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| Square # | Venn, Karnaugh region | x | y | z | (~ | (y | & | z) | & | (x | → | y)) | → | (~ | (x | & | z)) | ||
| 0 | x'y'z' | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | ||
| 1 | x'y'z | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | ||
| 2 | x'yz' | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | ||
| 3 | x'yz | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | ||
| 4 | xy'z' | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | ||
| 5 | xy'z | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | ||
| 6 | xyz' | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | ||
| 7 | xyz | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 |
PREFACE: THE Lectures comprised in the present Volume form the second and concluding portion of the Biennial Course on Metaphysics and Logic, which was commenced by Sir William Hamilton on his election to the Professorial Chair in 1836, and repeated, with but slight alterations, till his decease in 1856. The Appendix contains various papers, composed for the most part during this period, which, though portions of their contents were publicly taught at least as early as 1840, were only to a very small extent incorporated into the text of the Lectures. The Lectures on Logic, like those on Metaphysics, were chiefly composed during. the session in which they were first delivered (1837-8); and the statements made in the Preface to the previous volume, as regards the circumstances and manner of their composition, are equally applicable to the present course. In this, as in the preceding series, the Author has largely availed himself of the labors of previous writers, many of whom are but little known in this country. To the works of the German logicians of the present century, particularly to those of Krug and Esser, these Lectures are under special obligations.
In the compilation of the Appendix, some responsibility rests with the Editors; and a few words of explanation may be necessary as regards the manner in which they have attempted to perform this portion of their task. In publishing the papers of. a deceased writer, composed at various intervals during a long period of years, and treating of difficult and controverted questions, there are two opposite dangers to be guarded against. On the one hand, there is the danger of compromising the Author's reputation by the publication of documents which his maturer judgment might not have sanctioned; and, on the other hand, there is the danger of committing an opposite injury to him and to the public, by withholding writings of interest and value. Had Sir William Hamilton, at any period of his life, published a systematic treatise on . Logic, or had his projected New Analytic of Logical Forms been left in a state at all approaching to completeness, the Editors might probably have obtained a criterion by which to distinguish between those speculations which would have received the final imprimatur of their Author, and those which would not. In the absence of any such criterion, they have thought it better to run the risk of giving too much than too little; - to publish whatever appeared to have any philosophical or historical interest, without being influenced by its coincidence with their own opinions, or by its coherence with other parts of the Author's writings. It is possible that, among the papers thus published, may be found some which are to be considered rather as experimental exercises than as approved results; but no papers have been intentionally omitted, except such as were either too fragmentary to be intelligible; or manifestly imperfect sketches of what has been published here or elsewhere in a more matured form.
The Notes, in this as in the previous volume, are divided into three classes. Those printed from the manuscript of the Lectures appear without any distinctive mark; those supplied from the Author's Commonplace- Book and other papers are enclosed within square brackets without signature; and those added by the Editors are marked by the signature" ED." These last, as in the Lectures on Metaphysics, are chiefly confined to occasional explanations of the text and verifications of references. In conclusion, the Editors desire to express their acknowledgments to those friends from whom they have received assistance in tracing the numerous quotations and allusions scattered. through this and the preceding volume.
In particular, their thanks are due to Hubert Hamilton, Esq., whose researches among his father's books and papers have supplied them with many valuable materials; and to H. W. Chandler, Esq., Fellow of Pembroke College, Oxford, who has aided them from the resources of a philosophical learning cognate in many respects to that of Sir William Hamilton himself.∃∀ℵ