The other person who, along with Piero Sraffa, helped Ludwig Wittgenstein to recognize the ‘grave mistakes’ contained in his first book was Frank Ramsey. Alas, Ramsey died in 1930, aged 27. Had he lived on, I think Wittgenstein would not have taken as long to articulate the concepts expressed in his last manuscript, On Certainty, written shortly before his own death in 1951.
Another thing Wittgenstein sorely missed was a Word Processor. A sharp analytical mind, he was, by his own admission, ‘a weak draughtsman’ when it came to synthesizing his thoughts and ‘proceed from one subject to another in a natural order and without breaks’. He recognized as much in the Preface to his second book, Philosophical Investigations: ‘After several unsuccessful attempts to weld my results into such a whole, I realised that I should never succeed’. In his mind, ‘this was, of course, connected with the very nature of the investigation’. But I am convinced that cut-and-paste (and delete!) would have done wonders to condense the plethora of manuscripts, typescripts, notebooks and drafts he left behind, and help him in his strenuous effort to adhere to Boileau’s rule.
The central theme in On Certainty is the relationship between knowledge and evidence, belief and proof, trust and doubt:
8. The difference between the concept of ‘knowing’ and the concept of ‘being certain’ isn’t of any great importance at all, except where “I know” is meant to mean: I can’t be wrong. In a law-court, for example, “I am certain” could replace “I know” in every piece of testimony. We might even imagine its being forbidden to say “I know” there.
30. When someone has made sure of something, he says: “Yes, the calculation is right”, but he did not infer that from his condition of certainty. One does not infer how things are from one’s own certainty.
Certainty is as it were a tone of voice in which one declares how things are, but one does not infer from the tone of voice that one is justified.
46. But then can’t it be described how we satisfy ourselves of the reliability of a calculation? O yes! Yet no rule emerges when we do so. – But the most important thing is: The rule is not needed. Nothing is lacking. We do calculate according to a rule, and that is enough.
66. I make assertions about reality, assertions which have different degrees of assurance. How does the degree of assurance come out? What consequences has it?
We may be dealing, for example, with the certainty of memory, or again of perception. I may be sure of something, but still know what test might convince me of error. I am e.g. quite sure of the date of a battle, but if I should find a different date in a recognized work of history, I should alter my opinion and this would not mean I lost all faith in judging.
105. All testing, all confirmation and disconfirmation of a hypothesis takes place already within a system. And this system is not a more or less arbitrary and doubtful point of departure for all arguments: no, it belongs to the essence of what we call an argument. The system is not so much the point of departure, as the element in which arguments have their life.
115. If you tried to doubt everything you would not get as far as doubting anything. The game of doubting itself presupposes certainty.
166. The difficulty is to realize the groundlessness of our believing.
196. Sure evidence is what we accept as true, it is evidence that we go by acting surely, acting without any doubt.
What we call “a mistake” plays a quite special part in our language games, and so too does what we regard as certain evidence.
253. At the foundation of well-founded belief lies belief that is not founded.
299. We are satisfied that the earth is round.
368. If someone says that he will recognize no experience as proof of the opposite, that is after all a decision. It is possible that he will act against it.
And so on. In the end, Wittgenstein landed squarely in Bayesland, where Ramsey would have plausibly led him earlier. As I am sure it would have been the case if Wittgenstein had had the chance to meet Ramsey’s near contemporary, Bruno de Finetti, who fortunately lived a long and fruitful life and was able to develop Ramsey’s framework – independently conceived at about the same time – into a fully-fledged Theory of Probability. The theory was subsequently adopted and spread in Anglo-American academia by, among others, Harold Jeffreys and Leonard Savage, and has been known since then as Subjective Probability Theory (see Gillies, Chapter 4 and Galavotti, Chapter 7).
De Finetti’s work is undeservedly hard to find in English, as well as in Italian. So much so that a brilliant essay he wrote in 1934, L’Invenzione della Verità (The Invention of Truth), has been first published only a few years ago:
An explanation … is not a metaphysical task, a miraculous step towards the absolute. Concepts are invented by us: no one will say that scientific concepts and truths come from a supernatural revelation (…). Therefore, we cannot look for the explanation of any concept outside and independently of the framework of our sensations and experiences, beyond which the concept itself would not even exist. To ask, with a critical attitude, what is the meaning of a certain concept means simply to analyse the deep and essential motives that constituted, if only unconsciously, the purpose for which that concept was introduced, and that explain the intimate reason of its utility. (p. 84).
Everything is built on quicksand, although we naturally try to lay the pillars on relatively less dangerous points. However, not only laws and predictions are not certain but only probable, but even the fact that certain schemes in which we consider appropriate to represent phenomena, such as the very concepts of space and time and the measurement criteria of distances and times, continue to appear as appropriate or even only as preservable, is a fact that cannot be considered certain, but only probable (even if immensely probable). (Last sentence, p. 146).
An affinity between Wittgenstein and de Finetti has been spotted by Donald Gillies here (p. 256), together with a resonant metaphor in Popper, interestingly written at the same time:
Science does not rest upon solid bedrock. The bold structure of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or ‘given’ base; and if we stop driving the piles deeper, it is not because we have reached firm ground. We simply stop when we are satisfied that the piles are firm enough to carry the structure, at least for the time being. (The Logic of Scientific Discovery, p. 94).
It reminds me of another verse – this one by Jorge Luis Borges – that I happened to come across a long time ago:Nada se edifica sobre la piedra, todo sobre la arena, pero nuestro deber es edificar como si fuera piedra la arena… (Fragmentos de un Evangelio Apócrifo, in Elogio de la Sombra).
That is: Nothing is built on stone, everything on sand, but it is our duty to build as if sand were stone… (Fragments from an Apocryphal Gospel, In Praise of Shade [not Darkness, as it has been wrongly translated in English]).