Logicism

Logicism is the idea that thinking is identical to performing logical operations.  This idea is rooted in philosophical work of the 17^th century.  Descartes equated thinking with the kind of reasoning engaged by mathematicians.  Thomas Hobbes’ writings on the nature of the mind (Hobbes, 1651/1967) have led him to be claimed as one of the philosophical fathers of classical cognitive science.  “When a man Reasoneth, hee does nothing else but conceive a summe totall, from Addition of parcels; or conceive a Remainder, from Substraction of one summe from another” (p. 32).  Such operations were not confined to numbers: “These operations are not incident to Numbers onely, but to all manner of things that can be added together, and taken one out of another” (p. 32).  Hobbes noted that geometricians applied such operations to lines and figures, and that logicians applied these operations to words.  With respect to the notion that thinking might involve the manipulation of logical or linguistic expressions, Hobbes called thought mental discourse. 

By the 19^th century, these notions were reified in modern logical systems.  In 1854, with the publication of An Investigation of the Laws of Thought, George Boole (1854/2003) attempted to move the study of thought from the domain of philosophy into the domain of mathematics. “There is not only a close analogy between the operations of the mind in general reasoning and its operations in the particular science of Algebra, but there is to a considerable extent an exact agreement in the laws by which the two classes of operations are conducted” (Boole, 1854/2003, p. 6).  Views of this sort have prevailed into 21^st century cognitive science, refined by advances in mathematics and computer science.  Classical cognitive science – which views cognition as the product of the rule-governed manipulation of mental symbols – is the most obvious example of modern logicism.  Consider, for instance, Chomsky (1965, p. 25): “Clearly, a child who has learned a language has developed an internal representation of a system of rules that determine how sentences are to be formed, used, and understood.”

References:

1. Boole, G. (1854/2003). The Laws of Thought. Amherst, N.Y.: Prometheus Books. (Originally published in 1854).
2. Chomsky, N. (1965). Aspects Of The Theory Of Syntax. Cambridge, MA: MIT Press.
3. Hobbes, T. (1651/1967). Hobbes's Leviathan. Oxford: Clarendon Press

(Added September 2010)