Some considerations about semiotic machines from the point of view of Charles S. Peirce's Philosophy

Lauro Frederico Barbosa da Silveira
Dept. of Philosophy
State University of S.Paulo at Marília
S.Paulo - Brazil


Peirce's writings offer a special interest to the consideration of semiotic machines. Some of them consider specifically the role that can be exercised by logical machines in order to produce inferences, while others have as their subject the physiological basis of mental activities.

Peirce had been interested in logical machines, even considering that it was impossible to a machine to reason. A machine could never take decisions from its own account and could only work with a very limited number of operations. Although a machine could draw true conclusions from the premises furnished to it, it would never produce a true inference, because inferences always suppose the observation of the conditions offered by the diagram and only in appearance and in very trivial cases can a machine draw the conclusion.

Nevertheless, Peirce supposed that the rational life follows the laws of the sensitive being. For human beings specially, it would follow that of the nervous system. By his own, he produced some theoretical hypotheses on this subject. Despise of recognizing the narrowness of the disposable knowledge, he tried to show the possibility of finding an acceptable explanation of this phenomenon both by proposing the interaction between the nervous cells, forming a kind of a network and by considering the nervous cell's protoplasm as capable of feeling, and then of mental action.

For Peirce, a semiotic machine could not be represented as a necessitarist one. Perhaps it could be thought as a neurosimile connectionist one, organizing itself in order to elaborate information and to find the best way of representing its object.

Some considerations about semiotic machines from the point of view of Charles S. Peirce's Philosophy

Nowadays increasing use is made of Peirce's Philosophy in considering the possibility of simulating the cognitive functions of mind.

The relatively recent and very well written book of Barbara Von Eckardt, What is Cognitive Science ( Von Eckardt (1995)), may be considered a good example of this, where the author chose the conception of representation proposed by Peirce as the best available in order to test cognitivist theories. As she considered that it was necessary for her purposes to simplify Peirce's original approach, she took into account only the triadic structure of sign as the best approach to representation, and worked with it until the end of her book, making abstraction of all the other elements present in the theory.

It is precisely this kind of choice over Peirce's Philosophy and, particularly, over his proposed Semiotics, that seems specially important to be considered , since probably what will be assumed as useful to a present proposal will not convey anymore the same idea that could be found in its original place.

Discarding the phenomenological categories of firstness , secondness and thirdness, as Barbara Von Eckardt does when she intends to assume the peircean conception of sign, she is not considering all the effort made by Peirce during the construction of Semiotics as a science, including the contribution that that categorical framework brought to the development of this same conception of sign.
Indeed, although Peirce had represented sign as a triadic entity early in his philosophical career, he only accomplished the purpose of constructing a full theory of the logic of reasonable conduct when, in the first three years of the 20th century, he elaborated Phaneroscopy and inserted the three categories into his system of sciences .

If account is not taken of these implications, what remains of Peirce's conceptions may be seen as interesting to the development of certain arguments, as is the case of Barbara Von Eckardt's about the foundations of the Cognitive Science. However, we cannot but guess how these arguments would present themselves if account were taken of the phenomenological character the categories confer to sign, to thought and to representation when worked by Semiotics.

If the insertion of sign, thought or representation into the context determined by the categories had been respected, the evolutionary character of semiosis could not be discarded. It would also not be possible to ignore the dialogic and social character of all the semiotic processes, especially when the human adult normal semiosis is taken as the main reference to thought simulation, as the author does.

Considering how frequent is this partial use of many of Peirce's ideas as had been often denounced (Peirce (1976) v.5 pp. 411 -434; Silveira (1993)) , before choosing some of those ideas as interesting to be incorporated in one's work while rejecting others as dispensable , it always seems opportune to search in the work of Peirce for the presence in it of the subject matter or of some other that could be akin to it. It will not be very surprising if there we find an unexpected richness of bright ideas and critical approaches on that matter, resulting from the very presence of those ideas initially considered as inopportune . And surely this will be the case when the question is that of simulating thought , with emphasis on the possibility of conceiving and constructing semiotic machines .

It is widely acknowledged the intense interest Peirce manifested on logical machines since his father tried to install a Babbage's one at the Albany Observatory (see Ketner (1988)). During the period he stayed at the Johns Hopkins University he had Allan Marquand as one of his best students, and when this latter proposed to construct a logical machine, Peirce contributed with all his knowledge in Logic and Physics to the best execution of the project. But while he was an enthusiast of the computational findings with machines, he was very critical about the possibilities of a machine showing genuine logical reasoning. As Peirce increasingly identified Logic with Semiotics, we may conclude that his critical attitude included the possibility of the existence of a true semiotic machine.

Before the moment when Peirce definitively settled Phaneroscopy and Semiotics as well formed theories, his critical attitude was shown, for example, through his denouncement of the intrinsic limitations presented by a machine in order to solve logical and mathematical problems.

The machine he knew was very limited in its calculating capacity, and this was the first handicap Peirce denounced in 1887 (Peirce (1976-(b)) vol.III.1, p.625-632), for a machine proposed to operate satisfactorily in Logic and Mathematics.

Nowadays, it seems evident that this denounced limitation has to be considered both as a question of fact and as a question of right. If considered as a question of fact, settled exclusively in the empirical observation, we have to conclude that this limitation has been surpassed day by day, since electronic computers were invented. However, if it is to be considered as a question of right, when what is to be considered is its essential computing possibility, this limitation must be attributed, at least, to all finite automaton, being this kind of machine the one Peirce was talking about.

Indeed, the greater could be its computing capacity, for a finite automaton all the operations it can effect would be limited to a finite number of steps, being impossible for such a machine to process a large number of important functions.
In the same text, the other limitation acknowledged in a machine was its impossibility of taking its own decisions. The answer given by Peirce to this handicap remains sound until now. Peirce remembered that, first of all, the answers expected to be given by a machine correspond to our own problems and not those of the machine itself. Thus, it would be nonsense consider that limitation as a true handicap for the artifact itself.

Understanding as Peirce probably had done the machine as a physical artifact, the answer once given may be repeated today. However, probably the question could receive different answers if its purpose was other. If, under the concept of a machine, was included the possibly self-organizing entities , then the capacity of taking decisions and proposing its own problems would be considered as a very pertinent question that perhaps would receive an affirmative answer.

One or two years before, Peirce made explicit other important aspects of the logical and mathematical inferences (Peirce (1976-(b)) vol. IV. p.353-356) that, in his opinion, laid beyond the processing capacity of any machine. Just in this period Peirce was giving lectures on Logic at Johns Hopkins, having the opportunity to develop his research into what later would become known as the Logic of Relatives . For this undertaking, he took profit of the presence of some exceptional students working under his orientation, and of accompanying the work of some of the more excellent mathematicians of that moment.

By the Logic of Relatives, the apparent mechanic character of deductive reasoning could not be accepted anymore. Under this theory all reasoning is seen as a diagrammatic set of relations that Reason produces in order to represent some class of objects. The simplest syllogistic form will be considered as a field of experimentation where, by the mere observation of the initial conditions that serve as premises or by the construction of new relations onto the diagram, the Reason makes explicit some other relations also elicited necessarily by this same diagram. These later are considered the conclusions of a reasoning.

If at Johns Hopkins all the development of a logic based on the diagrammatic constructions had not yet taken place, the observational nature of all reasoning was explicitly claimed, as can be seen in the following argument.

All kinds of reasoning imply observation, and since observation consists of a creative operation of Reason, although a machine may show itself as being able to "solve" syllogisms through the exhibition of the necessitated conclusion, this same conclusion will only be considered as true by a mind that interprets its consistency with the premises. And mind proceeds to this interpretation by implicitly observing the relations that were mechanically established. And more, reasoning so important as that belonging to Geometry whose structure is explicitly diagrammatic , depends so much on observation in order to draw its conclusions that it could never be effected by a mechanical machine. This reasoning, however, has been produced by mankind since remote Antiquity.

The inference produced by a diagrammatic thought, or by any thought that grows with the experience, implies the observation of an object imposing itself to the spirit, and its conversion into a constructed relational object produced by this same spirit.
This new object so constructed is not only equally observable but it is also a place, it could be said, where the spirit can work on either by comparing the relations initially represented in this object or by producing others, the leading principle of the construction being respected. To this constructed relational object, Peirce gives the name of a diagram.

What is constructed onto the diagram is ipso facto ascribed as true to the object. Only the observation can give rise to the discovery of the new relations elicited by the diagram and it is by the construction of these relations that thought takes place. The necessitated character of inference is essentially logic and can not be submitted to any mechanical determinism.

What gives place to the illusory attribution of the most necessitate of these operations to the processing capacity of a machine, which frequently happens with deductive syllogism, is the attention the reasoner must pay to take account of the almost imperceptible moment when he is solicited to observe the data and take a necessitate but not deterministic decision.

So, we can read in the text: "We found among inferences ... cases in which the necessity for observation of diagrams forces itself upon our recognition; for without a very sensible exertion of the observing faculty we are impotent to draw the conclusion. Now the act of observation , having once been fully acknowledged in such a case, we easily trace it through a succession of simpler and simpler cases differing little from one another, until we are brought to perceive ( what is so unobtrusive that at first we could not make sure of it) the existence of a perfectly analogous act of observation even in a ordinary syllogism."(p.354)

Some of these simple operations may be transferred to specially constructed machines to be effectuated by them. In some cases the presence of such machines may be considered as indispensable to the effectuation of the scientific thought, but nobody will consider these machines as being one of the authors of scientific research. Indeed, the questioning, the planning, the decision-taking, the observation and the evaluation always considered as the essential parts of scientific research, are exclusive attributions of the humans working in them. Scientists working in Chemistry, where the indispensable presence of instruments is unquestionable, never hesitate in associating the authorship of the research only to the humans working in it. Therefore, it would be very insensate that the same would not happen among the scientists working in Logic and in Mathematics.

In this discussion, it is also interesting to perceive that it is the whole thought process that confer to its parts its specific character. In fact, some of these parts, if taken separately, can be executed by mere mechanical ways, being able to be satisfactorily if not exclusively done by a machine.

The differences between Logic and Mathematics would become gradually clearer to Peirce's mind, resulting as he confessed from his assiduous talking with his father, an eminent mathematician and professor at Harvard. In 1902, taking position before Dedekind's thesis (Peirce (1976) vol.4 # # 227-307) that Mathematics had to be considered as a part of Logic, Peirce contrarily defended that of the specificity of each of them.

By this argument, Peirce distinguishes Mathematics as the science that produces true conclusions from Logic considered as the science of the production of true conclusions . From this distinction, it follows that while mathematics is strict hypothetical and apoditic science, Logic is characterized as being a representational and categorial one. This, it is important to be noted, makes all the difference when computability is to be considered in both the sciences.

Although mathematical reasoning is irreducible to mechanical operations since it implies observation in order to effectuate its demonstrations, it does not seem that the attainment of the immediate goal of producing true conclusions, although under the narrow limits of its exequibility, could not be reached by a machine. The same could not be said of logical reasoning, exception being made of its mere formal operations.

Logic being considered as the science that searches for the conditions of the production of true conclusions is, eminently, a science of rational conduct aiming at a goal. And so, it cannot satisfy its essential character only by producing true conclusions.

Peirce considered Logic more akin to Ethics than to Mathematics, once it is for the Reason a way for the attainment of the perfection . In this sense, the more a machine could contribute with to the achievement of logical reasoning, it never would be able to effectuate this reasoning integrally and by itself.

Abstraction made of the ethical aspect of the logical conduct and of the way by which a true conclusion is drawn, it becomes possible only to take account of the conventionally stated truth , we could say, of these conclusions produced by logical operations. In this very partial sense, identified by Peirce with that of the logical criticism (Peirce (1976) vol. 2. p.1-78), not only the logical operations can be effectuated by machines but man himself can be considered as a machine.

Peirce not only does not admit that the integrity of mathematical or logical thought is preserved with the adoption of this point of view, but finds by the occasion of this discussion a chance for emitting some interesting considerations about the difference Mathematics maintains relatively not only with Logic but with all other kind of sciences.

The concepts constructed by Mathematics are always particular in the sense that they do not represent as its Object, a general class of beings. These concepts only represents their own production.

Meanwhile, the concepts with which Logic as well as the other sciences elaborate their knowledge do represent general classes of objects that do not depend on those sciences for their being. In this relative independence of the object concerning the knowledge that Logic and the other sciences try to have of them, lies the very reason why these sciences intrinsically depends on the ethical choice made by Reason, in the search for its goodness . Computing can give account, at least, of a great part of the mathematical reasoning. The same, however, cannot be said of logic and of any other scientific reasoning. So, it is possible to conclude that although computation is a kind of reasoning , reasoning cannot be reduced to computation.

In the first decade of the present century, Peirce's theoretical thought attained its full development.

Phaneroscopy assumed, then, the role of establishing the primordial organization of the unrestricted universe of the appearances on proposing for this task the three coenopythagoric categories of firstness , secondness and thirdness . The first would represent the element of spontaneity , freedom or positive potentiality at that universe; the second, the element of actuality, factuality, struggle or otherness; and, finally, the third, the element of generality, necessity, continuity, law and thought properly.

To Semiotics, these categories could furnished the most adequate framework for the development of its own concepts. With their presence it became possible to deduce all the classes of signs by which the representation of the whole universe of experience takes place, by not subsuming anymore the cognitive functions under the paradigm of the propositional form of enunciation.

All intelligence representing the universe of experience could find in a so universal science a theory interested in well describing their own thinking.

The concept of thought, we could say, becomes extraordinarily enlarged in its depth and breadth, since pre-symbolic forms of representations which had not found yet an adequate treatment by Logic, find in Semiotics a formal and systematic representation.

It also becomes possible to incorporate under a scientific approach the forms of thought that could be exerted by non-humans or by human beings, not corresponding to the paradigm imposed for and by the traditional theories. The infants, the people not related to the occidental linguistic and cultural patterns, as well as all the kinds of impaired people, may be no more considered as consisting of deviant or inferior cases when considered in their thinking performance and capacity.

The question of the possibility and of the limits of simulating thought now free of the propositional and symbolic paradigm, transforms itself by the effect of this new approach. Probably, the main questions to be posed in order to verify if a machine can effectively produce thought will not be bound anymore to the propositional and symbolic model .

Thought will be found not only within the range of the conceptualization but also in all that can modify the conduct in the future, in order to establish a better relation toward an aimed object. But thought to be recognized, will imply the manifestation at least in some degree, of a process of generalization, diversification and growth. Thought will be recognized where can be found a true learning process.

Now, it is possible to anticipate some future conclusions, saying that there will be a semiotical machine where we can find a machine capable of learning or of acquiring a general habit of conduct.

Peirce's crescent recognition of all the subtlety of semiosis as the typical way of proceeding of any intelligence being able to learn

with the experience enlarged the distance separating it from any mechanical processing. Notwithstanding, it becomes clearer by the reading of the texts that develop the diagrammatic model of representing thought ( see Peirce (1976) vol. 4. p.530-538) that what Peirce proposes as the very essence of thought offers some hope for continuing research on the possibility of thought being simulated if not produced, by a machine, at least in one of its lower degrees.

In an article dated of 1908 (Peirce (1976) vol.4. p. 585-642) the author discards once more the pretense deterministic and mechanical character of the necessary reasoning, and claims for the thesis that the necessity found in reasoning does not suppress the exigency of observation and creativeness. Indeed, as several equally necessitate conclusions may be drawn from the same premises, the free choice of one of them would contradict the strict determinism supposed to be inherent in apoditic reasoning.

Together with this statement he insisted, as he had done in the past, on the radical impossibility of attributing thought to any mechanical machine. However, sequentially to his reasoning it seems that a way is open to be considered on the possibility of conceiving a machine that could operate semiotically.

The essential differences between the mechanical and deterministic computing process and a creative one do not derive from property found in all and in each of its parts, but depend on a characteristic of the whole as such.

Therefore, it would be perfectly possible that by the analysis of a genuine thinking process, all the components taken as isolated parts will present a mere mechanical character. However in the unity formed by very special assemblage of its components, the process being considered as a whole, thinking will be made present by a creative, evolutionary and time-irreversible conduct.

The apparent paradox present into a crucial distinction denounced as existing between life and thought could only find an acceptable answer by considering that phenomenologically life is understood by Peirce as a manifestation of freedom and spontaneity, since marked by the category of firstness. Meanwhile, thought is considered as a mediation and so, marked by the category of thirdness . The author, indeed, claims that differently from life that is present in each component of the living being , thought, as well as the ethic conduct, defines properties that are exclusive of some beings considered in their wholeness (see Peirce (1976) vol. 4. p.610-611).

Accordingly, we could conclude that if a machine could direct its operations toward an object by progressively modifying its proceeding way, becoming progressively better fitted to reach in the future the same object or some other similar, - i.e. by learning or by taking a habit -, we could find ourselves before a semiotical machine . Although this process supposes this machine as being endowed in some degree by generalizing capacity, Semiotic itself does not establish a threshold above which this capacity could be considered as an index of the occurrence of a thinking process.

The same can be said about the nature of the object considered as an end to be reached by the machine, since what is essential is the pursuit of this end and the capacity manifested by the thinking being of promoting a progressive adjustment of its operations in order to reach the object.

Some instruments where known in the moment that presented a behavior very similar to the one required for characterizing learning. That was , for example, the case of some instruments used in hydrology that were able to correct their operations before their object. Peirce, however, did not recognize in them the most adequate model of an intelligent machine, not because they did not successfully reach their aim, but because they were so well fitted to reach it that they seemed to not manifest in themselves the fallible and evolutionary characteristic of a true learning. A genuine semiotic machine, we may conclude, must be fallible in its behavior in order to be recognized as a learning machine . Learning it must be noted, is above all learning after its own errors.

Finally, in a text of 1911 (Peirce (1976) vol. 3. # 636-643), it is possible to find some complementary considerations that may enlighten the concept of thought as a diagrammatic construction, offering some important contributions for the characterization of a machine processing semiotically.

Two properties of the diagrammatic thought are taken as the object of special consideration, e.g. the successive stages by which the thought advances in the process of constructing and exploring the diagram and the process of abstraction, by which what is inferred in one stage of the diagrammatization will become the subject of a new diagrammatic representation in the following stage.

Without either of the processes, no thought could advance, in generalization. Wherever what is considered is the possible effectuation of the higher rational functions such as symbolization and scientific theorization, the presence of both the properties is absolutely required.

If phenomenological thought is time-bound, since it represents the own growth of the spirit, reasoning as the most explicitly mediated of its realizations may only be understood if an irreversible time is taken into account.

To operate by successive stages is the result of a semiotic way of thinking and, very specially, of reasoning. Diagram , it must be remembered, is precisely the class of signs that permits for the intelligence to represent the object and to determine its self-conscious and self-controlled conduct before the future presence of that object as an exemplar of the general class represented by the diagram.

Therefore, the diagram consists of a place where a constant dialogue is sustained by the spirit and the tradition . In this dialogue, the tradition representing the Past offers a set of values and objects to be accepted by the spirit, this latter as the authentic representative of Present being invited to make his choice to the future, after having critically and creatively interpreted the received message, through the production of a new sign.

The initial stage of the diagrammatic thought is constituted of the relations already established and that insist before the intelligence trying to persuade it to accept a certain way of conducting itself before the object (see Peirce (1976) vol. 5 p. 421; Silveira (1988 ).

The intelligence at this moment, taking access to a new stage, will establish a comparison between the representation that is offered for its acceptance and the idea it has of the object wanted to be reached.

Then, it will investigate those relations that can be established or accepted on the diagram , all of them concerning its own conduct in order to see ... "whether the same ardent desire is there to be discerned" (Peirce (1976) vol. 2. p. 227). This operation may be repeated as long as needed for the intelligence to give an adequate basement for its decisions, considering that the modifications made on the diagram, each time the conditions for the representation have changed.

This process of representation and evaluation consists of the role played by the interpretant of the sign and the transformation that will be taking place in the intelligence while enlarging its self-control and self-conscience and confering to its conduct a higher level of spontaneity. The determination of the rational conduct is of the nature of a habit and consists of the learning process.

The second property mentioned, namely the capacity of producing abstractions, is the unique way the reason has of constructing genuine symbolic signs as the most genuine kind of thought, based in the particular experimentation effectuated upon the diagrams.

It is only by this property of Reason that Mathematics and all the formal scientific thought become possible.

All that transcends the particularity of the experiment consists of abstract but no less real entities. The continuous, the infinite as well as the transcendental ideas of Truth, Goodness, Beauty and Being only take place in the universe of thought by an act of abstraction, and by this same act Reason becomes able to represent the supreme ideal where it can find its ultimate end and the object of its perfection (Peirce (1976) vol. 1. p.591-615) . Peirce's realism conferring real consistence to the spiritual realm, acknowledges that thought is a general but effective mode of being , conferring to the cosmos this same generality.

So thought can develop itself without any limit, penetrating through the infinite domain of reality. Although any phenomenal intelligence would be constrained in its exercise by the circumstances specially concerning the irreversible time of their growth, it could never propose a priori a limit to its capacity of investigation.

Intelligence, it must be noted, is the concretion of the infinite thought and not its cause. The work of abstraction, therefore, is neither an imaginative extrapolation of legitimate knowledge or a mere jeu de mots . Abstraction, indeed, is the unique and privileged resource that a phenomenal and semiotic intelligence disposes of for representing the most important aspects of Reality (Peirce (1958) vol. 8. # 327; Peirce (1976) vol. 5. p. 431-434).

It is not required for a machine to advance so highly in its thinking capacity in order to be recognized as a semiotic one. Nevertheless, it is convenient not to forget that thought in a peircean philosophical point of view even if it could be some day effectuated by a machine, by its own nature belongs to a sphere that transcends the limits imposed by any particularity.

From this present survey, it could be concluded that the exigencies for a machine to process data semiotically involves something more than the mere capacity of data computing. It must show competence in observing the data and in progressively elaborating by itself a more adequate program to represent its object.

Some competent experts in Peirce's Philosophy and Semiotics have sometime taken position before the question of the possibility of conceiving if not of constructing a semiotic machine, taking into account the theoretical exigencies of the doctrine.

In an article dated of 1977 (Ransdell (1977)), Joseph Ransdell considering dispensable to take account of the teleological aspect that Peirce attributed to semiosis, and transforming all final causation in a efficient one, proposed that a semiotical machine could be conceived as a cybernetic machine endowed of an appropriate feed-back circuit. The argument supposed as being true W. Ross Ashby's thesis of the traductibility of a self-organizing system into a deterministic one if the end to be attained consisted in a definite object of experience. (see Ashby (1962), (1963)).

For Ransdell his proposal was perfectly acceptable by Peirce's theoretical thought. In order to assume the peircean semiotics within the new parameters introduced by Cybernetics it was only required to translate an inadequate metaphysical language into a more operational one.

Against this proposal, T.L. Short (Short (1978)) ) claims by the irreductibility of final causation to the efficient one, arguing by the precedence exerted by growth, purpose and evolution over all the mechanical processes, if what is being considered is Nature as an organized whole. Then, if some thought processes may receive an approximate mechanistic explanation it cannot be denied their insertion in a teleological reality. Semiosis itself being a genuine triadic process, can only be understood by its teleological character and cannot be reduced to the mechanical and deterministic circuits proposed by Cybernetics.

Claudine Engel-Tiercelin (Teircelin (1984 )) takes position contrary to the tendency of conferring to a machine some capacity of processing semiotically. She calls the attention to the fact that Peirce's texts in which even when it is admitted the existence of logical machines it is the Reasoning simulation that they are being referred to, and not to thought in all its extensivity. But also to a machine operating deductively, it lacks the decisive properties of an authentic mental act. No machine proceeds deliberately , indefinitely or with a purpose. Only a genuine triadic process can manifest a purpose, and is able to assume its errors and to advance toward the perfection.

Kenneth Laine Ketner in the above mentioned article of 1988 (see Ketner (1878)) claims that a theorematic machine being able to proceed creatively in the elaboration of the diagrams and that could precisely correspond to the semiotic machine , could be the answer required by Turing in last design of constructing a machine that could learn.(see p.52).

If a machine could develop a creative method on its own and could operate non deterministically, the limits imposed to computability by the proof effectuated through the universal computing machine, known as the Turing universal machine, would not be imputed to it. The triadic representation of semiosis proposed by Peirce could lead to a future definition of an authentic theorematic, semiotical or learning machine.

George W. Stickel (Stickel (1993)) presented in The Charles Sanders Peirce Sesquicentennial Congress in 1989 the outline of a machine that as he claimed, could process data semiotically. The author took as a ground to his proposal the continuity claimed by Peirce between material and spiritual causation as well as the analogy that Peirce supposed to exist between the structure of thought and the structure of the world.

Then, the author advanced the hypothesis that it would be possible to represent semiosis by constructing a theoretical model elicited by the connectionist PDP ( Parallel Distributed Processing) machine.

The triadic character of sign would be adequately represented if it were possible to matricially represent the three peircean categorical modes of being. A similarity could be found between this operating process and that which characterizes the pyramidal neuron in the cerebral cortex.

The matrix to be constructed would have had to be a cubic one where in a plane it would be represented by the product of two vectors orthogonally disposed one relatively to the other. The vectors would be considered as representing firstness by its phenomenological realization as the qualities of feeling. The vectorial product would correspond to the phenomenological element of conflict, represented by the category of secondness.

Habit taken as the possibility of generalizing the past experience in order to determine the future conduct, would be represented by a third vector orthogonally disposed to the plane formed by the product of the first two vectors. Thirdness would be represented by this triadic matricial construction.

Assuming for the semiotical machine the neuronal form proposed by the connectionism to the machine's computing units and endowing them with three functions, respectively of activation , of inhibition and of neutrality, the machine processing will be effectuated according to the principle of competitiveness. By this principle it seemed to the author that the impending character of the determinism in order to represent semiosis, could be surpassed.

Despite the sound position assumed by Peirce against the possibility of a genuine logical and semiotic machine , it is a good surprise to find all a set of writings where he claims the need of not dissociating the mental activity, including thought, from its sensible ground.

This hopeful surprise was augmented when in a very recent declaration on the occasion of the anniversary of ENIAC, the first electronic computing machine in whose construction he had collaborated, (see Burks (1995/96)) Professor Arthur Burks, as one of the more eminent researchers in theoretical computing sciences as well as one of the editors of the workings of Peirce, evaluated the importance of this set of writings in order to consider the contribution of Peirce's thought to the historical study of physical bases of computability.

Especially in the human case, Peirce insisted in considering the physiological substratum of these activities, even the higher of them.

The vehemence with which this claim was presented in a paper dated of 1879 (Peirce (1986) p.38-44) must now to be considered. Therein it can be read: "Thinking is done with the brain , and brain is a complexus of nerves; so far that thinking is necessarily subject to the general laws of nervous action"(p.38), and after, "we meet no sure indications of a consciousness unconnected with a nervous organism; and the more complicated the organism, the higher is the consciousness. Whether the soul exists as an independent substance or not, certain it is that intelligence, as we know it, resides in the nervous system ; so that the laws of the former necessarily correspond to those of the latter. To trace the correspondence throughout, with scientific accuracy, would not at present be possible ; but such rough sketch as we can make of it, though not free from error, will not fail to shed a strong light upon the theory of logic."(p.40)

Peirce was perfectly conscious of the narrow limits presented by the disposable scientific knowledge about so complex a phenomenon. Nevertheless, at the same time that he was asking for news to his friend William James about the state of the question (Peirce (1958) v.8. p. 270-275), Peirce personally insisted in advancing some hypothetical explanations on these matters. These explanations, he hoped, being formally deduced from some acceptable premises, could open the way for future research.

He thought it could be found in the chemical structure of protoplasm of the nervous cells, the siege of the sensible activity. For him, the degree of viscosity presented by that substance permitted it to feel . And feeling for Peirce, it must be remembered (Cf. Peirce (1982), p.10 ff.), had always been considered the first manifestation of thought and, as a quality, the original mode of being.

The nervous cells being able to feel, Peirce proposed some ways by which the nervous system can effectuate the dual experience of sensation and the most complex of all the mental functions, namely that of learning .

Feeling could be considered as a monadic property of the nervous cells. The sensations would follow from the capacity shown by the cells of acting one upon the other as well as of reacting to stimuli coming from the environment.

Finally, learning would be the result of the capacity presented by the nervous cells to form networks and, in the future, of acting through them, preferentially. Faced with this capacity identified with the property of taking habits, it could be possible to conclude that the system formed by the nervous cells can effectively surpass the mechanic principle of action and reaction and sustain a rational conduct. (Peirce (1976). vol.1. #385-394 ).

Peirce's claim of the possibility of setting a physiological basis for all the mental activities, as well as the approach he did to the representation of the nervous system as a network formed by the interaction of the nervous cells, anticipated, it could be said, the efforts of conceiving a connectionist machine. Several of the properties of this machine are, indeed, very similar to those conferred by Peirce to the nervous system.

Nowadays, the disposable knowledge about the anatomy and the physiology of the nervous system as well as of the morphological and functional constitution of the nervous cells, do not permit anymore to hold with the same singleness the hypothesis of protoplasm as a chemical substance with such an extraordinary property as sensibility. Certainly, biochemical and cytological researches must advance by a long time before reaching a satisfactory conclusion about the way the nervous cells could sustain feeling and the other mental processes.

Nevertheless, the theoretical possibility of obtaining the simulation of the semiotical activities that seemed excluded when Peirce considered the so called logical machines , receives a new encouragement when one takes into account the defense he promoted of the role exerted by the anatomo-physiology of the nervous system and of the biochemistry of the nervous cells in the mental phenomena, including thought.

It is not certain yet whether connectionism will be able to conceive and to construct a genuine semiotical machine . Further, it is not possible to say that some day all authentic semiotical activities will be effectuated or simulated by a machine. Maybe, in the future, another theoretical model other than the connectionist one will be needed in order to undertake this work. Certain it is that, in spite of all these limitations, the search both for conceiving and constructing a semiotic machine finds in the philosophical thought of Peirce a important basis for its legitimacy.

Just returning to our first considerations, namely ,that mainly when it is the case that a certain subject-matter had been worked by an author like Peirce, it does not seems to be the best way for taking profit of one's Philosophy in order to undertake a research, to make a summary choice of some its constructions or of some of its concepts without considering if the integrity of the doctrine has been preserved, and can now receive a better evaluation.

The present survey into Peirce's Philosophy trying to recover what was said in it about the possibility of conceiving a logic and semiotic machine, although not proposing itself to be exhaustive, certainly has been able to make manifest how much interest to the research of nowadays may be offered by the patient reading of that Thinker's works. Perhaps for a strict technical preoccupation such a study may not show itself to be so interesting. However, for a research that intends to reach the philosophical dimension of the question about the possibility of conceiving if not of constructing a genuine learning or semiotical machine , the density and the depth of Peirce's considerations surely will be of the most inestimable value.

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