Context Kultur → Lebensform, Aspects vs. Techniques Turing

The “Machine” Self-Symbolizing Its Own Actions: Philosophical Investigations §§189ff.

Juliet Floyd, Boston University

University of Indiana, Bloomington, Center for Theoretical Inquiry Discussion of Philosophical Investigations §§189ff., via Zoom 3 13 2021 Context Kultur → Lebensform, Aspects vs. Techniques Turing

Table of Contents

Context

Kultur → Lebensform, Aspects vs. Techniques

Turing Context Kultur → Lebensform, Aspects vs. Techniques Turing

Wittgenstein’s Idea

Wittgenstein always envisioned a book with the structure of: • Part I: The Proposition and Meaning • Part II: Applications of the View to the Foundations of Logic and Mathematics

All his major drafts of books exhibit this structure: • Philosophical Remarks (1930) • The Big Typescript (213) (1931-1934) • Philosophical Grammar (1934) • Frühversion, Bearbeitete Frühversion, Philosophical Investigations (1937-38) Context Kultur → Lebensform, Aspects vs. Techniques Turing

Versions of Philosophical Investigations, 1936-1944

• MS 155: Fall 1936, Attempt to Translate The Brown Book into English • MS 142: Urfassung of PI, pp. 1-76, Norway before Nov.-Dec. 1936 • MS 142: Urfassung of PI, pp. 77-167, Norway Jan.-May 1937 • TS 220: Urfassung, Cambridge, Summer 1937 • TS 221: Norway, fall 1937-Spring 1938; Dictated in 1938 • TS 220+TS 221 = Frühfassung of PI, Submitted to Cambridge Press Summer 1938 • TS 222: Bearbeitete Frühfassung of PI, Submitted to Cambridge Press September 1943, accepted but withdrawn from publication 1944 Context Kultur → Lebensform, Aspects vs. Techniques Turing

Wittgenstein’s Later Philosophy of Mathematics, 1937-1944

• Remarks on the Foundations of Mathematics: 1937-1944. • Many other manuscripts, Lecture Courses (WCL, LFM) • Floyd and Mühlhölzer, Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics: An Investigation of Wittgenstein’s Non-Extensionalist Understanding of the Real Numbers (Springer 2020). • Floyd, Wittgenstein’s Philosophy of Mathematics, Cambridge Element (forthcoming) • Floyd, Wittgenstein’s Later Philosophy of Mathematics, Cambridge Element (in progress) Context Kultur → Lebensform, Aspects vs. Techniques Turing

What’s New in 1937?

1. Interlocutory style; non-linearity as opposed to The Blue and Brown Books. 2. "Forms of Life" go deeper than language-games. 3. Simplicity is fluid: absolutely fluid, not relative to language-games. 4. Logic is not gap-free Luckenlose (see PI Preface). 5. The idea of a “technique”. Context Kultur → Lebensform, Aspects vs. Techniques Turing

“Forms of Life” in Wittgenstein

• In 1936 Wittgenstein failed to turn the dictated Brown Book into a book. It was too linear, too anthropological (“tribes”, “culture”), naive about “general” rule-following. • He also heard about Turing’s “On Computable Numbers, with an application to the Entscheidungsproblem” (partial routines, command structures, are fundamental, absolute, unified and in general undecideable). PI is a book of incompleteness. • He began anew. The interlocutory style of Philosophical Investigations emerges: first person voices, multilogues, contestations. • Neither Kultur nor Wert occur in Philosophical Investigations (except PI §119, the “value” of bumping up against limits of language). They are concertedly replaced by Lebensformen. Context Kultur → Lebensform, Aspects vs. Techniques Turing

The Urfassung of Philosophical Investigations (MS 142, fall 1936)

76 pages of the Urfassung were done by Christmas 1936. • The remarks on Plato’s Theaetetus and simples are added in more or less their final position. • “Forms of life” enter the manuscript concertedly (PI §§19, 23-25). • “Culture” [Kultur] and “common sense” are dropped from the manuscript, never entering again. • Wittgenstein’s remarks about Ramsey, logic as a calculus, and logic as a “normative science” are written down. • The rule-following remarks are broached, but the notion of “technique” is absent. Context Kultur → Lebensform, Aspects vs. Techniques Turing

End of the Urfassung, Chrismas 1936

The manuscript stops with the question—which remains as yet unanswered:

“In what sense is logic something sublime?” (UF 86, cf. PI §89) Context Kultur → Lebensform, Aspects vs. Techniques Turing

Simplicity Revisited, Norway, Spring 1937

Turing sent Wittgenstein an offprint of “On computable numbers, with an application to the Entscheidungsproblem” by 11 Feb. 1937. Throughout the spring, in his notebooks Wittgenstein struggles with the notion of simplicity, which he says must be domesticated: “The simple as a sublime term and the simple as an important form of representation [Form der Darstellung] but with homespun [hausbackener] application” (152, 96).

Wittgenstein is subliming the simple, transforming the sublime into the simple. But not in the manner of the Tractatus any longer, in contrast to it (Engelmann 2013). Turing shows that analysis must have a “homespun” use. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Wittgenstein on Simplicity: 4 Stages

• Simplicity as an absolute ideal (1914-1921) TLP • Simplicity as relative to Satzsysteme (1929-1932) [“Insight”] • Simplicity given in language-games (1933-1936) BB • Simplicity as fluid and ubiquitous (1937-1951)

Floyd 2020: In the final stage, forms of life are the dynamic arenas with and in which human lives with language play themselves out. What is “simple” (evident, right before our eyes, the “given”, the “unthinkable”) is contestable, changing, subject to drift, etc. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Urfassung of PI: Spring 1937

Wittgenstein completed the UF before leaving Norway on May 1st, 1937.

Substantial development of a mature philosophy of logic: • Warmup exercises Jan. 1937 with theory of continued fractions (MS 152) • Ideal of the “sublimity” of logic reworked • Rule-following theme developed

(The Urfassung is the manuscript source of PI §§1-189.) Context Kultur → Lebensform, Aspects vs. Techniques Turing

The Ending of the Urfassung

The manuscript ends with:

“But are the steps then not determined by the algebraical formula?” — The question contains a mistake. (PI §189)

And indeed it does contain a mistake, if we think of Turing’s way of analyzing the idea of “determining the steps” in something other than a miraculous or “purely formal” way. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Turing 1936, “On computable numbers, with an application to the Entscheidungsproblem

Turing shows that there is no machine (no human acting like a machine, reckoning according to a rule) that can decide, Yes or No, according to a gap-free, general method, "Is a sentence s of a formal system of logic P valid or not?

(Wittgenstein had first formulated this question in a letter to Russell of 1913, calling it the “Grundproblem der Logik”.) Context Kultur → Lebensform, Aspects vs. Techniques Turing

Wittgenstein, RPP I §1096 (MS 135, 1947)

Turing’s “Machines”. These machines are humans who calculate. And one might express what he says also in the form of games. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Cambridge Summer 1937

• Wittgenstein shows the Urfassung to Moore. He tells Moore that in The Brown Book he had used a “false method”, but that now he has found “the correct method”. Moore does not know what this means, but notices the new remarks on simplicity. • Turing, Alister Watson and Wittgenstein discuss “On Computable Numbers” and the foundations of mathematics, especially the recent undecidability results (Mind 1938 paper by Watson). Context Kultur → Lebensform, Aspects vs. Techniques Turing

Wittgenstein 1937-1938: the Frühfassung of PI

• In Norway 1937-1938 the Frühfassung is extended. The perspective developed in §§1-189 is applied to logic the foundations of mathematics (= RFM I). The machine as a “symbol of its own way of operating” (PI §§193ff). “Technique” enters (Watson mentioned here explicitly, FF §322 (= RFM I §133)). • Writes RFM II, remarks on Cantor’s Diagonal Argument. • Lectures at Cambridge on Gödel (negation, “provability”). • Submits the Frühversion of PI to the Cambridge Press with a Preface emphasizing that the method is not “gap free” [Luckenlose], it doesn’t run along one “track”. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Fall 1937: The Machine Symbolizing Its Own Actions (PI §193)

This remark is drafted in Norway immediately upon Wittgenstein’s arrival from Cambridge fall 1937. It enters Wittgenstein’s manuscripts just after the discussion with Watson and Turing of Gödel, Turing, etc. in summer 1937.

These manuscripts echo many remarks in Watson’s Mind paper of 1938 (which explicitly thanks Turing and Wittgenstein for its content).

See MS 119, 28; cf. Frühfassung §349, RFM I §122, PI §193. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Notebook 160, 1938

W. realizes he “must get used to seeing a variety of techniques of sign usage (i.e., thinking)”.

A sentence will have a variety of techniques associated with its meaningful applications (Travis 2008: Occasion Sensitivity).

160: This whole issue hangs together with: Are you clear about the inapplicability of the usual conception of reference [Bedeutung], meaning [Sinn] and truth [Wahrheit]? Context Kultur → Lebensform, Aspects vs. Techniques Turing

“To imagine a language is to imagine a form of life” (PI §19)

What is taken to be “simple”, “clear”, “unthinkable” is important, part of how we live, embedded in our bodily life with language. But this is something fluid, evolving, contestable, partial, contingent, and without necessary hierarchies, analyses, or a fixed bottom level. Putnam: necessity relative to a conceptual scheme (Monist Special Issue 2020). As both Wittgenstein and Turing appreciated, there is a need for Lebensformen at the foundations: the human embedding of “phraseology” in life, explored in dialogue and discussion. Context Kultur → Lebensform, Aspects vs. Techniques Turing

“Forms of Life” in Wittgenstein

• Forms of life are not the “Life World” of the phenomenologist (Lebenswelt never occurs in Wittgenstein’s writings). “Life Worlds” contain already-meaningful, culturally-saturated forms and holistic norms of living at the level of a whole world. • “Form of life” is a norm of elucidation of portions of human life, not something “given” to be described: the possibility of structure in life (cf. TLP 2.032), schematicity, automaticity vs. dynamic transformations (e.g. film, Cavell 1979). • Forms of life in Wittgenstein have a biological, as well as an ethnological aspect (Cavell 1988). • Forms of life require the first-person voice (a specific, unique ‘I’), the claims of an individual within a larger social structure: these are fundamental to the embedding of words in life (Cavell passim, Laugier 2015). Context Kultur → Lebensform, Aspects vs. Techniques Turing

Examples of Forms of Life: PI §23

• Walking, chatting, playing, giving orders and commands, calling things by their names, pointing at things • Feeling grief, describing things, constructing an object from drawings • Reporting events, speculating about an event, making up a story, smiling at newborns, playing with picture books and children • Acting in a play, singing rounds, guessing riddles, cracking a joke • Solving a problem in applied arithmetic, translating from one language to another • Requesting, thanking, cursing, greeting, praying Context Kultur → Lebensform, Aspects vs. Techniques Turing

Technik also Enters W.’s Manuscripts 1st in 1937

The propositions of logic are “laws of thought” “because they express the essence of human thought” – but more correctly: because they express or show the essence, technique (Watson), of thinking. They show what thinking is and also ways of thinking. (MS 118, 87r; Frühfassung §322, RFM I §133.)

The notion of "technique" occurs 117 times in Wittgenstein’s 1939 Lectures on the Foundations of Mathematics, in discussion with Turing. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Aspects vs. Techniques: Aspect “Realism”

Aspects are discovered, whereas techniques are invented.

BT, §134; RFM II §38, RFM III §§46ff; MS 122, pp. 15, 88-88, 90; PI §§119,124-129,133,222,262,387,536; xi, p. 196; PPF xi, §130. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Wittgenstein and Turing

• Wittgenstein and Turing shared a matrix of foundational ideas about the nature of logic. • They also discussed the nature, limits, and foundations of logic over many years. • They drew from one another, as they both recognized. • We have here a confluence of ideas forged over many years, not a conflict.

Wittgenstein → Turing Wittgenstein ← Turing Context Kultur → Lebensform, Aspects vs. Techniques Turing

Turing’s Analysis

Turing’s 1936 paper bears the stamp of Wittgenstein’s way of thinking about logic “anthropologically”, rather than “metamathematically”: Turing’s ‘machines’ are humans who calculate” (RPP I §1095). (We self-mechanize).

Turing analyzed what a step in a formal system is by thinking through what it is for, i.e., what is done with it.

Turing made the very idea of a formal system (or a “step in accordance with the simplest rules of a logical system”) plain, or “homespun”. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Turing Re-Read

• Turing’s philosophical attitude has been distorted by controversies in recent philosophy of mind (Putnam): computationalist and behaviorist reductionisms, functionalism, AI, and the “the singularity”, in which machines will inevitably become the primary drivers of cultural change and creativity.

• Turing was neither a behaviorist nor a reductive mental mechanist. Philosophy of logic, not philosophy of mind, was central for his work on foundations. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Turing Re-Read

• Turing focussed on taking what we say and do with words seriously, and on the limits of formal methods, not only their power.

• Everyday language, including our “typings” of objects as they occur naturally in science and everyday life, are an evolving framework or technology. Turing stressed human conversation, “phraseology”, and “common sense”, as foundational.

• Turing reported (1942/44) that he had learned this lesson from Wittgenstein’s (1939) Lectures (Floyd 2013). Context Kultur → Lebensform, Aspects vs. Techniques Turing

Turing’s Machines: Compare PI §§188,190

• A human computor works locally, step-by-step, and can only take in a certain number of symbols at a glance. • The computor takes in “simple operations ... so elementary that it is not easy to imagine them further divided”. • We “avoid introducing the notion of a ‘state of mind’ by considering a more physical and definite counterpart: it is always possible for the computor to break off from his work, to go away and forget all about it, and later to come back and go on with it. If he does this he must leave a note of instructions (written in standard form) explaining how the work is to be continued. This note is the counterpart of the ‘state of mind”’. Context Kultur → Lebensform, Aspects vs. Techniques Turing

The Extensional vs. the Non-Extensional Perspective (PI §§191-192, Floyd and Mühlhölzer 2020)

§191. “It is as if we could grasp the whole use of the word at a stroke.” Like what, for example? – Can’t the use – in a certain sense – be grasped at a stroke? And in what sense can’t it? – It is indeed as if we could ’grasp it at a stroke’ in a much more direct sense. – But have you a model for this? No. It is just that this mode of expression suggests itself to us. As a result of the crossing of different pictures.

§192. You have no model of this inordinate fact, but you are seduced into using a super-expression. (It might be called a philosophical superlative.) Context Kultur → Lebensform, Aspects vs. Techniques Turing

Turing’s Diagonal Argument: Two Faces of a Turing Machine, Extensional and Non-Extensional In his 1936 paper Turing does not use the “Halting Argument” in order to show that there is no decision procedure for logic. Instead, he constructs an idiosyncratic machine, one that turns up the following command:

Do What You Do or “I Do What I Do”

This expresses a rule that cannot be followed. The point of this is purely philosophical, not only mathematical. The human interface, the human context of a shareable command, is demonstrated to be fundamental to the nature of logic. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Turing (1936)

The simplest and most direct proof ... is by showing that, if this general process [of determining whether a machine is “circle free”] exists, then there is another [“contradictory”] machine β. This proof, although perfectly sound, has the disadvantage that it may leave the reader with a feeling that “there must be something wrong”. The proof which I shall give has not this disadvantage, and gives a certain insight into the significance of the idea “circle-free". It depends not on constructing β, but on constructing β0, whose nth figure is φn(n). Context Kultur → Lebensform, Aspects vs. Techniques Turing

Contrast with Carnap’s “Principle of Tolerance” (Floyd 2012)

• Choice of logic not at issue (no reliance on law of excluded middle, bi-valence, law of contradiction). • Choice of linguistic framework not at issue. • Consistency of a command structure not at issue. • Internal coherence/strength of a metastance not at issue. • Formalization alone doesn’t settle the analysis, but not for general reasons, for specific reasons having to do with the special problem context. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Gödel 1946 Praises Turing’s Analysis

In all other cases treated previously, such as demonstrability or definability, one has been able only to define them relative to a given language, and for each individual language it is clear that the one thus obtained is not the one looked for. For the concept of computability, however, although it is merely a special kind of demonstrability or definability, the situation is different. By a kind of miracle it is not necessary to distinguish orders, and the diagonal procedure does not lead outside the defined notion. Context Kultur → Lebensform, Aspects vs. Techniques Turing

The Stored Program Computer Concept

• This is the idea of a machine that can work on its own commands (Wittgenstein: the idea of a machine “symbolizing its own actions”). • Turing’s Universal Machine makes possible the ubiquity of computational processing in our world, and its indefinite extent of application and ability to compress what is definable. • The Universal Machine shows that there are no dichotomies between hardware, data, and software. • The Universal Machine shows us the robustness in the idea of the fluidity of “simplicity”. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Wittgenstein, RPP I §1096 (MS 135, 1947)

Turing’s “Machines”. These machines are humans who calculate. And one might express what he says also in the form of games. And the interesting games would be such as brought one via certain rules to nonsensical instructions (unsinnigen Anweisungen). I am thinking of games like the “racing game”. One has received the order “Go on in the same way” when this makes no sense, say because one has got into a circle. For that order makes sense only in certain positions. (Watson.) Context Kultur → Lebensform, Aspects vs. Techniques Turing

But what about Turing and AI? Context Kultur → Lebensform, Aspects vs. Techniques Turing

Turing, “Intelligent Machinery" (1948): The “Intellectual” Search

We might arrange to take all possible arrangements of choices in order, and go on until the machine proved a theorem which, by its form, could be verified to give a solution of the problem ... Further research into intelligence of machinery will probably be very greatly concerned with “searches” of this kind. We may ... call such searches “intellectual searches”. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Turing, “Intelligent Machinery", The Evolutionary Search

It may be of interest to mention two other kinds of search in this connection. There is the genetical or evolutionary search by which a combination of genes is looked for, the criterion being survival value. The remarkable success of this search confirms to some extent the idea that intellectual activity consists mainly of various kinds of search. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Turing, “Intelligent Machinery", The Cultural Search

The remaining form of search is what I should like to call the ‘cultural search‘... [T]he isolated man does not develop any intellectual power. It is necessary for him to be immersed in an environment of other men, whose techniques he absorbs during the first 20 years of his life. He may then perhaps do a little research of his own and make a very few discoveries which are passed on to other men. From this point of view the search for new techniques must be regarded as carried out by the human community as a whole, rather than by individuals. Context Kultur → Lebensform, Aspects vs. Techniques Turing

Turing’s 1950 Test: Machine “Intelligence”, an “Imitation Game" Context Kultur → Lebensform, Aspects vs. Techniques Turing

The Turing Test is a Social Test Context Kultur → Lebensform, Aspects vs. Techniques Turing

Thank You!