For Aristotle, then, logic is the instrument the "organon" by means of which we come to know anything. He proposed as formal rules for correct reasoning the basic principles of the categorical logic that was universally accepted by Western philosophers until the nineteenth century. This system of thought regards assertions of the subject-predicate form as the primary expressions of truth, in which features or properties are shown to inhere in individual substances. In every discipline of human knowledge,then, we seek to establish the things of some sort have features of a certain kind. Aristotle further supposed that this logical scheme accurately represents the true nature of reality.
Logic; or, The analytic of explicit reasoning
Thought, language, and reality are all isomorphic, so careful consideration of what we say can help us to understand the way things really are. Beginning with simple descriptions of particular things, we can eventually assemble our information in order to achieve a comprehensive view of the world. The initial book in Aristotle 's collected logical works is the Categories , an analysis of predication generally. It begins with a distinction among three ways in which the meaning of different uses of a predicate may be related to each other: homonymy, synonymy, and paronymy in some translations, "equivocal," "univocal," and "derivative".
Homonymous uses of a predicate have entirely different explanations, as in "With all that money, she's really loaded," and "After all she had to drink, she's really loaded. So long as we are clear about the sort of use we are making in each instance, Aristotle proposed that we develop descriptions of individual things that attribute to each predicates or categories of ten different sorts. Substance is the most crucial among these ten, since it describes the thing in terms of what it most truly is.
Logic; Or, the Analytic of Explicit Reasoning - esarynezivak.gq
For Aristotle, primary substance is just the individual thing itself, which cannot be predicated of anything else. But secondary substances are predicable, since they include the species and genera to which the individual thing belongs.
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Thus, the attribution of substance in this secondary sense establishes the essence of each particular thing. Categories 4 Used in combination, the ten kinds of predicate can provide a comprehensive account of what any individual thing is. She is in my apartment at a. Aristotle supposed that anything that is true of any individual substance could, in principle, be said about it in one of these ten ways. Another of Aristotle 's logical works, On Interpretation , considers the use of predicates in combination with subjects to form propositions or assertions, each of which is either true or false.
We usually determine the truth of a proposition by reference to our experience of the reality it conveys, but Aristotle recognized that special difficulties arise in certain circumstances. Although we grant and can often even discover the truth or falsity of propositions about past and present events, propositions about the future seem problematic. If a proposition about tomorrow is true or false today, then the future event it describes will happen or not happen necessarily; but if such a proposition is neither true nor false, then there is no future at all.
Aristotle's solution was to maintain that the disjunction is necessarily true today even though neither of its disjuncts is.
It deals only with propositions declarative sentences, used to make an assertion, as opposed to questions, commands or sentences expressing wishes that are capable of being true and false. It is not concerned with the psychological processes connected with thought, or with emotions , images and the like.
It covers core topics such as the study of fallacies and paradoxes , as well as specialized analysis of reasoning using probability and arguments involving causality and argumentation theory. Logical systems should have three things: consistency which means that none of the theorems of the system contradict one another ; soundness which means that the system's rules of proof will never allow a false inference from a true premise ; and completeness which means that there are no true sentences in the system that cannot, at least in principle, be proved in the system.
But modern logic descends mainly from the Ancient Greek tradition. Both Plato and Aristotle conceived of logic as the study of argument and from a concern with the correctness of argumentation. Aristotle produced six works on logic, known collectively as the "Organon" , the first of these, the "Prior Analytics" , being the first explicit work in formal logic.
Aristotle espoused two principles of great importance in logic, the Law of Excluded Middle that every statement is either true or false and the Law of Non-Contradiction confusingly, also known as the Law of Contradiction , that no statement is both true and false. He is perhaps most famous for introducing the syllogism or term logic see the section on Deductive Logic below. His followers, known as the Peripatetics , further refined his work on logic.
In medieval times, Aristotelian logic or dialectics was studied, along with grammar and rhetoric , as one of the three main strands of the trivium , the foundation of a medieval liberal arts education. Logic in Islamic philosophy also contributed to the development of modern logic, especially the development of Avicennian logic which was responsible for the introduction of the hypothetical syllogism , temporal logic , modal logic and inductive logic as an alternative to Aristotelian logic.
In the 18th Century, Immanuel Kant argued that logic should be conceived as the science of judgment , so that the valid inferences of logic follow from the structural features of judgments , although he still maintained that Aristotle had essentially said everything there was to say about logic as a discipline.
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This new logic, expounded in their joint work "Principia Mathematica" , is much broader in scope than Aristotelian logic , and even contains classical logic within it, albeit as a minor part. It resembles a mathematical calculus and deals with the relations of symbols to each other. Formal Logic : Formal Logic is what we think of as traditional logic or philosophical logic , namely the study of inference with purely formal and explicit content i.
follow site See the section on Deductive Logic below. A formal system also called a logical calculus is used to derive one expression conclusion from one or more other expressions premises. These premises may be axioms a self-evident proposition, taken for granted or theorems derived using a fixed set of inference rules and axioms, without any additional assumptions. Formalism is the philosophical theory that formal statements logical or mathematical have no intrinsic meaning but that its symbols which are regarded as physical entities exhibit a form that has useful applications.
Informal Logic : Informal Logic is a recent discipline which studies natural language arguments, and attempts to develop a logic to assess, analyze and improve ordinary language or "everyday" reasoning. Natural language here means a language that is spoken , written or signed by humans for general-purpose communication , as distinguished from formal languages such as computer-programming languages or constructed languages such as Esperanto. It focuses on the reasoning and argument one finds in personal exchange, advertising, political debate, legal argument, and the social commentary that characterizes newspapers, television, the Internet and other forms of mass media.
Symbolic Logic : Symbolic Logic is the study of symbolic abstractions that capture the formal features of logical inference.
It deals with the relations of symbols to each other, often using complex mathematical calculus , in an attempt to solve intractable problems traditional formal logic is not able to address. It is often divided into two sub-branches: Predicate Logic : a system in which formulae contain quantifiable variables. See the section on Predicate Logic below.
Propositional Logic or Sentential Logic : a system in which formulae representing propositions can be formed by combining atomic propositions using logical connectives , and a system of formal proof rules allows certain formulae to be established as theorems. See the section on Propositional Logic below. Mathematical Logic : Both the application of the techniques of formal logic to mathematics and mathematical reasoning, and, conversely, the application of mathematical techniques to the representation and analysis of formal logic.
The earliest use of mathematics and geometry in relation to logic and philosophy goes back to the Ancient Greeks such as Euclid , Plato and Aristotle. In the s and s, researchers predicted that when human knowledge could be expressed using logic with mathematical notation , it would be possible to create a machine that reasons or artificial intelligence , although this turned out to be more difficult than expected because of the complexity of human reasoning.
Mathematics-related doctrines include: Logicism : perhaps the boldest attempt to apply logic to mathematics, pioneered by philosopher-logicians such as Gottlob Frege and Bertrand Russell , especially the application of mathematics to logic in the form of proof theory , model theory , set theory and recursion theory. Intuitionism : the doctrine which holds that logic and mathematics does not consist of analytic activities wherein deep properties of existence are revealed and applied, but merely the application of internally consistent methods to realize more complex mental constructs.
Signs, Symbols, Signifiers and Signifieds
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