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laws of logic
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• logic • rules of inference

 

Definition:
In informal logic, people use three basic, logical principles which are regarded as the three basic "laws of logic" or "laws of thought":

1. The law of identity: p is p at the same time and in the same respect. Thus: George W. Bush is George W. Bush, and George W. Bush is the son of George Bush.

2. The law of non-contradiction: a conjunctive proposition (one that uses "and", as in "p and q") cannot be both true and false at the same time and in the same respect. Thus the proposition "p and not-p" cannot be true. For example, the proposition "It is raining and it is not raining" is a contradiction, and must be false.

Note: technically, the above example stated fully should read "It is raining and it is not raining at this location and at this time." This additional phrase encompasses the crucial factors of "at the same time" and "in the same respect," but in natural language it isn't common to state them explicitly. When evaluating a person's statements, it is sometimes helpful to consider whether or not they are indeed assuming the truth of such factors.

3. The law of the excluded middle: in any proposition "p," the related disjunctive claim (one that uses "or", as in "p or not-p") must be true. A more informal and common way of stating this is to simply say that either a proposition is true or its negation must be true - thus, either p is true or not-p must be true.

For example, the disjunctive proposition "Either it is raining or it is not raining" must be true. Also, if it is true that it is raining, then the proposition "Either it is raining, or I own a car" must also be true. It really doesn't matter what the second phrase is.

The above "laws of logic" are part of the basic logical rules of inference.

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Related Resources:

What is the Logic and the Philosophy of Language?
The two fields Logic and the Philosophy of Language are often treated separately, but they are nevertheless close enough that they are presented together here. Logic is the study of methods of reasoning and argumentation, both proper and improper. The Philosophy of Language, on the other hand, involves the study of how our language interacts with our thinking.

What is Philosophy?
What is philosophy? Is there any point in studying philosophy, or is it a useless subject? What are the different branches of philosophy - what's the difference between aestheitcs and ethics? What's the difference between metaphysics and epistemology?

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