Many other propositions have also been mentioned as laws of thought, including the dictum de omni et nullo attributed to Aristotle, the substitutivity of identicals ( or equals ) attributed to Euclid, the so-called identity of indiscernibles attributed to Gottfried Wilhelm Leibniz, and other " logical truths ".
32.
But Frege's work is ambiguous in the sense that it is both concerned with the " laws of thought " as well as with the " laws of truth ", i . e . it both treats logic in the context of a theory of the mind, and treats logic as the study of abstract formal structures.
33.
Modern logicians, in almost unanimous disagreement with Boole, take this expression to be a misnomer; 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.
34.
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, he named his second logic book " An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities " ( 1854 ).
35.
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, he named his second logic book " An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities " ( 1854 ).
36.
The goal is to derive all of mathematics, starting with the counting numbers and then the irrational numbers, from the " laws of thought " alone, without any tacit ( hidden ) assumptions of " before " and " after " or " less " and " more " or to the point : " successor " and " predecessor ".
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