Aristotle's Conception of Technology

 


Nature and Techne

Aristotle presents basically the same conception of technology as Plato, except for the emphasis on mathematics: technology has a low social and epistemic status and it imitates nature. Nevertheless, Aristotle does not simply repeat Plato but he has a more comprehensive treatment of technology. Aristotle establishes in his Physics that there are four causes for every thing that exist, either naturally or by art: the material cause, the formal cause, the efficient cause, and the final cause. For example, a bronze statue is made out of bronze (material cause), having its particular form (formal cause), it is made by artist's actions with the help of tools (efficient cause), and it serves for religious worship (final cause) (Ross, 2005: 45-47). An important distinction that Aristotle draws is between the cause being in the thing itself and its being external to the thing, i.e. the thing is caused by something else. Technological things are the things that have their causes (the formal, the efficient and the final causes) in men, i.e. the things that are made by the work of men who imprint in matter a form that preexist in man's soul for some human purpose.

The craftsman imprints on matter a certain form that pre-exists in his soul. Aristotle tries to explain where this form comes from. Is it a human invention or is it an imitation of nature? He takes the example of a house and shows that the form of a house comes neither from pure imitation nor from pure invention. In fact, the form of the house is an innovation, a completion of nature's purposes.

Thus if a house, e.g., had been a thing made by nature, it would have been made in the same way as it is now by art; and if things made by nature were made not only by nature but also by art, they would come to be in the same way as by nature. The one, then, is for the sake of the other; and generally art in some cases completes [epiteleitai] what nature cannot bring to a finish, and in others imitates [mimeitai] nature (Physics, 199a).

The form of the house is a natural end; it is a final stage of natural development. The only problem is that nature cannot accomplish by itself its purposes partly because of accident (health is damaged by illness), partly because of complexity (building houses requires too complex operations). Consequently, human technology is a natural way to complete what nature cannot finish. 

The question might be raised, why some things are produced spontaneously as well as by art, e.g. health, while others are not, e.g. a house. The reason is that in some cases the matter which determines the production in the making and producing of any work of art, and in which a part of the product is present, is such as to be set in motion by itself and in some cases is not of this nature, and of the former kind some can move itself in the particular way required, while other matter is incapable of this; for many things can be set in motion by themselves but not in some particular way ... Therefore some things cannot exist apart from some one who has the art of making them, while others can exist without such a person (Metaphysics, 1034a).

This feature, of completing natural purposes, is not particular to human technology, because nature creates nests, spider-webs and other things through the work of animals (birds, spiders, etc.) that do not have rational souls: “This is most obvious in the animals other than man: they make things neither by art nor after inquiry or deliberation. That is why people wonder whether it is by intelligence or by some other faculty that these creatures work,—spiders, ants, and the like” (Physics, 199a)¹. Thus, in cases in which the product of technology does not exist naturally, it is made by following the natural path of development. If the thing exists naturally, the craftsman should faithfully imitate nature. Therefore, technology is a matter of imitating natural things or completing the natural evolution of things without inventing new forms. Technology's end is nature or the aim of technology is to produce things exactly as nature would have produced them. Moreover, to complete nature is more or less the same thing with imitation. If imitation means to do things in the same way they are in nature, to complete nature is to do things in the same way they naturally should be. The technician should always consider the intent of nature. The passage quoted earlier from Physics should be read both as descriptive and as normative. It describes that technology is a imitation, but it also prescribes that technology should be so, and this is indeed how the scholastics understood it. The normative element of the passage rejects the possibility and the desirability of invention. One should not try to modify the technology, except by imitating nature, otherwise he may come to be in conflict with nature. Aristotle rejects technological inventions that are totally new and do not complete the existing potentialities of nature, either because that would impair natural perfection or because it is impossible to create things that do not exist potentially in nature.

Technology needs to imitate nature not only in its final products but also in its ways of proceeding. Tools used in technology are best suited for an operation if they are copies of natural objects: “in the ordinary crafts the best tools were discovered from nature” (Fragments, Dialogues, Iamblichus, Protrepticus 54.10-56.12 Pistelli, B47). The purposive character of technology is an imitation of the purposive character of nature. “If, then, art imitates nature, it is from nature that the arts have derived the characteristic that all their products come into being for the sake of something” (Fragments, Dialogues, Iamblichus, Protrepticus 54.10-56.12 Pistelli, B14). Similarly, the order of technological operations should follow the sequence of natural processes.

Nevertheless, the imitation and the completion of nature do not amount to identity between natural products and technological products. It is true that a house made by art is similar to a house that would have been made by nature. The similarity holds as far as the actual function of a house is concerned. However, a certain property of natural objects, that of self-reproduction is an absolute limit for technology. From the point of view of the natural order, technology has the character of the accident and, like monsters, artefacts are not self-reproducible:

if you planted a bed and the rotting wood acquired the power of sending up a shoot, it would not be a bed that would come up, but wood which shows that the arrangement in accordance with the rules of the art is merely an accidental attribute, whereas the substance is the other, which, further, persists continuously through the process (Physics, 193a)

Technology is external to its products while nature is not. The efficient, final and formal causes of technology lie in the technician that imprints them on matter. This imprinting is only accidental to the imprinted substance and it does not change the real nature of things. Only the material cause (what the thing is made of) is wholly present in the technological product and it retains its own principles of change.

The principles of change are external to technological products and thus they cannot change by themselves: “a bed and a coat and anything else of that sort, qua receiving these designations – i.e. in so far as they are products of art – have no innate impulse to change” (Physics, 192b). Technological products cannot move by themselves. The cause of movement is external to the thing. Movement is either internal or external. If it is external, some mover must exist that have to be, in general, in permanent contact with the thing moved. Thus, artificial autonomous movement requires explanation. In the case of an arrow or of an automaton, the mover does not cause the movement continuously:

In addition to the naturally occurring up or down motion of bodies composed of earth, water, fire, and air, non-spontaneous motion observed in the world around us, such as the flight of an arrow, requires explanation. Aristotle envisioned all such motion as forced or violent (as against natural) motion. He proclaimed that such motion always requires an external mover, someone or something to apply an outside force of some sort to cause the motion in question. Moreover, the mover must be in constant contact with the object. In the vast majority of instances Aristotelian movers can be easily identified and the principle apparently confirmed: the horse pulls the cart, the wind blows the sail, and the hand guides the pen. But paradoxical counterexamples exist: the arrow or the javelin in flight after it has lost contact with its mover. Where is the mover in those cases? (Aristotle himself said the medium somehow does the pushing.) (McClellan & Dorn, 2006: 75).

Aristotle explains that a movement can sometimes be so violent that it can continue to act for some time without any contact between the mover and the moved thing:

pushing off occurs when the mover does not follow up the thing that it has moved; throwing when the mover causes a motion away from itself more violent than the natural locomotion of the thing moved, which continues its course so long as it is controlled by the motion imparted to it (Physics, 243a).

If this argument explains the flight of an arrow, the movements of automata remain still unexplained, for they tend to move autonomously for a too long period of time without the help of any external mover.

Aristotle considers the movement of automata and explains their capacity to move quasi-autonomously. Discussing animal movements, Aristotle compares animals with automata in Movement of Animals and Generation of Animals. Automata present a kind of self-movement by the fact that they, on the basis of design, can transform one kind of locomotion into another kind of locomotion. They are set in motion by a mover through a causal chain. This causal chain that affects only local motion is their substantial form and this is similar with the animal motion caused mechanically by the environment. The motion is potentially contained in the automata, i.e. the potential motion of automata was imprinted in them by the artisan.

It is possible, then, that A should move B, and B move C; that, in fact, the case should be the same as with the automatic puppets. For the parts of such puppets while at rest have a sort of potentiality of motion in them, and when any external force puts the first of them in motion, immediately the next is moved in actuality. As, then, in these automatic puppets the external force moves the parts in a certain sense (not by touching any part at the moment, but by having touched one previously) (Generation of Animals, 734b).

Aristotle accepts a limited² similitude between animals and automata – their constitutive physical parts are similar, their movements can be affected by their environment.

The movements of animals may be compared with those of automatic puppets, which are set going on the occasion of a tiny movement (the strings are released, and the pegs strike against one another); or with the toy wagon (for the child mounts on it and moves it straight forward, and yet it is moved in a circle owing to its wheels being of unequal diameter – the smaller acts like a centre on the same principle as the cylinders). Animals have parts of a similar kind, their organs, the sinewy tendons to wit and the bones; the bones are like the pegs and the iron; the tendons are like the strings; for when these are slackened or released movement begins. However, in the puppets and the toy wagon there is no change of quality (Movement of Animals, 701b, my emphasis).

However, automata lack qualitative change and also the internal principles of change. They can only transform the motion they receive without adding a surplus of motion. An automaton's causal chain can affect only local motion. For Aristotle, local motion is just one type of motion alongside change in quality, change in quantity, and generation-destruction. The four changes (change in quality, change in quantity, change of place and the generation-destruction) cannot be reduced just to one: “Aristotle ... never tries to reduce one kind of change to another; the difference of category stands as a barrier against any such attempt.” (Ross, 1995: 51). Although a change of place, locomotion, is involved in every change, this one is not fundamental and cannot explain the process of change as such. What is peculiar to automata is that based on their design they can transform the received motion. Automata cannot initiate movement and they cannot change into something else or evolve. The limit of the comparison is the local motion set by an external agent. Moreover, animals can continue to move by themselves while automata will stop when the imprinted artificial movement is consumed.

Knowledge and Techne

In the beginning of Metaphysics (980a-981b), Aristotle presents a historical evolution of knowledge from animal perception to philosophical contemplation. In this text Aristotle reaffirm the Platonic low status of technology as being an ignoble kind of knowledge. For Aristotle knowledge begins with perception, the possibility of every animal to distinguish differences. The faculty of perception gives rise to memory as the trace of perception in the soul. The next step is the experience that represents the creation of a certain universal based on multiple memories over the same thing. Experience is the origin, on the one hand, of science, epistheme, if the concern is Being as such, and, on the other hand, of art, techne, if the concern is becoming: “science and art come to men through experience” (Metaphysics, 981a). Art, techne, that comprises all Platonic classes, is inferior to knowledge because it is “limited in its interest by having some ulterior practical end” (Ross, 1995: 99): “when all such inventions were already established, the sciences which do not aim at giving pleasure or at the necessities of life were discovered” (Metaphysics, 981b). Utility is not a noble purpose for Aristotle. The real knowledge is the knowledge of universals and causes, not a description of how particulars are. Thus, in the first paragraphs of Metaphysics, Aristotle rejects techne as a lower activity, which obviously is not recommended for a citizen. At the end of his discussion on the origins of knowledge, Aristotle gives a hierarchy of knowledge with arts (techne) at the bottom and science (epistheme) at the top: “the man of experience is thought to be wiser than the possessors of any perception whatever, the artist wiser than the men of experience, the master-worker than the mechanic, and the theoretical kinds of knowledge to be more of the nature of wisdom than the productive” (Metaphysics, 981b).

Beside art (techne, making) and science (epistheme, “the disposition by virtue of which we demonstrate” (Nicomachean Ethics, 1139b)), Aristotle admits other three ways of knowing: a practical wisdom (phronesis, doing) dealing with living a good life, political or military actions, and taking good decisions; an intuitive reason (nous), the faculty that grasps the first principles, the universal truths; and finally the theoretical wisdom (sophia) that is the union of science and intuitive reason directed at the loftiest objects as heavenly bodies or God.³ Nevertheless, the faculties of knowledge can be reduced to three given that epistheme, nous and sophia have the common domain of studying the necessary and the immutable. Therefore, we have, in order of importance, proper knowledge dealing with the necessary, practical wisdom dealing with praxis and art dealing with making artificial things. The fact that techne does not possess real knowledge is made very clear in Magna Moralia, where Aristotle or its follower – the authenticity of the book is still disputed – considers the mechanics as being a bad branch of knowledge:

pleasure was held ... not to be good ... because some pleasures are bad. But this sort of objection and this kind of judgment is not peculiar to pleasure, but applies also to nature and knowledge. For there is such a thing as a bad nature, for example that of worms and beetles and of ignoble creatures generally ... In the same way there are bad branches of knowledge, for instance the mechanical (Magna Moralia, 1205a).

Knowledge
Of the necessary	Of the contingent
Science + Intuitive reason + Theoretical wisdom	Practical wisdom	Techne

Fig. 1. The division of Knowledge. After Ross, 1995, 137.

Technology posses a certain degree of knowledge, however ignoble. Aristotle affirms that mechanical knowledge is the practical subset of geometry. In fact, mechanics and music seem to be the only arts, techne, that possess a specific kind of knowledge: “But demonstration does not apply to another genus – except, as has been said, geometrical demonstrations apply to mechanical or optical demonstrations, and arithmetical to harmonical” (Posterior Analytics, 76a, my emphasis). On this account, mechanics and music seem to be, out of all other forms of techne, the most knowledgeable arts because they are most reducible to simple mathematical relations. Mechanics abstracts from real motions and it deals with geometrical figures and thus it has the characteristics of a science. Mechanics does not deal with objects qua objects but qua instantiating geometrical entities, lines and figures:

a science is most precise if it abstracts from movement, but if it takes account of movement, it is most precise if it deals with the primary movement, for this is the simplest; and of this again uniform movement is the simplest form. The same account may be given of harmonics and optics; for neither considers its objects qua light-ray or qua voice, but qua lines and numbers; but the latter are attributes proper to the former. And mechanics too proceeds in the same way (Metaphysics, 1078a, my emphasis).

Although mechanics is linked to geometry, the exchange between them is only in one direction: geometric principles can be applied in mechanics but geometry remains totally unchanged. Science is immutable while art only imitate some of its features. Science has nothing to gain from technical endeavours.

Classification of Techne

There are lower and higher forms of techne, based on the utility of technological products: higher utility of technological products corresponds to lower status of that technology. Artists belong to a higher level of human development than master artisans and artisans, although all of them deal only with particulars that do not qualify for real knowledge. Thus, if the products of artisans aim at satisfying the necessities of life, the associated techne has a lower status: “as more arts were invented, and some were directed to the necessities of life, others to its recreation, the inventors of the latter were always regarded as wiser than the inventors of the former, because their branches of knowledge did not aim at utility” (Metaphysics, 981b). This distinction classifies techne in two great domains, that of art – the playthings class in Platonic terminology – and technology as such.

Aristotle gives three criteria for classifying arts: the materiality involved in that art, the abilities that that specific art develops in men, and the contingency of that art. Thus, if an art requires an important involvement with material things, that art is more ignoble. Also, if an art requires more physical abilities at the expense of theoretical and practical ones, that art has a lower status⁴.

Those occupations are most truly arts in which there is the least element of chance; they are the meanest in which the body is most maltreated, the most servile in which there is the greatest use of the body, and the most illiberal in which there is the least need of excellence (Politics, 1258b, my emphasis).

Although in mechanics more geometrical principles are involved, this art is condemned by Aristotle because it requires a lot of physical work and its products are made for others to use them, transforming the technician into some kind of slave:

the artisan ... attains excellence in proportion as he becomes a slave. The meaner sort of mechanic has a special and separate slavery; and whereas the slave exists by nature, not so the shoemaker or other artisan (Politics, 1260b).

An art is nobler if it is closer to practical life, the exercise of citizenship. The practical life is attained only if one develops practical wisdom. Practical wisdom deals, like technology, with contingent beings. “The class of things that admit of variation includes both things made and actions done. But making is different from doing” (Nicomachean Ethics, 1140b). In the case of praxis there is on the one hand the nobility of purpose, the development of human personality, and on the other hand the fact that practical actions are ends in themselves. “[M]aking aims at an end distinct from the act of making, whereas in doing the end cannot be other than the act itself” (Nicomachean Ethics, 1140b). The separation between praxis and techne seems quite straightforward but in fact it is not so, at least for the modern mind, because if sculpture, architecture, mining, and carpentry belong to technology as expected, agriculture is on the borderline because it elevates the people who practice it:

Now in the course of nature the art of agriculture is prior, and next come those arts which extract the products of the earth, mining and the like. Agriculture ranks first because of its justice; for it does not take anything away from men, either with their consent, as do retail trading and the mercenary arts, or against their will, as do the warlike arts. Further, agriculture is natural; for by nature all derive their sustenance from their mother, and so men derive it from the earth. In addition to this it also conduces greatly to bravery; for it does not make men’s bodies unserviceable, as do the illiberal arts, but it renders them able to lead an open-air life and work hard; furthermore it makes them adventurous against the foe, for husbandmen are the only citizens whose property lies outside the fortifications. (Economics, 1343a-b)

Here Aristotle redesigns the Platonic classification of techne. Firstly, he divides techne into liberal and illiberal arts. Liberal arts, like music, are noble arts because they do not involve utility and develop human superior abilities. Secondly, Aristotle classifies the illiberal arts on the basis of their closeness to practical life. Thus, agriculture is the first of illiberal arts because it develops liberal character traits.

The ancients certainly used technologies and techniques in the actual practice of agriculture, but they considered it to be conducive to the development of good character traits in the landholder that would prepare him for political and military action. They believed that agriculture inculcated virtue, training elite males to be good leaders. It was a discipline appropriate to the praxis of political and military leadership, quite separate from lower-status occupations involving the technical arts. (Long, 2001: 16).

After agriculture comes what Plato called 'first-born' class, obtaining the raw materials. The last position is occupied by mechanics, which is closest to slavery, the opposite of citizenship. Aristotle shows that science and practice are superior to technical endeavours and beside that, he prohibits the mixing of these domains. The borders are clear and distinct and cannot be trespassed. It will be the task of the Renaissance to show the important links between science and technology.

The Social Status of Technology

As already mentioned, technology is classified between slavery and practical life with different degrees of excellence. Aristotle wrote many passages in which he denies citizenship to artisans and limits the involvement of citizens with arts, especially illiberal arts. Even music or gymnastics can become illiberal if pursued immoderately:

nor is there any difficulty in meeting the objection of those who say that the study of music is mechanical. ... it is quite possible that certain methods of teaching and learning music do really have a degrading effect. It is evident then that the learning of music ought not to impede the business of riper years, or to degrade the body (Politics, 1340b-1341a)

From the above quotes one can see that to become a technician is shameful. Artisans do not deserve to be citizens:

There still remains one more question about the citizen: Is he only a true citizen who has a share of office, or is the mechanic to be included? ... In ancient times, and among some nations, the artisan class were slaves or foreigners, and therefore the majority of them are so now. The best form of state will not admit them to citizenship; but if they are admitted, then our definition of the excellence of a citizen will not apply to every citizen, nor to every free man as such, but only to those who are freed from necessary services. The necessary people are either slaves who minister to the wants of individuals, or mechanics and labourers who are the servants of the community. ... so that under some governments the mechanic and the labourer will be citizens, but not in others, as, for example, in so-called aristocracies, if there are any, in which honours are given according to excellence and merit; for no man can practise excellence who is living the life of a mechanic or labourer. In oligarchies the qualification for office is high, and therefore no labourer can ever be a citizen; but a mechanic may, for an actual majority of them are rich. At Thebes there was a law that no man could hold office who had not retired from business for ten years. (Politics, 1277b-1278a)

The mechanic, because he works for others and is paid for that, is just a different kind of slave. In conclusion, it is dishonourable for citizens to involve in such activities:

Certainly the good man and the statesman and the good citizen ought not to learn the crafts of inferiors except for their own occasional use; if they habitually practice them, there will cease to be a distinction between master and slave ... There is, indeed, the rule of a master, which is concerned with menial offices – the master need not know how to perform these, but may employ others in the execution of them: the other would be degrading; and by the other I mean the power actually to do menial duties, which vary much in character and are executed by various classes of slaves, such, for example, as handicraftsmen, who, as their name signifies, live by the labor of their hands – under these the mechanic is included (Politics, 1277b).

Aristotle uses the Platonic argument that the technician does not even know the standards of what he is doing. His products are subject to users' opinions who best evaluate them.

Moreover, there are some arts whose products are not judged of solely, or best, by the artists themselves, namely those arts whose products are recognized even by those who do not possess the art; for example, the knowledge of the house is not limited to the builder only; the user, or, in other words, the master, of the house will actually be a better judge than the builder, just as the pilot will judge better of a rudder than the carpenter, and the guest will judge better of a feast than the cook. (Politics, 1282a)

An important Ancient work on technology is pseudo-Aristotle's Mechanics, which, in the introduction, critically analyses the relation between technology and nature, a book that tremendously influenced the Renaissance. This book is consistent with the Aristotelian corpus and during the Renaissance it was considered an original work of the Stagirite. All contemporary literature, however, agrees that the Mechanics is not written by Aristotle. 

The fact that it was attributed to Aristotle raises its value in the eyes of a Renaissance man. As for the real author, David Ross and G.E.R. Lloyd think that it is somebody from the Peripatetic School while Thomas Winter tries to show by elimination of possible authors that the book was written by a Pythagorean contemporary of Plato, Archytas of Terentum, the inventor of mathematical mechanics (Winter, 2007: iii-ix).

The book was considered unique amongst Aristotle's work because it focuses on simple machines, describing pulleys, gears, levers, and other devices that produce mechanical advantage and also because it mixes physics and mathematics in treating mechanical problems. Mechanics is copied in 1457 for cardinal Bessarion but at the time of its discovery there is little interest in its content.

“For nearly a hundred years thereafter, its main readers were humanist scribes and scholars who had little interest in its contents, but at the turn of the sixteenth century, around the time of its first Greek printing in the Aldine edition of Aristotle (1495-8), researchers began to look at the Mechanics more closely, creating demand for improved editions, Latin translations, vernacular versions, and commentaries that made the work more widely available.” (Copenhaver, 1992: 66).

The initial lack of interest shows the traditional contempt of both scholars and humanists for technology.

Mechanics begins by establishing the categorical difference between art and nature. Mechanics is not a part of physics because mechanics is para physin. This can be interpreted either as “contrary to nature” or as “beyond nature” in the sense of completion of nature. Anyway, nature and mechanics are separated. What is important and non-Aristotelian about the conception of technology in this book is the fact that mechanics use both physics and mathematics and mix them in creating artefacts.

They [mechanical problems] are not quite identical nor yet entirely unconnected with Natural Problems. They have something in common both with Mathematical and with Natural Speculations; for while Mathematics demonstrates how phenomena come to pass, Natural Science demonstrates in what medium they occur” (Mechanics, 847a)

The marvels of mechanics are all explained by the marvellous status of circular motion because the circle is a combination of opposites and the authors of Mechanics tries to demonstrate that any mechanism is reducible to circles:

there is nothing strange in the circle being the origin of any and every marvel. The phenomena observed in the balance can be referred to the circle, and those observed in the lever to the balance; while practically all the other phenomena of mechanical motion are connected with the lever (Mechanics, 848a).

The oppositions contained in the circle are the existence of concavity and convexity in the same circumference, the backward and forward movement in the same time¹, the possibility of movement in circumference while the centre is at rest and the fact that a point farther from the centre moves faster than a point closer to the centre. Therefore, the author will try to explain all the problems by reducing them to circular motion. After the introduction, the Mechanics continues with thirty-five problems or mechanical phenomena, some taken from everyday experience and others of more theoretical nature. It is important to notice that in the Aristotelian corpus there is no mention of mechanisms that use fire, water or wind. This characteristic is overcome by Hellenistic authors who made extensive use of these phenomena in constructing their mechanisms: both Hero and Vitruvius describe the aeolipile, the first recorded steam engine in history.

Apart from the works mentioned above, there is no other philosophical approach to technology before Renaissance. The most proeminent examples of Ancient technology authors are Hero of Alexandria, Vitruvius and Archimedes, who design and describe complex mechanisms but their intentions are neither philosophical nor scientific. The closest we get to a view on the role of technology in those authors is Hero's comment on the aim of his work, that of bringing “much advantage ... to those who shall hereafter devote themselves to the study of mathematics” (Hero of Alexandria, 1851:1). And after a short introduction on the problem of vacuum and on the elements, he proceeds to describe diverse mechanisms.

1A similar passage is found in Fragments: “art exists to aid nature and to fill up what nature leaves undone. For some things nature seems able to complete by itself without aid, but others it does with difficulty or cannot do at all; ... similarly, some animals too attain their full nature by themselves, but man needs many arts for his preservation, both at birth and in the matter of nutrition later” (I Dialogues, Iamblichus, Protrepticus 49.3-51.6 Pistelli, B13)


2 “Animals – unlike stones or artifacts – can instigate local motion when there are changes in their environment, but nothing pushing or pulling them. The automata he describes do not precisely do this, but they share with self-movers the capacity to transform one kind of input into motion of a different kind. In the puppets Aristotle uses as analogues, the unwinding of twisted cords is transformed into the motion of the limbs. The sequence of motion continues without an agent operating it, and unlike a projectile – which simply continues the motion it is given – it is the constitution of an automaton that determines the resultant motion” (Berryman, 2003: 358)


3 “Let it be assumed that the states by virtue of which the soul possesses truth by way of affirmation or denial are five in number, i.e. art, knowledge, practical wisdom, philosophic wisdom, comprehension; for belief and opinion may be mistaken.” (Nichomachean Ethics, 1139b)


4 “parents who devote their children to gymnastics while they neglect their necessary education, in reality make them mechanics” (1338b)

Plato's Approach to Technology

In the Statesman, Plato gives both a definition and a classification of his contemporary technology. The importance of this text comes from the fact that his purpose is not to define and classify technology but to show how one can analyze the art of the statesman. Therefore, he gives just a didactic example which means that the conception exposed here is a piece of common knowledge. Thus, Plato only clarifies what is commonly thought of technology. He refers to craftsmanship, carpentry and manufacture as the “practical actions... [that] complete those material objects they [the artisans] cause to come into being from not having been before” (258e). Thus, for Plato the technology is understood as the practice of creating and perfecting material objects that do not exist naturally. This practice is linked to a practical knowledge, a “knowledge... naturally bound up with practical actions” (258e). Knowledge, especially mathematical knowledge, is an important part of technological endeavour:

if someone is to take away all counting, measuring, and weighing from the arts and crafts, the rest might be said to be worthless... All we would have left would be conjecture and the training of our senses through experience and routine. We would have to rely on our ability to make the lucky guesses that many people call art, once it has acquired some proficiency through practice and hard work (55e, my emphasis).

If one is to eliminate knowledge from crafts, these will become worthless because all that is left is lucky guess and conjecture. However, for Plato, technology is a systematic endeavour that uses principles in making things. The principles, the knowledge that the artisan uses is mainly mathematics. Therefore, technology is mathematically embedded. Plato criticizes the (probably) popular view of technology as based only on routine, experience and lucky guesses, in which no real knowledge is involved. Although knowledge is involved in craftsmanship and Plato stresses that, in the Republic Plato shows that the type of knowledge that the artisan, the practical man, possess is impure and corrupt:

no one with even a little experience of geometry will dispute that this science is entirely the opposite of what is said about it in the accounts of its practitioners... They give ridiculous accounts of it, though they can't help it, for they speak like practical men, and all their accounts refer to doing things. They talk of 'squaring', 'applying', 'adding', and the like, whereas the entire subject is pursued for the sake of knowledge (527a, my emphasis).

The geometry of the artisan is an ignoble form of the real science and the craftsman does not possess the proper language and the principles of science. The practical geometry of the artisan is even the opposite of the real science because it is a geometry of the things that become, that come into being, while geometry as such is a science of being qua being, of the incorruptible: “If geometry compels the soul to study being, it's appropriate, but if it compels the soul to study becoming it's inappropriate” (526e). This distinction will be further used to argue for the low status of the artisan in the city.

In the Statesman, Plato discovers by analysis seven great technological classes based on the intended use of the things made: “it would be most appropriate if we put the [1] 'first-born' class of things at the beginning and after this [2] 'tool', [3] 'vessel', [4] 'vehicle', [5] 'defense', [6] 'plaything', [7] 'nourishment'” (289b). These seven classes comprise all that can be called 'craftsmanship' or, in contemporary terminology, technology. Of these classes, Plato distinguished tools-making as a special class because the production of tools is the basis of technology. Tool-making is called “contributory causes of production” (281e) because tools are used in all other classes. Without tools, no other technological class would be possible. Consequently, no civilization would be possible: “we must put down as being contributory causes all the sorts of expertise that produce any tool in the city whether small or large. Without these would never come to be a city, nor statesmanship” (287d). However, in the end of his analysis of technology, at 289b, he changes the order of classes, considering that obtaining the raw materials is the primal technological class. Nevertheless, this contradiction amounts to the view that technology necessarily proceeds from tools and raw materials in order to pursue further. The other important ingredient for making things is, as stated at 258e and 55e, the practical knowledge of the artisan.

Plato consequently classifies technology in seven domains based on the teleology of artefacts, on what they are good for. 'Tools' are the things made for “the purpose of causing the coming into being” (287e); the 'vessel' class comprises the things made “for the sake of preserving what craftsmen have produced” (287e); the 'vehicle' class comprises products of carpentry, pottery and bronze-working, which “it is all for the sake of some supporting or other, always being a seat for something” (288a); the 'defense' class comprises things made “for the purpose of defending”, “all clothing, most armor, and walls, all those encirclements made out of earth, or out of stone, and tens of thousands of other things” (288b); the 'playthings' class is “a fifth class of things to do with decoration, painting, and those representations that are completed by the use of painting, and of music, which have been executed solely to give us pleasures”, “not one of them is for the sake of a serious purpose, but all are done for amusement” (288b); the 'first-born' class consists of “gold and silver and everything that is mined”, “art of tree-felling”, “the art of stripping off the outer covering of plants”, “the art of the skinner”, and all the arts that “make possible the working up of classes of composite things from classes of things that are not put together” (288e); and finally, the 'nurture' class comprises “the arts of the farmer, the hunter, the trainer in the gymnasium, the doctor and the cook” (289a)¹. Technology comprises all human made products and the associated practices, whatever the mode of production, that are somehow necessary to human life.

To these Platonic technological classes, a new class will be added during Renaissance, that of scientific instruments, the class of things created to study nature.

An important part of Plato's approach to technology is the stress he puts on the lower social and ontological status of artisan. This is a recurrent theme that lasts until Renaissance and even beyond. As we already mentioned, one Platonic reason for this contempt is the fact that artisans deal only with becoming while the highest purpose of life is Being and the incorruptible Ideas. The science involved in craftsmanship is of a lower form because it deals with becoming and not with being. Another argument against the artisans is that they are not the real experts in their own domain: “a user of each thing has most experience of it and ... he tells a maker which of his products performs well or badly in actual use” (601d). In other words, the artisans are inferior to the users of technology and they should follow the users' prescriptions. Another argument against artisans is that they are only imitators of nature:

When a craftsman discovers the type of tool that is naturally suited for a given type of work he must embody it in the material out of which he is making the tool. He mustn't make the tool in whatever way he happens to choose, but in the natural way (389c).

This argument also deals with the relationship between technology and nature. Technology should imitate nature because the artefacts have pre-existing models in the natural world and the artisan should only discover these models. Moreover the artisans should be faithful to nature and should not bring any innovations because the natural way is the best one.

Finally, in the Laws, Plato explicitly regards craftsmanship as a disgrace for a citizen and argues for the ignobleness of such endeavour: “As for craftsmen in general, our policy should be this. First, no citizen of our land nor any of his servants should enter the ranks of the workers whose vocation lies in the arts or crafts” (846d). He specifies punishments for the citizens that would become artisans: “If a citizen born and bred turns his attention to some craft instead of to the cultivation of virtue, the City-Wardens must punish him with marks of disgrace and dishonour until they've got him back on the right lines” (847a). Plato argues in the Republic that the reason for banning artisans from citizenship is that they are made out of different base materials and that that diminishes their civil capabilities: 

'All of you in the city are brothers' we'll say to them in telling our story, 'but the god who made you mixed some gold in those who are adequately equipped to rule, because they are most valuable. He put silver in those who are auxiliaries and iron and bronze in the farmers and other craftsmen' (415a, my emphasis)

1Based on this classification, one can add, beside tools, raw materials and knowledge, a fourth important element of technology: the purpose of the thing made. But, this would amount to the Aristotelian analysis of the four causes, the efficient cause, the material cause, the formal cause and the final cause, which is not an explicit feature of the Platonic text.

Conștiința după Wittgenstein

Originea sinelui interior:

Platon: sufletul nu este un inteligibil, o Idee, pentru că admite schimbarea; nu este nici sensibil, dar este etern, asemănător inteligibilelor, legat de lumea sensibilă și vrea să se întoarcă în lumea inteligibilă.

Plotin: lumea inteligibilă devine mintea lui Dumnezeu; Ideile sunt în Mintea Divină, o sferă în al cărui centru este Unul; Sufletul o sferă exterioară concentrică sferei Minții Divine; sufletele individuale sunt ferestre către exterior ale Sufletului uitându-se către „lumea exterioară”, sensibilă; întoarcerea către interior face ca sufletele să vadă Ideile, Mintea lui Dumnezeu.

Augustin: inventatorul sinelui interior – inner self; Augustin nu poate prelua imaginea plotiniană pentru că în acest caz sufletul ar fi parte a lui Dumnezeu și nu ar exista indivizi și răspundere individuală (a te întoarce spre interior ar însemna a contempla Mintea lui Dumnezeu); sufletul este o lume interioară privată, un palat compus din memorii, iluminat de lumina divină.

John Locke: lumea interioară este o 'cameră obscură', privată, teatru intern compus din idei.

Descartes este cel ce introduce conștiința ca privire ce scrutează cutia neagră, interioară și privată, care este mintea. Peter Hacker: „Cu conștiința este o poveste curioasă. Grecii și romanii nu au avut un termen pentru conștiință, deși au ridicat probleme asemănătoare cu unele din problemele pe care Descartes și succesorii săi le-au ridicat. Descartes a introdus cuvântul în latină în 1641 folosind 'conscius', într-un sens diferit de utilizarea medievală. Pentru medievali 'conscius' însemna pur și simplu cunoștințe împărtășite, a fi la curent cu informația. Atunci când Descartes introduce noțiunea de conștiință, se referă la faptul că știu cum stau lucrurile cu mine mental, în interior sau în mintea mea. Utilizarea obișnuită a cuvântului în limba engleză începe un pic mai devreme - 1603 este prima apariție înregistrată - și se dezvoltă rapid într-un instrument util, chiar dacă specializat, a vocabularului cognitiv. Este utilizat drept unul dintre verbele cognitive care desemnează receptivitatea cognitivă – ca a-și da seama, a înțelege, a observa. Conștiința perceptuală, de exemplu, se referă la a avea atenția atrasă și menținută de ceea ce este perceput. De aceea nimeni nu poate să devină în mod voluntar sau intențional conștient de ceva – pentru că a deveni conștient de ceva nu este în general un act, cu atât mai puțin un act voluntar. ... Utilizarea filosofică a trecut de la o catastrofă intelectuală la alta.” (Peter Hacker, 2010, http://www.philosophypress.co.uk/?p=1583 )

În perioada Tractatusului Wittgenstein adoptă un solipsism transcendental schopenhauerian. Conștiința este limita lumii și a limbajului dar nu sub forma unui sine/subiect unitar ci ca șir de episoade mentale. Conștiința nu poate fi obiectul nici unei experiențe și nu poate fi inferată din conținutul experiențelor. În Tractatus conștiința este identificată cu eul și cu viața, iar viața este identificată cu lumea/realitatea. Unitatea aperceptivă este analoagă unității câmpului vizual. Conștiința este raza care luminează episoadele mentale private. (TLP 6.3-6.4)

Această viziune este contrazisă de Investigații:

Argumentul limbajului privat afirmă că nu are sens să vorbim despre fapte mentale private. Nu există un conținut intern privat pentru că noi înșine nu ne-am putea împărtăși acest conținut. (Ex.: am experiența privată „blabuca”. Dacă presupunem că e absolut privată atunci nu voi fi capabil să o recunosc când mi se va întâmpla iar și nici nu voi fi capabil să mi-o reamintesc – nu am criterii pentru „blabuca”. Dacă o descriu în limbajul natural și stabilesc criterii de identificare atunci „blabuca” nu mai este privată, ci un nume pentru o descriere accesibilă public)

Argumentul împotriva introspecției: „Eu sunt conștient” este doar un mod de a raporta că văd, aud, simt, etc. Nu există o experiență a conștienței. „Eu am experiența faptului de a fi conștient” are aceeași semnificație cu „Eu am o experiență”. Conștiința e un joc de limbaj care se aplică oamenilor și nu pietrelor. (PI §§ 416-420)

Problema conștiinței nu se rezolvă prin introspecție, prin a fi atent/a privi conștiința (atenție și privire fără conținut) ci prin analiza jocurilor de limbaj în care apare „conștiința”.

Ca urmare, conștiința nu este un fenomen (stare sau proces intern). Nu există o lume fizică și o lume a conștiinței ci doar o diferență categorială în limbaj între ființele care percep și reacționează la mediu și cele care nu fac acest lucru. „Ființele umane au conștiință” este o propoziție gramaticală (nu se bazează pe fapte, nu există justificări pro sau contra ei). (PI §§ 281-284)

Relația dintre conștiință și creier: Orice proces conștient poate fi relatat ca proces neuronal, ca proces al trupului fără a lua în calcul procesele neuronale sau pur și simplu ca descriere la persoana întâi. Toate acestea sunt descrieri diferite dar echivalente care nu aduc nimic nou descrierii filosofice.

Daniel D. Hutto – Wittgenstein and the End of Philosophy, 2003, cap. Without Explanation, pp. 128-173

Wittgenstein încearcă să demistifice conștiința (dar nu în sensul lui Dennet de reducere a ei la explicații 'științifice'). În filosofia analitică problema conștiinței are 2 opțiuni: dualismul (dualismul substanțelor sau dualismul proprietăților) sau materialismul. Dennet: problema este folosirea metaforelor de teatru (mental) intern, sinele care îl supravegheză și obiecte ale conștiinței. Wittgenstein: problema este că limbajul referitor la conștiință este greșit considerat ca fiind referențial. 'Mintea' nu se referă la vreun fel de entitate așa cum stările de conștiință nu sunt 'obiecte' speciale.

Dennet propune ca prim pas în analizarea conștiinței o heterofenomenologie care să identifice strict conștiința cu descrierea la persoana I a stărilor de conștiință (această descriere va fi considerată o lume ficțională, la fel de adevărată precum Sherlock Holmes). 'Textul heterofenomenologic' obținut (conștiința) trebuie explicat într-un mod naturalistic prin sub-sistemele subiacente care produc astfel de texte (mașini virtuale Joyceene) împreună cu explicația ontogenetică a formării acestor sisteme. (Copiii și animale, neputând produce astfel de texte, nu pot fi conștienți.)

Wittgenstein consideră că dările de seamă privind 'stările de conștiință' sunt expresive. ('I am in pain' este expresie a durerii și nu descriere a unei stări.) Ele nu sunt referențiale, ca pentru Dennet, unde referința este ficțională. Wittgenstein demistifică conștiința nu prin eliminarea ei ci printr-un nou mod de a analiza natura limbajului psihologic.

Paul Johnson – Wittgenstein. Rethinking the Inner, 1993, cap. „The Mind, the Brain and the Soul”, pp. 202-233

Cerința de a explica conștiința este greșită pentru că limbajul este format din practici, gesturi și expresii care nu pot fi parafrazate. Avem tendința de a prezenta Interiorul (the Inner) fie ca un lucru (substanță mentală), fie drept nimic (o metaforă reductibilă la comportament). Wittgenstein afirmă că Interiorul este un tip de concept radical diferit.

Analogia dintre vedere și conștiință: putem descrie experiențele vizuale dar nu vederea. A vedea este posesia unei tehnici speciale pe care orbii nu o au. Conștiința este posesia unei tehnici speciale pe care un automaton nu o are. Nu putem explica conștiința în termeni mecanici așa cum nu putem explica vederea unui orb. (a scrie după dictare poate fi explicat doar cuiva care deja știe; dacă în timpul dictării spun „șterge ultimul cuvânt”, cel ce a învățat din descriere ce este dictarea va transcrie și aceste cuvinte; nu există diferență între 'limbajul' și 'metalimbajul' dictării sau doar cel ce este familiarizat cu dictarea sesizează diferența; pentru a dicta unei mașini trebuie să am un supersimbol, care nu aparține nici 'limbajului' nici 'metalimbajului', care să facă alternarea; greșeala survine când modul de operare a mașinii este transferat în explicarea conștiinței). Imposibilitatea de a descrie vederea nu vine din faptul că este inefabilă sau că este un tip special de experiență ci din faptul că nu este o experiență. Conceptele psihologice sunt utilizate în interacțiunile dintre oameni și nu sunt definibile în afara acestui context.

Intențiile nu pot fi reduse la descrieri neurologice și orice descoperire din neuro-științe nu va adăuga nimic la rolul proceselor conștiente în viața noastră. Intenția de a vizita un prieten poate fi explicată prin dorința de a-l vedea, prin faptul că sunteți buni prieteni, prin dorința de a discuta despre noua slujbă, prin faptul că nu ai altceva mai bun de făcut, etc., dar descrierea neurologică a intenției nu ar putea cuprinde aceste motive și multe altele. Greșeala constă identificarea dintre o stare a creierului și conceptul psihologic asociat și nevoia de a da o explicație cauzală conceptului psihologic. Când cineva ghicește ce oră este fără a se uita la ceas nu trebuie să afirmăm că există un ceas interior pe care îl consultăm ci pur și simplu, ca ființe înconjurate de ceasuri, ne-am dezvoltat abilitatea de a ghici timpul. Procesele neuro-chimice implicate nu vor explica abilitatea ci doar vor oferi o descriere diferită (în alt joc de limbaj).

Cubul Necker



181 “But this surely isn’t seeing!” – “But this surely is seeing!” – It must be possible to give both remarks a conceptual justification.

182. But this surely is seeing! In what way is it seeing?

183. “The phenomenon is at first surprising, but a physiological explanation of it will certainly be found.” – Our problem is not a causal but a conceptual one. (Wittgenstein, Investigații, Partea a II-a, secțiunea xi )


Cubul Necker este un bun exemplu pentru a analiza conștiința prin analogie cu vederea. Richard Eldridge (Wittgenstein on Aspect-Seeing, the Nature of Discursive Consciousness, and the Experience of Agency, în William Day, Seeing Wittgenstein Anew, 2010, pp. 162-182) afirmă că doar ființele umane par capabile de a vedea ceva ca ceva sau ca altceva, sub un concept sau altul. A vedea un aspect (Wittgenstein – Investigații, partea a II-a, secțiunea xi), nu este 'parte a percepției', 'nu aparține percepției', pare a fi jumătate experiență vizuală și jumătate gândire. Cubul nu este un 'obiect în mintea mea'.

Când văd o față și apoi văd că seamănă cu cineva, nimic din vederea mea nu s-a schimbat, văd exact același lucru, și totuși văd altceva.

Când vedem 'roșu' nu vedem fizic o lungime de undă și mental o qualia privată. Ca și în cazul Necker sau a iepurelui-rață avem o experiență directă și imediată a unuia din aspecte. (împotriva dualismului și a argumentului spectrului inversat). În cazul vederii aspectelor nu este vorba de o interpretare ci de vedere imediată.

Înțelesul a ceva este, în general, modul de utilizare a acelui ceva (Meaning is use). În cazul survenirii unui aspect, a înțelegerii într-o clipă (A! Acum am înțeles! știu să continui!), înțelesul este mai mult decât utilizarea. (împotriva reducționismului și behaviourismului). Neurologia poate să descrie procesele asociate survenirii unui aspect dar nu să le explice.

În cazul în care cuiva i se spune să vadă și un alt aspect al cubului, acesta are o experiență vizuală actuală, este conștient în mod actual de un aspect, și în același timp încearcă să vadă diferit, are o intenție conștientă actuală referitoare la conținutul experienței sale. Dar, două aspecte ale cubului nu pot fi văzute în același timp. Vederea aspectului și intenția de a vedea alt aspect, cele două fluxuri de conștiință, aparțin aceluiași nivel de conștiință. Nu există un limbaj și un metalimbaj. (Fenomene asemănătoare: hipnoza – pacientul, în urma hipnozei, afirmă că a avut și nu a avut durerea; visul lucid – persoana visează și în același timp este conștientă că visează; scanările creierului confirmă în ambele cazuri cele două mărturii contradictorii).

Numbers as Tools

'What is a number?' would be a perfect meaningful question for Socrates to ask. But Wittgenstein stress that 'number' is a name for many different, yet interrelated, things that do not have a single thing in common. Take for example 5 and pi. While 5 is an odd, prime number, it is nonsensical to ask whether pi is even or odd, prime or non-prime. Acknowledging the fact that there are different kinds of numbers, Wittgenstein drops the questions 'What is a number?', 'What is the meaning of numbers?' and even “What is the meaning of the word 'five'?” (PI §1). Wittgenstein reverses Socrates maxim 'Don't look, think!' into “[First,] look and see whether there is anything common to all” (PI §66). Therefore, in order to know the meaning of 'five', one has to look at the different language-games in which the word 'five' is employed, like teaching numbers, using number in groceries, mathematics, etc.

In the first paragraph of Philosophical Investigation Wittgenstein tries to show how the Augustinian picture of language may be right by providing an example of how names stand for objects. In doing so he acknowledges that 'five', 'apple' and 'red', while all names, are names of different types. The use of 'apple' is different from the use of 'five'. While 'apple' is the name of an object that the shopkeeper takes in his hand to put it in the basket, the word 'five' is used in a series of actions in which the shopkeeper takes an apple for every word he recites (aloud or just for himself) and he stops at the word 'five'. Similarly, he can just take at once five apples because he knows that such configuration of objects correspond to the sign 'five'. Is the order of natural numbers or the fact that 5 is odd and prime playing any role in his actions? It may or it may not. The shopkeeper does not need to have the answer of what 'five' is the name. He just knows his use and that is enough for Wittgenstein to say that the shopkeeper knows what 'five' is. Wittgenstein does not pretend to have explained what 'five' means or what are the grounds for the shopkeeper's actions. He only shows the direction in which the explanation of 'five' should be looked for, i.e. in the common practices that employ this number.

The knowledge of what 'five' means is not beyond the practice of the shopkeeper when he fulfils the request 'five red apples'. To add at the description given by Wittgenstein that 'five' is 'a number' would not be at all informative. The explanation will be only more complicated because it will make use of a name more in need of definition, i.e. 'number', than the initial name, i.e. 'five'. “Explanations come to an end somewhere” (PI §1). We do not have access to the shopkeeper's brain and even if we did our explanation would not be more complex or more illuminating. Even if we have had looked in his brain we would have found only a different story of the same events and not an entity like the meaning of 'five'.

For Augustine and his subsequent tradition the word 'five' stands for a mental object or for another word in the 'language of thought'. “Wittgenstein always rejected both the formalist and nominalist tendency to identify numbers with numerals and the Platonist contention that numerals stand for abstract numbers [...] Numbers are what numerals signify, but the meaning of numerals is given not by abstract entities, but by the rules of their use.” (Glock, 1996, 267) Even such mental objects existed they would add nothing relevant to the description in §1, because what is important in everyday usage is the role and the use that number-words play in counting or picking the relevant objects.

What Wittgenstein is doing is to give the simplest examples of using the words, in order to rule out any metaphysical adds-on that make the use of concepts unclear. Such metaphysical additions are the presuppositions of necessary order and the a priori infinity of the series of natural numbers. The expansion of the language (2) in paragraphs 8 and 9 gives away with such presuppositions. Andrew Lugg affirms that “Nothing of significance turns on his [Wittgenstein's] use of 'a' to signify one, 'b' to signify two, 'c' to signify three and 'd' to signify four” (2004, 27), while acknowledging that previously Wittgenstein used '1', '2', '3' and '4'. The reason for the use of “the series of letters of the alphabet” is twofold. First, contrary to the series of natural numbers, the succession of letters in the alphabet is a contingent one. It is not a necessary feature that 'c' is after 'b' and before 'd'. Second, the series of letters do not bring about the presupposition of an infinite series. Moreover, had Wittgenstein used the name of cardinal points for numerals, the series would have been strictly reduced to four. The moral of using the letters of alphabet for numerals is that one should not view in a language-game more than is specifically described. One should stop adding unnecessary presuppositions when one is after the basic structures of grammar (in Wittgenstein's sense).

Enriching the language (2) Wittgenstein shows that there are different kinds of names, for building blocks, for numerals, for demonstratives and for colour samples. These words are used in many respects in similar ways in obeying orders, but there are many differences also. It is important to mention that when introducing the numerals Wittgenstein stresses that they are used in the same manner as the shopkeeper used numerals and not the way we do. This is to show that the use of numerals should be restricted to an activity-based use without any theory that underlies the use of number-words in more complex language-games. The language evidently could lack a general concept of numbers and also it may lack any words for designating numbers other than 'a', 'b', 'c' and 'd'. What the practice of obeying the order 'd-slab-there' could not lack is the knowledge by heart of the succession of letters in the alphabet. “From the stock of slabs B takes one for each letter of the alphabet up to 'd'” (PI §8). The knowledge of the alphabet is a circumstance that should obtain for every individual that can carry on the activities in §8 correctly. But, as shown in §9, this characteristic is not necessary either. A previous knowledge of any series could be missing as well.

Using the letters for signifying numbers Wittgenstein distinguishes between two ways of learning the numerals/numbers: teaching by counting and ostensive teaching. One way to learn numbers is to memorise a series of names, 'a', 'b', 'c', 'd', and when a 'c' command is given to recite the series up to 'c' doing for each letter/name/numeral the required action (the action may be just to say the letter). This seems to be a very natural way for Augustinian picture. One already knows the series of natural numbers in his thought language and all he has to do is to learn the names of those numbers. Wittgenstein makes this picture more appealing by showing that one has to know a series, for example the letters of alphabet, and to associate this series with the activity of counting. In other words, at a certain moment of time the activity of reciting the series of letters should become another activity, that of counting. Anyway this picture shows how the Augustinian conception can fail. The number-words are not linked to any kind of image whatsoever. The number-words are just parts of a complex activity.

But this is not the only thing one can do. One can learn numbers by learning to associate some configuration of objects with some specific names. This is to show that natural numbers could also be taught ostensively. This seems to be possible only for the first five or six numbers, but it is enough to dismiss the idea that numbers cannot be taught ostensively. The ostensive teaching is more like labelling objects: “Something more like the ostensive teaching of the words "block", "pillar", etc. would be the ostensive teaching of numerals that serve not to count but to refer to groups of objects that can be taken in at a glance.” (PI §9) In this case the whole idea of numbers being part of a series disappears. In this case 'c' is not between 'b' and 'd' but is a name similar to 'b' and ‘d’ that single out a certain configuration of objects of the same kind. “As in the case of the word 'slab', the child learns the use of a single word rather than a series of words.” (Lugg, 2004, 28) Such ostensive definition of numbers corresponds to the definition of names as labels. But some features that seemed necessary in the previous example are dismissed in this new practice of teaching. In this case the prerequisite knowledge is not that of a series of any kind but the ability to single out the kind that is shown to one. To say “This is c” pointing to a group of three slabs require that there is a place of 'c' in the language-game, i.e. pointing to that group of objects single out their number and not other feature of the group. For Wittgenstein the action of pointing is part of language, of the language-game. But again, pointing, the ostensive definition, does not give the whole meaning of number-words. To learn 'c' ostensively does not imply that one will be able to follow the order 'c-slab-there'. One will be able to identify correctly what 'c' stands for, he will know only part of the language-game, only one use. “Ostensive definitions specify only one rule among others for the use of a word. Indeed they presuppose the grammatical category of the word defined.” (Baker & Hacker, 2005, 16) For the language-game to be effective it should make sense to point to a group of objects and to associate the word said with the gesture. The student should know or guess to what kind the teacher is pointing. To say 'c is a number' can be used to define 'c' as a name for a particular of a kind one already knows, i.e. number, or to build up a new kind given that one already knows what 'c' is and how it is used.

Wittgenstein has constructed in §9 two ways in which numbers can be learned and used. He has shown that number-words are different from other kinds of words in this language-game. And that the number-words have a similar use. But is this use identical in the two cases? Let numbers1 be the numbers taught as members of a series and numbers2 the numbers taught as configuration of groups of objects. Does 'c' as number1 plays exactly the same role as 'c' as number2? It may be. But if the order 'c-slab-there' is given the results can differ in the two cases. In the case of numbers as members of series a man who cannot hold three slabs in his hands will probably bring only one slab three time in a row, namely bringing 'a-slab-there', then bringing 'b-slab-there' and then bringing 'c-slab-there'. But for the man who knows numbers only as configurations of objects the order may be simply disobeyed. If I am to use a Kantian vocabulary, numbers1 have a temporal meaning, of going through a series of action till the last member of that series, while numbers2 have a spatial meaning of objects being simultaneously present. But this kind of explanation adds nothing to the practices in language-game (8) and so it does not enrich the meaning of 'c'.

In normal cases however both number1 and number2 function in the same manner. It is true that for classical physics it is important that any number corresponds to a physical quantity and so physicists may prefer the ostensive numbers, while for pure mathematics only the relations between numbers are important. That does not mean that their numbers differ. They use numbers for slightly different ends. One can stress the differences or the similarities. But these considerations will not modify the use or the meaning of numbers. Extraordinary events like the impossibility to carry on an order may give rise to the question that the interlocutor of Wittgenstein asks: “Now what do the words of this language signify?” (PI §10) These words signify “the kind of use they have”. To ask if numbers1 differ or not from number2 is a metaphysical question that tries to go with the explanation further than is required by a normal use of language. This kind of questions is struggling for one right definition, for strict boundaries of a concept, strict boundaries that Wittgenstein dismissed by talking about family resemblance. Such a metaphysical question could bring about a new definition of numbers, that anyway adds nothing to the use of language as described in §9. “Wittgenstein noted [that] an exciting new definition of number is of no philosophical concern (MS 110 (Vol. VI), 222). For if it is new, it is not a rule that we use and that guides us in our use of number-words” (Baker & Hacker, 2005, 32n)

The 'significance of a word', say 'c', is an appropriate tool in distinguishing things inside one category, for example to say that 'c' signifies a different number, a different configuration, a different member of a series than 'd'. Also it may be used to distinguish between categories: 'c' cannot be a name for a building block. To state these differences does not require a sharp definition of numbers. It is part of the language-game that 'c' and 'd' are different and also that 'c' and 'slab' are different, yet 'different' in different ways. And to state this difference one does not have to have a metalanguage, a superior level of explanation. The competent speakers could state these differences without the need of a metaphysical theory that state a difficult entity for which the name stands. What 'c' signifies is not something outside the language-game, something hidden from the view of competent speakers. A competent speaker recognises the correct use of 'c' and can give definitions of 'c' by pointing or by counting objects.

Bibliography

Baker, G.P., Hacker, P.M.S. 2005. Wittgenstein: Understanding and Meaning, Part I: Essays. Blackwell.

Glock, H.J. 1999. A Wittgenstein dictionary. Blackwell.

Schroeder, S. 2006. Wittgenstein. The Way Out of the Fly-Bottle. Polity Press.

Wittgenstein, L. 1999. Philosophical Investigations. Blackwell.