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Harald Høffding’s own copy of Relation som Kategori (1921; the printed text is in this collection, transcribed and translated) carries notes in his hand, written in the years after publication. They show him reading the new physics and the new philosophy against his own book: Bohr on the limits of causal description, Russell’s The Analysis of Mind on belief, William James, Einstein, and Kierkegaard. Høffding died in 1931; the latest dated note so far is from August 1929.
What follows is provisional. The readings are made from photographs, not yet
checked against the volume, and Høffding’s hand is compressed and heavily
abbreviated. Words marked [?] are guesses; struck words are shown struck.
English quotations that Høffding copies from printed books have been checked
against those books, which also fixes the reading of the words around them.
The notes are numbered here in the order they were read, not in the order of
the volume.
On a lined sheet. The lecture is Bohr’s address to the Scandinavian Naturalists’ Meeting in Copenhagen, published as »Atomteorien og Grundprincipperne for Naturbeskrivelsen« (Beretning om det 18. skandinaviske Naturforskermøde, 1929, pp. 71–83; in English in Atomic Theory and the Description of Nature, 1934); the Collected Works confirm that it was given on 26 August 1929. Høffding quotes it from the report in Berlingske Tidende, not from the printed lecture, whose own phrase is »den ejendommelige Svigten af Aarsagsbeskrivelsen« (the peculiar failure of causal description).
I Bohrs Foredrag ved Nord. Naturforskermøde d. 26. August 1929 udtalte han iflg. Berl. T. bl. a.: „Kravet om en Aarsagsbeskrivelse kan vi altsaa ikke honorere. Vi kan ikke
[one word]forklare, kun beskrive. Vi befinder os i en lignende [?] Situation, hvor vi maa opgive alle Begreber og lære [?] os nye Grundbegreber [?].”„Aarsagsforklaring” maa betyde, at baade det rationale [?] og det empiriske [?] Moment er fyldestgjort. Naar nu „Beskrivelse” stilles [?] i Modsætning til „Forklaring”, maa det betyde, at det rationale Moment mangler Fyldestgørelse. Og kommer denne Mangel ikke
derafaf, at Kvantelæren gælder? —Kfr. Thiele om den Opgave at beskrive Tingene i alle Henseender med Tydelighed [?] … [two lines not yet read]
Albert Einst.: hvor [?] kan det [?], at Mathematikken … [continues]
In English: In Bohr’s lecture to the Scandinavian Naturalists’ Meeting on 26 August 1929 he said, according to Berlingske Tidende, among other things: “The demand for a causal description we cannot, then, meet. We cannot explain, only describe. We find ourselves in a similar [?] situation, where we must give up all concepts and learn [?] new fundamental concepts [?].” — “Causal explanation” must mean that both the rational and the empirical moment are satisfied. When “description” is now set against “explanation”, it must mean that the rational moment lacks satisfaction. And does this lack not come from the fact that the quantum theory holds? — Cf. Thiele on the task of describing things in every respect with clarity [?] … — Albert Einstein: how [?] can it be that mathematics …
The rational and the empirical moment of explanation are the terms of Relation som Kategori itself, so Høffding is testing Bohr’s claim on his own analysis of causality. The Einstein line looks like the opening question of Geometrie und Erfahrung (1921): how can it be that mathematics, a product of human thought independent of all experience, fits the objects of reality so well? Thiele is presumably the astronomer and actuary T. N. Thiele.
On a blank leaf of the volume. Høffding copies Russell’s The Analysis of Mind (London 1921), lectures XII (“Belief”) and XIII (“Truth and Falsehood”), and answers it.
Naar Russell (Analysis of Mind, p. 238) siger: „It is impossible for a belief to consist of sensations alone, except when, as in the case of words, the sensations have associations which make them signs possessed of meaning. The reason is that objective reference is of the essence of belief, and objective reference is derived from meaning” — maa dertil siges, at der kan gives en Tro i Betydning af praktisk Tillid, som forudsætter, at der mangler Grund til Tvivl. Princippet „Hvorfor ikke?” [?] — „den manglende Grunds Princip” — gør sig faktisk gjældende. — P. 242 f. fremhæver iøvrigt Russell dette, naar han siger: „Most of our beliefs, like most of our wishes, are ‚unconscious’ … such beliefs display themselves when the expectations that they arouse fail in any way.” Og videre, naar han siger, at „our more elementary beliefs … often remain at the level of images.” — Derimod kritiserer Russell den af James [& Taine] fremsatte Teori, at Tro skulde bestaa i Fraværelse af hæmmende Forestillinger (247–250). — Smlg. Russells Kritik af Kohærensteorien, 266–268 … at Selvfølgelighed [?] (subjektiv Vished) … som Kriterium [?]. Faktisk anerkender han dog det som et stadigt [?] … Kriterium (p. 27[?]).
In English (Høffding’s Danish only): When Russell (Analysis of Mind, p. 238) says […], it must be answered that there can be a belief in the sense of practical trust, which presupposes that there is no ground for doubt. The principle “why not?” [?] — “the principle of the lacking ground” — is in fact at work. — On pp. 242 f., moreover, Russell stresses just this when he says […]. And further, when he says that […]. — On the other hand Russell criticizes the theory put forward by James [and Taine], that belief should consist in the absence of inhibiting ideas (pp. 247–250). — Compare Russell’s criticism of the coherence theory, pp. 266–268 … that self-evidence [?] (subjective certainty) … as a criterion [?]. In fact he does recognize it as a constant [?] … criterion (p. 27[?]).
The theory Russell rejects on pp. 247–250 is the one James took over from Spinoza: “any object which remains uncontradicted is ipso facto believed and posited as absolute reality” (Principles of Psychology II, 288). Høffding’s practical trust, which needs no positive ground but only the absence of a reason to doubt, sides with James against Russell. On truth, Russell rejects self-evidence and coherence as intrinsic criteria but grants that “judgments having a high degree of subjective certainty are more apt to be true than other judgments”; Høffding seems to note that Russell thereby admits a criterion after all. The last two lines are the least certain part of this reading.
On a blank leaf of the volume, facing printed text. Høffding works through Bohr’s Atomernes Bygning og Stoffernes fysiske og kemiske Egenskaber (Copenhagen 1922), citing it by page and by a letter for the place on the page, and then copies the summary of a communication Bohr gave to the Royal Danish Academy in December 1926. The opening line is the least certain part.
(Svarende [?] til en anden Side af Bohrs Undersøgelser [?]: Rationel Analyse [?] p. 98 f.)
N. Bohr: Atomernes Bygning og Stoffernes fysiske og kemiske Egenskaber, p. 6 (Stationære Tilstande af Energien som forskellige Stadier af en Proces [?]). Jf. 24 b (Kvanteteorien som rationel Udvikling af vore sædvanlige Forestillinger). Korrespondensprincippet (ɔ: den Tanke, at en bestemt Overgang mellem et Atoms stationære Tilstande betinges ved en bestemt harmonisk [?] Svingningskomponent, cf. p. 25 c) lader trods [?] Kvanteteoriens Antagelser ane en indre Sammenhæng af lignende Art som den, der fordres i de klassiske Forestillinger om
[struck]elektrodynamiske Processer, som ved Forklaringen [?] af mange fysiske Fænomener, saavel som … [a line not yet read] … af Stoffernes Egenskaber … ud af Atombygningen (p. 60 d).Smlgn. Brunschvicg: L’expérience humaine et la causalité physique, p. 397–399.
— 17. Dec. 1926 gav Bohr i Videnskabernes Selskab en Meddelelse om „Atomteori og Bølgemekanik”, som han i Slutningen [?] resumerede saaledes: „I den kvanteteoretiske Beskrivelse af Atomernes Forhold indgaar et væsentligt Element af Diskontinuitet, der staar i afgjort Modsætning til de klassiske mekaniske og elektrodynamiske Teoriers Fordringer. De … Resultater … [continues on the next page]
In English: (Corresponding [?] to another side of Bohr’s investigations: rational analysis [?], p. 98 f.) — N. Bohr, The Structure of the Atoms and the Physical and Chemical Properties of Substances, p. 6 (stationary states of the energy as different stages of a process [?]). Cf. 24 b (quantum theory as a rational development of our usual ideas). The correspondence principle (that is, the thought that a definite transition between an atom’s stationary states is conditioned by a definite harmonic [?] component of vibration, cf. p. 25 c) lets one glimpse, despite [?] the assumptions of quantum theory, an inner coherence of a kind similar to that demanded in the classical ideas of electrodynamic processes, which in the explanation [?] of many physical phenomena, as well as … of the properties of substances … from the structure of the atom (p. 60 d). — Compare Brunschvicg, L’expérience humaine et la causalité physique (Paris 1922), pp. 397–399. — On 17 December 1926 Bohr gave the Academy a communication on “Atomic theory and wave mechanics”, which at the end [?] he summed up thus: “In the quantum-theoretical description of the behaviour of atoms there enters an essential element of discontinuity, which stands in decided contrast to the demands of the classical mechanical and electrodynamic theories. The … results …”
What draws Høffding is the correspondence principle: the hope that quantum theory, for all its discontinuity, keeps “an inner coherence” of the kind the classical theories demanded. Note 1, three years later, records Bohr saying that causal description has to be given up; this note shows Høffding following the theory before that step. The December 1926 summary, with its “essential element of discontinuity”, is the turn between the two.
On a blank leaf of the volume. Høffding takes Russell’s case against subject–predicate logic from Jean Nicod’s »Les tendances philosophiques de M. Bertrand Russell« (Revue de Métaphysique et de Morale 29, 1922) and answers it from his own Den menneskelige Tanke (1910). A footnote sends the answer on to Kierkegaard.
Russell kritiserer Aristoteles’ Logik, fordi den holdt sig til Forholdet mellem Subjekt og Prædikat og ikke tog Hensyn til andre Relationer. Dommen er iflg. Russell karakteriseret ved at udtrykke [interlined] et Forhold til et enkelt Emne, men de egentlige Relationer angaa altid flere Emner. (Nicod i Revue de M. et M. 1922, p. 78.) Smlgn. Den menneskelige Tanke p. 161 f. (Dommen forudsætter Udtagen [?] af et Emne,* der skal bestemmes, altsaa en Forskelsrelation. Dommens Subjekt er en udsondret Gruppe. Men overses [?] let, at allerede Dommens Subjekt forudsætter en Skelnen, fordi det forudsættes bekendt og ikke [?] altid udtrykkes (smlg. id. p. 83–87); den skelnende Akt, ved hvilken Dommens Subjekt udtages, kan … [?] gaa for sig, næsten ganske uvilkaarlig [?].) (Se nedenfor p. 102 B om de kosmologiske Konsekvenser af Relationslogiken.)
*) Smlgn. Kierkegaards „Spring” (se min Afhandling om Platons „Parmenides” p. 38–57).
In English: Russell criticizes Aristotle’s logic because it kept to the relation between subject and predicate and took no account of other relations. The judgment, according to Russell, is characterized by expressing a relation to a single object, whereas relations proper always concern several objects. (Nicod in Revue de Métaphysique et de Morale 1922, p. 78.) Compare Den menneskelige Tanke, p. 161 f. (The judgment presupposes the picking out of an object* that is to be determined, and so a relation of difference. The subject of the judgment is a group singled out. But it is easily overlooked that the subject of the judgment already presupposes a distinguishing, because it is presupposed as known and is not always expressed (cf. ibid., pp. 83–87); the distinguishing act by which the subject of the judgment is picked out can … take place almost wholly involuntarily [?].) (See below, p. 102 B, on the cosmological consequences of the logic of relations.) — *Compare Kierkegaard’s “leap” (see my treatise on Plato’s Parmenides, pp. 38–57).
The parenthesis follows Den menneskelige Tanke closely: there (pp. 161–162) the singled-out object, »det udsondrede Emne (Gruppen)«, corresponds to the subject of the judgment, and »At allerede Dommens Subjekt forudsætter en Skelnen, overses let, … da det forudsættes kendt og derfor ikke altid udtrykkes«. Høffding’s answer to Russell is that the subject–predicate judgment is relational already, since its subject has first to be singled out by an act of distinguishing. The footnote names that act Kierkegaard’s leap.
The treatise is Høffding’s »Bemærkninger om den platoniske Dialog Parmenides« (Filosofiske Meddelelser I, 2, 1920; now in this collection), and pp. 38–57 are its chapter 3, »Begrebet det Pludselige (τὸ ἐξαίφνης) i Platons Filosofi«. Two points in it explain the footnote.
Read together with the note, the act that singles out the subject of a judgment is such a leap: sudden and not deduced from what precedes, yet, like every leap, within relations, so that the subject–predicate judgment is relational from the start. The asterisk might instead belong to a second mark at the right margin, at »flere Emner«; the photograph does not settle which.