In physical reality one cause does not produce a given effect, but a multitude of distinct causes contribute to produce it, without our having any me… - Henri Poincaré

To doubt everything and to believe everything are two equally convenient solutions; each saves us from thinking.

Mathematicians study not objects, but relations between objects; the replacement of these objects by others is therefore indifferent to them, provided the relations do not change. The matter is for them unimportant, the form alone interests them.
Without recalling this, it would scarcely be comprehensible that Dedekind should designate by the name incommensurable number a mere symbol, that is to say, something very different from the ordinary idea of quantity, which should be measurable and almost tangible.

The continuum so conceived is only a collection of individuals ranged in a certain order, infinite to one another, it is true, but exterior to one another. This is not the ordinary conception, wherein is supposed between the elements of the continuum a sort of intimate bond which makes of them a whole, where the point does not exist before the line, but the line before the point. Of the celebrated formula “the continuum is unity in multiplicity”, only the multiplicity remains, the unity has disappeared. The analysts are none the less right in defining the continuum as they do, for they always reason on just this as soon as they pique themselves on their rigor. But this is enough to apprise us that the veritable mathematical continuum is a very different thing from that of the physicists and the metaphysicians.