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by Daniel Everett

Daniel Everett

The Pirahãs are firmly committed to the pragmatic concept of utility. They don’t believe in a heaven above us, or a hell below us, or that any abstract cause is worth dying for. They give us an opportunity to consider what a life without absolutes, like righteousness or holiness and sin, could be like.

Daniel L. Everett, Don't Sleep There are Snakes: Life and Language in the Amazonian Jungle

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Charles Sanders Peirce was a brilliant philosopher, mathematician and scientist. His polymathic work should be better known

The importance and range of Peirce’s contributions to science, mathematics and philosophy can be appreciated partially by recognising that many of the most important advances in philosophy and science over the past 150 years originated with Peirce: the development of mathematical logic (before and arguably better eventually than Gottlob Frege); the development of semiotics (before and arguably better than Ferdinand de Saussure); the philosophical school of pragmatism (before and arguably better than William James); the modern development of phenomenology (independently of and arguably superior to Edmund Husserl); and the invention of universal grammar with the property of recursion (before and arguably better than Noam Chomsky; though, for Peirce, universal grammar – a term he first used in 1865 – was the set of constraints on signs, with syntax playing a lesser role).

Beyond these philosophical contributions, Peirce also made fundamental discoveries in science and mathematics. A few of these are: the shape of the Milky Way galaxy; the first precise measurement of the Earth’s gravity and circumference; one of the most accurate and versatile projections of the 3D globe of the Earth onto 2D space; the chemistry of relations and working out the consequences of the discovery of the electron for the periodic table; the axiomisation of the law of the excluded middle, or Peirce’s Law: ((P→Q)→P)→P); existential graphs and the transformation of mathematics into an (quasi-)empirical component of studies on cognition; one of the first studies of the stellar spectra, particularly the spectral properties of argon; the invention of the then most accurate gravimetric pendulum; the first standardisation of the length of the metre by anchoring it to the length of a wavelength of light (which he figured out via his own experiments in multiple stations around Europe and North America). This is by no means an exhaustive list.

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Peirce’s influence in logic is second only to his work in semiotics. For example, while Frege’s notation was hardly ever used, the Peirce-Schröder notation was largely adopted by others. The important results of the mathematicians Leopold Löwenheim and Thoralf Skolem at the beginning of the 20th century were presented in the Peirce-Schröder system without any trace of influence by Frege or Russell. Guiseppe Peano’s use of the existential and universal quantifiers derives from Schröder and Peirce, not from Frege. Unlike Frege, Peirce recognised the utmost importance of dependent quantifiers, and experimented with that idea in various ways in the algebra of logic and in existential graphs, proposing new systems and dimensions of quantification that involve independent quantification. Peirce’s overall influence upon the development of modern logic was considerable, though its nature and scope remained ill-understood for a long time.

Before he moved to Milford, Peirce lived in Cambridge, Massachusetts. When Whitehead – one of Britain’s greatest philosophers, mathematicians and theologians – moved there himself many years later, he was so deeply impressed by the intellectual level of the new world that he drew a comparison with the greats of antiquity. With regard to Charles Peirce and William James, he claimed that, not only were they the equals of any European philosophers but that: ‘Of these men WJ is the analogue to Plato, CP to Aristotle.’

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