Critical notice Logical machines: Peirce on psychologism

This essay discusses Peirce’s appeal to logical machines as an argument against psychologism. It also contends that some of Peirce’s anti-psychologistic remarks on logic contain interesting premonitions arising from his perception of the asymmetry of proof complexity in monadic and relational logical calculi that were only given full formulation and explication in the early twentieth century through Church’s Theorem and Hilbert’s broad-ranging Entscheidungsproblem. In Gulliver’s Travels, Jonathan Swift relates that in his voyage to Balnibarbi Gulliver comes across a professor of the grand academy of Lagado who shows him a machine capable of improving and extending knowledge by ‘mechanical operations.’ (Swift 1735: 195) The academician explains that ‘by his contrivance, the most ignorant person at a reasonable charge, and with a little bodily labour, may write books in philosophy, poetry, politicks, law, mathematicks and theology, without the least assistance from genius or study.’ (Swift 1735: 196) So far as the other voyages are concerned, it is clear whom Swift meant to ridicule, the follies and foibles he wished to expose. Balnibarbi’s target is rather less obvious. Why was Swift so acutely roiled by mathematicians and natural scientists in a period when mathematics was being enriched by major discoveries, when mathematical physics was being systematically extended, and when experimental sciences were flourishing in almost every department? Nonetheless, the target of the above narrative is apparently to deride the Organons of Aristotle and Bacon by exposing the inanity of supposing that any machine or instrument can do the work of the mind. The ambition to mechanise logic, in particular, goes back to Leibniz’s dream of a lingua characterica – a logical language into which every clear question could be translated and then settled by calcula-