In the Appendix I have given a new version of the Problem of the "Five Liars." My object, in doing so, is to escape the subtle and mysterious difficulties which beset all attempts at regarding a Proposition as being its own Subject, or a Set of Propositions as being Subjects for one another. It is certainly, a most bewildering and unsatisfactory theory: one cannot help feeling that there is a great lack of _substance_ in all this shadowy host----that, as the procession of phantoms glides before us, there is not _one_ that we can pounce upon, and say "_Here_ is a Proposition that _must_ be either true or false!"----that it is but a Barmecide Feast, to which we have been bidden----and that its prototype is to be found in that mythical island, whose inhabitants "earned a precarious living by taking in each others' washing"! By simply translating "telling 2 Truths" into "taking _both_ of 2 condiments (salt and mustard)," "telling 2 Lies" into "taking _neither_ of them" and "telling a Truth and a Lie (order not specified)" into "taking only _one_ condiment (it is not specified _which_)," I have escaped all those metaphysical puzzles, and have produced a Problem which, when translated into a Set of symbolized Premisses, furnishes the very same _Data_ as were furnished by the Problem of the "Five Liars." pg-x The coined words, introduced in previous editions, such as "Eliminands" and "Retinends", perhaps hardly need any apology: they were indispensable to my system: but the new plural, here used for the first time, viz. "Soriteses", will, I fear, be condemned as "bad English", unless I say a word in its defence. We have _three_ singular nouns, in English, of plural _form_, "series", "species", and "Sorites": in all three, the awkwardness, of using the same word for both singular and plural, must often have been felt: this has been remedied, in the case of "series" by coining the plural "serieses", which has already found its way into the dictionaries: so I am no rash innovator, but am merely "following suit", in using the new plural "Soriteses". In conclusion, let me point out that even those, who are obliged to study _Formal_ Logic, with a view to being able to answer Examination-Papers in that subject, will find the study of _Symbolic_ Logic most helpful for this purpose, in throwing light upon many of the obscurities with which Formal Logic abounds, and in furnishing a delightfully easy method of _testing_ the results arrived at by the cumbrous processes which Formal Logic enforces upon its votaries.