Everything is copied from Being Logical by D.Q. McInerny
Basic Principles of Logic:
1. First Principles
A. The Principle of Identity
*A thing is what it is.
-The whole of existing reality is not a homogenous mass. It is a composition of individuals, and the individuals are distinguishable from one another. If a thing is what it is, obviously it is not something other than what it is. An apple is an apple. It is not an orange, a banana, or a pear. But an Apple.
B. The Principle of the Excluded Middle
*Between being and nonbeing there is no middle state.
-Something either exists or it does not exist; there is no halfway point between the two. There is no such thing as just becoming there are only things that become.
C. The Principle of Sufficient Reason
*There is sufficient reason for everything.
-Everything that actually exists in the physical universe has an explanation for its existence. What is implied in the principle is that nothing in the physical universe is self-explanatory or the cause of itself. One thing is said to be the cuase of another thing because (a) it explains the very existence of that thing, or (b) it explains why the things exists in this or that particular way, the "mode" of its existence.
D. The Principle of Contradiction
*It is impossible for something both to be and not be at the same time and in the same respect.
-For example: You are physically in Arroyo Grande but you can't get your mind off your family in Brentwood, so mentally you are in Brentwood, but you are not physically in Brentwood. The book explanation was to confusing, so this just means something cant physically be in two places at once. 
Distingush Among Causes:
1) Efficient Cause: Is an agent whose activity brings something unto existence or that modifies its existence in one way or another.
2) Final Cause: As applied to an activity it is the purpose of the activity. As applied to an object it is the use to which the object can be put.
3) Material Cause: The material out of which an object is composed.
4) Formal Cause: The identifying nature of a thing, that which makes it precisely what it is.
-Example: A birdhouse
Fred = the efficient cause = he brought the birdhouse into existence
Nails, Wood, Paint = the material cause = what the object is made of
Birdhouse shape = the formal cause = the shape is of a birdhouse (identifying nature)
Provide shelter for birds = the final cause = purpose of the birdhouse (object
Founding an Argument:
*EVERY ARGUMENT IS COMPOSED OF TWO BASIC ELEMENTS*
1) Premise Statement: Is a supporting statement, it is the starting point of an argument, containing the known truth.
2) Conclusion: A supported statement, the statement that is accepted as true on the basis of the premise.
-A single conclusion is always best
The simplest argument is one composed of two statements, a supporting statement or premise and a supported statement or conclusion.
Example: Because he was constantly disputing with his boss (premise), Dave was transferred to the Houston office. (Conclusion)
Deduction:
The simplest way to understand this is : If you have to think about, read, or research your conclusion than it is a conclusion reached by logical deduction.
With deduction:
The nature of a universal statement is such that, it is it true, a particular statement wit hthe same subject and predicate is also true.
So that basically means - your premise is true than you conclusion is true.
Induction:
The simplest way to understand this: You know because you just do. The sun gives off heat. You dont have to research this or think about the sun giving off heat because its a logical induction.
With Induction:
The move from universal to particular ensures a necessarily trule conclusion.
So that basically means - the premise could be true, but the conclusion does not have to be true.
I hope this helped. Let me know if you have anymore questions.
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