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. For example, consider this categorical syllogism:

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

This syllogism works from a general rule: "all humans are mortal" to a specific conclusion: "Socrates is mortal". However, it is not necessary that deductive arguments move from general or universal statements, to specific or particular statements , for example, a deductive argument can work from particular premises, consider this disjunctive syllogism:

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.