Fundamental Philosophy, Vol. 1 (of 2)

by Jaime Luciano Balmes

In every force there are three things to be considered: the direction, point of application, and intensity. The direction is represented by a line, and the point of application by a point in space. The intensity is represented only in the effect which it can produce, and this is expressed by a line, the length of which expresses the intensity of the force. The effect of the intensity which is represented by a line includes the time also; for the measure of a motion cannot be determined until we know its velocity, which is merely the relation of space to time. Therefore, although the idea of time is combined with that of extension, the result is expressed by lines, that is, by extension.

19. There is another circumstance still which shows the fruitfulness of the idea of extension. It is that in the expression of the laws of nature, it reaches cases which are beyond the idea of number. If we suppose two equal rectangular forces, AB and AC, acting on the point A, the resultant will be AR. Now, if we consider AR to be the hypotheneuse of a right-angled triangle, AR² = AB² + AC², extracting the square root AR = √(AB² + AC²). If we suppose each of the component forces equal to 1, AR = √(1² + 1²) = √2, a value which can neither be expressed in whole numbers nor in fractions, but which is represented by the hypotheneuse.

20. In the physical sciences, such words as force, cause, agent, etc., are frequently used, but the ideas which these terms express are a part of science only inasmuch as they are represented by effects. This is not because true philosophy confounds the cause with the effect, but as physical science regards only the phenomenon in all that relates to the cause, it limits itself to the abstract idea of causality, which presents nothing determinate, and consequently is not the object of its scientific labors. The system of universal attraction has immortalized the name of Newton, and he begins by confessing his ignorance of the cause of the effect which he explains. When we go beyond the phenomena and the calculations to which they give rise, we enter the field of metaphysics.

21. The natural sciences consider certain qualities of bodies which have no relation to extension, as, for example, heat and light, and this might seem to be a refutation of what we have said of extension. Still this objection disappears when we examine in what manner science takes note of these qualities, and instead of overthrowing our thesis, the result will strengthen, extend, and explain it.

Heat is not measured by the sensation which it produces in us. If we enter a room where the temperature is very high, we experience a strong sensation of heat, which gradually grows weaker, while the temperature remains the same. If we reach our hand to a friend we experience a sensation of heat or cold, in proportion as his hand is warmer or colder than our own.

Heat and cold are measured, not in themselves, nor in relation to our sensations, but in the effect which they produce. These effects are included in the modification of extension; for the thermometer marks the temperature by a greater or less elevation of the mercury in a line. Its degrees are expressed by parts of a line, on which they are marked.

I know that what is measured is distinct from extension; but, its measurement is only possible by relation to extension, and by attending to effects which are modifications of extension. Thus, the temperature at which water boils is 212°, and this is discovered by the motion of the water, and has relation to extension. So, also, the rarefaction and condensation of bodies are modifications of extension, since these states consist in the occupation of greater or less space, or in the increase or diminution of their dimensions.

22. All that science teaches us of light and colors relates to the different directions and combinations of the rays of light. Our observation goes no farther than sensation. We know that we can combine the rays in different manners, and direct them, so as to modify our sensation, but this is nothing more than the scientific knowledge of extension in the medium which we make use of, and of the sensation experienced in consequence. All beyond this is entirely unknown.

23. We may say the same of all other sensations, that of touch included. What is that quality of bodies which we call hardness? the resistance which we encounter when we touch them? But abstracting sensation, which only produces the consciousness of itself, what do we find? Impenetrability. And what do we understand by impenetrability? The impossibility of two bodies occupying the same space at the same time. Here, then, we meet with extension. If, by hardness, we mean the cohesion of molecules, in what does cohesion consist? In the juxtaposition of parts in such manner that they cannot, without difficulty, be separated. But, to be separated, is to be made to occupy a place different from that which was before occupied. Here, too, we find the idea of extension.