Was Carnap really advocating formal science?
My doubt on this score was re-enforced by my earlier realisation that in key passages of Bertrand Russell, he was not advocating that others do what he had done in Principia Mathematica, he was advocating what he intended to do thenceforth having learnt from that experience, viz.: use "the method of logical construction", without directly using formal notations or proofs.
If we look at what Carnap actually said, retrospectively in his intellectual autobiography, there is no explicit programme of formalisation, he talks of:
the application of the new logical instrument for the purposes of analyzing scientific concepts and of clarifying philosophical problemsThere is no suggestion here of any transformation to science, nor even a commitment to the use of formal notations by philosophers. Was my interpretation of Carnap's programme mere wishful thinking?
There is no doubt that Carnap was an advocate of the use of formal notations. Quite early in his development he tells us, having been introduced to modern logic by attending Frege's lectures on the Begriffsscrift, that he began to feel he did not really understand something until he had formalised it. A sequence of his most important works directly address problems which might be considered pre-requisite for extensive deployment of formal systems, beginning with his Abriss der Logistik (1929), a logic textbook to spread the word, through the classic Logical Syntax of Language (1934), advocating pluralistic precision through syntax, to Meaning and Necessity (1947), addressing formal semantics and modal logics. To what extent, if any, he expected scientists to take them up, rather than perhaps deriving benefit from conceptual analysis undertaken by philosophers, is unclear.
Why does this matter?
It is of particular interest to me because of my own special interest in a broadly scoped application of formal logic and its automation, and my identification of a triumvirate of philosophers whose aspirations were broadly in the same direction, and in whose footsteps I conceived of myself as following. Those three philosophers were:
- Aristotle - for his Organon and the conception of demonstrative science it enunciates.
- Leibniz - for his idea of a Universal Characteristic and Calculus Ratiocinator, providing a mechanical decision procedure for formalised science.
- Carnap - for his devotion to the application of formal logic to science.
They are placed in the triumvirate for the ideas which they conceived and promoted. None of the three were at all successful in realising their aims. Aristotle's best approach to formalised logic, the syllogistic, fell well short of the deductive needs of mathematics and science, but sufficed to give Leibniz the illusion that scientific truth might be decidable. Leibniz's ideas were prescient, but his ideas on how they could be accomplished (or even what could be accomplished) were fundamentally flawed. In many ways the promise of Carnap's Logical Positivism proved illusory, and was to be refined by him into a softer Logical Empiricism, moderated particularly in its approach to the meaning and confirmation of synthetic propositions. Many important parts of his ideas about the application of logic to science remained intact, including fundamental features such as the clean distinction between analytic and synthetic propositions, his linguistic pluralism and ontological conventionalism, and his positive attitude toward and work on semantics for formal notations.
It is Carnap's position in my trilogy of predecessors which might have been threatened by doubts about his commitment to formal science, but he remains for me, despite any such doubts, the man who sought to rework Russell's achievement (with Whitehead) in Principia Mathematica and deliver similar results across the whole of empirical science, and for that he stays well in place.
Beyond that incompletely realised vision, Carnap is significant for me as the philosopher who has seemed the closest predecessor to my own philosophical views. In consideration of that connection, as a part of articulating my own forward strategy, I will be considering how the changes which have taken place since Carnap was alive might have affected his vision and program.
If he were starting now, what would have been the vision, and how might he have sought to realise it?