAL. given the hypothesis If p then q, if the consequent is asserted (q), does not imply that the antecedent (P) be the condition for it. Thus, the argument is invalid and the sign must also be observed for calculating predicates.
- The last conditional argument model is the DISCLAIMER OF THE FOREGOING. With the premise If p then q, with the denial of what was said before (antecedent = not p), there is also no implication that the result is derived from it (consequent = non-q). Thus, the argument will also be invalid and as in other cases, the sign of the propositions must be observed so that the calculation is correct.
By calculus of signs, it is understood the classification of propositions. These can be negative or affirmative, universal or particular (also unique, necessary, not necessary or impossible and possible). Invalid modes are called fallacious because, only apparently, their content promotes mistakes. But understanding the correct forms of valid arguments, no content can deceive or mislead anyone who knows such distinctions.
Arguments with disjunctive propositions by themselves constitute their validity, as they deal with mutually exclusive alternatives. Given a proposition like Or A, or B, if we have A, then we don't have B and vice versa. Only the care with the signs must be respected in order to diagnose whether the arguments are valid or invalid.
These, then, are the forms of conditional arguments.
By João Francisco P. Cabral
Brazil School Collaborator
Graduated in Philosophy from the Federal University of Uberlândia - UFU
Master's student in Philosophy at the State University of Campinas - UNICAMP
Source: Brazil School - https://brasilescola.uol.com.br/filosofia/silogismos-condicionais.htm
