Deduction

From Logic

Deductive Logic is the method of non contradictory identification. It is based on the classical axioms of Aristotelean logic. Deductive arguments are akin to mathematical equations: they present a series of categories or definitions in a series of equivalencies. For this reason, the conclusion of a deductive argument necessarily follows from its premises, in the same way that 4 follows from the "premises" of 2+2=. In the opinion of this author, the most elegant form of a deductive argument is Aristotle's syllogistic logic, or classical deductive logic.

Generally, it is held by logicians that deductive arguments work from general rules to specific conclusions. This is a childish oversimplification of what deduction is. For example while the following categorical syllogism goes from the general to the specific:

All humans are mortal
Socrates is human
Therefore, Socrates is mortal

...it is not necessary that deductive arguments move from general or universal statements, to specific or particular statements , for example, the following disjunctive syllogism/deductive argument works from particular premises to a general conclusion:

If Socrates if human, then Socrates is mortal
Socrates is human
Therefore, Socrates is mortal

We can call a deductive logical system an a priori system. This means that we can make up such a system without any observation or experimental examination.We can create a set of categories like squares or circles or letters, and a set of self consitent rules that follow a set of definitions, all without having to ever experience such "things".

Philosophers like to say that a "brain in vat" set apart from the rest of the universe could create an a priori system.