§ 4. The principle of Identity is usually written symbolically thus: _A is A; not-A is not-A_. It assumes that there is something that may be represented by a term; and it requires that, in any discussion, _every relevant term, once used in a definite sense, shall keep that meaning throughout_. Socrates in his father's workshop, at the battle of Delium, and in prison, is assumed to be the same man denotable by the same name; and similarly, 'elephant,' or 'justice,' or 'fairy,' in the same context, is to be understood of the same thing under the same _suppositio_. But, further, it is assumed that of a given term another term may be predicated again and again in the same sense under the same conditions; that is, we may speak of the identity of meaning in a proposition as well as in a term. To symbolise this we ought to alter the usual formula for Identity and write it thus: _If B is A, B is A; if B is not-A, B is not-A_. If Socrates is wise, he is wise; if fairies frequent the moonlight, they do; if Justice is not of this world, it is not. _Whatever affirmation or denial we make concerning any subject, we are bound to adhere to it for the purposes of the current argument or investigation._ Of course, if our assertion turns out to be false, we must not adhere to it; but then we must repudiate all that we formerly deduced from it. Again, _whatever is true or false in one form of words is true or false in any other_: this is undeniable, for the important thing is identity of meaning; but in Formal Logic it is not very convenient. If Socrates is wise, is it an identity to say 'Therefore the master of Plato is wise'; or, further that he 'takes enlightened views of life'? If _Every man is fallible_, is it an identical proposition that _Every man is liable to error_? It seems pedantic to demand a separate proposition that _Fallible is liable to error_. But, on the other hand, the insidious substitution of one term for another speciously identical, is a chief occasion of fallacy. How if we go on to argue: therefore, _Every man is apt to blunder, prone to confusion of thought, inured to self-contradiction_? Practically, the substitution of identities must be left to candour and good-sense; and may they increase among us. Formal Logic is, no doubt, safest with symbols; should, perhaps, content itself with A and B; or, at least, hardly venture beyond Y and Z.