Hegel on Ars Combinatoria & Characteristica Universalis

§ 1480

The extreme example of this irrational treatment of the Notion determinations of the syllogism is surely Leibniz's subjection of the syllogism to the calculus of combinations and permutations and has reckoned thereby how many positions of the syllogism are possible — that is, with respect to the distinctions of positive and negative, of universal, particular indeterminate and singular judgments; 2,048 such combinations are found to be possible of which, after the exclusion of the useless figures, twenty-four useful figures remain. Leibniz makes much of the usefulness of the analysis of combinations for ascertaining not only the forms of the syllogism but also the combinations of other concepts. The operation by which this is ascertained is the same as that by which it is calculated how many combinations of letters are possible in an alphabet, how many throws are possible in a game of dice, how many kinds of play with an ombre card, etc. Here therefore we find the determinations of the syllogism put in the same class with the points of the die and the ombre card, the rational is taken as a dead and non-rational thing, and the characteristic feature of the Notion and its determinations as spiritual essences to relate themselves and through this relating to sublate their immediate determination, is ignored. This Leibnizian application of the calculus of combinations and permutations to the syllogism and to the combination of other notions, differed from the notorious Art of Lully solely in being more methodical on the arithmetical side, but for the rest, they were both equally meaningless. Connected with this was a pet idea of Leibniz, embraced by him in his youth, and in spite of its immaturity and shallowness not relinquished by him even in later life, the idea of a characteristica universalis of notions—a language of symbols in which each notion would be represented as a relation proceeding from others or in its relation to others as though in rational combinations, which is essentially dialectical, a content still retained the same determinations that it possesses when fixed in isolation.

SOURCE: Hegel, G.W.F. Hegel’s Science of Logic, translated by A. V. Miller, foreword by J. N. Findlay (London: Allen & Unwin; New York: Humanities Press, 1969), Vol. 2, section 1, chapter 3, subsection A: The Syllogism of Existence: (a) First Figure of the Syllogism, § 1480.

§ 459

In speaking of vocal (which is the original) language, we may touch, only in passing, upon written languages further development in the particular sphere of language which borrows the help of an externally practical activity. It is from the province of immediate spatial intuition to which written language proceeds that it takes and produces the signs (§ 454). In particular, hieroglyphics uses spatial figures to designate ideas; alphabetical writing, on the other hand, uses them to designate vocal notes which are already signs. Alphabetical writing thus consists of signs of signs – the words or concrete signs of vocal language being analysed into their simple elements, which severally receive designation. – Leibniz’s practical mind misled him to exaggerate the advantages which a complete written language, formed on the hieroglyphic method (and hieroglyphics are used even where there is alphabetic writing, as in our signs for the numbers, the planets, the chemical elements, etc.), would have as a universal language for the intercourse of nations and especially of scholars. But we may be sure that it was rather the intercourse of nations (as was probably the case in Phoenicia, and still takes place in Canton – see Macartney’s Travels by Staunton) which occasioned the need of alphabetical writing and led to its formation. At any rate a comprehensive hieroglyphic language for ever completed is impracticable. Sensible objects no doubt admit of permanent signs; but, as regards signs for mental objects, the progress of thought and the continual development of logic lead to changes in the views of their internal relations and thus also of their nature; and this would involve the rise of a new hieroglyphical denotation. Even in the case of sense-objects it happens that their names, i.e. their signs in vocal language, are frequently changed, as, for example, in chemistry and mineralogy. Now that it has been forgotten what names properly are, viz. externalities which of themselves have no sense, and only get signification as signs, and now that, instead of names proper, people ask for terms expressing a sort of definition, which is frequently changed capriciously and fortuitously, the denomination, i.e. the composite name formed of signs of their generic characters or other supposed characteristic properties, is altered in accordance with the differences of view with regard to the genus or other supposed specific property. It is only a stationary civilisation, like the Chinese, which admits of the hieroglyphic language of that nation; and its method of writing moreover can only be the lot of that small part of a nation which is in exclusive possession of mental culture. – The progress of the vocal language depends most closely on the habit of alphabetical writing; by means of which only does vocal language acquire the precision and purity of its articulation. The imperfection of the Chinese vocal language is notorious: numbers of its words possess several utterly different meanings, as many as ten and twenty, so that, in speaking, the distinction is made perceptible merely by accent and intensity, by speaking low and soft or crying out. The European, learning to speak Chinese, falls into the most ridiculous blunders before he has mastered these absurd refinements of accentuation. Perfection here consists in the opposite of that parler sans accent which in Europe is justly required of an educated speaker. The hieroglyphic mode of writing keeps the Chinese vocal language from reaching that objective precision which is gained in articulation by alphabetic writing.

Alphabetic writing is on all accounts the more intelligent: in it the word – the mode, peculiar to the intellect, of uttering its ideas most worthily – is brought to consciousness and made an object of reflection. Engaging the attention of intelligence, as it does, it is analysed; the work of sign-making is reduced to its few simple elements (the primary postures of articulation) in which the sense-factor in speech is brought to the form of universality, at the same time that in this elementary phase it acquires complete precision and purity. Thus alphabetic writing retains at the same time the advantage of vocal language, that the ideas have names strictly so called: the name is the simple sign for the exact idea, i.e. the simple plain idea, not decomposed into its features and compounded out of them. Hieroglyphics, instead of springing from the direct analysis of sensible signs, like alphabetic writing, arise from an antecedent analysis of ideas. Thus a theory readily arises that all ideas may be reduced to their elements, or simple logical terms, so that from the elementary signs chosen to express these (as, in the case of the Chinese Koua, the simple straight stroke, and the stroke broken into two parts) a hieroglyphic system would be generated by their composition. This feature of hieroglyphic – the analytical designations of ideas – which misled Leibniz to regard it as preferable to alphabetic writing is rather in antagonism with the fundamental desideratum of language – the name. To want a name means that for the immediate idea (which, however ample a connotation it may include, is still for the mind simple in the name), we require a simple immediate sign which for its own sake does not suggest anything, and has for its sole function to signify and represent sensibly the simple idea as such. It is not merely the image-loving and image-limited intelligence that lingers over the simplicity of ideas and redintegrates them from the more abstract factors into which they have been analysed: thought too reduces to the form of a simple thought the concrete connotation which it ‘resumes’ and reunites from the mere aggregate of attributes to which analysis has reduced it. Both alike require such signs, simple in respect of their meaning: signs, which though consisting of several letters or syllables and even decomposed into such, yet do not exhibit a combination of several ideas. – What has been stated is the principle for settling the value of these written languages. It also follows that in hieroglyphics the relations of concrete mental ideas to one another must necessarily be tangled and perplexed, and that the analysis of these (and the proximate results of such analysis must again be analysed) appears to be possible in the most various and divergent ways. Every divergence in analysis would give rise to another formation of the written name; just as in modern times (as already noted, even in the region of sense) muriatic acid has undergone several changes of name. A hieroglyphic written language would require a philosophy as stationary as is the civilisation of the Chinese.

SOURCE: Hegel, G.W.F. Hegel's Philosophy of Mind, trans. William Wallace, together with the Zusätze in Boumann’s text (1845), translated by A. V. Miller; with foreword by J. N. Findlay (Oxford: Oxford University Press, 1971). Encyclopaedia of the Philosophical Sciences, Part III: The Philosophy of Spirit [Mind] (1830); Section One: Subjective Spirit; C. Psychology. Mind; (A) Theoretical Mind; ii. Representation (or Mental Idea); [b] Imagination; § 459 (excerpt).

Hegel on Number Mysticism: Pythagoreanism, Astrology, I Ching

On the General Characteristic” by Gottfried Wilhelm Leibniz

Leibniz on the Universal Characteristic

Leibniz blog entry

"Leibniz, Couturat kaj la Teorio de Ido" de Tazio Carlevaro

Philosophical languages, Romantic historicism, Hegel, Marx

Philosophy of Early German Romanticism,
the Oriental Renaissance, and the Historiography of Philosophy:
An Introductory Bibliography

Leibniz & Ideology: Selected Bibliography

Philosophical and Universal Languages, 1600-1800, and Related Themes: Selected Bibliography

Jorge Luis Borges: Selected Study Materials on the Web

Esperanto & Interlinguistics Study Guide / Esperanto-Gvidilo

Ars Combinatoria Study Guide


Ars combinatoria, speculative computing, & creativity

Hegel’s Lectures on the History of Philosophy:
Part Two. Philosophy of the Middle Ages. Section Three: Revival of the Sciences.
B. Certain Attempts in Philosophy.
3. Bruno.

Ars Memoriae, Philosophy and Culture: Frances Yates and After
by John Michael Krois

Ars Combinatoria: Or, Hegel’s Logic as Chronotope for the Digital Age
by Christopher Vitale, 22 Nov 2009
or at orbis mediologicus

Liberty and Identity: A Scaravelli's Interpretation of Leibniz
by Nico De Federicis

The Archeology of the Computer Assemblage:
The Ars Combinatoria of Berlin philosopher-engineer Werner Künzel

by Geert Lovink

Logical and Mathematical Psychology: Dialectical Interpretation of Their Relations
Nicolae Margineanu

Home Page | Site Map | What's New | Coming Attractions | Book News
Bibliography | Mini-Bibliographies | Study Guides | Special Sections
My Writings | Other Authors' Texts | Philosophical Quotations
Blogs | Images & Sounds | External Links

CONTACT Ralph Dumain

Uploaded 28 March 2010
Links added 10, 12, 14 Aug 2011,
15 Dec 2018, 2 Oct 2019

Site ©1999-2023 Ralph Dumain