The term deduction, derived from the Latin word deductio, refers to the act and consequence of deducting. This verb, in turn, refers to drawing a conclusion or discounting a certain amount.
For example: “This morning when I woke up you weren’t home: so by deduction I guess you must have been out all night”, “The provincial government announced that it will apply a 2% deduction on all bank deposits that exceed 10,000 pesos”, “The treasury will allow the deduction of the rental expense from the Income Tax”.
In deduction, the conclusion is necessarily inferred from the premises.
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Deduction in logic
On the plane of logic, deduction is a type of reasoning through which the conclusion is necessarily inferred from the axioms or premises. After a succession of formulas, deductive reasoning allows drawing the conclusion through rules of inference.
Let’s see how the deduction from premises works:
Premise #1: “All dogs are mammalian animals”
Premise #2: “Bobby is a dog”
Conclusion: “Bobby is a mammalian animal”
As you can see, if all dogs are mammalian animals and Bobby is a dog, the logical deduction is that Bobby is also a mammalian animal since he is a dog. Deducing, in this framework, consists of extracting a particular truth from a general principle.
In the fiscal field, a deduction is an allowance.
The concept in a theorem
It is known by the name of deduction theorem, in the field of propositional logic, first order logic and other formal systems, a metatheorem that is used very frequently to carry out the proof of another. A metatheorem, meanwhile, is one of the branches of logic, and focuses on the study of the components and properties of logical systems; Among the latter, completeness, decidability and consistency stand out.
The deduction theorem can be defined as a formalization of the normal technique of proof: the assumption of A is enough to conclude that B, and thus show that B follows from A.
Everyday use of deduction as reasoning
In everyday life, outside the academic field and without strictly using the principles of logic, we apply deduction in countless situations, although we do not always do it with all the appropriate tools.
The premises of the previous example have been verified, both the first (which can be elaborated thanks to the fact that human beings have dedicated centuries to the study of the species that inhabit the planet Earth) and the second (since the observer makes sure that Bobby be a dog before affirming it). However, when we visit a natural space for the first time and see an animal unknown to us, it is normal for us to deduce its species, even if we do not have any scientific knowledge and without having examined it carefully.
This way of practicing deduction is very common, and sometimes it can cause us serious problems, especially when the message we think we are receiving makes us feel threatened or hurt. We cannot escape our curious nature, our need to have an opinion about everything that surrounds us, but very often we go overboard and make mistakes that ruin relationships, that leave us without a job or that harm others.
The notion in the tax field
In the tax field, a deduction is a deduction : the discount of an amount of the fee or the base of a certain tax.
Suppose a person must pay 5,000 pesos of Income Tax. A tax regulation, however, allows to deduct from said tax what is invested in productive activities. In the case of this individual, it is 1000 pesos. Therefore, the corresponding deduction is applied to the original settlement: the amount to be paid is 4,000 pesos.
