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.George Boole. > 1854/2003.
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Significant symbols always imply a context within which it has significance, a universe of discourse. The universe of discourse is constituted by a group of individuals carrying on a common social process, within which these symbols have common meaning within that group, regardless of whether the members are making the gestures or responding to them.
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Facsimile of 1854 edition, with an introduction by J. Corcoran. Buffalo: Prometheus Books (2003). Reviewed by James van Evra in Philosophy in Review 24 (2004): 167–169. One statement of his principle is in the sentence immediately following his definition of universe of discourse, which is his first use of the expression 'universe of discourse' and probably the first in the history of the English language.
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Due to the study of ratios in physics and economics where the quadrant is the universe of discourse, its points are said to be located by hyperbolic coordinates.
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The principle of nonvacuous contrast is a logical or methodological principle which requires that a genuine predicate never refer to everything, or to nothing, within its universe of discourse.
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Peirce (1909), A Letter to William James, The Essential Peirce, 2:492–502. Fictional object, 498. Object as universe of discourse, 492. See "Dynamical Object" at Commens Digital Companion to C.S. Peirce.
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REs carry a presupposition of the existence of the referent(s), in some universe of discourse, including fictional universes. There are many other technical issues surrounding the nature of reference. Some of these are discussed from the perspective of linguistics in Lyons (1977, vol. I: chapter 7); Cann (1993: chapters 9 and 10); Saeed (1997: chapters 2, 7, 11).
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For Boole, the essential first step in the process of conceiving of a proposition preliminary to making a judgement of its truth or falsity – or even using it in a deduction, however hypothetically – was to conceive of the universe of discourse. See Boole 1854/2003, xxi, 27, 42, 43.George Boole. 1854/2003. The Laws of Thought.
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An ontological commitment refers to a relation between a language and certain objects postulated to be extant by that language. The 'existence' referred to need not be 'real', but exist only in a universe of discourse. As an example, legal systems use vocabulary referring to 'legal persons' that are collective entities that have rights. One says the legal doctrine has an ontological commitment to non-singular individuals.
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Also evolving from NIAM is "Fully Communication Oriented Information Modeling" FCO-IM (1992). It distinguishes itself from traditional ORM in that it takes a strict communication-oriented perspective. Rather than attempting to model the domain and its essential concepts, it models the communication in this domain (universe of discourse). Another important difference is that it does this on instance level, deriving type level and object/fact level during analysis.
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The ontology of GST is identical to that of ZFC, and hence is thoroughly canonical. GST features a single primitive ontological notion, that of set, and a single ontological assumption, namely that all individuals in the universe of discourse (hence all mathematical objects) are sets. There is a single primitive binary relation, set membership; that set a is a member of set b is written a ∈ b (usually read "a is an element of b").
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In general, truth requires a proper fit of elements within the whole system. Very often, though, coherence is taken to imply something more than simple formal coherence. For example, the coherence of the underlying set of concepts is considered to be a critical factor in judging validity. In other words, the set of base concepts in a universe of discourse must form an intelligible paradigm before many theorists consider that the coherence theory of truth is applicable.
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The plural form "houses", however, does have cumulative reference. If two (groups of) entities are both "houses", then their combination will still be "houses". Cumulativity has proven relevant to the linguistic treatment of the mass/count distinction and for the characterization of grammatical telicity. Formally, a cumulativity predicate CUM can be defined as follows, where capital X is a variable over sets, U is the universe of discourse, p is a mereological part structure on U, and \oplus_p is the mereological sum operation.
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All of those are special or partial objects. The object most accurately is the universe of discourse to which the partial or special object belongs. For instance, a perturbation of Pluto's orbit is a sign about Pluto but ultimately not only about Pluto. An object either (i) is immediate to a sign and is the object as represented in the sign or (ii) is a dynamic object, the object as it really is, on which the immediate object is founded "as on bedrock".
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The (restricted) "first-order predicate calculus" is the "system of logic" that adds to the propositional logic (cf Post, above) the notion of "subject-predicate" i.e. the subject x is drawn from a domain (universe) of discourse and the predicate is a logical function f(x): x as subject and f(x) as predicate (Kleene 1967:74). Although Gödel's proof involves the same notion of "completeness" as does the proof of Post, Gödel's proof is far more difficult; what follows is a discussion of the axiom set.
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The distinguishing feature of FCO-IM is that it models the communication about a certain Universe of Discourse (UoD) completely and exclusively, i.e.: it does not model the UoD itself, but rather the facts users exchange when they communicate about the UoD. FCO-IM is therefore a member of the family of information modeling techniques known as fact-oriented modeling (FOM), as are Object-Role Modeling (ORM), predicator set model (PSM) and natural language information analysis method (NIAM). Fact- oriented modeling is sometimes also indicated as fact-based modeling.
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It is argued that the unstructured interview can sometimes be more valid than the highly structured interview. According to Gorden, more valid responses may be created by letting the respondent follow what he calls "the natural paths of free association". "The universe of discourse" varies from respondent to respondent so that the interviewer must change the question wording to meet the understanding of each individual participant. Another situation where the unstructured interview is said to be more valid than the structured interview is where the respondent is experiencing memory failure.
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Leibniz enunciated the principal properties of what we now call conjunction, disjunction, negation, identity, set inclusion, and the empty set. The principles of Leibniz's logic and, arguably, of his whole philosophy, reduce to two: # All our ideas are compounded from a very small number of simple ideas, which form the alphabet of human thought. # Complex ideas proceed from these simple ideas by a uniform and symmetrical combination, analogous to arithmetical multiplication. The formal logic that emerged early in the 20th century also requires, at minimum, unary negation and quantified variables ranging over some universe of discourse.
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Different models of the life cycle of content may have important differences, not least in the specific meaning attached to the names of terms they employ. FRBR, indecs and CRM were each informed by different functional requirements, and so evolved different mechanisms for dealing with the issues that seemed most important to them. Each is a particular view on the "universe of discourse" of resources and relationships: there are many valid views. Broadly, they are compatible, and effective integration of metadata from schemes based on them should be achievable, but they must be handled with care.
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Systematics is the name given by John Godolphin Bennett (1897–1974) to a branch of systems science that he developed in the mid-twentieth century. Also referred to as the theory of Multi-Term Systems or Bennettian Systematics, it focuses on types, levels, and degrees of complexity in systems, the qualities emergent at these levels, and the ability to represent and practically deal with ("understand") complexity using abstract models. Thus to understand the notions of sameness and difference requires a system or universe of discourse with a minimum of two terms or elements. To understand the concept of relatedness requires three, and so on.
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The letters that are created by writing are physical objects that can be destroyed by various means: these are letter TOKENS or letter INSCRIPTIONS. The 26 letters of the alphabet are letter TYPES or letter FORMS. Peirce's type–token distinction, also applies to words, sentences, paragraphs, and so on: to anything in a universe of discourse of character-string theory, or concatenation theory. There is only one word type spelled el-ee-tee-tee-ee-ar,Using a variant of Alfred Tarski's structural-descriptive naming found in John Corcoran, Schemata: the Concept of Schema in the History of Logic, Bulletin of Symbolic Logic, vol.
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LADD-FRANKLIN proposes to call them respectively the principle of exclusion and the principle of exhaustion, inasmuch as, according to the first, two contradictory terms are exclusive (the one of the other); and, according to the second, they are exhaustive (of the universe of discourse)." (italics added for emphasis) In Stephen Kleene's discussion of cardinal numbers, in Introduction to Metamathematics (1952), he uses the term "mutually exclusive" together with "exhaustive": :"Hence, for any two cardinals M and N, the three relationships M < N, M = N and M > N are 'mutually exclusive', i.e. not more than one of them can hold. ¶ It does not appear till an advanced stage of the theory . . .
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The album was re-released on March 21, 2006 as a CD/DVD with expanded Grammy-nominated artwork, two hours of extra footage, and "ShaunLuu" as bonus track which was also featured on the Masters of Horror soundtrack. This track was originally set to be 7 minutes long, but had to be cut short for the soundtrack. On the re-release, on a CD player, if rewind is held down until the display reads -2:20, there is a hidden instrumental song. Music videos were filmed for the songs "Bayonetwork: Vultures in Vivid Color", "Liarsenic: Creating a Universe of Discourse" and "Absentimental: Street Clam".
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Usually, an object in question, such as Hamlet or the planet Neptune, is a special or partial object. A sign's total object is the object's universe of discourse, the totality of things in that world to which one attributes the object. An interpretant is either (1) immediate to a sign, for example a word's usual meaning, a kind of interpretive quality or possibility present in the sign, or (2) dyanamic, an actual interpretant, for example a state of agitation, or (3) final or normal, a question's true settlement, which would be reached if thought or inquiry were pushed far enough, a kind of norm or ideal end with which any actual interpretant may, at most, coincide.
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Zermelo–Fraenkel set theory is intended to formalize a single primitive notion, that of a hereditary well-founded set, so that all entities in the universe of discourse are such sets. Thus the axioms of Zermelo–Fraenkel set theory refer only to pure sets and prevent its models from containing urelements (elements of sets that are not themselves sets). Furthermore, proper classes (collections of mathematical objects defined by a property shared by their members where the collections are too big to be sets) can only be treated indirectly. Specifically, Zermelo–Fraenkel set theory does not allow for the existence of a universal set (a set containing all sets) nor for unrestricted comprehension, thereby avoiding Russell's paradox.
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Weizenbaum originally wrote ELIZA in MAD-Slip for the IBM 7094, as a program to make natural-language conversation possible with a computer. To accomplish this, Weizenbaum identified five "fundamental technical problems" for ELIZA to overcome: the identification of critical words, the discovery of a minimal context, the choice of appropriate transformations, the generation of responses appropriate to the transformation or in the absence of critical words and the provision of an ending capacity for ELIZA scripts. Weizenbaum solved these problems in his ELIZA program and made ELIZA such that it had no built-in contextual framework or universe of discourse. However, this required ELIZA to have a script of instructions on how to respond to inputs from users.
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The text leaps from section ✸14 directly to the foundational sections ✸20 GENERAL THEORY OF CLASSES and ✸21 GENERAL THEORY OF RELATIONS. "Relations" are what is known in contemporary set theory as sets of ordered pairs. Sections ✸20 and ✸22 introduce many of the symbols still in contemporary usage. These include the symbols "ε", "⊂", "∩", "∪", "–", "Λ", and "V": "ε" signifies "is an element of" (PM 1962:188); "⊂" (✸22.01) signifies "is contained in", "is a subset of"; "∩" (✸22.02) signifies the intersection (logical product) of classes (sets); "∪" (✸22.03) signifies the union (logical sum) of classes (sets); "–" (✸22.03) signifies negation of a class (set); "Λ" signifies the null class; and "V" signifies the universal class or universe of discourse.
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In a formal system a symbol may be used as a token in formal operations. The set of formal symbols in a formal language is referred to as an alphabet (hence each symbol may be referred to as a "letter")John Hopcroft, Rajeev Motwani and Jeffrey Ullman, Introduction to Automata Theory, Languages, and Computation, 2000 A formal symbol as used in first-order logic may be a variable (member from a universe of discourse), a constant, a function (mapping to another member of universe) or a predicate (mapping to T/F). Formal symbols are usually thought of as purely syntactic structures, composed into larger structures using a formal grammar, though sometimes they may be associated with an interpretation or model (a formal semantics).
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Despite the fact that we lack background knowledge to indicate that there are dramatically fewer men than short people, we still find ourselves inclined to reject the conclusion. Hintikka's example is: "... a generalization like 'no material bodies are infinitely divisible' seems to be completely unaffected by questions concerning immaterial entities, independently of what one thinks of the relative frequencies of material and immaterial entities in one's universe of discourse." His solution is to introduce an order into the set of predicates. When the logical system is equipped with this order, it is possible to restrict the scope of a generalization such as "All ravens are black" so that it applies to ravens only and not to non-black things, since the order privileges ravens over non- black things.
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The restriction is that the generalization "for all" applies only to the variables (objects x, y, z etc. drawn from the domain of discourse) and not to functions, in other words the calculus will permit ∀xf(x) ("for all creatures x, x is a bird") but not ∀f∀x(f(x)) [but if "equality" is added to the calculus it will permit ∀f:f(x); see below under Tarski]. Example: : Let the predicate "function" f(x) be "x is a mammal", and the subject-domain (or universe of discourse) (cf Kleene 1967:84) be the category "bats": : The formula ∀xf(x) yields the truth value "truth" (read: "For all instances x of objects 'bats', 'x is a mammal'" is a truth, i.e. "All bats are mammals"); : But if the instances of x are drawn from a domain "winged creatures" then ∀xf(x) yields the truth value "false" (i.e.
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Wholistic reference is reference to the whole—with respect to the context. In its strongest, unqualified form, the principle of wholistic reference is the proposition that each and every proposition, regardless how limited the referents of its non-logical or content terms, refers to the whole of its universe of discourse. According to this principle every proposition of number theory, even an equational proposition such as 5 + 7 = 12, refers not only to the individual numbers that it happens to mention but to the whole universe of numbers. The relation verb ‘refers’ is being used in its broad sense (loosely “is about”) and not as a synonym for ‘names’ in the sense of “is a name of”. George Boole (1815–1864) introduced this principle into modern logic: Even though he changed from a monistic fixed-universe framework in his 1840s writings to a pluralistic multiple-universe framework in 1854,Corcoran, John, and Sagüillo, José Miguel, 2011. “The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper”, History and Philosophy of Logic 32: 359–80.
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In classical logic a sentence in a language is true or false under (and only under) an interpretation and is therefore a truth-bearer. For example, a language in the first-order predicate calculus might include one or more predicate symbols and one or more individual constants and one or more variables. The interpretation of such a language would define a domain (universe of discourse); assign an element of the domain to each individual constant; assign the denotation in the domain of some property to each unary (one-place) predicate symbol.See also First-order logic#Semantics For example, if a language L consisted in the individual constant a, two unary predicate letters F and G and the variable x, then an interpretation I of L might define the Domain D as animals, assign Socrates to a, the denotation of the property being a man to F, and the denotation of the property being mortal to G. Under the interpretation I of L, Fa would be true if, and only if Socrates is a man, and the sentence x(Fx Gx) would be true if, and only if all men (in the domain) are mortal.
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