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Let us sto

p here a moment and glance over the journey we have just made. We will note two limits within which almost all of the certain knowledge that is accorded to our natural intelligence is concentrated, so to speak. [34] One of those limits, our point of departure, is the idea of ourselves, which leads to that of the Omnipotent Being, and of our principal duties. The other is that part of mathematics whose object is the general properties of bodies, of extension and magnitude. Between these two boundaries is an immense gap where the Supreme Intelligence seems to have tried to tantalize the human curiosity, as much by the innumerable clouds it has spread there as by the rays of light that seem to break out at intervals to attract us. One can compare the universe to certain works of a sublime obscurity whose authors occasionally bend down within reach of their reader, seeking to persuade him that he understands nearly all. We are indeed fortunate if we do not lose the true route when we enter this labyrinth! Otherwise the flashes of light which should direct us along the way would often serve only to lead us further from it. The limited quantity of certain knowledge upon which we can rely, relegated (if one can express oneself this way) to the two extremities of space to which we refer, is far indeed from being sufficient to satisfy all our needs. The nature of man, the study of which is so necessary and so highly recommended by Socrates, is an impenetrable mystery for man himself when he is enlightened by reason alone; and the greatest geniuses, after considerable reflection upon this most important matter, too often succeed merely in knowing a little less about it than the rest of men. The same may be said of our existence, present and future, of the essence of the Being to whom we owe it, and of the kind of worship he requires of us. Thus, nothing is more necessary than a revealed Religion, which may instruct us concerning so many diverse objects. Designed to serve as a supplement to natural knowledge, it shows us part of what was hidden, but it restricts itself to the things which are absolutely necessary for us to know. The rest is closed for us and apparently will be forever. A few truths to be believed, a small number of precepts to be practiced: such are the essentials to which revealed Religion is reduced. Nevertheless, thanks to the enlightenment it has communicated to the world, the common people themselves are more solidly grounded and confident on a large number of questions of interest than the sects  [35] of the philosophers have been.

The advantage men

found in enlarging the sphere of their ideas, whether by their own efforts or by the aid of their fellows, made them think that it would be useful to reduce to an art the very manner of acquiring information and of reciprocally communicating their own ideas. This art was found and named Logic. It teaches how to arrange ideas in the most natural order, how to link them together in the most direct sequence, how to break up those which include too large a number of simple ideas, how to view ideas in all their facets, and finally how to present them to others in a form that makes them easy to grasp. This is what constitutes this science of reasoning, which is rightly considered the key to all our knowledge. However, it should not be thought that it [the formal discipline of Logic] belongs among the first in the order of discovery. The art of reasoning is a gift which Nature bestows of her own accord upon men of intelligence, and it can be said that the books which treat this subject are hardly useful except to those who can get along without them. People reasoned validly long before Logic, reduced to principles, taught how to recognize false reasonings, and sometimes even how to cloak them in a subtle and deceiving form. [38]

Too much communication can sometimes benumb the mind and prejudice the efforts of which it is capable. If one observes the prodigies of some of those born blind, or deaf and mute, one will see what the faculties of the mind can perform if they are lively and called into action by difficulties which must be overcome.

The science of communication of ideas is not confined to putting order in ideas themselves. In addition it should teach how to express each idea in the clearest way possible, and consequently how to perfect the signs that are designed to convey it; and indeed this is what men have gradually done.

The general system of the sciences and the arts is a sort of labyrinth, a tortuous road which the intellect enters without quite knowing what direction to take. Impelled, first of all, by its needs and by those of the body to which it is united, the intelligence studies the first objects that present themselves to it. It delves as far as it can into the knowledge of these objects, soon meets difficulties that obstruct it, and whether through hope or even through despair of surmounting them, plunges on to a new route; now it retraces its footsteps, sometimes crosses the first barriers only to meet new ones; and passing rapidly from one object to another, it carries through a sequence of operations on each of them at different intervals, as if by jumps. The discontinuity of these operations is a necessary effect of the very generation of ideas. However philosophic this disorder may be on the part of the soul, [57] an encyclopedic tree which attempted to portray it would be disfigured, indeed utterly destroyed.

It is only after having considered their particular and palpable properties that we envisaged their general and common properties and created Metaphysics and Geometry by intellectual abstraction. Only after the long usage of the first signs have we perfected the art of these signs to the point of making a science of them. And it is only after a long sequence of operations on the objects of our ideas that, through reflection, we have at length given rules to these operations themselves.

nature of the different minds that determines which route is chosen

Natura non facit saltum

learning as a lasting changed state (emotional, mental, physiological (i.e. skills)) brought about as a result of experiences and interactions with content or other people.

Objectivism (similar to behaviorism) states that reality is external and is objective, and knowledge is gained through experiences. Pragmatism (similar to cognitivism) states that reality is interpreted, and knowledge is negotiated through experience and thinking. Interpretivism (similar to constructivism) states that reality is internal, and knowledge is constructed.