Lesson 28 Ideas and the Power of Abstraction
In the natural attitude we are so imbued with the need of feeling ourselves in the presence of “concrete” things that we are wary of ideas because we deem them to be too “abstract”. The natural attitude is extraordinarily thingish.
Yet what is a thing if not an object-identity? And is not an object-identity a concept? We may well believe ourselves to be more realistic than we really are. We are not aware for instance of the influence upon us of language. Were we more aware of it we would see that we live very much among words! Our ordinary waking state perception is full of ideas.
When asked what an idea is and that we reply that it is an “abstraction”, we believe ourselves to be in the concrete and to be able to situate the idea far away, as some kind of spectral thing that is not part of our “reality”. The idea must have some kind of connection to the concrete and we believe ourselves to be in the concrete right from the start. Yet it is precisely our so to speak relation to the concrete that has been strongly worked at by our whole culture and by our ideas!
The issue of the status of ideas is therefore more complex than it would appear. It is perfectly possible that the idea is not at all derived from perception. Could there be a procedure that would account for how our ideas are formed?
A. Abstracting and generalising.
The answer this question first appears to call for consists in saying that ideas are formed by abstraction from a previously given data, the sensation. The concept is effectively abstract. Why then not think that it is derived from something concrete, from a perception?
The elements of representation are complex. The idea of the house is different from the image of the house. The concrete is anything that can be given to me by the senses or that comes from the senses, what is impregnated with sensibility, sentiment. The perception of a waterfall and a forest beneath the snow are concrete. Concrete too the image of the sunrise for a child in Sarajevo playing among the ruins of his parents’ house. A feeling too is concrete. Sadness is an experience that is not abstract.
However if I now observe what sadness is, and above all if I analyse it, what will be the object of my thinking is the meaning, the essence of sadness and this essence precisely is not sad. It is an idea. Only sadness is sad because it is an experience, a pathos, of consciousness. In perception there is the strength of the presence of what is there, that of clouds in the sky, that too of a linden tree and the fragrance it yields on a fair spring day. Were I a botanist I would view it as a specimen of its class, “the” linden, a linden of this or that species. I would use a genre and then species within the genre. Yet, whatever distinctions one makes there will in any case always remain some generality, that idea will remain an idea, that is an abstraction. Thinking with ideas, I see in the given sensibilia of what is there (within me or outside of me) a representation that is intelligible and impersonal. I am not altogether on the level of sensible and personal experience. I leave the concrete perception of the linden ,the house for the idea of the linden, the house.
This means that out of the concrete totality given in perception I have abstracted certain elements common to a genre, summed up by a particular name. The linden is a category defined through grouping together the particularities of a certain tree, the house is defined by its function, which consists in providing a shelter for the sedentary man. One defines the abstraction as being the operation by means of which the mind seizes hold of certain elements of perception, isolates them by thought and collects them under a name. What presents itself as a totality in perception, as a concrete totality is decomposed into elements that have themselves been clearly identified by a specific term. Thinking fragments, generalises and isolates. One creates an abstract concept thanks to other concepts. This way the concept of a house keeps the features that could be applied to any possible house: foundation, windows, roof, door and so on. The concrete particularities of this or that specific house are not taken into account. Hence the building material is not very important, the colour, the sloping of the roof, the height of the windows, whether the roof is tiled or thatched and so on, all that is outside. Or else we would have to form another more particular concept: the house found in the Landes, that of the Basque country, Switzerland or Brittany. Once formed the concept gives an object-identity that will enable one to identify something in perception. The concept is the summary of a certain knowledge that, once had, can easily be applied to other similar objects by simple comparison. Once I know what a Basque house is I am able to identify among many houses the one that may receive this attribute and to distinguish it from others that do not possess the required characteristics. When the mind abstracts characteristics it immediately tends to gather them under a common term that then becomes a class, a given genre. We say that it is performing a generalisation. A generalisation consists in gathering under a common concept specificities observed in many singular objects. A river overflowing is here one fact. Another river flowing over is another fact. The concept of flooding makes it possible to think these two singular events on the basis of their observable common characteristics.
The characteristics retained in a concept are not immediately obvious, they are deliberately chosen, spotted, identified. For instance in the concept of a windmill one cannot retain an arrow-shaped roof, a terrace and a veranda. These elements are not necessary for a windmill. It is perfectly possible to conceive of a mill that would have none of these and still be a mill. But it must have a big wheel exposed to the wind and mounted high on the mill as a device to convert the energy of the wind. The concept must contain the essence of the object, it is the product of a judgement relating to an object regarded as an example of a specific class. The concept therefore fixates a sum of knowledge we have of an object inside a general and abstract symbol, the word. It allows the constitution of a class in such a way that the concept of the house or the windmill will be applied to all houses and all windmills.
If all knowledge derives from experience one may think that a concept is merely “extracted” from renewed perceptions, or more exactly, it is what allows one to denote a common element. This extraction can be obtained only if we have first perceived things in reality. Differences, resemblances, analogies exist in perception. In order to extract the common element by abstraction we must first have observed it in the perception of many objects. It is the words of language that make possible the generalisation of the idea. Thus Hume writes: “when we have discovered a resemblance between many objects that often present themselves to us, we apply the same name to all of them”. Once we are accustomed to the repetition of certain perceptions, accustomed to the repetition of names we are provided with general ideas.
One calls empiricism the doctrine that derives the idea of experience from perception. From this point of view one can consider that experience introduces in a kind of empty capacity, called the soul, marks that would be the origin of ideas. According to Locke experience engraves on the blank tablet of the mind all the elements of thoughts, the ideas. He concedes only one difference, that experience is of two sort: sensation, in the case of the experience of sensory perceptions, and reflection when the mind turns upon itself. The mind would therefore be fundamentally passive and dependent upon experience for the formation of ideas. “In this respect the mind is purely passive as to having or not having the rudiments, so to speak the materials of knowledge. For the particular ideas of objects of the senses are introduced into our souls whether we want it or nor.” It is not within our power to put an end to the flux of sensations that assail us and we cannot refuse them “no more than a mirror would be able to refuse, alter or erase the image that the objects produce on the glass in front of which they are placed”. “Since the bodies that surround us hit our organs in different manners, the soul is forced to receive the impressions and could not prevent itself from having the perception and the ideas attached to it.” Simple ideas therefore come from one sense only: sound, colour, cold or heat. Or they come from many senses such as motion, rest, space and so on. Finally Locke sees in certain ideas the intervention of reflection: such as the concept of existence, unity, power and succession. If the understanding is first of all passive in simple ideas, it becomes active in the formation of complex ideas, composed of simple ideas.
This empiricist analysis is quite satisfactory as regards simple ideas that are effectively meaningless if detached from perception. Such are the ideas of “red”, “heavy”, “light”. It is less satisfactory if one considers more abstract ideas. What can be the origin of ideas such as “God”, “the square root” or “potential”? One does not understand either why one should speak of “experience” when referring reflection. It is rather hard to understand by which procedure one could derive the most abstract ideas of the mind. How for instance would one derive the mathematical concepts? Is it not rather absurd a task to want to reduce all ideas at any cost to forms of experience? Is there not a faculty to conceive that would be distinct from perception?
B. Conceiving and Thinking
In order to conceive what Nature is it is not enough to look at it or to reflect the memory of it in our mind; it has to be scientifically explained or understood and this understanding has to be formulated in a language. To do this the mind isolates certain common elements, resemblances, and names them. Plato has Socrates say (pointing at ossicles): “I see ossicles, I do not see the number five”! True, I see objects that I identify as being ossicles, but I cannot see a concept that I could use to think the perception. One could be even more pernickety: ossicle is already a concept! Ossicle is for me a thing endowed with a very particular form once I have correctly identified it by means of a name. Ossicle is a signifying name that I can understand insofar as it relates to a certain number of objects found in groups of five and used for playing. This is already a concept. The mind is capable of applying a same name to distinct realities in perception because it possesses a primary aptitude to perceive resemblances by dismissing the differences. It has this capacity by virtue of its thing-oriented intentionality that orients it towards the identification of an object by means of a name.
The “word”, taken as a mere sound, does not mean anything; for a given name to serve as substitute for a diversified reality, it must already have a meaning and for this it has to relate to a certain content, or knowledge, that I possess about the object. The meaning of a name contains a virtual judgement. The concept is not a perception, nor a passive image, nor an auditory image; it is essentially a mental creation enveloping a piece of knowledge.
In order to better grasp this we must first of all distinguish, as does Leibniz, necessary truths and factual truths. Factual truths are relative to observations, to considerations of the mind, the very ones we encounter in all the empirical sciences relating to the measuring of certain phenomena. It is a fact that the sky is blue today, for the historian that Louis XVI was beheaded or for the chemist that salt added to water attacks iron and makes rust away faster. We say of factual truths that they are a posteriori because they depend on experience.
Necessary truths on the other hand are only relative to the mind itself and pertain more to logic than to facts. The concepts of equality, proportion or circle are pure ideas of the mind. All reasoning presupposes the principle of non-contradiction. Is that a concept derived from experience? No. It is a principle that is not derived from nature but that corresponds to a demand of the mind. Even the most ignorant man will startle when dealing with a liar who contradicts himself. The mind experiences contradictions and these are not sensory experiences, they are intellectual experiences. The principle of contradiction is rather in ourselves than in things. As soon as we have recognised in this way what is a priori, what therefore precedes the experience, we realise that there is a large number of ideas that are a priori. Indeed what about mathematical ideas? Has anyone ever been able to derive the concept of number from any experience? Of square root? Must we not say that the mathematical notions are derived from the mind itself and not from facts? In this respect “one must say that all arithmetic and all geometry is innate and are in us as potential, in as such a way that one can find them if one considers carefully and if one sorts what one has in the mind already and this without using any truth learned from experience or from any tradition, as Plato has shown.”
In Meno Plato gives a remarkable demonstration of this. While talking to Meno, Socrates has a young slave come forward and begins to question him while he draws figures on the ground. Socrates does not teach him anything, he merely pushes him to enquire while examining the relations in the figures. The slave ends up himself finding the solution to the problem of the duplication of the square. The procedure of interrogation that is sustained makes the slave literally discover of himself an intelligible relation. The mind draws the idea out of its own depths. Looking at things in this way one may say that all truths that stem from the mind and possess this characteristic are necessary truths. It is not experience that teaches me that the three angles of a triangle add up to 180°, this truth is not the result of having measured thousands of triangles with a compass! A very simple geometrical demonstration from parallel lines is enough to perceive it. What then is the role of experience? Experience only provides examples, particular cases to which the idea is applied. The reverse does not hold. Through accumulating examples and observations one will only establish general truths, not necessary truths. “All these examples that confirm a general truth, however many they may be, do not suffice to establish the universal necessity of this truth: because it does not follow that what has happened will always happen in the same way.” This means that certitude and truth come from the mind itself. Ideas are present in us as potential and experience is the occasion that awakes them. Physics does not progress from mere experience, it would be nothing without the mind’s power to invent and conceptualise. The concept is a production that springs from the mind but is applied to experience.
We must do justice to what the word concept does already indicate: the intellect possesses a capacity of conception with which it weaves a representation of reality. When we speak of a clear and distinct idea it is not in relation to the perception of the corresponding object, but in relation to the precise knowledge we have of it. An idea is clear when it is present and manifest to an attentive mind; an idea is distinct when it is differentiated from all others and is not mixed up with them. The model of the clear idea is the mathematical essence, it is not a perception. Clear and distinct ideas do not come from the senses, because what comes from mere sensation is rather confuse. The idea of heat or cold as applied to for instance the temperature of my bath is quite a vague one, relative to myself, how I feel and so on. 40° is a clearer idea. Heat expresses how at a particular moment I relate to a certain experience without describing with precision a measurable phenomenon that I could objectively relate to the water I bathe in. Also, when the mind thinks with clear and distinct concepts, it tends to think in a rational way.
We call rationalism the doctrine that proposes to show that the idea is essentially a conception of the mind and is not only derived from experience. A concept from this point of view is rather forged by the mind than extracted from experience. The rationalist point of view appears to better account for the nature of the idea and allows to better grasp the theoretical construction that is science.
More generally if we examine carefully the mode of operation of the intellect we will see that it is within its power to construe representations. It is in the nature of the mind to elaborate mental constructions of which the framework is upheld by ideas.
C. The Status of Ideas
If the idea is not a reflection of the real, but a conception of the real, if the idea envelops a certain knowledge and allows a representation, its status seems above all one pertaining to logic. Yet what is an idea from the logical point of view? A concept can be characterised in two ways:
We spoke above of genre and class. From that point of view there is a logical status of ideas.
1. To speak of a genre first of all implies that the concept has an extension or denotation. The concept of man can be applied to a large number of individuals, to the approximately 6 billion people alive on earth. The extension of the concept of man is therefore very large. The extension of Frenchman or American is much smaller. That of a Welshman or a Parisian even more so.
2. The concept is a collection of knowledge. We say that it has a comprehension or a connotation. In the comprehension of the concept of dog we find the whole of qualities and attributes that define this concept. A dog is a vertebrate, mammal, quadruped, omnivore, it is a domestic animal, it is the animal that barks and that can guard the house etc… When I use the concept of dog I must include its whole comprehension. For instance the attributes “able to fly with wings” or “equipped with fins” are not included. These two attributes do enter in the comprehension of the concept of bird and fish respectively.
What do we do when judging? We connect concepts, we establish relations of concepts, we make deductions from properties of concepts.
a. The bitch must have teats because it is a mammal.
b. A magpie must lay eggs because it is a bird.
c. An American is a man who resides in the USA and has the status of an American citizen.
In these everyday judgements, every time we make a statement about reality in a judgement that may be true or false, this one necessarily includes concepts. In a) bitch, teat, mammal; b) magpie, eggs, bird; c) American, man, USA. We cannot make judgements without disposing of concepts. Conversely a concept is above a condensed judgement, a compact form of knowledge which is the product of a judging activity. The idea contains in itself a collection of potential judgements that another judgement will actualise in a series of propositions.
What then is thinking? It is to develop ideas, to establish relations between ideas, it is affirming or denying by means of ideas, in such a manner that a knowledge can develop. To think is for the mind to conceptually represent reality to itself. It is to access the intelligible beyond the sensible offered to us in perception, imagination or souvenirs. This is the meaning most commonly retained from Plato’s theory of Ideas. We think the sensible by means of ideas. Since the sensible world is changing, flowing, since it is a domain in which difference is present everywhere, we use ideas to structure an object-identity in the midst of phenomena. When this particular meteorological phenomenon takes place out there, at this unique moment that is the present one, then I connect it to other similar phenomena already catalogued in the past and I say that it rains outside. "Rain" is a concept that allows me to subsume a collection of similar phenomena. I say that Paul is “mean” by relating his mania of having and saving money to a general category, that of “meanness”. I pretend knowing something about him by making this judgement. Would this mean that language is a sort of mediator between the sensible and the intelligible?
Everyone of us has a great number of ideas about all sorts of things: these are our opinions. When we have an idea, but are not really aware of having it, we have an opinion. When on the contrary the idea is held together with precise reasons that we are conscious of, we say that we have convictions. Thus the idea plays a part as a mental construction for the thinking mind, but this mental construction has or does not have as the case may be a certain truth, that we may or may not possess. It is entirely possible to manipulate ideas without having a clear understanding of what they represent. It is reflection which, turning back upon itself, forces the mind to become aware of its non reflected content, to differentiate ignorance from knowledge. Thinking is a perpetual effort at justification. The clarification of the intellect demands this endless self-justification on the part of the thinking Mind. More generally we can say that any philosophical procedure is this systematic concern with self-justification that Thinking enforces.
The quest for the “origin of ideas” takes us to a mythical interprÉtation of ideas and too far away from the precise awareness of what there is. What is important is not to speculate about the origin of ideas, but above all to become aware of what an idea is and of the role it plays in our life.
It is in the nature of the mind to operate constructions and any mental construction includes ideas. To form ideas is not an operation that would be an appendage to science or to philosophy. All men think using ideas, and this whether he wants to or not, whether these ideas be confuse or clear and distinct. When asking what plays a part in the formation of ideas we must turn our attention to the powers of our own mind.
Nevertheless we have not yet studied a question which remains in abeyance: does the idea have an existence in itself that would be accessible to us as an intuition? Can there be a lucid perception of ideas? What is the relationship between the Idea and the domain pertaining to existence?
dialogue : questions and answers
Home © Philosophy and spirituality, 2004, Serge Carfantan. Translated by Catarinna Lamm