Mathesis Universalis 4, 1997 http://www.pip.com.pl/MathUniversalis/4/basic .html
When using any part of this text - by Witold Marciszewski - refer, please, to the above original URL.
Intelligent Beliefs which Lack Clearness
On Pascal's Esprit de Finesse and Demon Procedures
That intellegent, or, rational beliefs should enjoy clearnes of their content, is a commonplace among philosophers. Rare exceptions from that common tenet, to wit Leibniz and Pascal, are those which inspire the present discussion (Pascal is referred to in Sec.2; as for Leibniz, the subject would require a special study).
Other items of this issue exemplify different approaches to the requirement of clearnes, that of Descartes, that of Peirce, and that of James (though in the last case only a special sense of clearnes is at stake). This one is meant to advocate an opposite point. This is to the effect that a lack of clearnes in a belief may accord with its being intelligent, and even may impart it this quality.
Why? Following the lead of Pascal, we can see the reason in some laws of information processing.
First, let us notice that any belief can be seen as conveyed by a process of transforming information.
Second, only some among these processes are consciously perceived by the mind. Those which the mind is aware of are, for instance, the successive steps in a formalized proof (as a procedure to produce a belief). However, sometimes one is aware of the conclusion without being aware of its premisses. Sometimes, even the conclusion remains hidden to `the eye' of consiousness, and its existence is displayed just in an overt behaviour (as that of a driver, mentioned in Sec.1).
Third, such unconsiously attained beliefs happen to provide a true and useful solution of a problem which was to be solved. Thus they should be deemed intelligent. Striking examples of such unclear intelligent beliefs can be found in applying the principle of expected utility in decision making. The extent of the utility, the risk involved, and the principle being applied are no consciously experienced contents, hence there is no room for clear beliefs; nevertheless, the estimations so unconsiously made prove, fortunately, right in quite a number of cases.
Fourth, sometimes, only unconscious processes can ensure the success of problem solving. There is no riddle in that if one takes into account the feature of computational complexity combined with the following fact. Information processing at the level of consiousness may require much greater capacities of the processor and memory, when faced with an enormous complexity, than the capacites required by unconscious processing. Sometimes, it is easier, quicker, and wiser to made an instinctive decision without a conscious deliberation (the case of a driver's, again); and there is always a belief, concerning a state of the world, behind every decision. This is why some beliefs attained instinctively deserve to be called intelligent, though - as not being conscious - they can not enjoy the quality of clearness. They are intelligent as much as they contribute to solving the problem in question.
1. On demons, or situation-triggered computational processes
The allegory of demons is inspired by the operating system Unix in which the name "demons" stands for processes incessantly going on in the system without user's commands and without interfering with other processes, also those having been set off by the user. Each process of this kind is managed by an appropriate segment of Unix.
This looks as if the system acting in a machine had an internal life of its own, independent from any intercourse with the machine user. For instance, the demon called "cron" (to allude to the god of time Chronos) is ever ready to launch any program in the time situation defined by the programmer. Another one, named "sendmail demon" is like an atttentive messanger who delivers the mail to the address in question without being asked to do so, just because of the occurring of the situation in which a mail is ready for delivery. This is one of those features which make Unix superior to MS DOS and other operating systems. In fact, there is something like demons in other systems, namely residential programs, but this is only a remote resemblance. Let us try analogy between such an advanced system and some features of mental life.
Let it be noted, that some AI theorists use the term "demon" in the way as suggested above. For example, the AI classic Winston (1984, p. 257) when considers a demon acting in a database, describes its role as follows. "[These] demons lurk about in the database to be used whenever needed, rather than when specifically asked to help by name. They are friendly, as demons go."
That there are similar processes in humans, and that some of them yield reliable beliefs, can be seen, for example, in a drivers behaviour. His reactions are conditioned by certain beliefs which, in turn, are produced by demon-like processes. If the driver, say, suddenly turns to the border, this is because he believes that another car approaches too near to the middle of the road.
However, such a belief does not result from any conscious activity of the mind. Instead, it is produced by something acting in the brain like a demon in a Unix system. This demon is ever ready to do his task if necessary, without receiving any command from the mind. In the above example, his task consists in a sequence of information processing operations which result in the judgments determining driver's decision, as the moment of turning the wheel, the proper angle of the turn, the appropriate acceleration, etc, etc. Sometimes such calculations carried out by the demon prove correct and result in true beliefs, sometimes they do not. This is why some drivers make right decisions, and some wrong ones.
In contradistinction to demons, there are processes, both in the computer universe and in other worlds, which do no arise unless caused by a command. Let such a process be called a servant, and the entity or the process to produce a command be called a master. Servants are those processes with which any computer user is most familiar as being caused by his conscious will (in this relation, the user deserves the title of a master).
Both kinds of processes belong to operations. The difference consists in that for a demon it is a situation, ie a state of the system, which takes the role of an operator, while the argument is indicated by the program which is being executed by this demon. For instance, the sendmail demon starts in the situation in which a new mail for sending - ie the argument of the operation involved - has been produced by the system user. On the other hand, a servant becomes active when both the operation and its argument(s) are explicitly stated by the master, and the operation is put by him into action, eg with pressing Enter.
What this allegory, so extended as to comprise both demons and servants, has to do with the problem of beliefs? Now we can classify beliefs into those which are due to demons and those due to servants, and then consider their relations to the conscious mind as their master.
The mind's conscious activity can be compared to that of the master of a machine, namely the user of brain machinery or - to take into account all possible factors (hormons, etc) - the whole body machinery. We need not care here about intricacies of the mind-body problem; every allegory is crippled, and only those aspects should be here considered which are relevant to the problem involved.
Our allegory works if we agree that there is a sense in such sayings as "I waved my hand to say goodbye" or "I raised my finger to my lips as a sign for silence". Sentences like these express a conscious plan which controls bodily movements mastered by the mind and carried out by servants in the nervous system. Such planned activities contrast with unconscious information processing performed by the nervous system demons.
Some conscious operations, especially reasonings, produce beliefs, possibly with the help of suitable servants. Some demon operations produce beliefs too. One should also consider the third category - that of mixed beliefs. This is to mean that some beliefs result from information processing procedures which involve conscious acts as well as servants and demons. Each of them can influence, eg, the content of premisses in reasoning and even the form of reasoning (the latter may be exemplified by instinctive induction carried out by a demon).
The theory that human mental life is to some extent controlled by demons may be called demonology ; though having a hint of joke in it, this name can serve as a handy abbreviation for the viewpoint argued in this essay. According to this view, we should acknowledge not only the existence of demons (a psychological point) but also their right to participate in processes of forming rational beliefs (a logical point), provided that certain conditions are satisfied.
Demonology so conceived deviates from the philosophical orthodoxy; the latter term can be used in the singular in spite of so numerous philosophical approaches, because the anti-demon attitude is shared by almost all of them. We find it both in the Cartesian epistemology and at the opposite extreme represented by Peirce, a defender of empiricism and pragmaticism. At either extreme, as well as in the spectrum between, it is the clearness of apprehension that endows beliefs with rationality. Clearness may be either direct or indirect, the latter consisting in reduction of a belief to other ones being directly clear.
With Descartes, the paradigm of clearness is found in Cogito and in mathematical insights. With Peirce it is found in our experiencing own activities - as in the example of how hardness of a stone should be understood in terms of its resistance to our scratching it (an activity clearly apprehended in a direct way by the agent in question).
The requirement of clearness, whatever form it takes, cannot be satisfied by demons. The clearness of apprehension is an attribute of conscious acts alone while demons do not appear at the level of consciousness. This is why their reliability, and even existence, is suspect both for philosophers and for laymen.
However, there was a philosopher who was surprisingly aware of the role and value of unconscius beliefs and attitudes. It was the solitary genius of Pascal that anticipated not only the modern theories of probability and decision, but also the modern knowledge about non-conscious information-processing. To resort to his thoughts will be a good strategy to explain the point of this essay.
2. Esprit de finesse according to Pascal; its relation to demons
Esprit de finesse, as Blaise Pascal called the ability to be now discussed, resembles what underlies demon processes. Pascal in his Pens'ees examines the difference between two intellectual skills which he calls esprit de finesse and esprit de g'eometrie . These terms do not appear in the passage quoted below, but are introduced earlier and tacitly referred to in the cited one. Here is Pascal's text (The Thoughts of Blaise Pascal translated by C. Kegan Paul, London 1895, Section "Various Thoughts").
The reason that mathematicians are not practical is that they do not see what is before them, and that, accustomed to the precise and distinct statements of mathematics and not reasoning till they have well examined and arranged their premises, they are lost in practical life wherein the premises do not admit of such arrangement, being scarcely seen, indeed they are felt rather than seen, and there is great difficulty in causing them to be felt by those who do not of themselves perceive them. They are so nice and so numerous, that a very delicate sense is needed to apprehend them, and to judge rightly and justly when they are apprehended, without a rule being able to demonstrate them in an orderly way as in mathematics; because the premises are not before us in the same way, and because it would be an infinite matter to undertake. We must see them at once, at one glance, and not by a process of reasoning, at least up to a certain degree.Pascal took from Desartes the notion of mathematical clearness. However, he went far away from Descartes when admitting of the other kind of mental activity which did no satisfy the requirement of clearness of apprehension; the premisses in that non-mathematical reasoning are "scarcely seen", "rather felt than seen" what, obviously, is very far from the clear and distinct apprehension as demanded by Descartes.In Pascal's context, owing to the opposition involved, we may better understand the postulate of distinctness which by Descartes himself was not satisfactorily explained. The premisses in the reasoning which lack the Cartesian traits are seen "at once, at one glance"; this means that they appear like a mass with giving us no chance of a distinct seeing, so to speak, the contours of its components. Even more significant is the saying that the seeing of all the premisses involved "would be an infinite matter to undertake". Here "infinite" means, in practice, "impossible". Hence the process of reasoning has to be carried out, partly at least, beyond any conscious apprehension, thus being devoid of clearness and distinctness.
Pascal never blaims esprit de finesse as irrational or unreliable. He treats it as the trustworthy guide in practical life and in other matters whose complexity goes far beyond what is capable of being clearly and distinctly apprehended. However, since the Cartesian approach was acknowledged in his intellectual environment as the only method recommended by reason, in some contexts the second approach was attributed by him to the heart. Thus "reasons of heart" were to mean the same as "reasons of esprit de finesse".
Hence a mistake is committed by those historians who misled by his reference to the heart present Pascal as a typical representantive of philosophical irrationalism. In his times, when one looked for a concept to oppose it to that of reason, the concept of heart must have been a suggestive option. Had Pascal lived in our times, he might have used Unix as the model of a very complex information processing system. Then he might have chosen the notion of demon to account for a rationally behaving process not remaining, though, under the control of consciousness. By the way, this seems so likely because Pascal was not only a zealous mystic but also a very able engineer.
3. A demon-like conceptual equipment resulting in beliefs
Conceptual equipment, or - as Ajdukiewicz (1934) calls it - conceptual apparatus (Begriffsapparatur) belongs to those factors in mental life which are like demons in the processes of forming beliefs. The esprit de finesse (in the Pascalian sense, as above) of an individual mind much depends on a set of concepts possessed, that is either inborn or acquired, by the person in question.
This can be illustrated by differences between the scientific mind and the magic mind. Having the same factual information, say, the symptoms of an illness, but accompanied by different general premisses - as to the forces acting in the world - each of them attains entirely different beliefs pertaining the cause of the illness.
Such explanations are due to esprit de finesse because no conscious step-by-step reasoning is carried out, but the diagnosis is made immediately to the effect that the event is due a natural or to a supernatural cause, respectively. To prove the point of one side in order to convince the other one would be - as Pascal rightly observes - "an infinite matter to undertake". For it is not a single judgement but the whole mental history of an individual that decides what attitude he or she takes in cases like those under discussion. As for primitive mentality, among the crucial factors influencing one's beliefs there is the ceremony of initiation, and this, in turn, is deeply rooted in most early experiences of the given tribe members.
On the other hand, a child in a civilized community from the very start becomes familiar with natural forces as acting in every moment of life. Hence, the question which natural force is reponsible for the event in question appears instinctively, without any moment of conscious deliberation. In this sense, both civilized and primitive conceptual equipments may act like demons in the processes of attaining beliefs.
To explain the very notion of conceptual equipment, we should take advantage of the possibly simplest paradigm, and then make it more and more involved to aproach commonsensical reasonings and beliefs. A possibly best paradigm for these purposes in found in axiomatic systems of, say, arithmetic or geometry as being both duly precise and known to every educated person.
From that lesson we learn that the meaning of the primitive terms, to wit those occurring in axioms, is characterized by a net of their mutual interrelations, while the meaning of all the remaining terms is defined on the basis of those primitive ones. The axioms of a system, when appearing in this definitional role (the other role being that of first premisses) have been fittingly called meaning postulates (cf Ajdukiewicz 1958, Carnap 1956). A set containing both the primitive and the defined concepts of a deductive system forms a conceptual equipment that may be possessed and employed by individual minds.
Thus the class of conceptual equipments becomes partially characterized by this paradigmatic ideal extreme. At the opposite extreme there is a set of non-connected terms, not controlled either by rules of defining or by rigours of entailment, as can be observed in some mental illnesses. Such a set can be hardly called an equipment for it is not apt to be a tool in any problem solving; or, one may call it an equipment in degree zero. In between, there extends a large spectrum of less or more coherent sets of concepts. Each of them the more deserves to be called a conceptual equipment the more it approximates the ideal case as discussed above.
In the forming of a conceptual equipment either for an empirical science or for everyday life, we approximate postulate sets by using ostensive procedures, sometimes called ostensive definitions (cf Marciszewski 1993). These are like meaning postulates except for the fact that besides a verbal part they involve the producing of a specimen - namely, a thing denoted by the expression being defined - in the role of definiens. Hence, with an ostensive procedure one approximates a meaning postulate, and this can be done in varying degrees of preciseness (depending on a proper choice of specimens, on the receiver's knowledge, etc).
Other desired qualities of meaning postulates equal those required from axiom systems, such as consistency, completeness, mutual independence within the set of axioms. Strictly speaking, these properties do not allow of degrees. A system either is, eg, consistent or is not, without any third option; the same is true of the remaining properties.
However, not all inconsistencies should be treated on the same footing. There is a difference between an obvious contradiction which can be noticed even by an idiot, and such one as detected by Russell in Frege's system. That system, even after that blow, retained very much of its cognitive value, since it was the one which paved the way to discovering a previously unknown kind of antinomy, and, moreover, to the search for remedies. Thus, conceptual equipments, even if not free of inconsistencies, may have cognitive values, dependent on the behaviour of the contradiction involved. Analogously, one can so reformulate the notions of completeness, indepedence, decidability, etc that they receive degrees and so serve to distinguish degrees of cognitive advantages of the conceptual equipment in question.
The preceding passages hinted that a conceptual equipment behaves like a demon, and tried to make this notion more precise owing to the notion of an axiomatic system. Now it is in order to complete the discussion with demonstrating that a conceptual equipment should behave in demon-like manner to produce rational beliefs. Before we reach the final conclusion, a case study, concerning a particular demon, should exemplify a more general point; let it be be a study on how we perceive time with a conceptual equipment acting in demon-like manner.
4. A case study: time perception as determined by a conceptual equipment
The perception of time is a simple example of how a demon, to wit a conceptual equipment, processes information to produce a belief.
Suppose, you look at the genealogical tree of a dynasty or read a text like that beginning St. Matthew's Gospel: "Abraham begat Isaac; and Isaac begat Jacob; and Jacob begat Judas and his brethern", etc. In the same instant, without any discourse or reasoning, you become ready to make such inferences as the following:
- Abraham's birth preceded in time that of Isaac.
- Isaac's birth preceded in time that of Jacob. Etc.
- Some parts of Abraham's and Isaac's lives may have coincided in time.
- Some parts of the lives of Judas' brothers may have coincided in time. Etc.
There are quite a number of such conclusions you reach in the course of reading Christ's genealogy. This does not mean that you recite them, either loudly or tacitly, during the process of reading. This is just to mean that you are ready to answer with a sentence, one from among those listed above, whenever the respective question is put to you. Any such conclusion is a belief that so-and-so is the case.
Such beliefs are generated, as said above, without any reasoning one be aware of, and moreover, without any conscious intention to attain a belief. Let us compare such a process with a servant-like process, eg, that of recalling a name or looking for a rhyme.
Any search like those starts from a command which puts into action a program to be executed somewhere in nerve cells. Such a process is like a service done by an obedient servant. The master does not bother about the way the service is to be performed, he just orders it and waits for the result, to be brought about by a string of machine operations following the operator's command. Contrary to that, a demon process does not issue from any command. It arises from a situation which triggers the chain of operations acording to a preestablished program. Such is the case under discussion. The situation of reading a genealogy triggers a conceptual apparatus as a demon to produce inferences which, in turn, produce beliefs.
What inferences? What beliefs? For instance, the belief that Jacob was born later than Abraham, inferred from the first two sentences of Christ's genealogy. This belief issues from a knowledge on biological procreation, acting as a set of premises, combined with a conceptual equipment concerning properties of time. This equipment can be reconstructed either as another set of premisses (besides the biological ones) or as a set of rules. Let it be presented as premisses, ie, declarative propositions, forming the set of axioms.
These axioms define the structure which consists of events, sections (segments, intervals) of time, and the relation: section B Follows section A. This relation is as follows:
(1) transitive;
(2) asymmetric;
(3) connected, ie, holds for any two sections.
These conditions mean that the set of events is linearly ordered. Moreover, this linear order is:
(4) dense, ie, every section contains a section as a proper part;
(5) infinite in both directions, ie, for every section there is another one which either follows it or is followed by it. To render the whole content of the concept in question, still the relation between time sections and events should be stated, namely that
(6) for every event there is exactly one section in which it occurs;
(7) in any section there may occur arbitrarily many events. Thus we have a demon defined in simple set-theoretical terms. At the same time this definition appears to render our everyday, commonsensical, idea of time. What does it mean "our"? This is an important question since when trying to answer it we are likely to discover how a demon may originate, that is, be programmed. "We" means here the people living in the 20th century and some centuries earlier in the Western urban civilization. This is a cultural circle in which the time is measured by clocks .
What is crucial for our discussion it is that people living in different cultures have different notions of time. It must have been different, for instance, in rural communities which did not used any clocks. They seem to have had no reason, eg, to accept density condition (4) as their time did not mirror any sequence of rational numbers.
Also philosophical or religious views can influence the conceptual equipment concerning time. The ancient Greeks, eg, conceived time as circular, not linear; linearity and infinity had derived from Christian eschatology before Newton postulated it in his mechanics.
5. McCarthy's claim and one's believing that he believes
McCarthy's claim is to the effect that even a simple automaton, as a thermostat, has certain beliefs. As John R. Searle (1984) reports, John McCarthy once asked, what beliefs does possess his thermostat, replayed that there are three such (alternative) beliefs: here is too warm, here is too cool, here the temperature is as required. The "demonological" approach adopted in this essay may seem to lead to similar conlusions, though these by no means are intended by the author. McCarthy's opinion, therefore, should be taken as a thought-provoking challenge (similar to that made by Peirce).
That great AI pioneer is not the only one to conceive beliefs as states which can attach to automata, in the sense that proper reactions amount to true judgments. For instance, in a report on shuffle flights, it was said that the computer which controls landing "makes four milions decisions per second." Since a proper decision presupposes a true belief, it follows that there is a similar number of beliefs entertained by the computer in the course of landing. Such utterances demonstrate that McCarthy's statement ceases to be paradoxical in the nowadays culture dominated by automata.
The bias towards this way of speaking may derive from the lack of sufficiently rich vocabulary - that would both cover a large class of the phenomena in question and distinguish those subclasses which essentially differ from one another. In fact, those human beliefs which are due to demons as processes triggered by situations according to certain programs, in certain respect do resemble the behaviour od homeostats or other automata.
However, there is a crucial difference. For our purposes it will be best rendered in terms of object language and metalanguage. There are beliefs which potentially form subject-matter of other beliefs of the same believing subject, and only those deserve the name of beliefs in the strict sense , while beliefs in the broad sense are those shared by humans with animals and some machines. A thermostat, eg, has no capability to critically discuss its reactions to the environment and modify its behaviour by itself. Therefore it is not said to have any beliefs in the strict sense.
This distinction is important for AI projects as it hints at an ambitious long-term goal of AI reserch, to wit that of equipping artifically intelligent agents with that metalinguistic attitude toward their beliefs. Let us examine this distinction in the example of the time demon as discussed above.
Let us imagine a person, named Jim, whose perception of time and issuing beliefs is determined by the conceptual equipment described in postulates 1-7 above. This does not mean that Jim has somewhere in his head the same list or a part of it. He may be unable to term the propeties in question and even he may have no awareness that time is capable of any verbal description of this kind. Nevertheless, he behaves as if he believed in the existence of time having such properties.
Thus, if Jim believes that, in a set of time segments, B follows A and C follows B, then he believes that C follows A. The process of transition to this conclusion is spontaneous and issued by the situation itself, without any command from anybody, and so it resembles demon processes.
Other tests will confirm that Jim's beliefs happen to be generated by the conceptual equipment expressed in 1-7, even without any awareness of him concerning the actual origin of these beliefs. So far we attribute him some beliefs in the sense similar to that in which we can speak of beliefs of a computer.
However, Jim - provided he is a normally intelligent human being - can learn that other people have different attitudes regarding time, and can learn those set-theoretical and other concepts which make it possible to distinguish from each other different conceptions of time. Then he gets able to raise a set of critical questions concerning his views on time.
This means that his beliefs concerning time become the subject matter of propositional attitudes, such as questioning, doubt, denial, and also acceptance amounting to a belief. Then he not only believes, say, in postulate 1, but also he believes that he believes in 1. This metalinguistic stage gives a new status to his belief in 1, namely the status to be called that of critical belief .
The reaching of the metalinguistic stage, that is obtaining the status of a critical belief, is a sufficient condition of being a belief in the strict sense. We should not regard it as necassary (this would damage the intended construction). We look for demarcation line to distinguish some states of animals and computers from some human beliefs. This line arises when we distinguish states capable of becoming critical beliefs from those devoid of this capability.
For instance, Jim even in the phase in which he was not aware of having beliefs induced by a demon (a conceptual equipment regarding time), was able to attain such awareness. Therefore, such a belief of him as that inferred from 1 in the precritical phase, though actually did not involve the awareness of the equipment controlling the inference, potentially it did. This potentiality is also a sufficient condition to regard a mental state as a belief in the strict sense. Since this condition is not satisfied by any homeostat, the distinction here proposed meets McCarthy's challenge. Critical beliefs form a typical class of explicit beliefs.
6. Interaction of demons with explicit reasonings and beliefs
An interplay od demon-like processes with what can be called explicit reasonings is a melting pot in which our beliefs are produced. It is the reactions ocurring in that pot which gives our beliefs a fair chance to become rational. Not only the demon of time perception yields a typical example of such interaction but also the demon of space perception which enjoyed a brilliant success in the history of fundamental ideas of science. Let us take advantage of both examples.
The English adjective explicit is very apt to term the class of reasonings which occur at the level of consciousness owing to complete verbalization. Thus its antonym implicit , when predicated of reasonings, means those which remain unconscious, recognizable at most from outside, by observing their effects (an overt behaviour). The other meaning of this term, which refers to something being just potential , also perfectly fits into the content in question; for an implicit reasoning is potentially explicit, provided a suitable procedure is adopted. Moreover, still other meaning of "implicit", that identical with "lacking doubt or reserve", or "unquestioned", proves to be appropriate for implicit reasonings; these cannot be questioned or critized since cannot be controlled by conscious reflexion.
There are four manners in which a resoning turns explicit. Or, so to speak, four levels of explicitness.
(i) All premisses and their consequences are verbalized except those which are so obvious to the audience in question (eg, that of the experts in the matter discussed) that their omission increases economy without any loss of clearness. Criteria of obviousness considerably depend on cultural patterns, as can be seen in the evolution of mathematics (cf Wilder 1981).
(ii) Not only premisses and the subsequent steps are verbalized but also respective rules of inference are mentioned to justify each inference.
(iii) In addition, the following rigour is observed: all the rules of inference are stated in the corresponding metalanguage in the form of structural-descriptive expressions (as Tarski (1956, p.167) calls them). This means that they describe just the structural connexions between forms of premises and forms of their consequences, and the validity of inference is entirely dependent on such connexions (ie, no understanding of their meaning is required).
The last level of explicitness amounts to a formalization of reasoning . It provides an algorithm to check the validity of inferences. The algorithm consists in checking each step of reasoning whether the transformation involved equals that being described by the rule referred to. If the algorithm is rewritten into a programming language, so that it can be executed with a machine, we reach the stage of mechanization of reasoning (cf Marciszewski 1994, Marciszewski and Murawski 1995).
A fruitful interaction with a demon may occur even at the first of the listed levels. This has been clearly shown in the history of geometry, in which the space demon interacted with axiomatization procedures (appearing at each level, though with varying degrees of preciseness). Our perception of space is a typical instance of demon process. The space demon induces us to believe that space is three-dimensional, continuous, infinite, that any two points determine a line, that two paralells never intersect, etc.
It is the principal method of imparting explicitness to a reasoning. At its most elementary level, it was successfuly applied by Euclid. Owing to his axioms, called also postulates, esp those in Book I, the demon's activity has been described in various aspects, each one treated with a particular postulate. Thereby we can investigate which features are independent from other ones; when modifying some of them we can construct a different space. Thus people arrived at non-Euclidean spaces.
This result is so much important since new geometries proved to be valid in certain physical conditions, radically different from those in which our human perception of space has been moulded. One of them holds in giant cosmic regions where gravitational effects modify the space, another one in the microcosmic world of quanta.
A story which is somewhat similar can be told about the time demon. True, we have not had any axiomatized theory of time which would have such a great impact on science as the Euclidean theory of space had. Nevertheless, we can state our time intuition in a fairly explicit way (as in postulates 1-7, Sec.4), and so check if they match the current state of science. The result is partly destructive since the evolutionary cosmology undermines the belief in the infinity of time, other results or, at least, thought experiments may oppose its continuity or density, and so on.
Such facts shed light at some limitations of cognitive competences of our demons. They prove reliable, indeed, but within certain limits. Thus their contributions to producing beliefs should be critically assessed in a research in which a major role is to be played by procedures of detecting implicit reasonings and implicit beliefs, and then making them explicit.
No wonder that a demon lacks absolute reliability. We should take into account that demons' development is an evolutional response to those conditions in which our race tries to survive and expand. In spite of being so limited, demons render us invaluable services as providing the cognitive capital to start with. Then there comes that astonishing phaenomenon that the human kind proves capable of overcoming so deeply rooted intuitions or habits of thought, owing to the methods of explicit reasoning.
After having been made explicit, the reasonings and the issuing beliefs may need serious corrections, as was the case in the development of the notions of space and time. On the other hand, no explicit reasonings could have been carried out unless were preceded by that intuitive perception, that is, those demons which provide us with an implicit conceptual equipment and perform implicit reasonings. Thus both computational processes, the implicit one due to demons, and the explicit one due to the conscious cognitive activity interact with each other to advance our knowledge, that is, a system of rational beliefs.
There opens a vast field of research in "cognitive demonology" in which the demons guiding the human mind should be listed, classified, and critically assessed. Especially, the teaching of logic will profit from recognizing inborn skills of logical thinking and deciding which of them are worth preserving and which should be improved by the study of logical theories accompanied by suitable training.
Moreover, new demons can be designed to explore the world in those cognitive and technological conditions in which the human race starts to live. Why not to project, for instance, a demon whose space and time perception would be adjusted to exploring a remote outer space? Such a new generation of demons would belong to the realm of Artificial Intelligence, involving perceptions, reasonings, beliefs. But how much artificial? Inasmuch as the mankind participates in a Creative Power of the Universe, there is no sharp boundary between what is artificial and what is natural among the creations of that immense computational power.
References
Ajdukiewicz, K. (1934), Das Weltbild und die Begriffsapparatur, Erkenntnis IV, pp 259-287. Ajdukiewicz, K. (1958), Le probl`eme du fondement des propositions analytiques, Studia Logica VIII, pp 259-282. Breger, H. (1988), Das Postulat der Explizierbarkeit in der Debatte um die k"unstliche Intelligenz, in: Leibniz, Tradition und Aktualit"at. V. Internationaler Leibniz Kongress, Vortr"age. Hannover 1988 , Hannover: Leibniz Gesellschaft. Carnap, R. (1956), Meaning and Necessity. A Study in Semantics and Modal Logic (Appendix B), Chicago: The University of Chicago Press. Descartes R. (1946), Regulae ad directionem ingenii in: AT (Oeuvres publi\'ees par Charles Adam, Paul Tannery), vol. 10, Paris. Descartes, R. (1956), Discours de la m'ethode, in AT, vol. 6, Paris. Hintikka, J. (1962), Knowledge and Belief. An Introduction to the Logic of the Two Notions, Ithaca, NY: Cornell University Press. Hume, D. (1952), A Treatise on Human Nature, vol. 1, in: A. Ayer and R. Winch (Eds.), British Empirical Philosophers, London. Leibniz, G.W. (1982), Monadologie, Hamburg: Felix Meiner Verlag. Marciszewski, W. (1993), Ostensive Definition as Prototype of Real Definition, in: Poli (1993). Marciszewski, W. (1994), Logic from a Rhetorical Point of View, Berlin, etc: Walter de Gruyter. Marciszewski, W. and Murawski, R. (1995), Mechanization of Reasoning in a Historical Perspective, Amsterdam etc: Editions Rodopi. Pap, Arthur (1957), Beliefs and Propositions, Philosophy of Science {\bf 24}, pp 123-136. Pascal, B. (1895), The Thoughts of Blaise Pascal translated by C. Kegan Paul, London. Peirce, Ch. (1878), How to Make Our Ideas Clear, Popular Science Monthly 12, pp 286-302. Poli, R. (Ed.) (1993), Consciousness, Knowledge, and Truth. Essays in Honour of Jan Srzednicki , Dordrecht, etc: Kluwer. Rescher, N. (1968), Topics in Philosophical Logic , Dordrecht: Reidel. Searle, J. (1984), Minds, Brains and Science , Cambridge, Mass: Harvard University Press. Tarski, A. (1956) The Concept of Truth in Formalized Languages. in: Tarski, A. Logic, Semantics, Metamathematics , Oxford: Clarendon Press. Tokarz, M. (1990), On the Logic of Conscious Belief, Studia Logica , 49, pp 321-332. Wilder, R.L. (1981), Mathematics as a Cultural System , Oxford, etc: Pergamon Press. Winston, P.H. (1984), Artificial Intelligence , Reading (Mass.), etc: Addison-Wesley.
