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Introduction, Important Definitions and Related Concepts:

A fallacy is a component of an argument which, being demonstrably flawed in its logic or form, renders the argument invalid in whole. In logical arguments, fallacies are either formal or informal. Because the validity of a deductive argument depends on its form, a formal fallacy is a deductive argument that has an invalid form, whereas an informal fallacy is any other invalid mode of reasoning whose flaw is not in the form of the argument. In logic, an argument is a set of one or more declarative sentences known as the premises (singular is also spelt "premiss" in British English), along with another declarative sentence known as the conclusion. A deductive argument asserts that the truth of the conclusion is a logical consequence of the premises; an inductive argument asserts that the truth of the conclusion is supported by the premises. Each premise and the conclusion are only either true or false, not ambiguous. Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The field of logic ranges from core topics such as the study of fallacies and paradoxes, to specialized analysis of reasoning using probability and to arguments involving causality. Invalid means not valid: being without foundation or force in fact, truth, or law <an invalid assumption> <declared the will invalid> logically inconsequent. Formal in Philosophy means relating to form, i.e. appearance rather than essence. Relating to Formalism, i.e. emphasis on form over content or meaning.

  • formal logic logical argument based only on the form and not on the meaning. Formal cause, Aristotle's intrinsic, determining cause. An informal fallacy is an argument pattern that is wrong due to a mistake in its reasoning. In contrast to a formal fallacy, the error has to do with issues of rational inference that occur in natural language; which are broader than can be represented by the symbols used in formal logic. Informal fallacies, when deductive, commonly occur in an invalid form. A set is a collection of distinct objects considered as a whole. Sets are one of the most fundamental concepts in mathematics. The study of the structure of sets, set theory, is rich and ongoing. A declarative sentence states an idea. It does not give a command or request, nor does it ask a question. A declarative sentence usually ends in a period, though it may end in an exclamation point. In discourse and logic, a premise (also "premiss" in British usage) is a claim that is a reason (or element of a set of reasons) for, or objection against, some other claim. In other words, it is a statement presumed true within the context of an argument toward a conclusion. Premises are sometimes stated explicitly by way of disambiguation or for emphasis, but more often they are left tacitly understood as being obvious or self-evident ("it goes without saying"), or not conducive to succinct discourse. A conclusion is a proposition, which is arrived at after the consideration of evidence, arguments or premises. In research and experimentation, conclusions are determinations made by studying the results of preceding work within some methodology (for example the scientific method). These often take the form of theories.

    Logical consequence or syntactic consequence, arguably the most fundamental concept in logic, is the relation that holds between a set of sentences (or propositions) and a sentence (proposition) when the latter "follows from" the former. For example, Kermit is green is a logical consequence of All frogs are green and Kermit is a frog. The certainty of the above consequence depends on the first postulates being true and complete. In a deductive argument, the premises are intended to provide support for the conclusion that is so strong that, if the premises are true, it would be impossible for the conclusion to be false. An inductive argument is an argument in which it is thought that the premises provide reasons supporting the probable truth of the conclusion. In an inductive argument, the premises are intended only to be so strong that, if they are true, then it is unlikely that the conclusion is false. The meaning of the word truth extends from honesty, good faith, and sincerity in general, to agreement with fact or reality in particular.[1] The term has no single definition about which the majority of professional philosophers and scholars agree. Various theories of truth continue to be debated. Ambiguous means doubtful or uncertain especially from obscurity or indistinctness <eyes of an ambiguous color> b: inexplicable2: capable of being understood in two or more possible senses or ways <an ambiguous smile> <an ambiguous term> <a deliberately ambiguous reply>.  A classical language, is a language with a literature that is "classical"—ie, "it should be ancient, it should be an independent tradition that arose mostly on its own, not as an offshoot of another tradition, and it must have a large and extremely rich body of ancient literature."[1] (George L. Hart of UC Berkeley). In another sense of the word, an important criterion is that a language should have a broad influence over an extended period of time, even after it is no longer a colloquial mother tongue in its original form. If one language uses roots from another language to coin words (in the way that many European languages use Greek and Latin roots to devise new words such as "telephone" etc.), this is an indication that the second language is a classical language. Greek (ελληνική γλώσσα IPA: [eliniˈkʲi ˈɣlosa] or simply ελληνικά IPA: [eliniˈka] — "Hellenic") has a documented history of 3,400 years, the longest of any single natural language in the Indo-European language family. It is also one of the earliest attested Indo-European languages, with fragmentary records in Mycenaean dating back to the 15th or 14th century BC, making it the world's oldest recorded living language. Today, it is spoken by approximately 17–25 million people in Greece (official), Cyprus (official), Albania, Bulgaria, the Former Yugoslav Republic of Macedonia (FYROM), Italy, Turkey, Armenia, Georgia, Ukraine, Moldova, Romania, Russia, Egypt, Jordan and emigrant communities around the world, including Australia, United States, Canada, Germany and elsewhere. Logos (Greek λόγος) is an important term in philosophy, analytical psychology, rhetoric and religion. It derives from the verb λέγω legō: to count, tell, say, or speak.[1] The primary meaning of logos is: something said; by implication a subject, topic of discourse or reasoning. Inference is the act or process of deriving a conclusion based solely on what one already knows. Inference is studied within several different fields.

    Human inference (i.e. how humans draw conclusions) is traditionally studied within the field of cognitive psychology.

    A scientific demonstration is a scientific experiment carried out for the purposes of demonstrating scientific principles, rather than for hypothesis testing or knowledge gathering (although they may originally have been carried out for these purposes). Many scientific demonstrations are chosen for their combination of educational merit and entertainment value, which is often provided by dramatic phenomena such as explosions. Note: many scientific demonstrations are potentially dangerous, and should not be attempted without considerable laboratory experience and appropriate safety precautions. Science (from the Latin scientia, 'knowledge'), in the broadest sense, refers to any systematic knowledge or practice. In a more restricted sense, science refers to a system of acquiring knowledge based on the scientific method, as well as to the organized body of knowledge gained through such research.[1][2] This article focuses on the more restricted use of the word. Fields of science are commonly classified along two major lines:

    • Natural sciences, which study natural phenomena (including biological life), and Social sciences, which study human behavior and societies.

      System (from Latin systēma, in turn from Greek σύστημα systēma) is a set of interacting or interdependent entities, real or abstract, forming an integrated whole. The concept of an 'integrated whole' can also be stated in terms of a system embodying a set of relationships which are differentiated from relationships of the set to other elements, and from relationships between an element of the set and elements not a part of the relational regime. There are natural and man-made (designed) systems. A paradox can be an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition; or it can be, seemingly opposite, an apparent contradiction that actually expresses a non-dual truth (cf. Koan). Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the premises themselves are not all really true or cannot all be true together. The word paradox is often used interchangeably with contradiction. Probability is the likelihood or chance that something is the case or will happen. Probability theory is used extensively in areas such as statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems. The word probability does not have a consistent direct definition. Causality or causation denotes a directional relationship between one event (called cause) and another event (called effect) which is the consequence (result) of the first.[1] This informal understanding suffices in everyday usage, however the philosophical analysis of causality or causation has proved exceedingly difficult. The work of philosophers to understand causality and how best to characterize it extends over millennia. Form (Lat. forma Eng. mould), refers to the external three-dimensional outline, appearance or configuration of some thing - in contrast to the matter or content or substance of which it is composed (compare with shape).The word form refers to a phenomenon. Thus a speech may contain excellent arguments (the matter may be good), whereas the style, grammar, arrangement (the form) may be bad. The term formalism describes an emphasis on form over content or meaning in the arts, literature, or philosophy. A practitioner of formalism is called a formalist. In general in the study of the arts and literature, formalism refers to the style of criticism that focuses on artistic or literary techniques in themselves, in separation from the work's social and historical context. Cause means a reason for an action or condition : motive something that brings about an effect or a result a person or thing that is the occasion of an action or state; especially : an agent that brings something about sufficient reason <discharged for cause> a ground of legal action casea matter or question to be decided. Nature, in the broadest sense, is the natural world, physical universe, material world or material universe. "Nature" refers to the phenomena of the physical world, and also to life in general. Manufactured objects and human interaction are, in common usage, not considered part of nature unless qualified in ways such as "human nature" or "the whole of nature". A language is a system of visual, auditory, or tactile symbols of communication and the rules used to manipulate them. Language can also refer to the use of such systems as a general phenomenon. Language is considered to be an exclusively human mode of communication; although other animals make use of quite sophisticated communicative systems, none of these are known to make use of all of the properties that linguists use to define language. Deductive means of, relating to, or provable by deduction employing deduction in reasoning. As the term is used in mainstream cognitive science and philosophy of mind, a concept or conception is an abstract idea or a mental symbol, typically associated with a corresponding representation in a language or symbology. A vast array of accounts attempt to explain the nature of concepts. According to classical accounts, a concept denotes all of the entities, phenomena, and/or relations in a given category or class by using definitions. Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".[2] Other practitioners of mathematics maintain that mathematics is the science of pattern, and that mathematicians seek out patterns whether found in numbers, space, science, computers, imaginary abstractions, or elsewhere.[3][4] The word theory has a number of distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. In science, a theory is a mathematical or logical explanation, or a testable model of the manner of interaction of a set of natural phenomena, capable of predicting future occurrences or observations of the same kind, and capable of being tested through experiment or otherwise falsified through empirical observation. It follows from this that for scientists "theory" and "fact" do not necessarily stand in opposition. Discourse is communication that goes back and forth (from the Latin, discursus, "running to and from"), such as debate or argument. The term is used in semantics and discourse analysis. In semantics, discourses are linguistic units composed of several sentences — in other words, conversations, arguments or speeches. British English (BrE, BE, en-GB) is the broad term used to distinguish the forms of the English language used in the United Kingdom from forms used elsewhere in the Anglophone world.[1] British English encompasses the varieties of English used within the UK, including those in England, Scotland, Northern Ireland, and Wales. Some may also use the term more widely, to include other forms such as Hiberno-English (spoken in Ireland).[2] In western philosophy, reason has had a twofold history. On the one hand, it has been taken to be objective and so to be fixed and discoverable by dialectic, analysis or study. On the other hand, since the seventeenth century rationalists, reason has been taken to be a subjective faculty, or rather the unaided ability (eg., pure reason) to form concepts. In informal logic an objection, also known as a refutation, is a reason arguing against a premise, lemma or main contention. An objection to an objection is known as a rebuttal. Argumentation theory, or argumentation, embraces the arts and sciences of civil debate, dialogue, conversation, and persuasion. Self-evident means evident without proof or reasoning; producing certainty or conviction upon a bare presentation to the mind; as, a self-evident proposition or truth. In philosophy and logic, proposition is used to refer to either (a) the content or meaning of an assertion or (b) the string of symbols marks or grunts that make up a written or spoken declarative sentence. In either usage, propositions are meant to be the truth-bearers, i.e they are what is either true or false. The existence of propositions (in usage (a) above), and the existence of meanings is disputed, and where admitted their nature is controversial. Evidence in its broadest sense includes anything that is used to determine or demonstrate the truth of an assertion. Philosophically, evidence can include propositions which are presumed to be true used in support of other propositions that are presumed to be falsifiable. The term has specialized meanings when used with respect to specific fields, such as policy, scientific research, criminal investigations, and legal discourse. Research is a human activity based on intellectual investigation and is aimed at discovering, interpreting, and revising human knowledge on different aspects of the world. Research can use the scientific method, but need not do so. Scientific research relies on the application of the scientific method, a harnessing of curiosity. Experimentation means

      The act, process, or practice of experimenting. A search for knowledge; "their pottery deserves more research than it has received". A preliminary experiment whose outcome can lead to a more extensive experiment.

      Methodology is defined as "the analysis of the principles of methods, rules, and postulates employed by a discipline", "the systematic study of methods that are, can be, or have been applied within a discipline" or "a particular procedure or set of procedures" [1]. Scientific method refers to the body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. It is based on gathering observable, empirical and measurable evidence subject to specific principles of reasoning.[1] A scientific method consists of the collection of data through observation and experimentation, and the formulation and testing of hypotheses.[2] Relation, in logic and philosophy, a property or predicate ranging over more than one argument. See also Logic of relatives, Relation of ideas, Relational theory, Relational philosophy. A Relation of Ideas, in the Humean sense, is the type of knowledge that can be characterized as arising out of pure conceptual thought and logical operations (in contrast to a Matter of Fact). In a Kantian philosophy, it is equivalent to the analytic a priori. In linguistics, a sentence is a unit of language, characterized in most languages by the presence of a finite verb. For example, "The quick brown fox jumps over the lazy dog." A simple complete sentence consists of a subject and a predicate. Certainty is perfect knowledge. It is total security from error.



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