Aristotelian logic has been developed in ways that allow us to translate many kinds of natural language statements into statements about relationships between classes. A full unit on this topic would show you how to translate statements like the following:
One final point needs clarification. The logical form of the inductive syllogism, after the convertibility maneuver, is the same as the deductive syllogism. In this sense, induction and deduction possess the same (final) logical form. But, of course, in order to successfully perform an induction, one has to know that convertibility is possible, and this requires an act of intelligence which is able to discern the metaphysical realities between things out in the world. We discuss this issue under non-discursive reasoning below.
Argumentation theorists (less aptly characterized as informal logicians) have critiqued the ascendancy of formal logic, complaining that the contemporary penchant for symbolic logic leaves one with an abstract mathematics of empty signs that cannot be applied in any useful way to larger issues. Proponents of formal logic counter that their specialized formalism allows for a degree of precision otherwise not available and that any focus on the substantive meaning or truth of propositions is a distraction from logical issues per se. We cannot readily fit Aristotle into one camp or the other. Although he does provide a formal analysis of the syllogism, he intends logic primarily as a means of acquiring true statements about the world. He also engages in an enthusiastic investigation of less rigorous forms of reasoning included in the study of dialectic and rhetoric.
In a short work entitled Sophistical Refutations, Aristotle introduces a theory of logical fallacies that has been remarkably influential. His treatment is abbreviated and somewhat obscure, and there is inevitably scholarly disagreement about precise exegesis. Aristotle thinks of fallacies as instances of specious reasoning; they are not merely errors but hidden errors. A fallacy is an incorrect reasoning strategy that gives the illusion of being sound or somehow conceals the underlying problem. Aristotle divides fallacies into two broad categories: those which depend on language (sometimes called verbal fallacies) and those that are independent of language (sometimes called material fallacies). There is some scholarly disagreement about particular fallacies, but traditional English names and familiar descriptions follow. Linguistic fallacies include: homonymy (verbal equivocation), ambiguity (amphiboly or grammatical equivocation), composition (confusing parts with a whole), division (confusing a whole with parts), accent (equivocation that arises out of mispronunciation or misplaced emphasis) and figure of speech (ambiguity resulting from the form of an expression). Independent fallacies include accident (overlooking exceptions), converse accident (hasty generalization or improper qualification), irrelevant conclusion, affirming the consequent (assuming an effect guarantees the presence of one possible cause), begging the question (assuming the point), false cause, and complex question (disguising two or more questions as one). Logicians, influenced by scholastic logic, often gave these characteristic mistakes Latin names: compositio for composition, divisio for division, secundum quid et simpliciter for converse accident, ignoranti enlenchi for nonrelevant conclusion, and petitio principii for begging the question.
Although Aristotle provides a logical blueprint for the kind of reasoning that is going on in ethical decision-making, he obviously does not view moral decision-making as any kind of mechanical or algorithmic procedure. Moral induction and deduction represent, in simplified form, what is going on. Throughout his ethics, Aristotle emphasizes the importance of context. The practice of morality depends then on a faculty of keen discernment that notices, distinguishes, analyzes, appreciates, generalizes, evaluates, and ultimately decides. In the Nicomachean Ethics, he includes practical wisdom in his list of five intellectual virtues. (Scholarly commentators variously explicate the relationship between the moral and the intellectual virtues.) Aristotle also discusses minor moral virtues such as good deliberation (eubulia), theoretical moral understanding (sunesis), and experienced moral judgement (gnome). And he equates moral failure with chronic ignorance or, in the case of weakness of will (akrasia), with intermittent ignorance.
Aristotle's work in logic is an attempt to understand and justify how people think about philosophy and the world in general. Logic is a philosophical field that studies accurate reasoning or inference. Logic generally involves rules that determine what a given set of facts allows one to infer. Aristotle examined the sorts of inferences that people make all the time, both in philosophy and everyday thinking. He tried to explain precisely what logical rules justify or invalidate such inferences. In particular, Aristotle focused on a logical process called deduction. The central feature of a deductive argument is that it is justified by necessity; the inferences it makes must be true according to the sorts of logical rules that Aristotle laid out. An example of a deductive argument might be the following:
The first two sentences, which are called the premises of the argument, make the third sentence, the conclusion of the argument, certainly true: it would not make logical sense to claim that every river contains water, but also that the Nile river does not contain water. This reasoning means that the argument is deductively valid. Aristotle's logic was important to his views on science because he thought science involved using deductions to infer causal facts about reality.
Aristotle focused much of his work in logic on a particular type of deductive argument called the syllogism, which is defined in terms of a certain structure. Aristotle syllogism consists of three successive assertions; the first two are the premises, and the third is the conclusion. The combination of a subject and a predicate forms an assertion; the subject is the thing that the assertion is about, and the predicate is the claim made about that subject. For instance, in the assertion, ''Every tree is a plant,'' the subject is tree, and the predicate is being a plant, which is claimed to be true of all trees. A key feature of a syllogism is that either the subject or the predicate of the first premise must appear again in the second premise; this shared term is a link that allows the conclusion to be a combination of the unrepeated terms. An example of a syllogism is the following argument:
Causality is related to Aristotelian logic because, in Aristotle's view, the scientific investigation involves observing and deducing the causal links and the patterns by which the natural world functions. Aristotle held that there were four types of causes and that explaining something generally involves all four types:
Aristotle's influence on philosophy throughout history has been immense. Although his work on logic was respected and accepted by many philosophers for hundreds of years, recently, a new type of logic has been developed that is viewed as much more accurate and comprehensive than Aristotle's original ideas. Many scholars think that Aristotle's work on logic, specifically his method of inquiry, has some elements in common with modern logic.
Aristotle's work has also been very influential in areas other than logic. For example, many philosophers in the centuries after Aristotle produced their own work as commentaries on Aristotle's original books. Aristotle's ideas impacted many different philosophical traditions, including European philosophy, Byzantine philosophy, Islamic and Arabic philosophy, Jewish philosophy, and Christian philosophy. Aristotle's impact has continued to the present day, and some of Aristotle's ideas have been recently rethought within modern philosophy. For example, virtue ethical positions similar to those advocated by Aristotle have become prominent in contemporary ethics. Contemporary philosophers have also drawn on Aristotle's work in other fields, such as philosophy of mind and metaphysics.
One field Aristotle worked in was logic, where he turned everyday reasoning into a formalized system that could show what sorts of inferences are correct. He primarily examined deduction, which includes only necessary inferences wherein the conclusion is definitely true unless the argument has a false premise. The syllogism is a form of a deductive argument that Aristotle wrote about a lot. It involves two premises and a conclusion. One idea from the first premise must appear again in the second, and the conclusion links the ideas that were not repeated. Aristotle believed that syllogisms about causality that explained what caused aspects of nature to exist or occur were important to science. According to Aristotle, most things should be explained regarding four types of causes, not just one. Another important Aristotelian idea is the golden mean, as Aristotle thought virtue was about having qualities in moderation. Aristotle's work was highly influential throughout history, and contemporary philosophers still draw on his ideas, especially in the field of virtue ethics.
Aristotle produced a lot of work on many different philosophical subjects, including logic, ethics, political theory, and metaphysics. He also did extensive work in biology, zoology, and other areas of science. In general, Aristotle's approach involved examining the empirical world and trusting perceptions rather than doubting them.
Aristotelian thinking or Aristotelianism refers to the ideas and methods of the Ancient Greek philosopher Aristotle. The expansiveness of Aristotle's work means that many different ideas fall under Aristotelianism. For example, in logic, Aristotelian thinking refers to a particular system of reasoning that focuses on syllogism, a three-step argument used to reach a logical conclusion. 041b061a72