Symbolic Thought and Artificial Languages
In what follows here, one is interested in further exploring the relationship between language and the world – not by exploring the ‘pure experience of order’ as Foucault does, but by understanding specific reflections upon that order. More specifically, our past is inundated by attempts to formulate perfect languages – to conceive of a word that invokes the purity of the Word by precluding any arbitrariness between language and what it represents. This has been imagined in several ways: some have tried to historically recover the original word by positing a monogenetic hypothesis (a common mother-tongue), some have tried to purify and reduce existing languages while others have tried to conceive of radically artificial languages denying precedent (a priori philosophical languages). In this project, I will imagine coding to be the most recent and heightened manifestation of this quest towards artificial universal languages. Positioned thus, it becomes possible to understand 'code' as a specific attempt towards an ordering thought, which is made possible by a novel relationship between language and the world that has had a rich and extremely varied genealogy. This part of my project will then be an attempt towards a genealogical understanding of artificial languages (such as code). Once this genealogy is established, it will become possible to understand coding as a certain kind of practice made possible under modernity, which reveals the positioning of other language-systems (natural language, formal language, mathematical and scientific language) in relation to our thought and materiality. The attempt then is to comment on scientific and quasi-scientific languages in general as a specific manifestation in the epistemic configuration of 'modernity'.
The Ars Magna of Raymond Lull
Composed in the 13th century by the Catalan friar Raymond Lull, the Ars Magna Ultima is not really an a priori philosophical language, nor is it the first philosophical statement on the need for a universal language (Lull, 1305). It is included here as a foundational text in the ars combinatoria, or the art of combination – a system of manipulation of words (and later used for symbolic manipulation in general) that would influence subsequence work on a priori languages and their systems of manipulation of expression and content.
The Ars may be understood briefly through its four principle figures (see figures I-IV in the following page). Its alphabet consists of nine characters B, C, D, E, F, G, H, J, K. As the occasion demands, each character may refer to a co-relating nine Absolute Principles (see figure I), Relative Principles, Questions, Subjects, Virtues and Vices. Since they are placed on a circular wheel, each alphabet may be connected to any of the other eight; also the arrow is vector and not scalar (the direction is relevant, since either of the letters can serve as a subject or a predicate).
Example 1: connecting B and E in figure I (arrow pointing at E) will give us the proposition:
“Greatness is the being because of which goodness, eternity etc. are great, encompassing all extremes of being. By “etc.”, we mean the other principles although not absolutely, because if we say that in God there is goodness, greatness, etc. we do not mean that there is any majority, minority or contrariety in God.”
The second figure that has the letters arranged according to Relative Principles, works in a similar way with a triangulation among three elements at a time (represented by colour) representing an additional ternary criteria of relationship between terms. The third figure is an additional mnemonic aid that helps in the combining of alphabets. These need not concern us here in detail.
The fourth figure has extremely interesting resonances through history and merits some discussion. Here we have the three concentric circles, each with the nine letters inscribed upon them. They are movable, dynamic circles and each turn of the circle will generate a juxtaposition of three letters. This in essence is the ars combinatoria or the art of combination. Although commonplace at first glance, its possibilities were to have profound consequences that would be lost for the next couple of centuries, but re-discovered to great effect by Giordano Bruno, with greater consequence by Leibniz and also by the German cryptographers in World War II[2]. The possibilities are twofold – a dynamic system of randomized generation (for cryptography) as well as the adoption of the unit in creating new combinations that would enable Leibniz’s logical machines and allow a vast multiplicity of arrays possible by just additions of more wheels (Couturat, 1901).
Lull’s attempt here is to generate a vast mnemonic library of propositions and questions, one that would provide the answer to every possible question. By combining different elements (elements he considers ‘universal’ and in that sense – primitive) in a multitude of ways, Lull hopes for the art to be able to produce every possible kind of definition, proposition or question. The limitations of such a system are of course extremely apparent. One would be hard pressed to be able to justify the universality of Lull’s primitives for instance, or even demonstrate that they are anything more than a very particular manifestation of a certain Christian theology. To make matters worse the combinations that can be exacted to occur from the system are often meaningless and even to Lull, often false. Furthermore, the selection of which propositions may be deemed true are hardly mechanical; for most part they are exhaustively annotated in the ars magna itself (over hundreds of pages of definitions) and for the rest his solution is to laud this as a concession to the artistry of the user.
The limitations on its universality are strikingly clear; however, paradoxically in this weakness lay its strength. While the mechanical ‘universality’ of the system may be a compromised one, in this compromise emerges the figure of the user, the artist - no less - in Lull’s terms. In this maneuver, language becomes not something that synonymous with the objects it represents, but an instrument of calculation – an object that aids thought. It is in this sense that it becomes an absolutely crucial influence on later work of interest here, as will soon become evident.
However, dwelling for another few moments on the Ars magna may profit us further. As has been mentioned, the Ars is a system for generation universal propositions and questions. While the former (propositions) have been analysed in detail by Rossi, Eco and several others, here one pauses on its simultaneous attempt at posing ultimate and general questions. (Eco, 1994; Rossi, 2000)
As mentioned before, one of the sets of nine in the Ars is a list of questions; this list provides us with the most general means of conducting philosophical enquiry. Let us concentrate further on entry against alphabet C of this list – ‘quid’. The question is essentially one of definition of a thing; we are urged here to interrogate its essence and its ‘what’-ness. The quiddity (what-ness) of a thing can be contrasted to its haeccity (this-ness). The question of essences is one that cannot be elided in the search for universality. The Renaissance episteme will conceive of a set of similitudes that establish strong patterns of resemblance that will underlie the singleness of their origins. The Classical episteme will similarly ground this search in the classificatory pattern of tabled identities and differences. To establish universality therefore rests squarely on an ability to establish an essence and relationships of commonality. It contrasts to the unasked question of haeccity (this-ness) or a particularity. Therefore how this text establishes a what-ness in a thing will give us clues to how it establishes relationships between things, how it constitutes a universal essence.
To reach this essence, the Ars Magna urges the artist to ask the following question:
(i) The definition of the subject itself as a general principle. How does the definition itself establish the generality of a thing?
Example: What is general ‘greatness’? The principle whose proper function is to magnify and with which great things cause magnification.
(ii) What does a thing have in itself without which it cannot exist? What are its own active, passive and functioning parts?
Example: What does ‘greatness’ have in itself? Answer: Corporeal things that causes substantial extension in subjects and Spiritual things that causes great acts.
(iii) What is a thing in other things?
Example: What does ‘greatness’ do to other things? It forms all others things with more form and matter.
(iv) What does a thing have in other things?
Example: What does ‘greatness’ have in other things? It has great action and great passion in other subjects.
Lull’s belief is that these questions define the difference of this system from other kinds of logical analysis. While dismissing ‘logic’ as concerned only with words, with merely the definition (the first question), he holds the advantage of the Ars in that it asks further questions about the thing in itself and the relation of the thing to other things (questions two three and four). In this way, Lull maintains that the confines of words are escaped and that a definite movement is made towards an essential generality. While Eco’s criticism stands perfectly validated – there is no doubt the second, third and fourth species are defined according perfectly particular and contextual considerations – it seems clear that this is a path that Ars magna attempts to take to break out of the expression-system and constitute a language that is at one with things in the world. As Eco recognizes, the distinction that Lull makes between his art and logic is that while the former is able to access the conception of things (second intentions), logic is confined to merely an initial apprehension (first intentions).
The brief philosophizing in the Ars on essence and languages demonstrates the belief that if language is deployed in a certain way, words can almost mechanically arrive at the universal content of things. There is an almost mechanical correspondence then, between words and the things they represent. The relationship is neither arbitrary nor conventional. It is this indistinguishibility between words and things that makes possible the belief that it is possible to reach a philosophical truth through manipulations of language. However, the method itself conjugates only at the level of words, playing around with the expression-system to arrive at true propositions and definitions. In other words, a strong affinity between words and things is conceived; but this affinity can be accessed by a transparent manipulations and combinations of the expression system. These two simultaneous possibilities in the Ars rendered it susceptible to all kinds of appropriations over the next few centuries. It was almost as if it was prefiguring two contrasting epistemic configurations – both of which were to employ it for very different ends.
Figure 1: Ars Magna Ultima - I
Figure 2: Ars Magna Ultima - II
Figure 3: Ars Magna Ultima - III
Figure 4: Ars Magna Ultima – IV
The Renaissance Episteme and the Impossibility of Language as an Object[3]
In the Renaissance that followed two centuries after Lull’s writing, Foucault imagines language to have assumed a very specific relationship with the its referents: it was a repetition of the world it existed in; a mirror that resembled and not a representation that had an autonomous existence. Language did not point to the world but was a sign among other signs - a signature of a hidden configuration of truth and divine knowledge. The relationship of language to the world was that of analogy rather than signification.
Further, if language was not an autonomous entity, grammar could not be a possible form of knowledge; it could only exist as exegesis - to make signs speak is to interpret the world. However, this correspondence between language and the world had been interrupted by the Babelic curse; it was now the task of philosophers to recover the primordial Word that spoke the divine truth. This configuration of language and being explains the proliferation of interest in the monogenetic hypothesis and the outbreak of linguistic nationalism claiming their own tongues as God’s chosen Word. It becomes evident why Lull’s Ars and its belief that language could mechanically access essences becomes particularly interesting to thinkers of this times – especially those who nurtured similar hopes of discovering universal truths.
The Renaissance witnessed therefore a coming together of the techniques of combination in the Ars and the Kabalist techniques of manipulation. In contrast to Christian exegetes, The Kabalists of the 10th the 13th centuries altered the expression-plane of the sacred texts in the process of study. Eco points to three techniques that were employed in the anatomization of the expression substance: notariqon (when initial letters generate new words), gematria (when numerical values of letters are exploited) and temurah (when words are taken as anagrams). This kind of intervention at the level of letters and not words made possible an enormous possibility of combinations. Also, in a pre-emption of the status of language during the Renaissance, words were taken for not their meaning content but as already divine in their very letters. The ecstatic kabala used a free combination of single letters which – since they shared a non-arbitrary relationship with the world – brought the interpreter closer to God.
The dissolution of the differences between the Ars and the techniques of the Kabala was made possible by the shared technique of combination. The absolutely anarchic possibilities that this technique allowed serve the purposes of the Renaissance scholars interested in discovering truth in words themselves and not through their meanings. Eco points to the work of Cornelius Agrippa, who saw the unlimited possibilities of the Ars as an advantage and not as something that needed to be censored by the user (Lull’s original intention). Opposed to Lull’s closed finite world, Agrippa was inaugurating the idea of an open, expanding cosmos; the ‘thrill of an infinity of worlds’ was beginning to be felt (Eco, 132).
Giordano Bruno envisaged a similar project. Working with a modified Lullian concentric wheels system, and placing agents, actions, insignia, bystanders and circumstances on these wheels, Bruno was able to create a vast array of random articulations (150 elements in 5 combinations) with absolutely no limitations on permissible permutations. While this did no more to the Lullian system than greatly magnify its possibilities, Eco (following an interpretation by Sturlese) makes an even more radical claim. The propositions thus formed by the concentric wheels did not constitute meaningful utterances in themselves, but were really tools for generating absolutely new words (for which these generated utterances were merely mnemonic aids). We are now entering the terrain of absolutely novel a priori combinations, the possibility of naming anew, of generating new elements of expression itself that have no prior status in knowledge. Only now are we arriving at the conditions necessary for development of truly new artificial languages, of wholly new expression-systems that will prove amenable to calculation. However, for the languages of calculation to emerge it will be necessary for a new configuration of knowledge, a configuration that will break the unity of the word and the world and herald the retreat of the magical from formal knowledge and erudition.
The Classical Episteme, Kircher’s Polygraphia and Cryptography
The process of Kircher’s polygraphy is easy to understand (Kircher, 1663). The first exhaustive table contained an alphabetically arranged list of words [Fig. 5]. These words were arranged in a column and there were five columns adjacent to each other – one for each language (Latin, Italian, Gallic, Hispanic and German). Further each word was assigned a roman and an Arabic numeral. Across languages, the words with the same meanings were assigned the same numerals. To be clear, there was a straightforward vertical series of words, with a horizontal correspondence across columns (or across languages) of numbers. Of course, the horizontal relationship was not immediately visible since the words had been arranged alphabetically and not according to their meaning.
In a second table, the words were arranged according to their numbers, and consequently – their meanings [Fig. 6]. A visible horizontal relationship was now established. The process of translation then was to encode a word into a number with table I, and the second step was to decode it using the table arranged numerically (hence in horizontal rows of synonyms across the five languages) in table II. In a third table [Fig. 7] Kircher formulated a series of marks that would indicate grammatical characteristics such as verbs, tense, mood and so on.
Figure 5: Kircher’s Polygraphia - I
Figure 6: Kircher's Polygraphia - II
Figure 7: Kircher's Polygraphia - III
Kircher’s project would be no different from an early multi-lingual dictionary and of no interest here if it was not for two crucial differences. First, it postulates a translation of words into numbers and marks that can then stand apart from context. It is an early instance of a meta-language that in this case makes possible a ‘universality’, and later will enable symbolic manipulation and a philosophical calculus of enquiry. This will be a crucial precursor to the further development of symbolic logic and will consequently be taken up again. Second, it demonstrates the emerging status of language in the configurations of this new episteme. We are placed precariously between two modes of thought – the unity of the sign and its referent has been broken; but we are not yet in the realm of comparative linguistics that posits language as an object and an internal system decisively unable to access any truth or essence. We are in a liminal stage; horizontal comparisons such as these are not yet a comparative linguistics that examines each language on its own terms. Yet the vertical ordering of language (that harks back to Babel) is giving some way to some horizontal comparison; the decisive principle is still an original language that provides roots, but the definitive role of historical events outside language are also recognised as an influence upon its form. As Foucault puts it, language is no longer hidden in the enigma of a mark, but it has not yet appeared in the history of signification. The unity of the word and its referent is broken, but representation still is perceived to be analogous to thought - only separate from it.
Kircher’s project is an early instance of this shift. The vertical ordering – the urge towards a primal word – is accommodating a horizontal movement across languages. This horizontal movement presupposes the first (in the assumption of common roots) but also involves a concession to a comparison across languages on their own terms. The direct link between language and thought is still acknowledged, but it is now possible to differentiate between the two. Language is no longer thought itself, but the faithful bearer of the historical development of thought. Kircher’s horizontal table points precisely to this new status of language in the classical episteme. The quest for a perfect language in the sense of one that embodies divine marks is no longer possible. Instead, language directly represents thought, and if perfection is to be sought, it is not the past that one must look to but at the inventiveness of the present, a new form of representation that unfolds thought in the most precise and opportune ways. This must be found not in the essences of words, but also now in the rules of grammar and syntax – processes of unfolding that mimic the unfolding of thought. The quest now for a perfect language must begin to take this unfolding into account.
John Wilkins
The conditions for artificial languages and grammars rooted in the present were now coming into place. The old problem of finding comprehensive and ethno-neutral primitives did not disappear. However, since representation began to appear in a plane not coincident with thought, it becomes necessary to establish its specific ordering and syntactical principles. Grammar took the function of unfolding thought in a syntactical structure; for those interested in formulating new perfect languages, it became as imperative then to establish a system of relationships between the units as it was to correctly name the units themselves
Foucault demonstrates the primary relationships that were established as relationships of identity and difference. It transplanted resemblance (in the work of Bacon and principally Descartes) by perfecting and systemising it: what was once a magical transversal across time and space was reduced to a comparison in terms of measure and order. Identity analysed relationships of inequality and equality, and series were established by ordering differences in the smallest possible degree. Through a comparison of things, a watered down operation of resemblances – a certain series and system was brought into being which although not thought itself, engendered the same murmurs.
Let us return first to the problem of primitives. For those who took natural languages as their model (Kircher as an example) this posed no problem. For those positing a wholly new artificial language, concepts that existed in language had to be systematically limited in order to pose a system of a realistic system of representation that would exhaust these primitives. As Eco suggests, the Porphyry Tree structure became the accepted model of classification: the division of each object into two differences – which constitutes a pair of opposites, which are further subdivided through other constitutive differences.
Like Lull and many others before him, Wilkins derived his primitives from experience and arranged them in a Porphyry tree system that encoded all the particularity and ethnocentrism of his thought (Wilkins, 1668). Again, we will not dwell on this failure, but concentrate on a remarkable innovation in terms of the expression-system of this content. Hoping to reach beyond the limitations imposed by words, like Bruno and the ecstatic Kaballists before him Wilkins formulated his representation on the basis of letters. Of course the rational Wilkins did not imagine that the letters themselves shared some primordial relationship with magical or divine truth. However in a new operationalisation of techniques of combination, Wilkins hoped to use combinations of these units of characters to form completely novel words that would – by their very structure – bespeak the object they referred to. A glance at Fig. 8 shows how each of the 40 primary primitives (or genus) in his exhaustive table were to be represented by a two letter combination. Each additional movement into a sub-species or sub-division was to be represented easily with an additional character. For example, colours would be represented thus:
‘Thus, if (Ti) signifie the Genus of Sensible Quality, then (Tid) must denote the second difference, which comprehends Colours; and Tida) must signifie the second Species under that difference, viz. Redness: (Tide) the third Species, which is Greenness, &c…’
Figure 8: Wilkins 'Real Character' - I
Figure 9: Wilkins 'Real Character' – II
The second figure [Figure 9] is Wilkin’s transcription of the Lord’s prayer in his new language. It is immediately apparent that a certain transformation has taken place at the level of the expression-system, a radical movement away from natural language into a new method of organising knowledge. We have moved into the domain of symbolic characters that stands in for language or words themselves; in this instance – a precise position in a classificatory grid that Wilkins himself has developed. The formulation of meta-languages has now begun in earnest – with letters standing in for concepts, arranged in a non-arbitrary way to point to a particular systematic position. It is a movement that has been made possible by the configuration of the classical episteme – the discrimination of thought from representation, while retaining its essential connectedness. It is similarly possible only before the modern configuration of knowledge, where language is engrossed in its own internal economy and loses its non-arbitrary relationship with thought.
What is also enabled by a movement into real characters is a distinct form of grammar – where grammar is understood as an unfolding of language. Foucault finds that in the classical episteme, the unfolding of the proposition is an act of analysis – both horizontal and vertical. A horizontal analysis groups and differentiates elements, a process of which Wilkin’s system is an example par excellence. It also exercises a vertical articulation that distinguishes things from each other. Preserved in all this is the representative function of language, its ability to name and designate things. In Wilkin’s analysis, the process of establishing identities and difference and naming are all present in a nascent form. We are witnessing how a proposition orders space while it unfolds. This very principle of ordering (achieved through establishing identities, differences in a structure of names) is one that will culminate in a mathesis universalis, an ordering of simple natures to enable manipulation and calculation. For this to be achieved, language will have to represented by units that it are easily calculable – a further movement into symbolic logic whose first manifestation we have already seen in Wilkins. Leibniz’s project – although obviously dependent on Lull, derives in part then from Wilkins as well as the developments in the idea of a symbolic mathesis in the 16th century – algebra. While the latter will be the object of the next chapter, we will end here with a description of Leibniz’s attempt at a universal character. For his work in mathematical logic itself, we shall defer to the next chapter.
Leibniz and the Universal Character[4]
Leibniz’s complete work on language involves a multitude of endeavours; here we shall concern ourselves with two projects: an attempt towards a universal character and another towards a system of calculations upon this character. His work on mathematical logic will find a place in the next chapter.
Leibniz was dissatisfied with prior projects on two counts (Couturat, 1901). Firstly, the arbitrary relationship of correspondence set up between numbers and the ideas they represented detracted from the usefulness and workability of such systems (e.g. Kircher). Secondly, the emphasis on universal communication detracted from the scientific purposes of language; one could not manipulate its symbols to discover the truth or falsity of propositions (e.g. Wilkins and his contemporaries).
The first step – as in previous attempts – would be a rigorous reduction of knowledge into primitive concepts. Leibniz’s work was not very much more original than others in this respect; his radical contribution lay in how he organized these primitives. Each primitive concept would be assigned prime numbers. More complex phenomena (a combination of two or more primitive concepts) would then be thought of as an operation of multiplication upon the primitive concept-units (i.e. two or more prime numbers). In this way, we would have several orders of classes - from the simplest terms, to those that were combination of two terms, those that were combinations of three terms and so on.
Constructed numerically, these units would now be agreeable to operations of calculation. To find the definition of any complex term, all that would be necessary would be to reduce it (by a method of factorization to primes) to its primitive terms. To find the truth of a proposition, a simple operation of divisibility would suffice. To find the number of possible predicates for a given subject, the formula [2k-1] would be adequate, where ‘k’ would be the number of prime terms that have entered in the calculation of the subject. Similarly, to calculate the inverse (2n+k – 1) would return the number of possible combinations for a given subject, where ‘n’ is the total number of simple terms in a system, and ‘k’ is the number of prime factors in the given combination).
The process by which these numbers would be given back to language as pronounceable words was simplicity in itself. Consonants would represent digits, and vowels would refer powers of 10 in ascending order. Thus any number could now be assigned an alphabetical value, and any word could now be represented by a number.[5]
With the modern episteme, Foucault believes that representation turns upon itself, detached completely from being and thought. It is now thought to be structured by an internal economy, unable anymore to reach the essence of things. Language is relegated to a mode of being, and a transcendental subjectivity is placed beyond its grasp. The unified mathesis that structured both empirical and natural sciences is now fractured – leading to disciplinary boundaries. All talk of ‘mathematicising’ the human sciences will now purely be an urge towards a previous unity, a shadow that confirms its impossibility. While language was one sign among others, it now becomes one object among others. It’s pre-eminence as either a sign itself (Renaissance episteme) or as an entity analogous with logic (classical thought) is now lost; it becomes now an instrument subservient to philosophy which becomes the discipline closest to the truth.
Leibniz’s project is situated along this epistemic rupture. It has not yet abandoned an affinity towards being (in seeking to calculate upon primitive concepts drawn and given back to language), yet it is beginning to apprehend that for this to occur, a movement must occur towards another system, one that is placed outside language. The shift that occurs from the encyclopedia and the table towards Leibniz’s ‘blind thought’[6] (operations upon symbols whose relations to the real world have been lost) and symbolic logic is analogous to a corollary shift in the quest for truth from language to quasi-formal systems that will be placed in the interstices of mathematics and philosophy. Here we have seen the first instance of such a shift; over the next two chapters we shall attempt more effectively map out this epistemic transformation. In this chapter we have traced briefly the conditions of emergence of a symbolic meta-language in the quest for artificial and universal languages. The next chapter will concern itself with contemporaneous symbolic algebra as another instance of the development of a meta-language(Eco, 1994) of calculation. The third chapter will chart the entrance of this meta-language of enquiry (quasi-formal languages at the interstices of mathematics and philosophy) into modernity and the consequent debates regarding its relationship to truth, the method by which it establishes a continuous and reliable terrain of study and its status as a signifying system in general.
Bibliography
Couturat, Louis. La Logique De Leibniz. 1901.
Eco, Umberto. The Search for the Perfect Language. Trans. James Fentress: Blackwell, 1994.
Foucault, Michel. The Order of Things: An Archaeology of the Human Sciences. Tavistock, 1970.
Kircher, Athanius. "Polygraphia Nova." 1663.
Lull, Raymond. "Ars Magna Ultima." 1305.
Rossi, Paolo. Logic and the Art of Memory: The Quest for a Universal Language. 2000.
Wilkins, John. "An Essay Towards a Real Character and a Universal Language." 1668.
[1] Animals are divided into (a) belonging to the Emperor (b) embalmed (c) tame (d) sucking pigs (e) sirens (f) fabulous (g) stray dogs (h) included in the present classification (i) frenzied (j) innumerable (k) drawn with a very fine camelhair brush (l) et cetera (m) having just broken the water pitcher (n) that from a long way off look like flies.
[2] The Enigma Machines were build basically on a similar principle as further developed by Blaise Vigenere two centuries later. Its advantage was the rapid mechanization of the same wheel and its combination with other similar wheels. It proved unbreakable for decades to Allied cryptanalysis.
[3] Due to the regrettable non-availability of translated texts of Agrippa and Bruno, I will be referring extensively to Paolo Rossi and Umberto Eco for their work on the same authors.
[4] Most of Leibniz’s work is in unpublished manuscripts and fragments, and the world is indebted to Louis Couturat’s attention to Leibniz for our current knowledge of his work on logic. I will be referring to his detailed and exhaustive exegesis for this part of the paper.
[5] However, here a point of confusion arises which both Eco and Couturat elide. Why would it be necessary to return these calculable forms of numbers to a different form of language than the one upon which these calculations were made? In other words, when primitive concepts were being encoded into primes and complex concepts into their multiples, they are already being translated into universal forms (the number system); why then this second step? The answer seems to be – for the lack of any other explanation – the ease of mnemonic grasp, easier in the case of artificial words than long numbers.
[6] Leibniz thought it possible to not have to consciously recognize the content of the signs that were being manipulated, but to work upon the manipulation and calculation itself. As Eco perceptively points out, now the form of the proposition mirrors an objective thought. (Eco, 283). The unity of expression and content systems is now being abandoned consciously and comprehensively.
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