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Law of thought
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Law of thought
The laws of thought as described by logicians are the basic rules that guide each individual's thinking and all rational discussion. These rules have been clarified and formulated by philosophers over a long period of time. In recent times, these classical ideologies have been rejected and questioned throughout society.
According to the 1999 Cambridge Dictionary of Philosophy, laws of thought are laws by which valid thought proceeds, or that justify valid inference, or to which all valid deduction is reducible. These laws of thought are to be applied without exception to any subject matter. The term, rarely used in exactly the same sense by different authors, has long been associated with three equally ambiguous expressions: the law of identity (ID), the law of contradiction (or non-contradiction; NC), and the law of excluded middle (EM). Sometimes, these three expressions are taken as propositions of formal ontology having the widest possible subject matter.
Beginning in the middle to late 1800s, these expressions have been used to denote propositions of Boolean algebra about classes: (ID) every class includes itself; (NC) every class is such that its intersection ("product") with its own complement is the null class; (EM) every class is such that its union ("sum") with its own complement is the universal class. More recently, the last two of the three expressions have been used in connection with the classical propositional logic and with quantified propositional logic. In both cases the law of non-contradiction involves the negation of the conjunction of something with its own negation, ¬(A∧¬A), and the law of excluded middle involves the disjunction of something with its own negation, A∨¬A. The expressions "law of non-contradiction" and "law of excluded middle" are also used for semantic principles of model theory concerning sentences and interpretations: (NC) under no interpretation is a given sentence both true and false, (EM) under any interpretation, a given sentence is either true or false.
The expression "laws of thought" gained added prominence through its use by Boole (1815–64) to denote theorems of his "algebra of logic." In fact, Boole named his second logic book An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities (1854). Modern logicians, in almost unanimous disagreement with Boole, take this expression to be false; none of the above propositions classed under "laws of thought" are explicitly about thought per se, a mental phenomenon studied by psychology, nor do they involve explicit reference to a thinker or knower as would be the case in pragmatics or in epistemology. The distinction between psychology (as a study of mental phenomena) and logic (as a study of valid inference) is widely accepted.
Hamilton offers a history of the three traditional laws that begins with Plato, proceeds through Aristotle, and ends with the schoolmen of the Middle Ages; in addition he offers a fourth law (see entry below, under Hamilton):
The law of identity: 'Whatever is, is.'
For all a: a = a.
Regarding this law, Aristotle wrote:
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Law of thought
The laws of thought as described by logicians are the basic rules that guide each individual's thinking and all rational discussion. These rules have been clarified and formulated by philosophers over a long period of time. In recent times, these classical ideologies have been rejected and questioned throughout society.
According to the 1999 Cambridge Dictionary of Philosophy, laws of thought are laws by which valid thought proceeds, or that justify valid inference, or to which all valid deduction is reducible. These laws of thought are to be applied without exception to any subject matter. The term, rarely used in exactly the same sense by different authors, has long been associated with three equally ambiguous expressions: the law of identity (ID), the law of contradiction (or non-contradiction; NC), and the law of excluded middle (EM). Sometimes, these three expressions are taken as propositions of formal ontology having the widest possible subject matter.
Beginning in the middle to late 1800s, these expressions have been used to denote propositions of Boolean algebra about classes: (ID) every class includes itself; (NC) every class is such that its intersection ("product") with its own complement is the null class; (EM) every class is such that its union ("sum") with its own complement is the universal class. More recently, the last two of the three expressions have been used in connection with the classical propositional logic and with quantified propositional logic. In both cases the law of non-contradiction involves the negation of the conjunction of something with its own negation, ¬(A∧¬A), and the law of excluded middle involves the disjunction of something with its own negation, A∨¬A. The expressions "law of non-contradiction" and "law of excluded middle" are also used for semantic principles of model theory concerning sentences and interpretations: (NC) under no interpretation is a given sentence both true and false, (EM) under any interpretation, a given sentence is either true or false.
The expression "laws of thought" gained added prominence through its use by Boole (1815–64) to denote theorems of his "algebra of logic." In fact, Boole named his second logic book An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities (1854). Modern logicians, in almost unanimous disagreement with Boole, take this expression to be false; none of the above propositions classed under "laws of thought" are explicitly about thought per se, a mental phenomenon studied by psychology, nor do they involve explicit reference to a thinker or knower as would be the case in pragmatics or in epistemology. The distinction between psychology (as a study of mental phenomena) and logic (as a study of valid inference) is widely accepted.
Hamilton offers a history of the three traditional laws that begins with Plato, proceeds through Aristotle, and ends with the schoolmen of the Middle Ages; in addition he offers a fourth law (see entry below, under Hamilton):
The law of identity: 'Whatever is, is.'
For all a: a = a.
Regarding this law, Aristotle wrote: