Book details

Dialectics of the Ideal: Evald Ilyenkov and Creative Soviet Marxism
Edited by Alex Levant and Vesa Oittinen


The focus of this book is Ilyenkov’s essay “Dialectics of the Ideal”, which he wrote in 1974 but which was not published until 2009 (long after Ilyenkov’s death in 1979). This is the essay’s first translation into English in full (an incomplete translation was published in 2012). As well as the essay itself, there are various articles providing context and commentary.

“Dialectics of the Ideal” itself is a good introduction to Ilyenkov and, perhaps, a good introduction to (a certain kind of) Marxism. Ilyenkov’s is a “Classical” Marxism, in the sense that his references are to Marx, Lenin, and then to earlier sources like Hegel. Ilyenkov was strongly influenced by Vygotsky, and the two share an influence in Spinoza.

The essay is primarily a polemic against a reductionist interpretation of the Ideal, then current in Soviet philosophy, which interpreted ideal phenomena (e.g. concepts) as mental states, and thenceforth reduced them to neural events. This position is perhaps comparable to eliminative materialism and similar positions clustering around neuroscience.

Ilyenkov’s position is that ideal phenomena are social — kind of representations of social practices — which confront the individual, and consequently that any mental or neural states are effects of this pre-existing Ideal. Ilyenkov’s position can perhaps usefully be compared with social externalism in the analytical tradition.

the other essays

The other essays are variable, but some are very good. In particular, the essays about Ilyenkov and his context in Soviet (and current Russian) Marxism:

  • Alex Levant, the translator, and the kind of Maitre D’ of the book provides opening and closing essays;
  • Andrei Maidansky, an academic philosopher at Belgorod State University, who has an Ilyenkov web site, with texts in Russian, English and some other languages, writes a very good commentary essay “Reality of the Ideal”;
  • There is an interview with Sergei Mareev, author of “Из истории советской философии. Лукач-Выготский-Ильенков” (2008, “From the history of Soviet philosophy: Lukacs – Vygotsky – Ilyenkov”). Very nice interview — and I could hardly believe my eyes when I saw the title of this book: my three favourite Marxists (after Marx and Lenin). I need to read it!

Next Steps

Read next/soon: Ilyenkov’s “Dialectical Logic” (1974).

Keep up with Alex Levant’s papers — which he publishes on his page.

Read Mareev’s 2008 “Из истории советской философии. Лукач-Выготский-Ильенков”. Ha ha ha! No, really. First I am working my way through Maidansky’s 2009 review “Диаграмма философской мысли”. Reading that is interesting in its own right, and it will tone up my Russian so I can (slightly more) sensibly embark on Mareev’s book.

Re-familiarising myself with social externalism might be a worthwhile thing to do, as it might broaden out again my understanding of this area.

A New Year wish from Yang Lan

Saturday, 2nd January, 2016

Yang Lan (杨澜) sends a New Year message from her Weibo account:

** gloss

In the New Year, with love at the centre, extending life’s radius, your world flourishing brilliantly!

** original


** new words

圆心 yuán xīn centre (circle heart)
延长 yán cháng extend
半径 bàn jìng radius (half path)
繁盛 fán shèng thriving, flourishing, prosperous
精彩 jīng cǎi brilliant, splendid

A New Year Wish from Sammi Cheng

Friday, 1st January, 2016

Sammi Cheng sends a New Year message from her Weibo account:

** gloss

At last we are in 2016. All hope this year is better. But what do we mean by “good”? More successful? Richer? More beautiful? More “the best”? These definitions might conform to the standards of the world, but really in our hearts we might have a better “good”. For example: More loving. More forgiving. More kind-hearted. More humble. Let’s go!

** original


** new words

终于 zhōng yú finally, at (long) last; 于 (yú) = at (time)
处身 chǔ shēn dwell
定义 dìng yì definition
顶尖 dǐng jiān peak, centre, “best”
也许 yě xǔ perhaps
标准 biāo zhǔn standard, criterion
其实 qí shí in truth; 实 (shí) = solid
包容 bāo róng forgive
善良 shàn liáng kind-hearted
谦卑 qiān bēi humble

** constructions

[notes forthcoming]

任谁都 rèn shuí dōu
一年比一年好 yī nián bǐ yī nián hǎo
比这些更好的「美好」 bǐ zhè xiē gèng hǎo de “měi hǎo”
共勉之 gòng miǎn zhī

book details

L. E. J. Brouwer — Topologist, Intuitionist, Philosopher: How Mathematics Is Rooted in Life
Dirk van Dalen

the biography

This is a very good biography. Exasperatingly thorough and comprehensive (830 pages not including bibliography and index). It’s a very humane book, and a good example of what a humanistic project a biography is, or should be.

the maths

During Brouwer’s work on his PhD thesis — perhaps especially in correspondence with his PhD supervisor Korteweg, and in parts of the thesis that were later rejected — we see already many of the foundation stones of Brouwer’s intuitionism (p. 86-7): e.g., that “the points of departure of the theory” should be determined by “how mathematics roots in life” (p. 86), that “the primeval phenomenon is simply the intuition of time”, the “shift from goals to means”.

The “life” in which maths roots is not a social life, and the rooting is not an instrumentalism. It seems to be a kind of subjective idealist solipsism: “my mathematical thinking is non-sensory internal architecture”, “consciousness gains access to free creation — which is my mathematics — as soon as it knows itself autonomous and immortal, ignoring objective knowledge and common sense.” (p. 190-1, interview with Weissing ca 1913).

Brouwer was aware of and did tackle preceding work on mathematical foundations, including Kant, and especially the constructivist approaches of Kronecker, Poincare and Borel (p. 232f). Brouwer’s position differed from these earlier constructivists in important ways.

The constructivists’ main concern seems to have been that mathematical objects should be constructible in finitely many steps from the natural numbers — e.g., irrational numbers were admissable mathematical objects only if derivable from natural numbers by an algorithm with finitely many steps. Brouwer held to this rather weakly even in the beginning, for example including “free selection” as an algorithmic step. He does seem to have kept the “finitely many steps” idea, but in a less technical form.

Brouwer also differed from the earlier constructivists in his rejection of the principle of the excluded middle (p. 104f, 196). See his 1908 paper. In 1918 he went further and demonstrated that the law of double negation cannot be proved (p. 307). n.b. these constraints on logic are for infinite domains like mathematics.

However, Brouwer’s focus seems not to have been on the objects of mathematics, but on the subject of mathematics — the mathematician. Van Dalen refers to Brouwer’s “subjectivist approach to mathematics” (p. 306). The creating subject at the centre of Brouwer’s maths is an idealised mathematician (p. 738-9).

next steps

The two points most interesting to me are (a) the nature of the mathematical subject and (b) the constraints on logic.

Unlike Husserl’s “transcendental” subject, Brouwer’s subject exists in time. The “intuition” of time is a foundational experience for this subject, but what is meant by an “intuition” and why the subject’s appreciation of time can’t be ordinary learned experience is not explored here. Of course I am tempted to reach for some kind of psychologism, or maybe a kind of “abstract” psychologism a la Hegel.

Reading about Brouwer’s constraints on logic I kept thinking about Hegel’s logic (all those old slogans: “the unity of opposites”, “the negation of the negation”).


  • read more on the nature of the subject and the constraints on logic in Brouwer’s maths (see references below)
  • swot up on Hegel’s “Science of Logic”
  • it might be useful to read an introduction to the philosophy of maths, as it is a completely new field to me. Two likely-looking candidates are “Thinking About Mathematics” (Shapiro, 2001) and “Introducing Philosophy of Mathematics” (Friend, 2007).

annotated references

Brouwer, L. E. J. (1908). De onbetrouwbaarheid der logische principes (The unreliability of the logical principles). Tijdschr. Wijsb. 2, 152-58. (There are two English translations available: one in volume 1 of Brouwer’s Collected Works (1975); and a new translation by Mark van Atten & Göran Sundholm

Brouwer’s “revolutionary rejection of the general validity of the principle of the excluded third” (p. 104f, 106).

Brouwer, L. E. J. (1913). Intuitionism and formalism. Bull. Am. Math. Soc. 20, 81-96. (English translation of “Wiskunde, Waarheid, Werkelijkheid”).

This was Brouwer’s inaugural lecture, in which he differentiates his own intuitionism from the contructivism of Kroneker, Poincare, et al. (p. 218-20, 233f).

Brouwer, L. E. J. (1929). Mathematik, Wissenschaft und Sprache. Monatschefte Math. Phys. 36, 153-164. English translation in Mancosu (1998).

Presents “Brouwer’s views on the genesis of the basic entities of the subject’s inner and outer world”, motivated and developed more clearly here than in Brouwer’s PhD thesis (according to van Dalen. Plausible).

Brouwer, L. E. J. (1949). Consciousness, Philosophy and Mathematics. Proceedings of the 10th International Congress of Philosophy, Amsterdam, 1948, pp. 1235-1249.

This paper sounds like a summing up and a restatement of B’s fundamental intuitionist positions (p. 755-6): the phases of consciousness, the “move of time”, the “cunning act” (aka the jump from ends to means), the creating subject, the solipsism.

There also seems to be an innovation, in the “… phenomenon of play, occurring when conative activity or causal thinking or acting is performed playfully, i.e. without inducement of either desire or apprehension …”

Johan Huizinga is only mentioned once in the biography, when Brouwer mourns Huizinga’s death in a 1945 letter (p. 702), but I couldn’t help thinking of Homo Ludens when I read this passage. Huizinga published Homo Ludens in 1938.

Brouwer, L. E. J. (1955). The effect of intuitionism on classical algebra of logic. Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences Vol. 57 (1954 – 1956), pp. 113-116.

Brouwer’s last paper, stresses “the basic differences between classical and intuitionist logic”, “worth reading … because of its reflections on the nature of logic” (p. 798-800).

Heyting, A. (1956). Intuitionism, an introduction. North-Holland.

“Its role should not be underestimated, … its readability has always been praised.” (p. 800)

Mancosu, P. (1998). From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s. Oxford UP.

Translated papers of Brouwer, Weyl and others. Contains Brouwer (1929) and Weyl (1921).

van Dalen, D. (2004). Kolmogorov and Brouwer on constructive implication and the Ex Falso rule. Russ. Math. Surv. 59, 247-257.

This paper traces” the construction-meaning of implication in Brouwer’s famous ‘jump from ends to means'” (p. 612).

Weyl, H. (1921). Uber die neue Grundlagenkrise der Mathematik. Math. Z. 10, 39-79. English translation in Mancosu (1998).

This sounds like quite an exciting read, “beautiful provocative paper” (p. 311).

Paper details

M. van Atten, D. van Dalen, and R. Tieszen
Brouwer and Weyl: the phenomenology and mathematics of the intuitive continuum
Philosophia mathematica 10(3), 203-226


I thought this was a nice accessible paper (hardly any maths!). As well as “doing what it says on the tin”, it provides an introductory overview and a discussion of choice sequences.

Next stop for me is van Dalen’s biography.


The “intuition” in Brouwer’s intuitionism seems to be to do with our appreciation of time. Weyl’s definitions seem to be explicitly Husserlian, but Brouwer doesn’t explicitly use Husserl’s intuitionism. ADT quote Brouwer describing (what they repeatedly call) “the primordial intuition of mathematics” as “the substratum … of any perception of change, a unity of continuity and discreteness”. Related “intuitions” are the role of memory, and the asymmetry between past and future.

My questions here would be:

  • What does Brouwer mean by (an) intuition? Does it follow a Kantian distinction between learned knowledge and direct appreciation?
  • Why choose these particular things to be the “primordial” intuitions of mathematics? Time is a good candidate I concede. An even more “primordial” foundation might be eye movement: saccadic movement for the discrete counting; smooth pursuit movement for the continuum.
  • (Why) is it important that these things be unlearned intuitions? From my reading in developmental psychology, I would say these things — appreciation of time, memory, appreciation of an asymmetry between past and future — are learned by the human infant.

Related is the question of how Brouwer’s intuitionism differs from other constructivist approaches to mathematics. How much of this talk of “intuition” is really necessary?

Brouwer vs Weyl; Brouwer vs Husserl

Weyl seems to be much closer to Husserl than Brouwer does. It wasn’t clear to me from reading this paper whether Brouwer was just unfamiliar with Husserl or actively disagreed with Husserl’s position. Where differences are outlined in this paper, Brouwer’s position seems preferable to me.

Bits I like

I like Brouwer’s emphasis on the “creative subject” (or “transcendental ego”). This subject seems to exist in time: e.g., it can carry out only “finitely many acts of intuition”.

In what sense is this subject “transcendental”? What does it “transcend”? (and, again, why?)

Why am I interested in all this anyway?

My interest in Brouwer — and more broadly in the Constructivist approach to mathematics — is a digression from my main interests. However, it’s a digression from three of my main interests at the same time, which makes it hard to ignore.

  • Work: I am a computer programmer. The importance and role of type systems is a hot topic atm, and consequently type theories and proof systems. The constructivist approach to maths is relevant to computer programming because, like Brouwer’s creative subject, the computer program exists in time.
  • Schrödinger: I want to understand Schrödinger’s wave mechanics! That is the maths I am really interested in. I think I first heard about Brouwer — especially the Brouwer-Weyl connection — when I was reading Schrödinger’s biography late last year. Weyl was Schrodinger’s best friend in Zurich, and helped S with some of the maths for his breakthrough wave mechanics paper (1926).
  • Marx & Hegel: As well as the reference to Hegel on nLab, lots of the Brouwer in this paper is very reminiscent to me of Hegel: Brouwer’s “unity of continuity and discreteness” recalls Hegel’s “unity of unity and disunity”; the “two-ity” described early in ADT recalls the fundamental place Hegel gave to contradiction.

Notes on “The Young Hegel”

Friday, 28th August, 2015

Book details

The Young Hegel: studies in the relations between dialectics and economics
Georg Lukács
1966 (English translation 1975)
MIT Press


The point of “Young Hegel” is to show the development of Hegel’s thinking up to (and including) his Phenomenology of Mind. The special focus is to show how Hegel’s study of economics (primarily Adam Smith and David Ricardo) affected this development.

This is the most biographical treatment of Hegel I’ve read so far. It’s divided into sections with Hegel at Berne (1793-96), Frankfurt (1797-1800) and Jena (1801-03, 1803-07). The “very” young Hegel in Berne is depicted as idealising Classical civilisation, especially of Greece, which he would contrast absolutely with the “positivity” and dogma of the Christian world. In Frankfurt, Hegel became “reconciled” to the bourgeois/Christian reality, and this reconciliation brought with it (or was partly) a need to link the two worlds — for example to explain the historical changes (Hegel’s main source seems to have been Gibbon!).

I think “reconciliation” is Hegel’s word but, in Lukács’ telling, the process was more than only intellectual. Lukács talks of Hegel’s Frankfurt “crisis”, and how Hegel took much of the source material from his own personal experience of life.

Hegel’s debates with Kant, Fichte and Schelling are covered in detail. So Hegel is placed in historical context in terms of philosophy; also the political situation in Germany and France, and the political/economic situation in England are shown to influence (determine, Lukács would have it) Hegel’s thinking.

The exploration of Hegel’s study and use of economics is very good. Obviously at least part of the point of this exploration is to confirm and consolidate our understanding of the similarities between Hegel and Marx. Pinkard stressed how Hegel’s “idealism” (as in not materialism) is not quite as straightforwardly “idealist” as you might think (e.g., Hegel describes animals as idealists). What you might call Hegel’s “proto-materialism” is drawn out by Lukács.

Marx turns up from time to time in this book, but not really until the final chapter. After a synopsis of the Phenomenology, Lukács reviews Marx’s Economic and Philosophical Manuscripts of 1844 (EPM), which culminate in a critique by Marx of the Hegel’s Phenomenology.

Another frequent visitor in the book is Goethe. Lukács is always stressing the similarity of thinking between Goethe and Hegel.

For all the foibles of his style (see below), Lukács knows how to put a book together, and this book finishes in a kind of triple climax. The first is the one you expect and that the whole book has been building up to: the Phenomenology, dealt with in a huge crescendo of exposition. For the second, Marx steps out of the shadows and we plunge in to EPM. The third and final climax is announced on the very last page — “Historically, only one figure may be placed on a par with Hegel: …” — and it is Goethe who takes the final bow and receives the bouquet.

Lukács’ style

Lukács does have a tendency

  • to be a bit unmediated/deterministic with his explanations
  • not to shilly-shally about with minor issues
  • to make sure Stalin gets a mention every so often.

For the unsympathetic reader there is plenty not to like about Lukács. I like to think Lukács was writing assuming two particular audiences: (a) Marxists, so certain things don’t have to be explained, and certain things can be short-circuited, and (b) the censor and the KGB.

Next steps

Marx’s EPM is an obvious next stop.

For strengthening understanding of the development of the dialectic, with Hegel and Marx as two points on the timeline as it were, I should re-read Ilyenkov’s Dialectical Logic.

Goethe: the work most mentioned is Wilhelm Meister. Iphigenia on Tauris and Confessions of a beautiful soul also get interesting mentions (as does Faust obvs).

Smart Army Helmet

Thursday, 23rd July, 2015

Sometimes quite astounding where your work can end up:

Ivan Uemlianin, 2009, Developing speech recognition software for command-and-control applications.

J. Alejandro Betancur, Gilberto Osorio-Gómez, Alejandro Mejía, & Carlos A. Rodriguez, 2014, Smart army helmet: a glance in what soldier helmets can become in the near future by integrating present technologies.


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