PRINCIPLE : THAT FROM WHICH SOMETHING ELSE PROCEEDS (in any way whatsoever)   Click to Expand ⤵

Two Things Necessary to Constitute a Principle   ⤵

Priority
The principle must be prior to (i.e. come before) the Principiate in some way   ⤵

Real Priority
A principle could be prior to its principiate on the basis of something real   ⤵

1. Priority in Time
   This is when the principle is in extience before the existence of the principiate (the principle may continue or discontinue to exist after the principiate begins to exist)
   (e.g. a father is prior to his child in this way)
2. Priority in Nature
   This is when the existence of the principiate depends on the existence of the principle
   (e.g. the stone of a statue is prior to the statue it composes, as the statue's existence depends on the stone; thus the stone is a principle of the statue)
3. Priority in Origin
   This is when there is priority neither of in time nor of nature but only of procession of the one from the other
   (this is only said to be the case with regard to the Persons of the Trinity, namely how the Father is a principle of the Son, and how the Father and the Son are principles of the Holy Spirit)

1. Logical Priority
   The principle could be prior to its principiate only on a purely mental basis (that is, according to the manner of thought)
   (e.g. in a syllogism, the premises are logically prior to their conclusion; thus, a premise is a principle of a conclusion)

Special Connection
In addition to coming before the principiate, a principle must be connected to the Principiate in some special way either in reality and/or in the mind   ⤵

1. Ontological Connection (a.k.a. Real Connection)
   This is when the being of the principiate depends on the being of the principle
   Note: This is the case with causality, namely how the effect is ontologically dependent on its cause
2. Logical Connection (a.k.a. Purely Mental Connection)
   This is when the truth of a principiate (i.e. a statement) is dependent on the truth of the principle (i.e. another statement)
   (e.g. in a syllogism, the truth of the conclusion is dependent on the truth of the premises)

Four Supreme Principles
(the special connection that the Supreme Principles have are both ontological and logical)   ⤵

1. Principle of Non-Contradiction (a.k.a. Principle of Contradiction)
   A thing cannot both exist and not exist (in the same way and at the same time)
2. Principle of Identity
   A thing is the same as itself
3. Principle of Excluded Middle
   A thing must either be or not be (it cannot be somewhere between those two)
4. Principle of Sufficient Reason
   Everything exists for a reason (either because something caused it to exist or because it exists by its very nature)
   (God is the only thing said to exist by its very nature)

PRINCIPIATE : THAT WHICH HAS ITS ORIGIN IN A PRINCIPLE