One is, that the Proposition "some x are y" is to be interpreted, neither as "Some x _exist_ and are y", nor yet as "If there _were_ any x in existence, some of them _would_ be y", but merely as "Some x _can be_ y; i.e. the Attributes x and y are _compatible_". On _this_ theory, there would be nothing offensive in my telling my friend Jones "Some of your brothers are swindlers"; since, if he indignantly retorted "What do you _mean_ by such insulting language, you scoundrel?", I should calmly reply "I merely mean that the thing is _conceivable_----that some of your brothers _might possibly_ be swindlers". But it may well be doubted whether such an explanation would _entirely_ appease the wrath of Jones! Another view is, that the Proposition "All x are y" _sometimes_ implies the actual _existence_ of x, and _sometimes_ does _not_ imply it; and that we cannot tell, without having it in _concrete_ form, _which_ interpretation we are to give to it. _This_ view is, I think, strongly supported by common usage; and it will be fully discussed in Part II: but the difficulties, which it introduces, seem to me too formidable to be even alluded to in Part I, which I am trying to make, as far as possible, easily intelligible to mere _beginners_. (C) [See p. 173, § 4.] The three Conclusions are "No conceited child of mine is greedy"; "None of my boys could solve this problem"; "Some unlearned boys are not choristers." pg197 INDEX. § 1. _Tables._ I. Biliteral Diagram. Attributes of Classes, and Compartments, or Cells, assigned to them 25 II. do. Representation of Uniliteral Propositions of Existence 34 III. do. Representation of Biliteral Propositions of Existence and of Relation 35 IV. Triliteral Diagram. Attributes of Classes, and Compartments, or Cells, assigned to them 42 V. do. Representation of Particular and Universal Negative Propositions, of Existence and of Relation, in terms of x and m 46 VI. do. do., in terms of y and m 47 VII. do. Representation of Universal Affirmative Propositions of Relation, in terms of x and m 48 VIII. do. do. in terms of y and m 49 IX. Method of Subscripts. Formulæ and Rules for Syllogisms 78 § 2. _Words &c. explained._ 'Abstract' Proposition 59 'Adjuncts' 1 'Affirmative' Proposition 10 'Attributes' 1 'Biliteral' Diagram 22 " Proposition 27