ontology
A word used in the study of Metaphysics that refers to arguments that have to do with existence and being. From Gk. οντος + λογος, "the study of being." This philosophical study is easily seen in many philosophers' works, but it is especially pronounced in Aristotle's Metaphysics which accounts for one of the most influential and classical understanding of existence and essence.
theology
The study of divinity and/or God(s) from Gk. θεος + λογος, "The study of God." This is an important study in the Metaphysics, especially in book Λ which discusses God's existence and potential. Aristotle's arguments for God's existence and causal supremacy are well known (i.e. "Unmoved Mover" argument).
causality
Although this word is easily understood, the concepts it evokes are not as simply apparent. Aristotle's entire philosophy can be viewed paradigmatically with causality properly understood.
This word for Aristotle in Metaphysics can be understood to connote the reason a thing is a certain way. This involves conceptual essence and consequence, meaning broadly that some things imply others and things exist in ways that agree with their causality, and in no other way.
contradiction
This word is generally used to refer to any argument that seems to disagree with another, but in Metaphysics, the word is more formally used. This word has a specific meaning in Aristotle's "syllogistic" philosophy, (see below). It is an argument which specifically implies that another argument be false in order for its own validity. This is different than a logical defeater which just shows that an argument is false or invalid. In generic terms, an argument's contradiction is the argument opposite of it.
Aristotle argues in the Metaphysics that contradictory arguments can never both be true, and also that perfectly valid contradictions can never have a middle ground.
syllogism (also truth vs. validity)
Although these concepts are not primarily evident in Aristotle's Metaphysics, they are essential in understanding the Metaphysics' core arguments about philosophical systems and primary causation.
A syllogism occurs when a conclusion is drawn from two arguments that implies the conclusion if both postulates are true. A syllogism is said to be "Valid" if and only if the manner in which the arguments imply the conclusions is logical. A syllogism is said to be "True" if and only if that argument is valid and its component parts are in fact correct.
An example of an invalid syllogism (although not offered as formally as Aristotle might have demanded) is as follows: "All penguins are black and white: Some TVs are black and white; therefore, some TVs are penguins." This argument is not valid because the conclusion depends on illogical deduction of two truths.
