From his sickbed he kept up contact with the young Trinity mathematician William Walton, and dictated his thoughts on a wide range of topics, including etymology, bees'cells, Roman money, the principles of a projected Chinese dictionary, and Boole's " The Laws of Thought " ( 1854 ).
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.
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 ".
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.
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.
37.
In his investigation he comes back now and then to the three traditional laws of thought, singling out the law of contradiction in particular : " The conclusion that the law of contradiction is a law of " thought " is nevertheless erroneous . . . [ rather ], the law of contradiction is about things, and not merely about thoughts . . . a fact concerning the things in the world ."
38.
Other important points in which Hutcheson follows the lead of Locke are his depreciation of the importance of the so-called laws of thought, his distinction between the primary and secondary qualities of bodies, the position that we cannot know the inmost essences of things ( " " intimae rerum naturae sive essentiae " " ), though they excite various ideas in us, and the assumption that external things are known only through the medium of ideas ( " Syn.
39.
She argues that, " acknowledging matter as somehow akin to and penetrated by mind is not adding a new . . . assumption . . . it is becoming aware of something we are doing already . " She suggests that " this topic is essentially the one which caused Einstein often to remark that the really surprising thing about science is that it works at all . . . the simple observation that the laws of thought turn out to be the laws of things ."
40.
But whatever violates the laws of thought cannot be subject to rational language; it cannot be said to exist any more than a sentient stone ( i . e . a sentient non-sentient being ) can be said to exist . ( At the moment a stone becomes sentient, in other words, it ceases to be a stone . ) Goldblatt concludes that two theological statements, which seem irreconcilable, are nevertheless necessarily true : 1 ) God created the world; 2 ) God does not exist.
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