Induction vs. Deduction
These terms and their latin equivalents are often employed to represent a paradigmatic difference between Platonic philosophy and Aristotlean philosophy. Whereas Plato's philosophy is intergrally positioned around his understanding of the heavenly Forms, Aristotle's Metaphysics and other works depend on bottom-level truths that lead to truth.
Deduction refers to a logical system that draws conclusions from higher truths about the way things are or are not. Induction, its complementary oppositite, refers to a logical system that draws its conclusions via extrapolation of lower truths. Deduction relies on abstract truths trickling down into arguments, where as induction involves logical positions construction arguments from the ground up.
One complication is that Aristotle depends on logical syllogism to induce his arguments, which seems like deduction. However, syllogistic reasoning depends heavily on ultimatum language which necessitates some level of assumption.
In the Metaphysics, Aristotle creates arguments about the way things are true that depend heavily on observable or demonstrable conditions in the natural world.
Essentially, the difference can be understood this way. Plato looks up into heaven to find truth. Aristotle looks around and uses logic to find truth.
Causality
Since Aristotle's Metaphysics is concerned so much with logical systems, it is important to have a clear understanding of cause and effect, which can be understood as a type of logical process. Causality in the Metaphysics can have several layers, depending on intention, design, choice and many other variables.
Causality is essentially the philosophical word for asking all the reasons "why" a thing is the way it is. This could have several components including different facets of its being the way it is.
Logic and Truth
One of the first claims of the Metaphysics is that the systems by which we know truth are important and based in logic. Aristotle as the father of logic defined the term as a series of predications which imply a conclusive predication.
E.g. using Aristotlean logic:
1. All (that which is food) is some of (that which is edible)
2. All (that which is muffins) are some of (that which is food)
3. Therefore: All (that which is muffins) is some of (that which is food)
--which can be reduced to: "If food is edible and muffins are food, then muffins are edible.
This system is the vehicle by which the Metaphysics explores truths that are not easily apparent, such as the existence of God or the knowability of truth or the primacy of logical metaphysics above the natural sciences.
