The laws of thought are fundamental axiomatic rules upon which rational discourse itself is based. The three classic laws of thought are attributed to Aristotle. These three laws are samples of self-evident logical principles. Everyone should memorize these laws.
1. The Law of Identity (Whatever is, is.)
The law of identity states that an object is the same as itself: A = A.
"Being is."
- Parmenides the Eleatic (circa BC. 490)
"Now 'why a thing is itself' is a meaningless inquiry (for—to give meaning to the question 'why' — the fact or the existence of the thing must already be evident — e.g., that the moon is eclipsed — but the fact that a thing is itself is the single reason and the single cause to be given in answer to all such questions as why the man is man, or the musician musical, unless one were to answer, 'because each thing is inseparable from itself, and its being one just meant this.' This, however, is common to all things and is a short and easy way with the question."
- Aristotle, Metaphysics
2. The Law of Non-Contradiction (Nothing can both be and not be.)
The oldest statement of the law is that contradictory statements cannot both at the same time be true, e.g. the two propositions A is B and A is not B are mutually exclusive.
"It's plain that the same thing won't be willing at the same time to do or suffer opposites with respect to the same part and in relation to the same thing."
- Plato, The Republic
"It is not possible to say truly at the same time that the same thing is and is not a man."
- Aristotle, Metaphysics
"Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned."
- Avicenna, Metaphysics
3. The Law of Excluded Middle (Everything must either be or not be.)
The Law of excluded middle is the principle that for any proposition, either that proposition is true, or its negation is.
"It is impossible, then, that 'being a man' should mean precisely 'not being a man', if 'man' not only signifies something about one subject but also has one significance.... And it will not be possible to be and not to be the same thing, except in virtue of an ambiguity, just as if one whom we call 'man', and others were to call 'not-man'; but the point in question is not this, whether the same thing can at the same time be and not be a man in name, but whether it can be in fact."
- Aristotle, Metaphysics
"Every judgment is either true or false."
- Leibniz, New Essays
1. The Law of Identity (Whatever is, is.)
The law of identity states that an object is the same as itself: A = A.
"Being is."
- Parmenides the Eleatic (circa BC. 490)
"Now 'why a thing is itself' is a meaningless inquiry (for—to give meaning to the question 'why' — the fact or the existence of the thing must already be evident — e.g., that the moon is eclipsed — but the fact that a thing is itself is the single reason and the single cause to be given in answer to all such questions as why the man is man, or the musician musical, unless one were to answer, 'because each thing is inseparable from itself, and its being one just meant this.' This, however, is common to all things and is a short and easy way with the question."
- Aristotle, Metaphysics
2. The Law of Non-Contradiction (Nothing can both be and not be.)
The oldest statement of the law is that contradictory statements cannot both at the same time be true, e.g. the two propositions A is B and A is not B are mutually exclusive.
"It's plain that the same thing won't be willing at the same time to do or suffer opposites with respect to the same part and in relation to the same thing."
- Plato, The Republic
"It is not possible to say truly at the same time that the same thing is and is not a man."
- Aristotle, Metaphysics
"Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned."
- Avicenna, Metaphysics
3. The Law of Excluded Middle (Everything must either be or not be.)
The Law of excluded middle is the principle that for any proposition, either that proposition is true, or its negation is.
"It is impossible, then, that 'being a man' should mean precisely 'not being a man', if 'man' not only signifies something about one subject but also has one significance.... And it will not be possible to be and not to be the same thing, except in virtue of an ambiguity, just as if one whom we call 'man', and others were to call 'not-man'; but the point in question is not this, whether the same thing can at the same time be and not be a man in name, but whether it can be in fact."
- Aristotle, Metaphysics
"Every judgment is either true or false."
- Leibniz, New Essays
The laws of thought can be most intelligibly expressed thus:
1. Everything that is, exists.
2. Nothing can simultaneously be and not be.
3. Each and every thing either is or is not.
4. Of everything that is, it can be found why it is.
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