That science justifies a recourse to the ideography is an article of Gottlob Frege published in 1882 in the Zeitschrift für Philosophie und philosophische Kritik. Through this text of only four pages, the Logician and Philosophe of Iéna proposes to show for which reasons a ideographic writing is necessary in abstract sciences.
Utility and insufficiency of the natural language
Frege starts by developing the two following theses:
The first thesis is justified throughout the article: to determine which is the nature of this means, and to justify this means which is the ideography, it is the objective of the article. The second thesis is used as starting point with this justification. But as of the formulation of these theses in the first lines, the problems of Frege show through: if we think with signs, we are also mistaken by using them; which are then the errors which we make and which are the signs such as they can divert us? But, moreover, can we determine the nature of its signs?
- * “abstract sciences need a means of expression to prevent the mistakes in interpretation and the faults of reasoning. ”
- * “We need sensitive signs to think. ”
We need sensitive signs to think
It is, according to Frege, necessary to seek a means of expression which makes it possible to avoid two types of error: mistakes in interpretations, and faults of reasoning. However, these two types of errors are caused by the imperfection of the language, but it is this same language which enables us to conceptualize, by retaining the flow of the significant impressions by signs: by the use of signs, the man seizes concept, of what is common to different things:
“Without the signs, we would rise with difficulty with the conceptual thought. By giving the same sign to different things though similar, the singular thing strictly speaking any more is not indicated but what is common: the concept. And it is by indicating it that possession of the concept is taken; since it cannot be object of intuition, it needs an intuitive representative who expresses it to us. Thus the sensitive one opens it the world from what escapes the directions. ”
The language is thus essential for us, and this, even if we manage to pass to us from the word to think. The sign, such as Frege thinks it, also implies that, without him, we would be impotent from several points of view which are not developed in the article, but to which Frege makes some allusions which can be thus clarified:
- without the signs, we would be only not very free relative with our representations; however, the animal modifying its significant impressions by fleeing them or by seeking them, we would be reduced to useful and the pleasant one, the vermin and the pain;
- it would thus not have there an abstracted thought, which moreover is reinforced by the fact that the sign enables us to conceptualize;
- our actions would be limited so that our hands can work;
- without the signs, the memory would be lacking to us; one can deduce from it that we would not have or little concept of our own identity;
- it would not have there or little interiority: not being able to think by the means of the words, of more strong reason, we could not think without the word.
Limits of the usual language
The invention of the sign thus had deep Conséquence S for the development of humanity. Nevertheless, in spite of this power as an instrument of the thought, the language present of the imperfections which are the source of our errors.
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the usual language is not univocal.
The same word can indeed indicate at the same time a concept and a particular object:
- “the horse is a herbivore”: the horse as a species;
- “This horse”: the horse as a such individual subsumed under a concept.
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the usual language is not governed by logical rules.
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the usual language cannot express in an explicit and simple way all the logic elements of a deduction.
Since such confusions exist in the language, of the Hypothèse S can indeed be introduced without one taking Conscience of it: the usual language never expresses in an explicit way the unit of the assumptions of a series of deductions; and even, if we try to reformulate a reasoning, in the usual language, by expressing all the distinctions and deductions, it proves prolix and well too heavy to handle. Thus the logical reports/ratios remain always tacit. Frege gives the example of Euclide: the demonstration of proposal 19 of the book first of the Éléments does not make it possible to see in an obvious way that this last employs without saying it several not formulated proposals in an explicit way.
Written word and spoken word
After this logical criticism of the usual language, Frege continues by comparing the respective merits of the Mot written and the word spoken taking into consideration their utility to fix with precision and clearness of the Raisonnement S.
The written word is durable: one can, thanks to him, to traverse several times a succession of thoughts in a stable form; however, this quality is not sufficient, for the already evoked reasons: by the written word of the usual Language, the Différence S of direction of a word are not made manifest.
How to obtain precision in our use of the signs?
If we compare the language and the hand, we find this analogy: the Main has very varied uses; however, it is not enough to fill of the tasks which require more the utmost precision. To cure this defect, the men manufactured artificial hands, which complete a work of an impossible precision for a human hand.
From which does this precision come? For Frege, it comes from the rigidity and the indeformability of the parts of the Outil S frabriqués by the Homme. The tool which replaces the hand is thus more precise, but less skilful than the hand. However the spoken language has a similar insufficiency: it is flexible and full with resources, but this versatility excludes that it can be a whole of signs stripped of ambiguity. What it is thus necessary, it is a whole of signs strictly logical, therefore rigid and univocal, which however does not let escape the contents from thought.
Audible sign and visible sign
The first question is then, for Frege, to know if, to this end, in fact the audible Signe S have the advantage, or the visible signs.
Frege distinguishes the advantages from the audible signs:
- productions independent of the external circumstances;
- narrow affinity of the sounds and the facts of Conscience;
- modulations infinite of the voice, adapted to the most subtle variations.
But these advantages are clearly related to the physical and psychic conditions human: being appropriate for example for the expression of the feelings, these reports/ratios of dependence are not appropriate for logic. Frege is opposed to the Psychologisme which would reduce the logical Proposition S to the ways in which we are affected.
Frege distinguishes the advantages from the visible signs:
- delimited well and differentiated: precis and lights;
- lasted and immutability.
The visible sign is thus, according to Frege, similar to the concept: at the beginning of the article, Frege noted indeed that the concept enables us to rise above the current of the impressions and the thoughts. However, the writing also makes it possible it to fix thoughts at the same time by retaining them. The character of fixity of the writing thus makes it possible to concentrate the attention. But, moreover, the provision of signs in a space with two dimensions is also useful to express internal reports, which cannot do the audible sign.
To final, the properties of the writing move away us from run of our representations, and for this reason, these are the same properties which can mitigate the defects of our natural constitution.
The Idéographie appears thus as a Technique by means of which the thought gives itself the greatest possible independence with regard to the significant impressions and of the Grammaire, to manage to express visually, in a stable way and the internal coherence of the reasoning specifies.
Utility of the ideography: its place in the development of sciences
Frege answers an objection which evokes, in comparison with the history of the thought, the problem of the statute of the Logique in the Pensée of Aristote: shouldn't formalization come only once completed science? At Aristote, let us recall that the statute of logic is not known with precision: it is not known if it is about a method of discovery, or of a working of science once this one is completed. But, in the second case, logic is sterile.
Such is not the opinion of Frege: again resorting to an analogy with the Technical , he affirms that science makes it possible to build instruments which in their turn make it possible to develop science. The same will apply to the ideography.
This makes it possible to recapitulate the whole of the article in a draft of theory of the progress of the Connaissance:
- the Man, like Animal, is apparently subjected to the significant impressions: its attention is turned towards outside;
- but, like the animal, it can act on the course of its Représentation S (of manner basic: by the escape, or seeks it certain impressions);
- by the hand and the tools, and by the voice, the man has a greater independence with regard to its representations than the other animals;
- thanks to signs, the man gives itself the presence of things absences: the sign makes it possible to rise with the conceptual thought;
- however, the usual language is not governed by logical, but grammatical laws: it is thus a source of errors;
- it is thus necessary to invent new a whole of signs which make it possible to reach with an expression of the univocal thought and without ambiguity.
The article thus holds its unit of this design of the development of the science, evoked during a discussion of the scientific interest of the Idéographie, and this design justifies the title of the article: the development of the science, which asks for more detail and of clearness, requires the invention of it.
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