Logic studies the Syllogism or argument. This has its own forms capable of showing that a conclusion is derived from what was established in the premises or propositions given above. There are two ways to proceed when you want to form an argument, they are:
The syllogism or deductive argument is one that proceeds from increasingly universal propositions to particular propositions, providing what we call it a proof, since its inference (the conclusion is drawn from the premises) is the inclusion of a less extensive term in another of greater extension. The following examples may clarify better:
Every man is mortal. Every Brazilian is mortal.
John is a man. Every paulista is Brazilian.
Therefore, John is mortal. Therefore, every paulista is mortal.
It can be seen that in the first example the argument starts from a universal premise for a conclusion with a particular proposition (because the second premise is also particular). In the second argument, all the premises, as well as the conclusion, are universal. However, in both the inference occurs, since the given terms (mortal, man and João – first argument, mortal, Brazilian and São Paulo – second argument) have an extension relationship between them that goes from the longest term, through the medium (through which there is mediation) and finally reaching the term smaller.
The second type of argument is the inductive one. This proceeds from particular propositions or with terms relatively smaller than those in the conclusion, and reaches more universal or more extensive terms. See the examples below:
Iron conducts electricity. Every dog is mortal.
Gold conducts electricity. Every cat is deadly.
Lead conducts electricity. All fish are deadly.
Silver conducts electricity. Every bird is deadly.
... etc... etc.
Therefore, all metal conducts electricity. Therefore, every animal is mortal.
As in deductive terms, the terms have an extension relationship that allows their inclusion in each other, although in the first argument the propositions of the premises are particular and in the second they are universal. However, the inclusion occurs due to the smaller extension being part of the premises and not the conclusion, which must always be more extensive or universal than the premises.
Importantly, logicians prefer to work with deductive arguments. This occurs for two basic reasons: one of an ontological nature, since the substantial value of universal terms is questioned (the arguments inductives are widely used by philosophers and empirical scientists who understand that the universal is nothing more than a name given to a set of stuff). Another reason would be the fact that in induction nothing authorizes the conclusion to be related to the premises, because it is a term that was not given previously. The advantage of deduction is that all terms involved in the premises establish relationships that can be found in the conclusion. However, its premises are unprovable, as this would lead to a regression to infinity (deduction is often used by mathematicians). Even if there is a discussion about the substantiation of universals, the way the terms are related provides a demonstration.
Therefore, there are two ways to make arguments: by deduction or by induction. Each is applied according to the needs of the investigation and the nature of the problem raised by human reason.
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/argumentos-dedutivos-indutivos.htm
