Logic (Deduction and Induction) is one of the three roads from the Trivium.
The Subject of Logic: “Syllogisms”
All Aristotle’s logic revolves around one notion: the deduction (sullogismos). A thorough explanation of what a deduction is, and what they are composed of, will necessarily lead us through the whole of his theory. What, then, is a deduction? Aristotle says:
A deduction is speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so. (Prior Analytics I.2, 24b18-20)
Each of the “things supposed” is a premise (protasis) of the argument, and what “results of necessity” is the conclusion (sumperasma).
The core of this definition is the notion of “resulting of necessity” (ex anankês sumbainein). This corresponds to a modern notion of logical consequence: X results of necessity from Y and Z if it would be impossible for X to be false when Y and Z are true. We could therefore take this to be a general definition of “valid argument”.
When arguing with someone in an attempt to get at an answer or an explanation, you may come across a person who makes logical fallacies. Such discussions may prove futile. You might try asking for evidence and independent confirmation or provide other hypotheses that give a better or simpler explanation. If this fails, try to pinpoint the problem of your arguer’s position. You might spot the problem of logic that prevents further exploration and attempt to inform your arguer about his fallacy. The following briefly describes some of the most common fallacies: