Laws of Thought
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[edit] Definition
“Laws of Thought” is a designation given to various principles governing rational thought. A more accurate term might be “Laws of Reason”, since obviously, what we call thought is sometimes not rational. Laws of Thought may be considered axioms or self-evident principles, similar to the postulates of Euclidean Geometry.
[edit] Aristotle
Without further qualification, the “Laws of Thought” generally refer to those put forth by Aristotle:
- The Law of Identity: Each thing is identical with itself.
- The Law of Non-contradiction: Each thing cannot both have and not have a given property.
- The Law of the Excluded Middle: Each thing either has or does not have a given property.
Again, these are put forth as unprovable, and unfalsifiable axioms. As one medieval philosopher put it:
- 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.
The Law of the Excluded Middle becomes an interesting object of study in light of Gödel's Incompleteness Theorem. Since there exist statements that are neither provable nor disprovable (This itself is not a violation of the Law), it is at least conceivable that some statements might be neither true nor false.
[edit] Liebniz
Gottfried Liebniz added proposed two additional Laws of Thought in his philosophy. These are:
- The Principle of Sufficient Reason: Things are true for a reason.
- The Identity of Indiscernables: If two things are indiscernable, then they are the same thing.
It is problematic to reconcile The Principle of Sufficient Reason with human free will, and with the idea of the creation of the universe. Some philosophers have resolved this difficulty by supposing a “first cause”, often identified with God and with the “motive” for human will. Similar arguments are used today in attempts to provide a rational basis for The Existence of God.
Schopenhauer expanded the Principle of Sufficient Reason to the following four cases:
- Judgements about truth are based upon related external judgements;
- New states are preceded by existing states
- Existence of any thing depends on the existence of something else
- There is a reason or “motive” behind human choices.
[edit] Boole
The Laws of Thought, as expressed so far, suffered from the defect that they are rendered in natural human language, which is notoriously prone to equivocation and imprecision. The 19th-century philosopher George Boole placed logic on a mathematical basis by developing a system in which “true” and “false” were thought of as mathematical values, and logical connectives such as “and”, “not” and “or” were used as mathematical operators. In such a system, the Laws of Thought could be expressed in precise mathematical notation, and any supposed argument could be carried out and verified by formal manipulation of symbols.
