of thought, mathematical in its form." (with more explanation about this "dichotomy" comes about cf Boole 1854:49ff) Boole defines the notion "domain (universe) of discourse" This notion is found throughout Boole's "Laws of Thought" e.g. 1854:28, where the symbol "1" (the integer 1) is used to represent "Universe" and "0" to represent "Nothing", and in far more detail later (pages 42ff): " Now, whatever may be the extent of the field within which all the objects of our discourse are found, that field may properly be termed the universe of discourse. ... Furthermore, this universe of discourse is in the strictest sense the ultimate subject of the discourse." In his chapter "The Predicate Calculus" Kleene observes that the specification of the "domain" of discourse is "not a trivial assumption, since it is not always clearly satisfied in ordinary discourse ... in mathematics likewise, logic can become pretty slippery when no D [domain] has been specified explicitly or implicitly, or the specification of a D [domain] is too vague (Kleene 1967:84). Hamilton (1837–38 lectures on Logic, published 1860): a 4th "Law of Reason and Consequent" As noted above, Hamilton specifies four laws—the three traditional plus the fourth "Law of Reason and Consequent"—as follows: "XIII. The Fundamental Laws of Thought, or the conditions of the thinkable, as commonly received, are four: – 1. The Law of Identity; 2. The Law of Contradiction; 3. The Law of Exclusion or of Excluded Middle; and, 4. The Law of Reason and Consequent, or of Sufficient Reason." Rationale: "Logic is the science of the Laws of Thought as Thought" Hamilton opines that thought comes in two forms: "necessary" and "contingent" (Hamilton 1860:17). With regards the "necessary" form he defines its study as "logic": "Logic is the science of the necessary forms of thought" (Hamilton 1860:17). To define "necessary" he asserts that it implies the following four "qualities": (1) "determined or necessitated by the nature of the thinking subject itself ... it is subjectively, not objectively, determined; (2) "original and not acquired; (3) "universal; that is, it cannot be that it necessitates on some occasions, and does not necessitate on others. (4) "it must be a law; for a law is that which applies to all cases without exception, and from which a deviation is ever, and everywhere, impossible, or, at least, unallowed. ... This last condition, likewise, enables us to give the most explicit enunciation of