Marcelo Dascal

Hobbes's Challenge

Marcelo Dascal, Tel Aviv University

Introductions to the Cognitive Sciences, in their excessively brief historical surveys, usually attribute to Thomas Hobbes the merit of having been the first thinker to propose the computational theory of the mind. What they overlook is (a) the fact that Hobbes explicitly assigned to natural language the role of providing the symbols through which we perform our mental computations and (b) the context within which this proposal was made and the challenge it raised for 17th and 18th century thinkers. Believing, as I do, that the meaning of a theory can only be gathered through careful attention to the controversies within which it takes shape, I will try in this paper to reconstruct the debate to which Hobbes's proposal belongs. It will be apparent, from this reconstruction, how much of the current debate on central methodological and substantive issues in the Cognitive Sciences echo, to a large extent, the debate that animated the Classical Age.
In a nutshell, Hobbes's challenge consisted in calling into question the then prevalent view that the units of mental activity consisted in ideas, whose representational powers were left unexplained or vaguely explained by suggesting that ideas represented their objects like images do. Hobbes, instead, suggested that mental representations represent like words do, i.e., not naturally but arbitrarily or conventionally. This seemed ridiculous and at the same time dangerous (for it would, ultimately, make truth itself arbitrary) to thinkers such as Descartes, Arnauld, Spinoza, Malebranche, and Kant. They banned language from the inner sanctum of the mind, and continued to grapple with the problem of how to account for the nature of mental representation and its relationship with the world. Hobbes=s suggestion seemed fruitful as a possible way of solving these problems in the eyes of thinkers such as Leibniz, Locke, Berkeley, Condillac, and Humboldt, who tended to attribute to language a central role in cognitive processes. They had, however, to face the issue of the eventual relativization and arbitrariness of a knowledge achieved by manipulating socially and historically produced public signs. It is significant that the two camps on this central issue do not correspond to the divide between rationalists and empiricists, which calls into question this traditional classification of classical -- and contemporary -- views.
Hobbes, then, can be credited not only with proposing the computational theory of the mind, but also with raising to center stage the issues of the nature of mental representations and of the role of language and conventionality therein, which continue to be with us. If we are to overcome the deadlock of present-day debate on these and related issues, we should understand why we have not been able to move beyond the quite analogous deadlock that put an end to the classical debate on the same issues.

Introductions to the Cognitive Sciences, in their excessively brief historical surveys, usually attribute to Thomas Hobbes (1588-1679) the merit of having been the first thinker to propose the "computational theory of the mind". Unfortunately, they overlook the details of Hobbes's proposal, the theoretical program it served, the intellectual context within which it was made, the reactions it provoked, and the issues it put in the agenda of 17th and 18th century thought. In this paper I will try to reconstruct the significance of Hobbes's proposal in the light of such contextual factors.

It will be apparent, from this reconstruction, how much of the current debate on central issues in the Cognitive Sciences addresses the problems raised by Hobbes's challenge and elaborates types of solutions adumbrated by himself and his contemporaries. Hobbes, then, can be credited not only with proposing the "computational theory of the mind", but also with defining -- along with his contemporaries -- the problem-space within which present-day Cognitive Sciences still operate. Awareness of its historical roots may eventually help to tap hidden or forgotten potentialities in that space and/or to overcome its inherent limitations.

1. Verbalizing the mind?

The the most often quoted passage where Hobbes makes his "computational" statement belongs to the first two paragraphs of Chapter 5 ("Of Reason, and Science") of Part I ("Of Man") of the Leviathan:

When a man reasoneth, he does nothing else but conceive a sum total from addition of parcels, or conceive a remainder from subtraction of one sum from another; which (if it be done by words) is conceiving of the consequences of the names of all the parts to the names of the whole, or from the names of the whole and one part to the name of the other part. [...] In sum, in what matter soever there is place for addition and subtraction, there also is place for reason; and where these have no place, there reason has nothing at all to do.

Out of all which we may define (that is to say determine) what that is which is meant by this word reason, when we reckon it amonst the faculties of the mind. For REASON, in this sense, is nothing but reckoning (that is, adding and subtracting), of the consequences of general names agreed upon for the marking and signifying of our thoughts; I say marking them when we reckon by ourselves, and signifying, when we demonstrate or approve our reckonings to other men (Leviathan I, 5, 1-2).

Under the grip of the "computational metaphor", we tend nowadays to be impressed by its forceful -- albeit a bit too arithmetical perhaps -- formulation in this passage, and to quickly see it as a forerunner of the "physical symbol system" hypothesis. In so doing, we overlook its peculiarity, namely that the symbol system by means of which we perform our reasoning is claimed to be linguistic. Natural language itself, and not some sort of "Mentalese", is the vehicle of mental reckoning.1 And this is stressed, in the last sentence, by pointing out that the very same "names" are used in mental operations (as "marks") and in communication (as "signs").2

This was a far cry from the commonplace that language and reason, the two distinctive characteristics of humans and both forms of the Greek logos, should be somehow connected. Hobbes was claiming that language is directly involved in the process of reasoning and that without it reasoning cannot go very far, if it could at all exist. It was this intrusion of language in the inner sanctum of the mind and its consequences, rather than the `computational' aspect of his thesis, that caught the attention of Hobbes's contemporaries and provoked violent reactions. His proposal was considered either ridiculously wrong (if people think with words, how can the thoughts of an Frenchman and an Englishman ever be the same? -- asked Descartes and Arnauld) or else scandalously dangerous (since words are arbitrary, truth itself, resulting from mental manipulations of words, would be arbitrary).

Such reactions can be better understood against the background of the linguistic implications of the intellectual struggles that accompanied the rise of "modern" philosophy and science in the first half of the 17th century. One should first recall the struggle against late medieval scholasticism, perceived by the new philosophers as a sterile form of manipulation of words, unable to advance our knowledge of the world. Renaissance thought was also seen as guilty of verbalism: on the one hand, for its excessive reliance on the authority of ancient texts and on futile hermeneutic exercises; on the other, for the widespread belief in language as a source of occult knowledge about the world -- to wit the popularity of cabbalistic ideas up to the end of the seventeenth century. Reliance on words -- whatever its source -- was perceived as diametrically opposed to reliance on reason and observation -- the only sure ways to achieve knowledge.

Recall, further, the rise of the vernacular languages, which were replacing Latin as languages of culture. To be sure, in order to be broadly read and understood, authors had to write"vulgar" languages, whose eloquence Dante Alighieri had long before praised. But, in addition to their lowly (and hence unreliable) origin, they had not yet achieved the stability, richness, and precision necessary for scientific and philosophical purposes. Montaigne, for instance, complained about the fluidity of the orthography, the rapid semantic changes and the lack of precision of the French of his time, and felt compelled to create a great number of new French words and expressions (cf. Essais II, 2 and III, 9). Similarly, Locke, nearly one century after Montaigne, introduced an estimated 500 new English words, expressions, or new senses for old terms (Hall, 1976); and Leibniz, while emphasizing the advantages of German (a language more "concrete" than those related to Latin), acknowledged its lack of philosophical terms (Schulenburg, 1973).

Under these circumstances, the dangers of a language-based pseudo-science, of incomprehensible mumbo-jumbo passing for knowledge, and of relativism, were not merely remote possibilities. A critical attitude towards natural language developed, which undertook to keep it strictly apart from the cognitive processes involved in the production of knowledge, and thereby to reduce its deleterious effects. Francis Bacon forcefully articulated this attitude early in the 17th century. For Bacon logic should supply to the intellect the tools necessary for overcoming the difficulties that endanger its endeavor to acquire and develop scientific knowledge. The art of detecting fallacies is one of such tools. The dangerous idola it helps to identify are "false notions" which, being deeply entrenched in our thinking habits, distort our understanding of the "nature of things" (NO, I, 38, 41). Thereby they create a barrier for the formation of correct judgments. Among the idols, those of the "market-place" are "the most troublesome of all" (NO, I, 59). They are the "false appearances imposed upon us by words, which are framed and applied according to the conceit and capacities of the vulgar sort" (Sp, III, 396), and thus "follow those lines of division which are most obvious to the vulgar understanding" (NO, I, 59). Therefore, they obstruct the way to scientific knowledge, for "whenever an understanding of greater acuteness or a more diligent observation would alter those lines to suit the true divisions of nature, words stand in the way and resist the change" (ibid.).

Paradoxically, Bacon's critique of language led to an enhanced interest in language. For it suggested that only a better understanding of language and, eventually, its radical reform or even replacement could protect us from its dangers. The former suggestion led to the development of "philosophical grammar" -- the attempt to discover the principles underlying the variety of languages; the latter, to the projects of "universal" or "philosophical" languages. Such projects -- which abounded in the second part of the 17th century (and were the object of Swift's sharp satire in Gulliver's Travels) -- avoided natural language's problems simply by trying to create entirely artificial symbol systems (mostly only written). Furthermore, most of them accepted Bacon's assumption that language -- whether natural or artificial -- had no role to play in the production of knowledge, but at most in its transmission.3 In fact, they presumed -- like Descartes in his well-known reply to Mersenne (AT, I, 76-82) -- that the completion of science (at least in its foundations and basic categories) was not only totally independent of the availability of such languages, but also a precondition for their proper design.

Vis-a-vis this prevalent critical attitude towards language, Hobbes's claims were not only heterodox, but also appeared as regressive, for they seemed to promote a version of the old-fashioned verbalism every "modern" thinker was trying to get rid of. Yet Hobbes himself was, as much as Descartes, Bacon, Gassendi, Arnauld, Boyle or Leibniz, a "modern" philosopher/scientist. Like them, he adopted and contributed to the "mechanization or the worldview" -- perhaps even more than them, in so far as he tried to extend it to the scientific study of the mind and of society. Like them he sought to develop a systematic model of scientific thought and practice. His heterodox proposal relating thought with "linguistic computation" could not therefore be easily dismissed as retrograde. In fact, it forced his fellow moderns to ask fundamental questions they presumably would not have asked without his challenge. The ensuing sections spell out some of these questions.

2 A new model for mental representation?

If you were to ask a 17th or 18th century thinker what are the basic units of thought processes, he would certainly reply: "ideas". If you were to ask for a definition of this term, you would provoke puzzlement: "why do you need a definition for such a simple and clear notion?".4 Puzzlement apart, the term "idea" was carefully scrutinized and defined in quite different ways by different authors (and even by the same author) in the 17th and the 18th centuries, when its philosophical use peaked. Divergences about how to understand "idea" gave rise to divergent philosophical "schools" (e.g., rationalism vs. empiricism) and, within the same school, to bitter polemics (e.g., between Arnauld and Malebrance -- cf. Dascal 1990a). After two centuries of intensive debates, Voltaire, for one, was sceptical about their yield: "It is quite sad to have so many ideas, and not be able to know precisely the nature of ideas".5

In spite of their divergences, all parties at the time were particularly interested in one type of ideas, namely those endowed with the power to "represent" something other than themselves. Their interest in these representative building blocks of thinking was, of course, derived from their interest in the question of how thinking can provide knowledge of, among other things, the world. For this particular kind of ideas, the question "how do ideas represent?" is fundamental. Its importance notwhitstanding, surprisingly few alternative answers were seriously considered, and the most popular one cut across the divergences mentioned above. Voltaire, in 1765, suggests this answer, in the characteristically implicit way it was presented in both the empiricist and the rationalist traditions: "What is an idea? It is an image depicted in my brain".6 What this implies is that ideas represent as images do.

Images, for empiricists and rationalists alike, were (material) entities imprinted in the "phantasy" or "corporeal imagination"; as such, they are indeed "depicted in certain parts of the brain";7 in Hobbes's terminology, they are "phantasms" formed in the imagination by a series of "movements" beginning, usually, with sensorial stimuli.8 Consequently, they were supposed to represent their objects by virtue of a physiological causal chain, i.e., as indices or traces of the latter -- although it was widely assumed (and barely justified) that they were iconic representations too. On both counts, images are natural -- as opposed to conventional -- signs. By equating or comparing ideas with images, then, the former were also supposed to represent "naturally".

The empiricists tended to literally view ideas as images -- thereby identifying the former as either sensorial or directly derived from sensorial images through simple processes such as "association", "fading", etc. But this identification posed for them the problem of how to account for those ideas that could not simply be equated with images or traced back to them, such as general ideas and the ideas corresponding to the operations of the mind (e.g., predication, conjunction, disjunction, implication), usually denoted by syncategorematic expressions.9 What Hobbes was suggesting, in the footsteps of medieval nominalism, was a solution to this problem. The role of ideas, in the problematic cases in question, was to be fulfilled not by unavailable images but by words themselves.10

As for the rationalists, they obviously could not identify "ideas" with physiological or physiologically-derived phenomenona, not onlydue to their adherence to mind-body dualism, but also because such a move would suppress the basis for their doctrine of necessary truths, making all knowledge contingent. So, when characterizing ideas as images they were bound to claim that this was only "a way of speaking". Thus, Descartes, who had said in the third Meditation that (representative) ideas are "comme les images des choses" (AT IX, 29), quickly withdraws from this characterization in his reply to Hobbes's objection, and redefines idea as "everything that is immediately conceived by the mind" (AT IX, 141).11 Thus, ideas -- properly speaking -- are the products of the mental operation of "conceiving".

Although at first this operation was characterized in such a way as to eventually include also the products of the imagination,12 it was later on restricted to the intellect or understanding, and its products -- "concepts" -- were, accordingly, sharply distinguished (e.g., by Kant) from the products of the imagination, be it reproductive or creative. The problem is that, whereas when ideas were equated or likened to images it was possible to rely on an implicit commonsensical explanation for how they represent and for the accuracy or correctness of such representation, once they became concepts this was no longer the case.

The rationalist way of tackling this problem consisted, for obvious reasons, in looking for intrinsic or "formal" criteria for a concept's accurate representational power. Thus, Malebranche, drawing upon the Cartesian notions of "immediacy" and "clarity and distinction", characterizes an idea -- in its more specific sense of "concept" -- as an immediate object of the mind that represents clearly a thing, where a representation is clear when it permits one "to discover by a simple inspection whether such and such modifications belong to it".13 Whereas Arnauld, following Descartes, was satisfied with a psychological interpretation of such criteria and, accordingly, viewed ideas as "modifications of the mind" rather than as Malebranchean "representative beings" (cf. Dascal 1990a), Malebranche and Leibniz (as well as Spinoza) considered such an interpretation insufficient because liable to subjectivism. Malebranche finally opted for a Platonic solution, equating our clear ideas/concepts with God's perfect knowledge of essences, without however spelling out in what precisely such a knowledge consists.14 Leibniz, in a more practical spirit, sought to provide a clearcut logical criterion for the existence of an idea. According to him we have an "idea" only if are able to prove its logical consistency; otherwise, all we have is a (psychological) "notion", that may turn out to be devoid of representative content and hence, of epistemic value. We can speak and even think, say, of "the greatest number", but we have no "idea" therof, because we cannot give a real definition of this expression, i.e., a contradiction-free complete description of its content.

According to Leibniz, Hobbes was on the right track by pointing out the importance of words in thought and of their use according to precise definitions. But he created what Leibniz often refers to as "the Hobbesian difficulty"15 -- namely, the alleged dependence of truth upon the arbitrariness of definitions -- by overlooking the fact that real -- as opposed, say, to mere nominal -- definitions are not arbitrary in so far as they are subject to a powerful logical constraint.16 The association of concepts with definitions was not restricted to those who, like Hobbes and Leibniz, admitted a role for words in thought. It loomed large also in authors who denied such a role -- to wit, Bacon himself and, no less significantly, Port Royal Logic's three chapters devoted to definitions. Such an association clearly indicates the acceptance of an implicit "verbalization" of the notion of idea: if not straightforwardly identified with words themselves, ideas/concepts were conceived as language-like structured chains of components, closely corresponding to their verbal definitions -- a far cry from the earlier view of ideas as similar to images.

And this was not the only indication of the need for another -- possibly verbal -- model of mental representation. In fact, Descartes himself was not happy with the comparison between ideas and images. In the second Meditation he pointed out that the physiological chain producing images might induce subjectively convincing "similarities", that were however objectively false. The sun, for example, appears small to us, whereas scientific reasoning proves it to be many times bigger than the Earth. In the Dioptrics (chapter 4) he denounces the mistake of those philosophers who interpreted the visual metaphor too literally, leading to the belief that in order to feel, perceive, or think the mind must "contemplate images transmitted from the objects to the brain". Thought, according to Descartes, need not rely upon such mistaken-prone signs of things. The naturalness of the representativity of ideas -- which ensures their objectivity -- must come exclusively from their intrinsic properties, not from extrinsic similarities. In criticizing once more, in his posthumously published treatise The World or Treatise on Light, the literal interpretation of the analogy idea/image, Descartes significantly appeals to words which, "without having an similarity with the things they represent, nevertheless make us conceive them" -- these very words which, he insists, "signify something only by virtue of human imposition".17 And in the Discours de la Methode, as well as in a letter to Henry More (5 february 1649), he proposed the ability to use language appropriately in changing and unexpected circumstances as a sort of Turing Test for differentiating animals (or automata) from humans.18

None of this means, of course, that Descartes and most of his contemporaries were prepared to endorse Hobbes's idea of actually making public language or any other public signs part and parcel of mental operations of any kind. At most they would perhaps be willing to go along with something akin to the Fodorian hypothesis of a "language of thought", i.e., of an innate (and therefore "natural") language-like mental medium. But it clearly indicates the need to elaborate an alternative model of mental representation. Unlike the ancient Aristotelian idea of thought as "silent speech", which mysteriously allowed for the coexistence of a "non-natural" account of words with a "natural" account of thought-units, Hobbes's proposal forced his contemporaries to question such a dubious coexistence, regardless of whether they accepted or rejected his thesis of the actual intervention of public language in thought.

Hobbes's merit was to consider the linguistic model of mental representation as a serious alternative, and thereby to force everybody else to face its consequences, which raised far-reaching questions: (i) since the meaning of ideas is now to be modeled upon the meaning of words, linguistic semantics cannot anymore be "ideational" -- a new theory of meaning for both words and ideas is required; (ii) if ideas, like words, do not represent `naturally', does this entail the conventionality and presumably also the relativization of ideas and thought?; (iii) since language is typically a social phenomenon, should thought too be conceived as a public, rather than as a private affair?; (iv) what exactly does it mean to attribute to language and thought "computational" powers?

If the new, "verbal" model for mental representation was to take shape, pace Hobbes's opponents; if linguistic representation was to serve as a model for mental representation, both the nature and workings of language and mind had to be more carefully scrutinized and better understood. If, in addition, language was to be allowed to play any role in mental operations, Cartesian dualism should be reconsidered giving way, eventually, to a new architecture of the mind and its functions.

3. Mental computation: linguistic, logical, mathematical

The questions raised by Hobbes's proposal were -- intrinsically --of an interdisciplinary nature: they prompted reflecain tliof what was known about language (especially semantics) as well as logic and mathematics; and they benefited from the changes occurring in these areas at the time, and stimulated them as well.

Semantics had been concerned almost exclusively with the meaning of "categorematic" words (nouns, adjectives, verbs), which it was easy and natural to relate to the ubiquitous "ideas". Locke's main semantic principle, thus, was that "words, in their primary or immediate signification, stand for nothing but the ideas in the mind of him that uses them" (Locke, Essay, III.2.2). However differently "ideas" were understood by Locke and Descartes, they were for both what guaranteed -- point by point -- the meaningful use of language: "Whenever I express something with words, when I understand what I say, it follows with certainty that I have in me the idea of the thing signified by my words".19

This kind of "ideational" semantics was directly correlated with an "inspectionist" (cf. Reeves 1962: 11-12) conception of thought, according to which (a) the study of thought is the study of the elements of content which constitute it, (b) such elements are "ideas", whose (c) successive "presentation" to the mind in the course of cognitive processes is what cognition is all about. On this view, it is ther constant inspection of ideas by the "mind's eye" that ensures the validity of reasoning and the reliability of any mental process, especially those involving a measure of complexity.20 For thinking is performed upon ideas themselves, not upon their (verbal or other) signs, and complex ideas or sustained reasoning must be captured by the understanding uno intuitu -- at a glance -- if their truth or validity is to be properly assessed. Thus, Descartes recommended, in his Rules for the Direction of the Mind, the use of a sort of "mental gymnastics" whenever we are engaged in a complex mental task:

...if I have first found out by separate mental operations what the relation is between the magnitudes A and B, then that between B and C, between C and D, and finally between D and E, that does not entail my seeing what the relation is between A and E, nor can the truth previously learnt give me a precise knowledge of it unless I recall them all. To remedy this I would run them over from time to time, keeping the imagination moving continously in such a way that while it is intuitively perceiving each fact it simultaneously passes on to the next; and this I would do until I had learned to pass from the first to the last so quickly, that no stage in the process was left to the care of the memory, but I seemed to have the whole in intuition before me at the same time. This method will both relieve the memory, diminish the sluggishness of our thinking, and definitely enlarge our mental capacity (Rule 7; AT, X, 387-388; HR, 19-20).

To be sure, Descartes also considers the possibility of employing abridging signs in order to render the above process more efficient. Such signs, preferably written, should be short, so that, after having distinctly examined each thing, one would be able to "traverse them all with an extremely rapid movement of our thought and include as many as possible in a single intuitive glance" (Rule 16; AT, X, 455; HR, 67). But this use of signs is confined to a purely mnemonic function. They are useful only to evoke ideas, i.e. to place them before the mind's eye. The task of verifying the validity of a deduction or of actually drawing a conclusion from the premises of an argument is entirely left to the understanding itself. Descartes is suspicious of any attempt to formalize reasoning, for he does not trust the "precepts of the dialecticians, by which they think to control the human reason" (Rule 10; AT, X, 405; HR, 32). In order to avoid the danger represented by blind obedience to such formal precepts, the only means is, for him, to employ at each step the watching eye of the understanding:

Wherefore as we wish here to be particularly careful lest our reason should go on holiday while we are examining the truth of any matter, we reject those formulae as being opposed to our project, and look out rather for all the aids by which our thought may be kept attentive... (Rule 10; AT, X, 406; HR, 32).

Such an inspectionist model of mental computation is clearly opposed to Hobbes's suggestion of a mental manipulation of linguistic signs, just as it is very distant from the kinds of accounts we would associate today with the term `computation' -- influenced as we are by formal logic, by Turing machines, and by Physical Symbol Systems. But it is worth pointing out that it was not entirely alien to Hobbes himself -- as befits a citizen of his age. He too focused mainly on categorematic words, and his arithmetics of addition and subtraction can only work for subject-predicate sentences (where both subject and predicate are "general names"), and under the presupposition of a given hierarchy of nouns according to their extension and/or comprehension.21 Furthermore, he assumed a transducer model of speech, which presupposes a language-independent "train of thoughts" or "mental discourse", wherein the role of words as marks was restricted to "fixing" (general) ideas and bringing them to the mind's attention.22 And -- like Descartes -- he was wary of the scholastic allegedly vacuous use of words without referents, and considered the presence in the mind of the correctly defined "ideas of things" corresponding to the words as the only possible guarantee against such abuses. This is why he was suspicious of algebra, whose "symbols" were semantically empty symbols -- to be viewed at most as useful abbreviations -- and modeled his idea of mental computation upon the semantically interpreted signs of arithmetic (comparable to concrete geometric figures).23

It is algebra, however, that provides the clue -- for Leibniz, Berkeley, and others -- for a different approach to semantics and for a different model of mental computation, at odds with the inspectionist conception described above. Algebra is appealed to by Berkeley in the course of his argument against Locke's semantic principle -- the "received opinion that language has no other end but the communicating our ideas, and that every signifcant name stands for an idea":

And a little attention will discover, that it is not necessary (even in the strictet reasonings) significant names which stand for ideas should, every time they are used, excite in the understanding the ideas they are made to stand for: in reading and discoursing, names being for the most part used as letters are in algebra, in which, though a particular quantity be marked by each letter, yet to proceed right it is not requisite that in every step each letter suggest to your thoughts that particular quantity it was appointed to stand for (Principles, Introd., 19).

To "proceed right", Berkeley is suggesting, requires only the obedience to the "procedural rules" that regulate mathematical operations, not the actual presence of contentful "ideas".

Leibniz went a step further, stressing the psychological impossibility of satisfying the inspectionist requirement. For him, in algebraic reasoning, the ideas underlying the symbols employed are not evoked or presented to the mind at each step. If this were to be done, he contends, algebraic reasoning would become impossible, for the mind would be permanently busy trying to get hold of the evoked ideas, with no capacity left to proceed with the business of reasoning itself. It is essential, on the contrary, that in this kind of reasoning the mind concentrate exclusively on the signs themselves and on the operations performed upon them, without caring to interpret them as it proceeds. In this sense, algebraic reasoning is viewed as nothing but the manipulation of signs, performed according to rules which guarantee the validity of its results (cf. Dascal 1987: passim). He extends this observation to any thought process involving some degree of complexity, which essentially depends upon what he calls `blind thought':24

Similarly, nobody could follow a lengthy reasoning with his mind ifcertainames had nbeen . Through them, a great number of things can be comprehended in such a way as to allow one to run through many of them very quickly; this would be impossible if, suppressing the names and all equivalent signs, we should use the definitions instead of the defined. Thoughts of this kind I usually call blind thoughts, and there is nothing more common nor more necessary for men. Very few people, indeed, distinctly imagine all the units of the number nine, or the method of generating a hyperbola, when talking about them. If we were once conscious of ordering the words distinctly and constantly, then blind thoughts alone would be sufficient for distinct reasoning. This is why the modern Analysis Symbolica [i.e., Algebra] -- in spite of Hobbes's criticism -- is so useful for quick and sure reasoning (A, VI, ii, 481; transl. in Dascal 1987: 149).

Algebra's use of letters for "unknown quantities", along with the new "procedural" mathematics embodied in the calculus, which allowed to deal with infinite magnitudes without the need to refer to entities called "infinitesimals",26 further supported the emerging alternative -- a non-inspectionist model of cognition -- by demonstrating the possibility of performing computations with non-interpreted symbols. Reasoning, within this perspective, can be accounted for in "formal" terms, i.e., through a system of operational rules that defines the relevant "formal" properties of the symbols, and spells out their "valid" sequences, independently of their intepretations. In such a system, computation viewed as a manipulation of symbols, as that "playing with characters" in which "blind thought" consists, could thus indeed "go far, very far" -- as Leibniz says in a note (cf. Dascal 1987: vii). For the "cashing out" of the meanings of the symbols in terms of their referents -- be they "ideas", "things" or other kinds of "content" -- could be in fact postponed indefinitely until the end of the game, as suggested by Berkeley in his dialogue Alciphron:

Words, it is agreed, are signs: it may not therefore be amiss to examine the use of other signs, in order to know that of words. Counters, for instance, at a card-table, are used, not for their own sake, but only as signs substituted for money, as words are for ideas. Say now, Alciphron, is it necessary every time these counters are used throughout the progress of a game, to frame an idea of the distinct sum of value each represents? ... From hence it seems to follow, that words may not be significant, although they should not, every time they are used, excite the ideas they signify in our minds; it being sufficient that we have it in our power to substitute things or ideas for their signs when there is occasion (Works, III, 291-292).

Just as the circulation of goods, made possible by the replacement of gold and silver by banknotes, cheques, and letters of credit, is what matters for a healthy economy, so too the cognitive economy of the mind depends, on the non-inspectionist view, upon the regular and reliable circulation of contents -- which it achieves by replacing the problematic "ideas" by symbols which can be easily grasped by the senses and whose "exchanges" can be formally regulated in a precise and public way.26

The development of the notion of formalization in mathematics and logic was concomitant with a closer interest in the notion of linguistic form (cf. Land 1974; see also Aarsleff 1982). This implied a shift of attention from the word to the sentence as the basic unit of meaning, and from the categorematic to the syncategorematic words -- those "particles" (a term that included affixes and suffixes) that structure the sentence (and even larger linguistic units).27 Leibniz, here too, was a pioneer -- although most of his texts on linguistic matters remained unpublished until the beginning of this century, and some of them are still waiting for publication. The dominant trend, represented, for instance, by the Port Royal Grammar (Arnauld and Lancelot 1676), which -- consonant with the prevalent view that favored the direction of explanation: mental --> linguistic -- sought to explain linguistic "deep structure" in terms of "universal logical structure". Leibniz, instead, tried to define a level of "rational grammar" which, although underlying all languages, was not to be equated with "logic". It is at such a level that a specific notion of "linguistic form" -- hence, of "linguistic computation" -- could be defined. And Leibniz's detailed comparative analyses of the "particles" were intended to provide the the "meat" for this formal characterization of linguistic structure.28 Like the logico/mathematical notion of form, which permitted to ignore the local arbitrariness of the individual signs chosen by focusing on the structural non-arbitrariness of larger units and of the system of rules as a whole,29 so too at the level of their shared "rational grammar", languages could be viewed as non-arbitrary in spite of their surface differences.30 This made them fit for overcoming "Hobbes's difficulty" and, thereby, for playing a role in cognition.

In David Hartley's (1749) classification of four types of words -- 1. Such as have Ideas only; 2. Such as have both Ideas and Definitions; 3. Such as have Definitions only; 4. Such as have neither Ideas nor Definitions -- the close relation of the mathematical and linguistic developments described above is made apparent. Words of the first class are compared to "propositions purely geometrical, i.e. to such as are too simple to admit of Algebra" (e.g., the equality of the base angles of an isoceles triangle). Those of the second class are analogous to "that part of Geometry, which may be demonstrated either synthetically or analytically; either so that the Learner's Imagination shall go along with every Step of the Process painting out each Line, Angle, etc. according to the Method of Demonstration used by the ancient Mathematicians; or so that he shall operate entirely by algebraic Quantities and Methods, and only represent the Conclusion to his Imagination". Those of the third class are like "Problems concerning Quadratures, and Rectifications of Curves, Chances, Equations of the higher Orders, etc. as are too perplexed to be treated geometrically", requiring the use of signs for unknown quantities. And those of the fourth class "answer to the algebraic Signs for Addition, Subtraction, etc., to Indexes, Coefficients, etc.; these are not algebraic Quantities themselves; but they alter the Import of the Letters that are; just as Particles vary the Sense of the principal Words of a Sentence, and yet signifiy nothing of themselves" (Hartley 1749: 277-280; quoted in Land 1974: 149-150). It is apparent from these quotations that, from Hartley's vantage point, the recent history of mathematics provided a convenient model for distinguishing between different kinds of mental computations in terms of which linguistic expressions were to be classified -- a model where the inspectionist and formal approaches did not exclude each other but could be viewed as complementary.

The rapprochement between language and mathematics tended to favor a reading of `computation' that emphasizes the logically formalizable aspects of natural languages at the expense of other aspects -- e.g., those sometimes lumped under the label `rhetoric'. Such an emphasis naturally leads to texts such as Condillac's Langue des Calculs (1798), which is not just a treatise on algebra but an attempt to construct a model of a completely formalized non-arbitrary language for scientific thought and communication.31 Although coming from a declared empiricist, such a project corresponds to what Auroux (1992) calls "maximalist rationalism", which holds a conception of language that not only seeks to develop a formal theory of language but equates language itself with a formal calculus.32 A somewhat milder version of this idea is epitomized in Condillac's claim that the art of reasoning is nothing but a well-formed language, which was enthusiastically adopted by Lavoisier and his colleagues as the ideology underlying their major refnotatioat the end of 18th cen(cf. Crossland 1978: Chap. 5).

This tendency is no doubt the one stimulated by Hobbes's talk of reasoning as computation, while at the same time demanding strict adherence to definitions, proscribing metaphor, and -- generally -- conducting his theoretical discussion of language and speech within the framework of his methodology of science (cf. Jesseph 1996). But there was also another strand of reflection about language in Hobbes, that emerges in other parts of his work. He was also concerned both with language's daily uses and with its theological and political abuses, where feelings, emotions, ambiguities, and their linguistic expression cannot be overlooked. In fact, most of the Leviathan is devoted to these kinds of linguistic phenomenona. True, here too Hobbes wishes to provide a scientific account of society and to denounce superstition that passes for true religion only thanks to obscure and imprecise language. Nevertheless his approach to language here is notably more flexible: he withdraws from a rigid semantics of definitions, admits plausible metaphorical interpretations of the Scriptures (and provides guidelines for producing them), analyzes a variety of speech acts other than assertions, and calls attention to the role of context (e.g. the addressees' opinions, the situation of utterance, the historical circumstances, the possibly different stages of linguistic evolution) in determining meaning. He thus addresses themes that traditionally belonged to rhetoric, and adumbrates others that would later become central to pragmatics.33

These pragmatic and rhetorical aspects of language surely had nothing to do, in Hobbes's mind, with its computational cognitive role. But since they cannot be excised from the use of natural language, no matter how carefully one tries to purge it from them, why to insist that it is in natural language rather than in some artificial symbolism that we perform our mental computations? Hobbes had no clear answer to this question. But Condillac, at least prior to his "formal turn", had. And it was a genetic answer, namely that natural language is -- both ontogenetically and phylogentically -- our first "computational" tool. For it is through the acquisition of language that we acquire the capacity of analysis, without which our sensations would remain forever holistic, a situation that would not allow us to have any definite ideas nor to articulate them (cf.Dascal 1983). Natural language plays an essential role in thought, according to Condillac, because, prior to its advent, "lacking any source of organization, the thinking subject must rely entirely upon language in order to structure the representations themselves" (Formigari 1992: 181). Natural language may not be the most perfect computational tool for reasoning, but without it better tools could not be developed.34 It has the further advantage of being the first such tool acquired by the untutored child so that it is the cognitive tool every person is familiar with and can handle most naturally. Still, for Condillac's school the cognitively valuable, "analytic" powers of natural language had virtually nothing to do with its rhetorical and pragmatic uses, which were considered to be rather a disposable nuisance from the cognitive point of view.35

It is customary to associate the re-valuation of these rejected aspects of language with the rise of romanticism in the 19th century, i.e., with the decline of cognitivism. A refreshing and somewhat surprising exception to this view can be found in the Scottish philosopher Dugald Stewart (1753-1828) who was aware of the cognitive value of such features of natural language such as vagueness, ambiguity, context dependence, and the unending need of interpretive efforts -- all of which were shunned by the cognitivists. Stewart argued that Leibniz and Condillac overlooked

... the essential distinction between mathematics and the other sciences ... In the former science, where the use of an ambiguous word is impossible, it may be easily conceived how the solution of the problem may be reduced to something resembling the operation of a mill -- the conditions of the problem, when ones translated from the common language into that of algebra, disappearing entirely from the view; and the subsequent process being almost mechanically regulated by general rules, till the final result is obtained. In the latter, the whole of the words about which our reasonings are conversant, admit, more or less, of different shades of meaning; and it is only by considering attentively the relation in which they stand to the immediate context, that the precise idea of the author in any particular instance is to be ascertained. In these sciences, accordingly, the constant and unremitting exercise of the attention is indispensably neccessary to prevent us, at every step of our progress, from going astray (Stewart 1854/60: III, 106; quoted in Land 1974: 113).

Are we returning here to the Cartesian mental gymnastics? I don't think so. For, unlike Descartes, Stewart does not deny language's role in cognitive processes. Nor does he propose to bypass through "direct inspection" sequential logical processes. Quite on the contrary, he highlights the special nature of the logical-cognitive processes underlying language use in all sciences except pure mathematics, where

... the mind must necessarily carry on, along with the logical deduction expressed in words, another logical process of a far nicer and more difficult nature, -- that of fixing, with a rapidity which escapes our memory, the precise sense of every word which is ambiguous, by the relation in which it stands to the general scope of the argument... The improvements which language receives, in consequence of the progress of knowledge, consisting rather in a more precise distinction of these meanings in point of number, the task of mental induction and interpretation may be rendered more easy and unerring; but the necessity of this task can never be superseded, till every word which we employ shall be as fixed and invariable in its signification as an algebraical character, or as the name of a geometrical figure (Stewart 1854/60; III, 107; quoted in Land 1974:121).

I am tempted to say that Stewart anticipates some of Peirce's central ideas as well as of present-day pragmatic theory. He is telling us that only a broader notion of computation can do justice to the wealth of computational processes operative in natural language use -- many of which involve operations that cannot be "mechanically regulated by general rules" for they depend upon heuristic roles, fuzzy logic, non-monotonic logic, abduction, and similar "soft" procedures that do not fit "hard" computationalism. Nonetheless, these are definitely cognitive as well as computational processes, in the sense that they are inferential in nature (cf. Dascal and Gross 1999). We might perhaps say that Stewart's position represents, in Auroux's (1992) terminology a "minimal rationalist" position, which only claims that "computation has a role in linguistic activity" -- provided `computation' is understood in the broad sense just mentioned.36

4. The ontological challenge

Hobbes's linguistic computation thesis -- we should not forget --was part and parcel of his metaphysical onslaught on Cartesian dualism.37 The mental is not a separate substance (Hobbes lists `immaterial substance' as an example of a nonsensical expression); the senses and the imagination -- both continuous with the understanding -- are also continuous with material movement; hence, the sounds or written marks of language are, essentially, "of the same stuff" as the components of our mental life -- ideas, judgments, beliefs, and desires. If reasoning is nothing but linguistic computation -- he politely suggests to Descartes -- then "le raisonnement dependra des noms, les noms de l'imagination, et l'imagination peut-etre (et ceci selon mon sentiment) du mouvement des organes corporels; et ainsi l'esprit ne sera rien autre qu'un mouvement en certaines parties du corps organique" (Hobbes's fourth Obj; AT, I, 138).

This usof the linguisticomputationathesis to support monistic materialism was, for Descartes, a further -- perhaps the most powerful -- reason not to grant language any foothold whatsoever in the realm of the mental. This, regardless of the fact that he had no explanation for the interaction between the physical and semantic sides of linguistic phenomena, between which stood the unsurmountable barrier separating two entirely different substances -- body and mind. Hobbes's materialism seemed to overcome smoothly such a difficulty, by simply removing the barrier. But it remained largely programmatic, "explaining" the inteplay between linguistic and mental phenomena -- as well as, generally, that between body and mind -- only in the most general terms available to the incipient "mechanical physiology" of the time.

Perhaps the most challenging aspect of Hobbes's legacy for cognitive science is the materialistic research programme. While at first strongly opposed, with only a few courageous adepts such as La Mettrie (1709-1751) and Cabanis (1757-1808), the assumption that the mind has no other ontological substrate than the body became, in the present century, virtually unquestionable among scientists and philosophers alike -- to the point that hardly anyone would question the following principle:

[The anti-Cartesian principle] There can be no purely mental beings (for example, Cartesian souls). That is, nothing can have a mental property without having some physical property and hence without being a physical thing (Kim 1996: 11),

and perhaps also this one:

[Mind-body supervenience] The mental supervenes on the physical in that any two things (objects, events, organisms, persons, etc.) exactly alike in all physical properties cannot differ in respec of mental properties. That is, physical indiscernibility entails psychological indiscernibility (ibid., p. 10).

The challenge, of course, consists in finding out the relevant physical properties and the kinds of relations the "corresponding" mental properties hold with them.

In the history of the attempts to cash out this materialist programme, language has loomed large, ever since Hobbes -- sometimes providing arguments on its behalf, sometimes raising problems for it. Broca's discovery of a brain location associated with speech provided for the first time concrete evidence for the belief that higher cognitive functions can be investigated by finding their neural correlates, possibly neatly packed in "modules". But up to this day brain scientists and neuro-surgeons struggle with the task of finding exactly what corresponds, in the brain, to mental states, mental contents, and mental functions -- including the alleged components of the "language organ". Behaviorism, in its early Watsonian form, considered it possible to reduce all mental activity to sub-vocal speech. But its later, Skinnerian, account of verbal behavior had to posit "covert" stimuli and responses, in addition to their physical, observable counterparts, in order to come to grips with the basic psycho-linguistic phenomenon of "semantic generalization". Philosophers of mind and of language such as Searle or Fodor, who adhere to the materialist programme and see in the ability to explain linguistic behavior the touchstone for its success, provide elaborate arguments that show that such notions as "intentionality" or "content" occupy a special explanatory niche, which prevents their explanation in terms of the physical properties of linguistic symbols. Artificial Intelligence pioneering projects, which assumed the significance of the Turing Test, preferred to employ a simple transducer view of language use of the Cartesian type, and to model intelligent thought as occurring in a purely logical symbol space, underestimating the problems involved in "translating" public language utterances into that space.38 In all these cases it is as if language resisted a straightforward materialist account, leaving room for some sort of dualism -- albeit not avowedly ontological -- to silently creep in. It is, nevertheless, a tribute to Hobbes that he insightfully picked up what is both the most difficult and also the most promising phenomenon for the implementation of the materialist programme.


* *

In all likelihood, Hobbes's suggestion that the most distinctive form of human thinking, reasoning, is nothing but linguistic computation is not directly responsible for all the developments discussed in this paper. Nevertheless, it set in motion, in the 17th and 18th centuries, a research programme -- to which these developments belong -- which culminated with a conception of language and mental life quite different from the one prevalent in Hobbes's time. The change was so radical that, instead of Descartes's surprise and scorn at the mere suggestion that language might have any direct role in thinking, by the end of the 18th century, it is Kant's silence about this intensively debated question that causes puzzlement (cf. Dascal and Senderowicz 1992). The present century's impressive achievements in the study of language, cognition, mathematics, logic, and brain sciences have certainly provided new empirical and conceptual tools for pursuing this debate. But Hobbes's challenge remains, as yet, unsolved.


  1. Hobbes's "reckoning" refers mainly to syllogistic deduction. It is not clear whether he relied upon an intensional or an extensional interpretation of the terms and quantifiers in the Subject-Predicate sentences out of which syllogisms are made. Each of them would allow for relatively straightforward readings of "addition" and "subtraction". One should beware, however, not to employ set-theoretical tools -- unavailable at the time -- for such readings. Leibniz, presumably inspired by Hobbes, proposed several numerical calculi for syllogistic reasoning, thereby minimizing its linguistic aspect, emphasized by Hobbes. But he used the full range of arithmetical operations, rather than only addition and subtraction (cf. C 42-49, 70-77, 77-82, 84-89, etc.).
  2. In De Corpore, Hobbes elaborates upon the functional difference between marks (or "notes", as he calls them here) and signs: the former are created for ourselves, the latter, for the others ["Notae ergo et signi differentia est, quod illa nostri, hoc aliorum gratia institutum sit" - De Corpore I,2,2]. He also somewhat restricts the mental role of the former: Notes are said to have a mnemonic function and signs, a communicative one ["Notae ut recordari, signa ut demonstrari cotitationes nostras valeamus" - De Corpore I,2,3]. In principle, then, notes, being "private", need not be identical to public signs. If this were the case, however, the thoughts they made accessible to an individual would be lost to humankind with his or her death. The advantage of using public signs for both functions was evident, for Hobbes. Furthermore, neither notes nor signs are "natural", both being "conventional" or arbitrarily "instituted".
  3. For a survey of such projects of universal language, see Knowlson (1975). Leibniz's projects, vis-a-vis those of his contemporaries, were sui generis, because he was interested in symbolic systems useful for the production of knowledge (ars inveniendi), and not only for its communication (cf. Dascal 1978; Pombo 1987).Occasionally, Bacon's followers deviated from the two basic assumptions mentioned in the text, and lapsed into the beliefs of the previous era he most criticized. A case in point is John Webster. In his Academiarum Examen (1654), Webster proposed a reform of learning, largely inspired by Bacon, which purported to replace speculation by experimental philosophy -- the `philosophy of the Schools' by the `philosophy of the furnaces'. Accordingly, he contrasted the library with the laboratory, and condemned verbalism. And yet, he freely combined these Baconian views with a good deal of Renaissance Logosmystik, by looking for that original `language of nature' that "still reveals itself in the great book of nature, in the inward signatures of things, in the language of animals, etc." (quoted in Formigari 1988: 20). Our task, according to Webster, is to reconstruct our ability -- lost in the Fall -- to decipher this language, a task which is to be achieved by "the recovery and restauration of the Catholique language in which lies hid all the rich treasury of natures admirable and excellent secrets" (Webster ibid., p. 21). This cryptographic model of knowledge, rather than leading (as in Galilei) to an emphasis on the role of mathematics, takes hieroglyphs as the model for the `Catholique language' to be restored/reinvented. Webster was sharply criticized by Seth Ward (1654) -- an influential member of the Royal Society -- who condemned Webster's reliance on language mysticism as incompatible with Bacon's legacy and with the spirit of the new science.
  4. "Le mot d'Idee est du nombre de ceux qui sont si clairs qu'on ne les peut expliquer par d'autres, parce qu'il n'y en a point de plus clairs et de plus simples" -- write Arnauld and Nicole in the first chapter of their influential La Logique ou l'Art de Penser (1683: 65).
  5. "Il est bien triste d'avoir tant d'idees, et de ne savoir pas au juste la nature des idees". In the entry idee (written in 1765), of his Dictionnaire Philosophique (Voltaire, 1769, p. 224).
  6. "Qu'est-ce qu'une idee? C'est une image qui se peint dans mon cerveau" (Voltaire, 1769: 223). What I am considering typical in Voltaire's answer is its use of "image", not of "brain".
  7. "... images qui sont depeintes en la fantaisie; ... en la fantaisie corporelle, c'est a dire en tant qu'elles sont depeintes en quelques parties du cerveau..." (Deuxiemes Reponses; AT IX, 124).
  8. "... the immediate cause of sense perception consists in ... that the first organ of sense is touched and pressed; ... the pressure of the uttermost part proceeds from the pressure of some more remote body, and so continually, till we come to that from which ... we derive the phantasms or idea that is made in us by our sense" (De Corpore 4, 25; EW 1, 390). On Hobbes's psychology, see Gert (1996). A similar chain of transmission of "movements" is described in detail by Descartes in his Traite de l'Homme (AT XI).
  9. Berkeley's criticism of Locke's "general ideas" in the Principles is well-known. He also called attention, in Siris, to the second kind of problematic cases, using the term `notion' to distinguish the non-imagetic operations of the mind from ideas or images: "There are properly no ideas, or passive objects, in the mind but what were derived from the sense: but there are also besides these her own acts or operations: such are notions" (Siris, # 308).
  10. Hobbes, thus, is not claiming that all thought is verbal. He is only claiming that those mental processes where generality and orderly concatenation of thought are involved require the use of inner verbal means. "General names" are mentioned in the long passage quoted in section 1; as for syncategoremata, they are discussed, for example, in Leviathan (46, 16-17), as those words that "serve to show the consequence or repugnance of one name to another", along with the suggestion that even languages such as Hebrew with "no verb answerable to est, or is, or be)" actually express the appropriate relation of one name to another through the syntactic device of "placing two names in order".
  11. In his Fifth Objection to the Meditations, Hobbes points out (AT IX, 139-140) that this characterization of `idea' implies that we can have no idea of God, since we cannot have an image of an invisible and immaterial thing. In line with his linguistic thesis, he suggests that we do not need to have an image of God in order to use significantly the name `God', and to think about God. For this, he claims, it is sufficient that several trains of reasoning, beginning with this or that particular experience, lead us to conclude that there should be a being with such and such properties, to which we then attach the name in question. Descartes's reply (AT IX, 141) consists in withdrawing from his description of ideas as similar to images, so that the fact that we cannot have an image of God no longer counts against our having an idea of God, provided God is "immediately conceived" by our mind.
  12. "On appelle concevoir la simple vue que nous avons des choses qui se presentent a notre esprit; comme lorsque nous nous representons un soleil, une terre, un arbre, un rond, un quarre, la pensee, l'etre, sans en former aucun jugement expres. Et la forme par laquelle nous representons ces choses, s'appelle idee" (Arnauld et Nicole 1683: 59).
  13. Arnauld's (1683) criticism of his equivocal use of `idea' led Malebranche to distinguish, in the Eclaircissements, three senses of this term, through the use of three properties -- immediacy, representativity, and clearness -- only ideas in the sense of concepts possessing all three: "Ainsi ce mot, idee, est equivoque. Je l'ai pris quelquefois pour tout ce qui represente a l'esprit quelque objet, soit clairement, soit confusement. Je l'ai pris meme encore plus generalement pour tout ce qui est l'objet immediat de l'esprit. Mais je l'ai pris aussi dans le sens le plus precis et le plus resserre; c'est-a-dire pour tout ce qui represente les choses a l'esprit d'une maniere si claire, qu'on peut decouvrir d'une simple vue si telles ou telles modifications leur appartiennent" (Malebranche 1712: 822).
  14. This is hisoften mentioned but ill-understood theory of the "vision in God". For a brief but perceptive account of Malebranche's epistemological motives for such doctrine, see Popkin (1993: 322-324). Popkin felicitously compares Malebranche's ontological realism (esse est concipi = to be is to be conceived) to Berkeley's (esse est percipi = to be is to be perceived). In a sense, each draws the extreme consequences of the basic assumptions of rationalism and empiricism, respectively.
  15. For example: "De discrimine inter conceptus inadaequatos et adaequatos, sive definitionum nominalium et realium, ubi occurrendum Hobbesianae difficultati de veritate arbritraria, Cartesianae, de ideis eorum de quibus loquimur" (VE 732). He also calls Hobbes's position "super-nominalism", and contends that it is untenable: "... I confess that Hobbes seems to me to be a super-nominalist. For not content like the nominalists, to reduce universals to names, he says that the truth of things itself consists in names and what is more, that it depends on the human will, because truth allegedly depends on the definitions of terms, and definitions depend on the humal will. This is the opinion of a man recognized as among the most profound of our century, and as I said, nothing can be more nominalistic than it. Yet it cannot stand. In arithmetic, and other disciplines as well, truths remain the same even if notations are changed, and it does not matter whether a decimal or a duodecimal number system is used" (L 128; GP IV, 158).
  16. "... a means of distinguishing between nominal definitions, which contain only marks for discerning one thing from others, and real definitions, through which the possibility of the thing is ascertained. In this way we can meet the view of Hobbes, who held truths to be arbitrary because they depend on nominal definitions, not considering that the reality of the definition does not depend upon our free choice and that not all concepts can be combined with each other. Nominal definitions do not suffice for perfect knowledge unless it has been established by other means that the defined thing is possible" (L, 293; GP IV, 424-425). For Leibniz's theory of definitions, and its relationship to Hobbes's, see Dascal (1987: chap. 4). As I point out there, Hobbes implicitly held some criterion of the "correctness" of definitions, which prevented them from being purely a matter of the arbitrary "imposition of names".
  17. "Vous savez bien que les paroles, n'ayant aucune ressemblance avec les choses qu'elles signifient, ne laissent pas de nous les faire concevoir, et souvent meme sans que nous prenions garde au son des mots... Or, si les mots, qui ne signifient rien que par l'institution des hommes, suffisent pour nous faire concevoir des choses, avec lesquelles elles n'ont aucune ressemblance ..." AT, XI, 4).
  18. The relevant texts are in AT VI, 56-57 and AT V, 278. They have been highlighted by Chomsky (1966, 1968), who drawed from them the wrong conclusion that, according to Descartes, "language can serve as an instrument of thought" (1968: 11). For a discussion of this topic, see Dascal (1990b).
  19. "... je ne puis rien exprimer par des paroles, lorsque j'entends ce que je dis, que de cela meme il ne soit certain que j'ai en moi l'idee de la chose qui est signifiee par mes paroles" (Secondes Reponses; AT IX, 124).
  20. The same assumption underlies Port Royal Logic's requirement to always replace in the mind a word by its definition: "... toutes les fois qu'on se sert du mot qu'on a defini, il faut substituer mentalement la definition a la place du defini; et avoir cette definition si present, qu'ausitot qu'on nomme, par exemple, le nombre pair, on entende precisement que c'est celui qui est divisible en deux egalement, et que ces deux choses soient tellement jointes et inseparables dans la pensee, qu'aussitot que le discours en exprime l'une, l'esprit y attache immediatement l'autre. Car ceux qui definissent les termes, comme font les Geometres avec tant de soin, ne le font que pour abreger le discours ... mais ils ne le font pas pour abreger les idees des choses dont ils discourent" (Arnauld et Nicole 1683: 124).
  21. "By this imposition of names, some of larger, some of stricter signification, we turn the reckoning of the consequences of things imagined in the mind into a reckoning of the consequences of appellations" (Leviathan I.4.9).
  22. "The general use of speech is to transfer our mental discourse into verbal, or the train of our thoughts into a train of words; and that for two commodities, whereof one is the registering of the consequences of our thoughts, which being apt to slip out of our memory and put us to a new labour, may again be recalled by such words as they were marked by. So that the first use of names is to serve for marks, or notes of remembrance" (Leviathan I.4.3).
  23. "At symbolica, qua permulti hodie utuntur putantes esse analyticam, nec analyticam est nec synthetica, sed calculationum arithmeticarum quidem vera, geometricarum autem falsa brachygraphia, ars quidem non docendi neque discendi geometriam, sed inventa geometrarum celeriter et compendio in commentarios redigendi. Nam etsi inter propositiones longe dissitas, facilis sit per symbola discursus, an tamen is discursus, cum fiat sine ipsarum rerum ideis, valde utilis existimandus sit, certe nescio" (De Corpore III, 20) [But the so-called `symbolica', which is used by many scholars who believe that it is truly analytic, is neither analytic nor synthetic. It is merely an adequate abbreviation of arithmetical calculations, and not even of geometrical ones, for it does not contribute either to the teaching or to the learning of geometry but only to the quick and succint compilation of what was already discovered by geometricians. Even though the use of symbols may facilitate the discourse about propositions which are wide apart from each other, I am not sure whether such a symbolic discourse, when employed without the corresponding ideas of things, is indeed to be considered useful].
  24. The notion of blind thought plays a central role in Leibniz's philosophy of signs as well as in his epistemology. It is first used in his early work De Arte Combinatoria (1666; A, VI, i, 170), then in several intermediary papers, such as the one here quoted, to appear, finally, as a central piece of Leibniz's theory of knowledge, in his "On knowledge, truth, and ideas" (1684; GP IV, 422-426; L 291-295), in the "Discourse on metaphysics" (1684; GP IV, 427-463; L 303-330), etc.
  25. Berkeley, as is well-known, was critical of the new calculus, on the grounds that it made not explicit what kind of entities or ideas it was referring to. In fact, many of Berkeley's assertions -- especially in the Philosophical Commentaries were incompatible with the nominalism he expresses in his praise for algebra and in other passages quoted in the text. For example, he says that no reasoning about things of which we have no idea -- hence no reasoning about infinitesimals -- should be allowed (PC 354) and he affirms that one should not use any word without an Idea (PC 356) as well as that all signifying words represent Ideas (PC 378). For Berkeley's "semantic classicism", see Brykman (1993: 202-209) and for a discussion of its inconsistency with his nominalism, in the context of his philosophy of mathematics, see Robles (1993: Chapters 2 and 5).
  26. The comparison between language and money was -- and still is -- a popular topos. For a book-length study, see Shell (1992). For a specific study of the role of language in thought as expressed in the simile linking words with counters, tokens, or Rechenpfennige, as employed by Bacon, Hobbes, and Leibniz, see Dascal (1987: Chap. 1).
  27. In his Real Character, an artificial language for the purposes of scientific communication, commissioned by the Royal Society, Wilkins (1668) focuses on representational words, and his treatment of particles, which "do not have objective referents" is very problematic. Dalgarno's Ars Signorum (1661), on the other hand, devotes much more attention to this formal part of language.
  28. See Dascal (1990b). For a comparison between Leibniz's and the Cartesia's presumed anticipation of the notion of "generative grammar", see Dascal (1987: Chap. 7), and for a broader comparison between Leibniz's and Descartes's cognitivist paradigms, see Dascal (1988).
  29. See the final sentence of the second text quoted in note 15.
  30. Leibniz's rationalism abhorred arbitrariness of any kind. Accordingly, he attempted to show, through elaborate etymological and comparative analyses, that even individual words were not in fact "arbitrary", in so far as their roots could be shown to be in correspondence across languages and to be related to basic emotional and behavioral human reactions to shared circumstances. See for example his text "On the connection between words and things" (transl. in Dascal 1987), as well as Gensini (1990, 1991) and Dascal (1994).
  31. As pointed out by Rieu (1982: 37-39) Condillac's mathematical models changed from his early Essai sur l'origine des connaissances humaines to his posthumously published Langue des Calculs, from geometry, through arithmatic, to algebra -- an evolution that parallels Hartley's classification of words. For the influence of Condillac on the development of linguistic thought in the 18th century, see Aarsleff (1982).
  32. Auroux quotes Richard Montague as expressing clearly this view: "I reject the contention that an important theoretical difference exits between formal and natural language" (Montague 1974: 188).
  33. Hobbes published a summary of Aristotle's rhetoric under the title A Briefe of the Art of Rhetorique (1637), available from Southern Illinois University Press (1986), edited by J. T. Harwood. On Hobbes's rhetoric/pragmatics see Silver (1996) and Biletzki (1997).
  34. Some of these later developped tools -- e.g. arithmetical notation -- actually are nothing but imitations or extrapolations of grammatical and lexical rules, as pointed out in detail by Condillac's follower Destutt de Tracy (1817: Chap. 16), who insists that "les regles grammaticales font juste le meme effet que les regles du calcul"; ibid., p.340).
  35. The rhetorical tradition in the 18th and 19th centuries generally accepted this view, confining itself mainly to the study of the what it considered to be the "ornamental" effects of language use. Only in the present century a return to the Aristotelian view of rhetoric as concerned with argumentation, and hence as having cognitive value, was undertaken, mainly through the work of Chaim Perelman and his associates. On some of the dividends of this approach, see Dascal (1998) and Dascal and Gross (Forthcoming).
  36. Like in all "pre-historic" work of this kind, I have perhaps read more cognitive science pre-history in Stewart's text than there actually is there.
  37. In his objection to the second Meditation, Hobbes contends that Descartes is wrong in inferring from "I am a thinking [being]" that I am a spirit, a soul, an understanding, a reason, i.e. that I am a non-material being. According to him, Descartes's proof does not allow him to draw this conclusion: for all we know, the kind of being I am, the kind of being that does the thinking, may well be corporeal. He adduces further reasons to transform this possibility into a categorical statement to the effect that a being that thinks is material, rather than immaterial (AT, IX-1, 134-135). Descartes's elaborate reply reiterates that "intellectual acts have no affinity whatsoever with corporeal acts", and ultimately appeals, question-beggingly, to our having formed "two clear and distinct concepts of these two substances"(AT, IX-1, 137).
  38. I am referring here to Newell and Simon (1972), among others. For a critique of this approach, see Dascal (1987b, 1992). It should be said that, recently, Newell and his associates have revised the SOAR architecture, acknowledging a role for natural language in the inner workings of the model (cf. Lehman et al. 1993). For a critique of the representational assumptions underlying much of AI research, see Dascal (1989).




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