The ‘prehistory’ of philosophy of science (10): From logical stoicism to logical positivism.

According to the traditional myth, mentioned in passing in the first entry of this series, contemporary philosophy of science would have started in the post-WWI Vienna, when a group of young philosophers and scientists, under the heading of Moritz Schlick, attempted to show how scientific knowledge could be unambiguously derived from observational data (or at least, clearly verified by these) with the help of strictly logical arguments. Also, according to this mythology (in this case, with more than a spoonful of truth), the plausibility of such an arrogant and overambitious project (that didn’t survive in those terms the disintegration of the ‘Vienna Circle’ Logical Positivism in the years previous to the Second World War) derived in good part from the apparent successes of another philosophical project started in the last decades of the 19^th century: Gottlob Frege’s so called ‘logicism’, or his attempt to ‘reduce’ all mathematics (or more exactly, set and number theory, and what can be derived from that) to ‘logic’ (for Frege, contrary to e.g., David Hilbert, didn’t believe that geometry could be so reduced). This project has had as younger champions figures of the stature of Bertrand Russell and Ludwig Wittgenstein, forming together with Frege and with physicists Ernst Mach and Ludwig Boltzmann the Vienna Circle’s book of saints (for a lively history of the Vienna Circle, see Sigmund, 2017 ¹).

As the story goes, this reductionist project was ultimately grounded on one of the most remarkable achievements in a century as formidable in intellectual feats as the 19th: the invention of ‘modern logic’ by Gottlob Frege (1848-1925) himself. What Frege did, in his juvenile book Begriffsschrift (or ‘Conceptography’, 1879), was to invent a new type of ‘logic’, a rather different one from the classical ‘syllogistic’ (or ‘term’) logic of Aristotle, that have been the canon of rational thinking for more than two millennia, and that now sounds better fitting into books of theology, metaphysics or law than into contemporary scientific works. Fregean logic, instead, consisted of propositions connected by ‘truth-functional operators’, like negation, disjunction, conjunction, conditional and bi-conditional, and where the propositions themselves are analysed in a structure that links ‘variables’ and ‘constants’ (i.e., terms for individual entities) by means of ‘predicates’ (i.e., monadic, dyadic, or polyadic relations) and ‘quantifiers’ (expressions like ‘for every x…’ or ‘for at least one x…”). If you have read almost any mathematical handbook written in the last century, you will be perfectly familiar with that type of logic, with sentences of the form ‘a relation R is transitive if and only if for every x, y, z, if xRy and yRz, then xRz’, or, in the standard symbols: ‘R is transitive ↔ (∀x∀y∀z (Rxy ⋀ Ryz) → Rxz))’ (by the way, Frege’s Begriffsschrift originally employed a much more clumsy typography, but the essence is the same).

Frege’s logicism failed as a project in the foundations of mathematics because of eventual results like Russell’s paradox (‘the set containing those and only those sets not belonging to themselves, belongs to itself or not?’) and mainly by Gödel’s incompleteness theorem (‘for every consistent axiomatic system formalising arithmetic there is at least a true arithmetic proposition that can not be derived from those axioms’). But this does not preclude that almost all contemporary logical research, as well as mathematics and computer programming, and everything that depends on them… which now is nearly everything in all scientific fields, remains now absolutely dependent on the new type of logic the Gottlob Frege devised in his Jena solitude (for his work was not properly recognised till many decades after its publication).

Fregean logic’s departure from the classical, Aristotelian one (Kant, one century before Frege, famously said that logic ‘had born complete out of the mind of Aristotle’) is so huge that it can be taken as the clearest example of a Kuhnian ‘paradigm shift’, one of the greatest innovations in the history of human thought… save because it (as almost everything) did have precedents and precursors. Historians of logic, once they became familiar with Frege’s contrivance, indicated soon a kind of family resemblance with the ideas of a fistful of (who else?) obscure Greeks, who apparently had developed something like a theory of arguments (or ‘dialectical art’) one century more or less after the great Aristotle. The main figure within this group was Chryssipus of Soli (c. 279-206 BC), the third leader of the Stoic school, that we had mentioned in the past entry. His fame as a ‘logician’ (or master in the art of debating and arguing) was such in Ancient times, that the historian Diogenes Laërtius said that “if the gods used dialectics, they would employ that of Chryssipus’. Stoic logicians (and their own precursors, known as the ‘Megarians’, i.e., the disciples of Euclid of Megara –not to be confused with the mathematician Euclid of Alexandria, the former being a disciple of Socrates, and hence a contemporary of Plato) had defended a kind of analysis of arguments rather different from Aristotle’s syllogistics, and closer to what we (after Frege) call ‘propositional logic’, like for example modus ponens (if A entails B, and A, then B), modus tollens (if A entails B, and not B, then not A), or the ‘disjunctive syllogism’ (if either A or B, but not A, then B). Glimpses of this propositional logic (that Chryssipus had ‘reduced’ –i.e., axiomatised!– to just five formal types of propositional inferences from which all the other valid ones could be derived) had persisted through the centuries and reappeared in the writings of some medieval scholars, both Arabic, like Avicenna, and Christian, like Peter Abelard, and hence the idea of ‘a propositional logic’ was not something so absolutely new even in Frege’s times. The history of logic had also been a topic systematically studied (like almost everything imaginable) by the indefatigable 19^th-century scholars, in this case by one Carl von Prantl and his 4-volume Geschichte der Logik in Abendland (History of Western Logic, 1855-1870), a book the young Frege knew well.

Prantl’s Gechichte contains an almost one-hundred page section on the Stoic logic, collecting all the by-then known testimonies about those authors found in others’ works (for none of their original books –only Chryssipus is quoted has having authored around 700 works, 300 of them about logic– survives), though this didn’t seem to have arisen Prantl’s sympathies, for he (a good Aristotelian) repeatedly said that the Stoic’s ideas were just blödsinnig (‘idiotic’) and läppish (‘ridiculuous’). Obviously, Frege didn’t think the same, and, as it has been convincingly proved by historian of logic Sussanne Bobzien in a very recent paper ² that has provoked a lot of quarrels in academic circles, it is not only that Chryssipus’ ideas loosely ‘inspired’ Frege’s developments, but that our German hero almost literally copied in many dozens of places from the relic-like surviving lines about Chryssipus’s insights. Of course, this does not reach the complex formal apparatus developed by Frege, that is so central to modern logic, but runs through most of the ‘philosophical’ discussions Frege’s work contains about things like the ‘nature’ of propositions as ‘units of thought’ (for the Stoics: assertibles, or ‘complete contents’), the nature of negation and logical connectives, or even one the ‘most Fregean’ innovations: the analysis of universal statements not in the Aristotelian way (‘All men are mortal’) but in terms of universal quantifiers linking ‘incomplete –or sub-sentential– contents’ (i.e., ‘If something is a man, then it is mortal’). In a different context, the similarities are so patent (as is Frege’s omission of quoting his sources) that we wouldn’t doubt in affirming that “Frege plagiarized the Stoics”, as Bobzien’s paper title itself claims.

Without entering here in the debate whether this is a real case of ‘plagiarism’ or not, the truth is that ‘Logical Stoicism’ didn’t seem to have derived into something similar to a full-blown philosophy of science like that of ‘Logical Positivism’. It is not that Stoics had nothing to say about science (as I mentioned in the last entry of the series), but that they were not attempting to a kind of ‘formal reconstruction’ of scientific theories from scientific data (as Schlick or Carnap tried), nor, of course, a ‘reduction’ of mathematical theories to logical arguments (like Frege and Russell attempted). Or, if they said or wrote something along those lines, it has not reached us at all. What is undeniably true is that Stoicism became something like the ‘official philosophy’ amongst the upper classes of the Hellenistic times and the first centuries of Roman power, and hence it is very likely that many, if not most of the scientists working during that period would have considered themselves as something like ‘Stoics’ in their philosophical leanings. But, as I have said, nearly nothing about how those philosophical ideas on logic might have influenced their vision of science has survived.