A fallacy is the use of invalid or otherwise faulty reasoning in the construction of an argument that may appear to be well-reasoned if unnoticed. The term was introduced in the Western intellectual tradition by the Aristotelian De Sophisticis Elenchis.
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid. An argument is sound if it is valid and all its premises are true. One approach defines deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: it is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning.
The Summa Logicae is a textbook on logic by William of Ockham. It was written around 1323.
Special pleading is an informal fallacy wherein one cites something as an exception to a general or universal principle, without justifying the special exception. It is the application of a double standard.
A faulty generalization is an informal fallacy wherein a conclusion is drawn about all or many instances of a phenomenon on the basis of one or a few instances of that phenomenon. It is similar to a proof by example in mathematics. It is an example of jumping to conclusions. For example, one may generalize about all people or all members of a group from what one knows about just one or a few people:
Inductive reasoning is any of various methods of reasoning in which broad generalizations or principles are derived from a body of observations. This article is concerned with the inductive reasoning other than deductive reasoning, where the conclusion of a deductive argument is certain given the premises are correct; in contrast, the truth of the conclusion of an inductive argument is at best probable, based upon the evidence given.
Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises. The premises and the conclusion are propositions, i.e. true or false claims about what is the case. Together, they form an argument. Logical reasoning is norm-governed in the sense that it aims to formulate correct arguments that any rational person would find convincing. The main discipline studying logical reasoning is logic.
A statistical syllogism is a non-deductive syllogism. It argues, using inductive reasoning, from a generalization true for the most part to a particular case.
The fallacy of accident is an informal fallacy where a general rule is applied to an exceptional case. The fallacy of accident gets its name from the fact that one or more accidental features of the specific case make it an exception to the rule. A generalization that is largely true may not apply in a specific case for good reasons. It is one of the thirteen fallacies originally identified by Aristotle in Sophistical Refutations.
The fallacy of converse accident is an informal fallacy that can occur in a statistical syllogism, when a rule that applies only to an exceptional case is wrongly applied to all cases in general.
Informal fallacies are a type of incorrect argument in natural language. The source of the error is not just due to the form of the argument, as is the case for formal fallacies, but can also be due to their content and context. Fallacies, despite being incorrect, usually appear to be correct and thereby can seduce people into accepting and using them. These misleading appearances are often connected to various aspects of natural language, such as ambiguous or vague expressions, or the assumption of implicit premises instead of making them explicit.
Sophistical Refutations is a text in Aristotle's Organon in which he identified thirteen fallacies. According to Aristotle, this is the first work to treat the subject of deductive reasoning in ancient Greece.
An appeal to nature is a rhetorical technique for presenting and proposing the argument that "a thing is good because it is 'natural', or bad because it is 'unnatural'." In debate and discussion, an appeal-to-nature argument can be considered to be a bad argument, because the implicit primary premise "What is natural is good" has no factual meaning beyond rhetoric in some or most contexts.
In logic and mathematics, proof by example is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof.
An argument is a series of sentences, statements, or propositions some of which are called premises and one is the conclusion. The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persuasion.
In argumentation theory, an argumentum ad populum is a fallacious argument which is based on claiming a truth or affirming something is good or correct because many people think so.
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.
In argumentation theory, an argumentation scheme or argument scheme is a template that represents a common type of argument used in ordinary conversation. Many different argumentation schemes have been identified. Each one has a name and presents a type of connection between premises and a conclusion in an argument, and this connection is expressed as a rule of inference. Argumentation schemes can include inferences based on different types of reasoning—deductive, inductive, abductive, probabilistic, etc.
