In order that we may argue and infer truly we must treat our logical symbols according to the fundamental laws of Identity and Difference. But in thus using our symbols we shall frequently meet with combinations of which the meaning will not at first sight be apparent. If in one case we learn that an object is “yellow and round,” and in another case that it is “round and yellow,” there arises the question whether these two descriptions are identical in meaning or not. Again, if we proved that an object was “round round,” the meaning of such an expression would be open to doubt. Accordingly we must take notice, before proceeding further, of certain special laws which govern the combination of logical terms. In the first place the combination of a logical term with itself is without effect, just as the repetition of a statement does not alter the meaning of the statement; “a round round object” is simply “a round object.” What is yellow yellow is merely yellow; metallic metals cannot differ from metals, nor circular circles from circles. In our symbolic language we may similarly hold that AA is identical with A, or A = AA = AAA = &c. The late Professor Boole is the only logician in modern times who has drawn attention to this remarkable property of logical terms;[46] but in place of the name which he gave to the law, I have proposed to call it The Law of Simplicity.[47] Its high importance will only become apparent when we attempt to determine the relations of logical and mathematical science. Two symbols of quantity, and only two, seem to obey this law; we may say that 1 × 1 = 1, and 0 × 0 = 0 (taking 0 to mean absolute zero or 1 – 1); there is apparently no other number which combined with itself gives an unchanged result. I shall point out, however, in the chapter upon Number, that in reality all numerical symbols obey this logical principle. [46] *Mathematical Analysis of Logic*, Cambridge, 1847, p. 17. *An Investigation of the Laws of Thought*, London, 1854, p. 31. [47] *Pure Logic*, p. 15. It is curious that this Law of Simplicity, though almost unnoticed in modern times, was known to Boëthius, who makes a singular remark in his treatise *De Trinitate et Unitate Dei* (p. 959). He says: “If I should say sun, sun, sun, I should not have made three suns, but I should have named one sun so many times.”[48] Ancient discussions about the doctrine of the Trinity drew more attention to subtle questions concerning the nature of unity and plurality than has ever since been given to them. [48] “Velut si dicam, Sol, Sol, Sol, non tres soles effecerim, sed uno toties prædicaverim.”