50. The limits of our mind prevent it from comparing many objects at one time, and from easily recollecting the comparisons it has already made. To assist the memory, and the perception of these relations, we make use of signs. When we pass beyond three or four, our power of simultaneous perception fails, and we divide the object into groups which serve us as new units, and are expressed by signs. Ten is clearly the general group in the decimal system; but before we reach the number ten we have already formed other subalternate groups; since to count ten, we do not say one and one and one, etc., but one and one, two; two and one, three; three and one, four, etc. Each unit added forms a new group, which, in its turn, serves to form another. With two, we form three; with three, four, and so on. This affords an idea of the relation of numbers with their signs; but, as this matter is too important to be here dismissed, we will further develop it in the following chapters. CHAPTER VI. CONNECTION OF THE IDEAS OF NUMBER WITH THEIR SIGNS. 51. The connection of ideas and impressions, in a sign, is a most wonderful intellectual phenomenon, and at the same time of the greatest help to our mind. Were it not for this connection, we could scarcely reflect at all upon objects somewhat complex, and above all our memory would be exceedingly limited.[26] [26] See L. IV., C. XXVIII. and XXIX. 52. Condillac made some excellent remarks upon this matter: in his opinion, we cannot, unaided by signs, count more than three or four. If, indeed, we had no sign but that of unity, we could readily count two, saying one and one. Having only two ideas, we could easily satisfy ourselves that we had twice repeated one. But it is not so easy to be certain of the exactness of our repetition when we have to count three, by saying one and one and one; still, this is not difficult. It is more so to count four, and next to impossible to go as far as ten. If we undertake to abstract the signs, we shall find that it is impossible to form an idea of ten by repeating one; and that it will be alike impossible, if we employ no sign, to make sure that we have repeated one exactly ten times.