Monday 16 July 2018

Doubting my take

My last post here was started a long time ago, and as I recently completed it I began to have doubts about my own characterisation of Carnap’s “core programme” (as I have been calling it).

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 problems
There 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:
  1. Aristotle - for his Organon and the conception of demonstrative science it enunciates.
  2. Leibniz - for his idea of a Universal Characteristic and Calculus Ratiocinator, providing a mechanical decision procedure for formalised science.
  3. 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?


Wednesday 11 July 2018

Carnap's core programme

In his intellectual autobiography Carnap places front and centre, as his philosophical mission, a programme for the formalisation of philosophy and science (broadly taken) inspired primarily by Frege's concept notation and Russell's conception of "scientific method in philosophy".
Whereas Frege had the strongest influence on me in the fields of logic and semantics, in my philosophical thinking in general I learned most from Bertrand Russell. In the winter of 1921 I read his book, Our Knowledge of the External World, as a Field For Scientific Method in Philosophy. Some passages made an especially vivid impression on me because they formulated clearly and explicitly a view of the aim and method of philosophy which I had implicitly held for some time. In the Preface he speaks about "the logical-analytic method of philosophy" and refers to Frege's work as the first complete example of this method. And on the very last pages of the book he gives a summarizing characterization of this philosophical method in the following words:
The study of logic becomes the central study in philosophy: it gives the method of research in philosophy, just as mathematics gives the method in physics. 
All this supposed knowledge in the traditional systems must be swept away, and a new beginning must be made. 
To the large and still growing body of men engaged in the pursuit of science,  ...  the new method, successful already in such time-honored problems as number, infinity, continuity, space and time, should make an appeal which the older methods have wholly failed to make. The one and only condition, I believe, which is necessary in order to secure for philosophy in the near future an achievement surpassing all that has hitherto been accomplished by philosophers, is the creation of a school of men with scientific training and philosophical interests, unhampered by the traditions of the past, and not misled by the literary methods of those who copy the ancients in all except their merits.
I felt as if this appeal had been directed to me personally. To work in this spirit would be my task from now on! And indeed henceforth the application of the new logical instrument for the purposes of analyzing scientific concepts and of clarifying philosophical problems has been the essential aim of my philosophical activity.from his "Intellectual autobiography" in The Philosophy of Rudolf Carnap, p13.

What I want to draw attention to is the stark difference between this scarcely ever mentioned central aim of Carnap's philosophy, "the application of the new logical instrument for the purposes of analyzing scientific concepts and of clarifying philosophical problems has been the essential aim of my philosophical activity", and the aspects of his philosophy more frequently discussed.  Those two most prominent parts of Carnap's philosophy were his early work on the structure of appearances, and his attempt to identify the meaning to empirical propositions with their verification conditions, the "verification principle".

Not only have these two aspects been given undue prominence, but also their significance has been grossly distorted.  By many Carnap is thought of to this day as a phenomenalist, whose empiricism was so rooted in the verification principle that the whole edifice was discredited by critique of the verification principle.   W.V. Quine did not share in any mass delusion about the significance of these aspects of Carnap's philosophy.  He incisively zeroed in on a fundamental principle which really was central, the analytic/synthetic distinction.  His attack on this principle, in essence a radical scepticism about semantics, was enough to turn his contemporaries against Carnap and thrust himself forward into global pre-eminence.

In my next I will look closer at Carnap's core programme.