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MATHEMATICAL OBJECTS Mathematics is populated by many more Objects of the Mind than objects of the real world, because the rules of math are not bounded by real-world constraints. For example, a Möbius Strip is a one-sided and one-edged object, without beginning or end. Another example, the Klein Bottle , is a one-sided, sealed surface with no inside or outside. Such objects can be represented by twisting and cutting or taping pieces of paper together, and by mathematical formulas, as well as by computer simulations. To hold them in the imagination, abstractions such as extra or fewer dimensions are necessary. LOGICAL SEQUENCES The subjects of Logical Sequences are often objects of the mind. For example, a Counterfactual argument relates a Hypothetical or Subjunctive Possibility which ''could'' or ''would'' be true, but ''might not'' be false. Conditional sequences involving subjunctives use Intensional language, which is studied by Modal Logic , whereas Classical Logic studies the Extensional language of Necessary and Sufficient conditions. In general, a logical Antecedent is a necessary condition, and a logical Consequent is a sufficient condition, or the Contingency , in a logical conditional. When logical conditionals do not reflect every day if-then reasoning, they are sometimes known as Material Conditional s. Non-material conditionals describe if-then reasoning that involves hypotheticals, fictions, or counterfactuals. False antecedent A false antecedent is a premise known to be false, fictional, imaginary, or unnecessary. In a conditional sequence, a false antecedent may be the basis for any consequence, true or false. The subjects of Art and Literature are often objects of the mind. Other examples include the subjects of False Documents , the origins of Stand-alone phenomena, or the implications of loaded words; and artificial sources, personalities, events, or histories. False antecedents are sometimes referred to as nonexistent, whereas nonexistent referents are not usually referred to. False consequent A false consequent, in contrast, is a conclusion known to be false, fictional, imaginary, or insufficient. In a conditional statement, a fictional conclusion is known as a Non Sequitur , which literally means ''out of sequence.'' A conclusion that is out of sequence is not contingent on any premises that precede it, and it does not follow from them, so such a sequence is not conditional. A conditional sequence is a connected series of statements. A false consequent cannot follow from true premises in a connected sequence. But, on the other hand, a false consequent can follow from a false antecedent. As an example, the name of a Team , a Genre , or a Nation is a collective term applied Ex Post Facto to a group of distinct individuals. None of the individuals on a sports team is the team itself, nor is any musical chord a genre, or any person America. The name is an identity for a collection that is connected by Consensus or Reference , but not by sequence. A different name could equally follow, but it would have different Social or Political Significance . PHILOSOPHY OF MIND In philosophy, Mind-body Dualism is the doctrine that mental activities exist apart from the physical body. In '' The Concept Of Mind '', Gilbert Ryle characterizes the mind in relation to the body as the '' Ghost In The Machine '', contrary to the argument posited by René Descartes in '' Meditations On First Philosophy ''. The 'ghost' is the imagined identity of the bodily 'machine,' which, Ryle argues, consists of individual parts none of which is the purposed identity. In the argument of Descartes, the mind is held to be real because personal identity cannot be a deception. Ryle compares individual identity to a university. A university is composed of many buildings and offices, but none of them is the university. Similarly, an individual person is composed of limbs and a torso and a head, but none of these pieces is the person's identity. Identity may be located in the brain, or it may not be. Individual identity is like collective identity in the respect that it follows by some Association , but not necessarily by sequence. On the other hand, identity may begin as a consequent and become antecedent to further inclusions of individuals. INVENTED SOURCES Many objects in fiction follow the example of false antecedents or false consequents. For example, '' The Lord Of The Rings '' by J.R.R. Tolkien is based on an imaginary book. In the ''Appendicies'' to ''The Lord of the Rings'', Tolkien's characters name the '' Red Book Of Westmarch '' as the source material for ''The Lord of the Rings'', which they describe as a translation. But the ''Red Book of Westmarch'' is a fictional document that chronicles events in an Imaginary World . One might imagine a different Translation , by another author. The '' Necronomicon '' is a book invented by H. P. Lovecraft as an important document in his stories. His characters use it for special purposes, and often times excerpts are quoted from it. But the excerpts refer to an imaginary source. ''The Necronomicon'', and similar books, also appear in many other stories by other authors in the Cthulhu Mythos . They are open-ended books which new authors might add new chapters to, but they are not real books. '' The Hitchhiker's Guide To The Galaxy '' is an electronic book for documenting the whole Galaxy, in the novel of the same name by Douglas Adams . In that story, the characters use the Guide as a reference book. Therefore, the quotes from it accurately reflect the content of that book in the story. There was no such book prior to Adams quoting it. But, an ongoing project known as H2g2 also references the same ''Hitchhiker's Guide.'' At the time that ''The Hitchhiker's Guide'' was invented, an '' Electronic Book '' was an object of the mind. Douglas Adams wrote a whole radio series and several books about an electronic book, before any real electronic books actually existed. This object of his mind may have predicated the real invention. A '''', 'stand alone complex' refers to copycat crimes with no original criminal. Like the image of the executable, the copycat crimes now exist independently of any source. It is a metaphor for phenomena with imaginary origins that take on a life of their own. Quotes and excerpts from imaginary sources are unlike references to extant sources in that the references themselves comprise the only extant material available from imaginary sources. Imaginary sources cannot be looked up in the real world or checked for accuracy, aside from consulting the author who made references to them. They can, however, take on a life of their own. Conversely, extant referents exist distinctly apart from the references to them, but they do not have any independent existence. CONVENIENT FICTIONS Social Reality is composed of many Standards and Inventions that facilitate Communication , but which are ultimately objects of the mind. For example, Money is an object of the mind which Currency represents. Similarly, Language s signify Ideas and Thoughts . Objects of the mind are frequently involved in the roles that people play. For example, Acting is a profession which predicates real jobs on fictional premises. Charades is a game people play by guessing imaginary objects from short play-acts. Imaginary Personalities and Histories are sometimes invented to enhance the Verisimilitude of Fictional Universes , and the Immersion of Role-playing Games . In the sense that they exist independently of Extant personalities and histories, they are believed to be fictional characters and fictional time frames. Related also is the use of numbers to represent durations of time in fiction. In the novel '' Nineteen Eighty-Four '' by George Orwell , the number 1984 represented a year that had not yet passed. Science-fiction is abundant with future times, alternate times, and past times that are objects of the mind. Real life dates also represent objects of the mind, specifically, past and future times. In ''The . The number 2005 did not change, but object of the mind that it represents did change. Deliberate Invention also often refers to objects of the mind. The intentional invention of fiction for the purpose of Deception is usually referred to as Lying , in contrast to invention for Entertainment or Art . Invention is also often applied to Problem Solving . In this sense the Physical invention of materials is associated with the Mental invention of fictions. PSYCHIATRIC DIAGNOSIS The notion that Psychological problems are symptoms of a Chemical Imbalance is a Conjecture based on incomplete Evidence . Psychiatrists do not test for chemical balances or imbalances in the Brain , nor is there any known such test. The Etiology of Psychopathology might be exclusively in the Body , exclusively in the Mind , or in some combination of both. SELF-REFERENCE A Reference that names an imaginary Source is in some sense also a Self-reference . A self-reference automatically makes a comment about itself. Premises that name themselves as premises are premises by self-reference; conclusions that name themselves as conclusions are conclusions by self-reference. In their respective Imaginary World s the ''Necronomicon'', ''The Hitchhiker's Guide to the Galaxy'', and the ''Red Book of Westmarch'' are realities, but only because they are referred to as real. Authors use this technique to invite readers to Pretend or to make-believe that their imaginary world is real. In the sense that the stories that quote these books are true, the quoted books exist; in the sense that the stories are fiction, the quoted books do not exist. UNDECIDABILITY According to the Incompleteness Theorems of Kurt Gödel , a countable set of consistent Axioms cannot prove or refute a contradiction among themselves, or prove their own consistency. A Contradiction among truths in a Theory cannot be decided in the theory, but might be decidable in a broader theory. Axioms themselves are unprovable in their own theory, and only a broader theory can prove their consistency. Similarly, Truth in Fiction is commonly considered to be consistency with the assumptions of the fiction. By analogy, the contradiction of fictional truths cannot be decided in the fiction. For example, '' The Lord Of The Rings '' can be regarded fictional and its source Tolkien 's Imagination . But if the '' Red Book Of Westmarch '' is not real, then The Lord of the Rings is not a translation of it, which contradicts the assumptions of the story. Therefore, ''The Red Book of Westmarch'' is a true document in the story of ''The Lord of the Rings''. To characters in '' The Hitchhiker's Guide To The Galaxy '', the Guide that they refer to must be real. Similarly, the concept of Improbability must be taken as true, because it is an assumption of their universe. A novel purporting to be the '' Necronomicon '' contains much that is not included in the works of H. P. Lovecraft or any book in the Cthulhu Mythos . But the original book was fiction, so the book claiming to be real must not be that book. While the two books cannot be proved to be the same, nor can they be proved to be different books. They might both be excerpts from another ''Necronomicon''. FURTHER CONSIDERATIONS Many other examples of objects of the mind exist, and each in its own way poses unanswerable questions about truth, falsehood, reality, fiction, and imagination. The many unique modes of expression available to human beings permit us to sample a universe wider than the world of our personal experiences and immediate sensations. REFERENCES The Teaching Company, Course No. 1423. "Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas." Lecture 14 - "A One-Sided, Sealed Surface - the Klein Bottle." Professors Edward B. Burger, Michael Starbird. Ryle, Gilbert. '' The Concept Of Mind ''. Sobo, Simon, M.D. "ADHD And Other Sins of Our Children". Payne, W. Russ "The non-material conditional". |
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