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An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (axíōma), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.
In any of several fields of study that treat the use of signs—for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language—an intension is any property or quality connoted by a word, phrase, or another symbol. In the case of a word, the word's definition often implies an intension. For instance, the intensions of the word plant include properties such as "being composed of cellulose ", "alive", and "organism", among others. A comprehension is the collection of all such intensions.
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true. It is one of the three laws of thought, along with the law of noncontradiction, and the law of identity; however, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens or De Morgan's laws. The law is also known as the law / principleof the excluded third, in Latin principium tertii exclusi. Another Latin designation for this law is tertium non datur or "no third [possibility] is given". In classical logic, the law is a tautology.
The relativist fallacy, also known as the subjectivist fallacy, is claiming that something is true for one person but not true for someone else, when in fact that thing is an objective fact. The fallacy rests on the law of noncontradiction. The fallacy applies only to objective facts, or what are alleged to be objective facts, rather than to facts about personal tastes or subjective experiences, and only to facts regarded in the same sense and at the same time.
In metaethics, the naturalistic fallacy is the claim that it is possible to define good in terms of merely described entities, properties, or processes such as pleasant, desirable, or fitness. The term was introduced by British philosopher G. E. Moore in his 1903 book Principia Ethica.
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.
In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect."
The sorites paradox, sometimes known as the paradox of the heap, is a paradox that results from vague predicates. A typical formulation involves a heap of sand, from which grains are removed individually. With the assumption that removing a single grain does not cause a heap to not be considered a heap anymore, the paradox is to consider what happens when the process is repeated enough times that only one grain remains and if it is still a heap. If not, then the question asks when it changed from a heap to a non-heap.
In logic, a three-valued logic is any of several many-valued logic systems in which there are three truth values indicating true, false, and some third value. This is contrasted with the more commonly known bivalent logics which provide only for true and false.
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.
Antony Garrard Newton Flew was an English philosopher. Belonging to the analytic and evidentialist schools of thought, Flew worked on the philosophy of religion. During the course of his career he taught philosophy at the universities of Oxford, Aberdeen, Keele, and Reading in the United Kingdom, and at York University in Toronto, Canada.
Verificationism, also known as the verification principle or the verifiability criterion of meaning, is a doctrine in philosophy which asserts that a statement is meaningful only if it is either empirically verifiable or a tautology. Verificationism rejects statements of metaphysics, theology, ethics and aesthetics as meaningless in conveying truth value or factual content, though they may be meaningful in influencing emotions or behavior.
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.
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.
In literary criticism and rhetoric, a tautology is a statement that repeats an idea using near-synonymous morphemes, words or phrases, effectively "saying the same thing twice". Tautology and pleonasm are not consistently differentiated in literature. Like pleonasm, tautology is often considered a fault of style when unintentional. Intentional repetition may emphasize a thought or help the listener or reader understand a point. Sometimes logical tautologies like "Boys will be boys" are conflated with language tautologies, but a language tautology is not inherently true, while a logical tautology always is.
As the study of argument is of clear importance to the reasons that we hold things to be true, logic is of essential importance to rationality. Arguments may be logical if they are "conducted or assessed according to strict principles of validity", while they are rational according to the broader requirement that they are based on reason and knowledge.
References
- 1 2 "Fallacies". Internet Encyclopedia of Philosophy. Retrieved 2022-02-09.
- 1 2 Curtis, Gary N. "The No-True-Scotsman Fallacy". Fallacy Files. Retrieved 2016-11-12.
- 1 2 Antony Flew (1966). God & Philosophy. Hutchinson. p. 104.
- 1 2 3 4 Antony Flew (1975). Thinking About Thinking (or, Do I Sincerely Want to be Right?). Fontana/Collins. p. 47. ISBN 9780006335801.
- 1 2 Goldman, David P. (31 Jan 2006). "No true Scotsman starts a war". Asia Times. Archived from the original on 5 January 2019. Retrieved 1 December 2014.
political-science professors... Jack Mansfield and Ed Snyder distinguish between 'mature democracies', which never, never start wars ('hardly ever', as the captain of the Pinafore sang), and 'emerging democracies', which start them all the time, in fact far more frequently than do dictatorships
- ↑ Robert Ian Anderson (2017). P. Brézillon; R. Turner; C. Penco (eds.). Is Flew's No True Scotsman Fallacy a True Fallacy? A Contextual Analysis. Modeling and Using Context. CONTEXT 2017. Lecture Notes in Computer Science. Vol. 10257. pp. 243–253. doi:10.1007/978-3-319-57837-8_19.
- ↑ Pinker, Steven (2021). Rationality, What It Is, Why It Seems Scarce, Why It Matters. New York: Viking. p. 88. ISBN 978-0525561996. OCLC 1237806678.
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