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False Premises
A false premise is an incorrect proposition that forms the basis of an argument or syllogism. Since the premise (proposition, or assumption) is not correct, the conclusion drawn may be in error. However, the logical validity of an argument is a function of its internal consistency, not the truth value of its premises. For example, consider this syllogism, which involves a false premise: :* If the streets are wet, it has rained recently. (premise) :* The streets are wet. (premise) :* Therefore it has rained recently. (conclusion) This argument is logically valid, but quite demonstrably wrong, because its first premise is false - one could hose down the streets, the local river could have flooded etc. A simple logical analysis will not reveal the error in this argument, since that analysis must accept the truth of the argument's premises. For this reason, an argument based on false premises can be much more difficult to refute, or even discuss, than one featuring a normal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proposition
In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the non-linguistic bearer of truth or falsity which makes any sentence that expresses it either true or false. While the term "proposition" may sometimes be used in everyday language to refer to a linguistic statement which can be either true or false, the technical philosophical term, which differs from the mathematical usage, refers exclusively to the non-linguistic meaning behind the statement. The term is often used very broadly and can also refer to various related concepts, both in the history of philosophy and in contemporary analytic philosophy. It can generally be used to refer to some or all of the following: The primary bearers of truth values (such as "true" and "false"); the objects of belief and other propositional attitudes (i.e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syllogism
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defined by Aristotle in his 350 BCE book '' Prior Analytics''), a syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise) and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism. From the Middle Ages onwards, ''categorical syllogism'' and ''syllogism'' were usually used interchangeably. This a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Premise
A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion. A premise makes a declarative statement about its subject matter which enables a reader to either agree or disagree with the premise in question, and in doing so understand the logical assumptions of the argument. If a premise is logically false, then the conclusion, which follows from all of the premises of the argument, must also be false—unless the conclusion is supported by a logically valid argument which the reader agrees with. Therefore, if the reader disagrees with any one of the argument's premises, they have a logical basis to reject the conclusion of the argument. Explanation In logic, an argument requires a set of at least two declarative sentences (or "propositions") known as the "premises" (or "premisses"), along with another declarative sentence (or "proposition"), known as the conclusion. This structure of two prem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Validity (logic)
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. Valid arguments must be clearly expressed by means of sentences called well-formed formulas (also called ''wffs'' or simply ''formulas''). The validity of an argument can be tested, proved or disproved, and depends on its logical form. Arguments In logic, an argument is a set of statements expressing the ''premises'' (whatever consists of empirical evidences and axiomatic truths) and an ''evidence-based conclusion.'' An argument is ''valid'' if and only if it would be contradictory for the conclusion to be false if all of the premises are true. Validity doesn't require the truth of the premises, inst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false''). Computing In some programming languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions like the number zero, the empty string, empty lists, and null evaluate to false, and strings with content (like "abc"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called "truthy" and "falsy" / "false". Classical logic In classical logic, with its intended semantics, the truth values are ''true'' (denoted by ''1'' or the verum ⊤), and '' untrue'' or '' false'' (denoted by ''0'' or the falsum ⊥); that is, classical logic is a two-valued logic. This set of two values is also called the Boolean domain. Corresponding semantics of l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deductive System
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined system of abstract thought. The term ''formalism'' is sometimes a rough synonym for ''formal system'', but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. Background Each formal system is described by primitive symbols (which collectively form an alphabet) to finitely construct a formal language from a set of axioms through inferential rules of formation. The system thus consists of valid formulas built up through finite combinations of the primitive symbols—combinations that are formed fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Falsifiability
Falsifiability is a standard of evaluation of scientific theories and hypotheses that was introduced by the philosopher of science Karl Popper in his book ''The Logic of Scientific Discovery'' (1934). He proposed it as the cornerstone of a solution to both the problem of induction and the problem of demarcation. A theory or hypothesis is falsifiable (or refutable) if it can be ''logically'' contradicted by an empirical test that can potentially be executed with existing technologies. Popper insisted that, as a logical criterion, it is distinct from the related concept "capacity to be proven wrong" discussed in Lakatos' falsificationism. Even being a logical criterion, its purpose is to make the theory predictive and testable, thus useful in practice. Popper opposed falsifiability to the intuitively similar concept of verifiability. Verifying the claim "All swans are white" would theoretically require observing all swans, which in actuality, is not possible. In contrast, obs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epistemology
Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Epistemologists study the nature, origin, and scope of knowledge, epistemic justification, the rationality of belief, and various related issues. Debates in epistemology are generally clustered around four core areas: # The philosophical analysis of the nature of knowledge and the conditions required for a belief to constitute knowledge, such as truth and justification # Potential sources of knowledge and justified belief, such as perception, reason, memory, and testimony # The structure of a body of knowledge or justified belief, including whether all justified beliefs must be derived from justified foundational beliefs or whether justification requires only a coherent set of beliefs # Philosophical skepticism, which questions the possibili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Causal Relationships
Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cause is partly responsible for the effect, and the effect is partly dependent on the cause. In general, a process has many causes, which are also said to be ''causal factors'' for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future. Some writers have held that causality is metaphysically prior to notions of time and space. Causality is an abstraction that indicates how the world progresses. As such a basic concept, it is more apt as an explanation of other concepts of progression than as something to be explained by others more basic. The concept is like those of agency and efficacy. For this reason, a leap of intuition may be needed to grasp it. Accordingly, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Premise
A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion. A premise makes a declarative statement about its subject matter which enables a reader to either agree or disagree with the premise in question, and in doing so understand the logical assumptions of the argument. If a premise is logically false, then the conclusion, which follows from all of the premises of the argument, must also be false—unless the conclusion is supported by a logically valid argument which the reader agrees with. Therefore, if the reader disagrees with any one of the argument's premises, they have a logical basis to reject the conclusion of the argument. Explanation In logic, an argument requires a set of at least two declarative sentences (or "propositions") known as the "premises" (or "premisses"), along with another declarative sentence (or "proposition"), known as the conclusion. This structure of two prem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Co-premise
A co-premise is a premise in reasoning and informal logic which is not the main supporting reason for a contention or a lemma, but is logically necessary to ensure the validity of an argument. One premise by itself, or a group of co-premises can form a reason. Logical structure Every significant term or phrase appearing in a premise of a simple argument, should also appear in the contention/conclusion or in a co-premise. But this by itself does not guarantee a valid argument, see the fallacy of the undistributed middle for an example of this. Sometimes a co-premise will not be explicitly stated. This type of argument is known as an 'enthymematic' argument, and the co-premise may be referred to as a 'hidden' or an 'unstated' co-premise and will often be subject to an inference objection. In this argument map An argument map or argument diagram is a visual representation of the structure of an argument. An argument map typically includes the key components of the argument, tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inference Objection
In argumentation, an objection is a reason arguing against a premise, argument, or conclusion. Definitions of objection vary in whether an objection is always an argument (or counterargument) or may include other moves such as questioning. An objection to an objection is sometimes known as a rebuttal. An objection can be issued against an argument retroactively from the point of reference of that argument. This form of objection – invented by the presocratic philosopher Parmenides – is commonly referred to as a retroactive refutation. Inference objection An inference objection is an objection to an argument based not on any of its stated premises, but rather on the relationship between a premise and main contention. For a given simple argument, if the assumption is made that its premises are correct, fault may be found in the progression from these to the conclusion of the argument. This can often take the form of an unstated co-premise, as in begging the question. In othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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