Charles S. Peirce (1839 - 1914) achtte de 'geometrische orde' van de Ethica "merely a veil over the living thought"

Eigenlijk is deze Amerikaanse pragmaticus, wiskundige, wiskundefilosoof, historicus van de wiskunde en natuurkundige, te groot voor een blog als dit. Ik hoef het gelukkig over zijn eigen filosofie niet te hebben en kan me beperken tot alleen zijn relatie tot Spinoza. Nu is daarover niet veel geschreven. Eigenlijk is er slechts één filosofe die zich diepgaand met die relatie heeft bezig gehouden: Shannon Dea. Zij schreef diverse artikelen over Peirce & Spinoza en promoveerde op dat onderwerp. Laat ik haar dat in haar eigen woorden zeggen: “I ended up specializing in early modern philosophy, and writing a seemingly improbable dissertation on the 19th-20th century American pragmatist Charles Sanders Peirce and the 17th century continental rationalist, Baruch Spinoza.” [Hier]

In haar speurwerk diepte ze een recensie van Peirce uit 1894 op over een uitgave van de Ethica waarin hij veelzeggende opmerkingen over Spinoza maakte, maar nog véél meer deed; eigenlijk kaapte hij een recensie om er belangrijke toelichtingen op zijn filosofie en op de relatie wiskunde-logica in weg te stoppen. Daarover schreef Dea “‘Merely a Veil Over the Living Thought’: Mathematics and Logic in Peirce’s Forgotten Spinoza Review.”

Die recensie zou enig licht werpen op een onderwerp waarover hij altijd met zijn als groot wiskundige beroemde vader, botste: de verhouding tussen wiskunde en logica. Wiskunde achtte hij van een meer primordiale orde dan logica, in plaats van zoals veelal wordt gedacht (ook door z'n vader) dat wiskunde z’n fundering zou vinden in logica. Dea schrijft: “For Peirce, true (theoremic) mathematical thought is in some sense pre-logical, and thus, the logical demonstration of this thought in the form of mathematical proofs is in fact "merely a veil over the living thought." Volgens haar werpt deze recensie meer licht op het onderscheid dat Pierce maakte tussen logica utens en logica docens en op Peirce’s notie van de ‘mathematical diagrammatization’ of ‘skeletonization’, waarop ik allemaal niet in hoef te gaan, maar die het wel een boeiend en aan te raden artikel maken. Ik haal er slechts enige grepen uit:

Peirce's remarks about mathematics in the 1894 review begin with his observation that Spinoza himself had an entirely mistaken view of his own thought. Whereas both Spinoza and his adherents regarded his thought in the Ethics as mathematical by dint of his so-called "geometrical method", Peirce argues that, even in Euclid, traditional mathematical proofs are themselves not mathematical at all.

Daarna citeert ze Pierce zelf uit zijn recensie: “This appratus [sic] of Definitions, Postulates, Axioms, Problems, and Theorems is in geometry itself merely a veil over the living thought. Hence it is that Euclid's manifold slips in logic have scarce cast a shadow of doubt over the substantial truth of his propositions. The history of mathematics justifies the presumption that just in proportion to thei importance of a theorem is the demonstration of it likely to be fallacious - or, at least, it would be so were the proposition stated in the absolute style of Euclid. Thus, the fruitfulness of Cauchy s work is intimately connected with its logical inaccuracy. Dirichlet’s principle, which powerfully aided the development of modern mathematics, is well known to be logically unsound; and much of the foundations of the theory of functions which has never been called in question - even, for example, the passage from one branch of a function to another - cannot sustain cross-examination.”

Pierce eindigt zijn recensie met: “[…] you must penetrate beneath these [theorems, with demonstrations] if you would enter the living stream of Spinoza s thinking. You then find that he is engaged in a somewhat mathematical style in developing a conception of the absolute, strikingly analogous to the metrical absolute of the math- ematicians. He thus appears as a mathematical thinker, not in the really futile, formal way in which he and his followers conceived him to be, but intrinsically, in a lofty, living, and valuable sens.

Tien jaar later zei hij, in weer een recensie:  de geometrische vorm van de Ethica was "the only thing about [Spinoza] that is not venerable." Spinoza scholars overdreven het belang van de geometrische  methode volgens hem, wat tot overdreven benadrukking van zijn metafysica leidde en tot blindheid voor Spinoza's "extraordinary approaches to pragmatism.” Peirce was van mening dat, had Spinoza langer geleefd dan zijn 44 jaar, hij het pragmatisme ver vóór Peirce zelf ontwikkeld zou hebben.

Het is misschien aardig te eindigen met deze opmerkelijke karakterisering uit Joseph Brent, Charles Sanders Peirce: A Life. Met eerst een citaat, waarin Peirce op hoge leeftijd terugblikte op z’n tienerjaren, waarin hij o.a. Spinoza las… en zichzelf beter achtte…:

“... even in my teens, when I was reading Kant, Spinoza, and Hegel my father, who was the celebrated mathematician Benjamin Peirce, not a powerful analyst of thought, so that his demonstrations were sometimes faulty, but a mind who never once failed, as well as I can remember, to draw the correct conclusion from given premises, unless by a mere slip, my father, I say would induce me to tell him about the proofs offered by the philosophers, and in a very few words would almost invariably rip them up and show them empty. He had even less mercy for such philosophers as Hobbes, Hume and James Mill. In that way, the bad habits of thinking which would have been impressed upon me by those mighty powers were in great measure, though I confess not entirely, overcome."

Joseph Brent vervolgt na dit citaat: “One effect of this training for genius was to engender in the young man an arrogance toward and impatience with others who exhibited superficial understanding or lack of clarity in their thinking. It must be corrosive of character to be placed, at the age of sixteen, in the unlikely position of believing that your own philosophical abilities are demonstrably superior to those of some of the most respected and revered philosophers of the past, such as Kant, Spinoza, Hume, and Hobbes. I imagine Charles in 1859, at age twenty, brilliantly discoursing in class "that the PERFECT is the Great Subject of Metaphysics," elegantly dressed, in negligent posture, completely self-assured and cool, the picture of the arrogant Dandy. William James commented on this aspect of Peirce's character in 1861, writing, "There is a son of Prof. Peirce, whom I suspect to be a very 'smart' fellow with a great deal of character, pretty independent and violent though."

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Peirce schreef een grote hoeveelheid lemma’s voor de Century Dictionary. Van zijn hand is ook het lemma over Spinozism en Spinozist. Interessant is hoe hij 'sub specie aeternitatis' vertaalt.


Shannon Dea, “‘Merely a Veil Over the Living Thought’: Mathematics and Logic in Peirce’s Forgotten Spinoza Review.” [in: Transactions of the Charles S. Peirce Society 42.4 (Fall 2006) 501-517.] Het is als PDF op internet te vinden.

Shannon Jennifer Dea, Peirce and Spinoza's Surprising Pragmaticism - Canadian theses. University of Western Ontario (Canada), 2007

Dea, Shannon, Firstness Evolution and the Absolute in Peirce's Spinoza. Transactions of the Charles S. Peirce Society; Fall 2008, Vol. 44 Issue 4, p603

Joseph Brent, Charles Sanders Peirce: A Life [Revised and Enlarged Edition. Indiana University Press, 1998] []

Jonathan Rocco Gangle, Spinoza in a Postmodern Context: Reading the "Ethics" with Peirce, Levinas and Deleuze. University of Virginia, 2007

Jonathan Beever, Vernon Cisney, All Things in Mind: Panpsychist Elements in Spinoza, Deleuze, and Peirce. Biosemiotics March, 2013


De 'sepiakleurige' foto is een uitsnede van 'n foto van de website van zijn universiteit.