Information about validity

This article is about validity in logic. For the term in the social sciences, see validity (statistics).

The term validity as it occurs in logic refers generally to a property of deductive arguments, although many logic texts apply the term to statements as well (a statement is a sentence that “has a truth value,” i.e., that is either true or false). For the purposes of this article, an argument is a set of statements, one of which is the conclusion and the rest of which are premises. The premises are reasons intended to show that the conclusion is, or is probably, true.

When an argument is set forth to show that its conclusion is true (as opposed to probably true), then the argument is intended to be deductive. An argument set forth to show that its conclusion is probably true may be regarded as inductive. To say that an argument is valid is to say that the conclusion really does follow from the premises. That is, an argument is valid precisely when it cannot possibly lead from true premises to a false conclusion. The following definition is fairly typical:

*An argument is deductively valid if it cannot possibly have all true premises and a false conclusion.

An argument that is not valid is said to be ‘’invalid’’.

The following is a famous example of a deductively valid argument:

:All men are mortal

:Socrates is a man

:Therefore, Socrates is mortal.

What makes this a valid argument is not the mere fact that it has true premises and a true conclusion, but the fact of the logical impossibility of things being otherwise. No matter how the universe might be constructed, it could never be the case that this argument should turn out to have simultaneously true premises but a false conclusion. The above argument may be contrasted with the following invalid one:

:All men are mortal

:Socrates is mortal

:Therefore, Socrates is a man

In this case, there is no impossibility of true premises but false conclusion: it is easily imagined that there is a woman named ‘Socrates’, so that in fact the above premises would be true but the conclusion false—hence it is possible that the argument has true premises and a false conclusion. This possibility is what constitutes invalidity. (Although whether or not an argument is valid does not depend on what anyone could actually imagine to be the case, this approach helps us evaluate some arguments.)

A standard view is that whether an argument is valid is a matter of the argument’s logical form. Many techniques are employed by logicians to represent an argument’s logical form. A simple example, applied to the above two illustrations, is the following: Let the letters ‘P’, ‘Q’, and ‘s’ stand, respectively, for the set of men, the set of mortals, and Socrates. Using these symbols, the first argument may be abbreviated as:

:All P are Q

:s is a P

:Therefore, s is a Q

Similarly, the second argument becomes:

:All P are Q

:s is a Q

:Therefore, s is a P.

These abbreviations make plain the logical form of each respective argument. At this level, notice that we can talk about any arguments that may take on one or the other of the above two configurations, by replacing the letters P, Q and s by appropriate expressions. Of particular interest is the fact that we may exploit an argument's form to help discover whether or not the argument from which it has been obtained is or is not valid. To do this, we define an “interpretation” of the argument as an assignment of sets of objects to the upper-case letters in the argument form, and the assignment of a single individual member of a set to the lower-case letters of the argument form. Thus, letting P stand for the set of men, Q stand for the set of mortals, and s stand for Socrates is an interpretation of each of the above arguments. Using this terminology, we may give a formal analogue of the definition of deductive validity:

*An argument is formally valid if its form is one for which no interpretation exists under which the premises are all true but the conclusion false.

As already seen, the interpretation given above does cause the second argument form to have true premises and false conclusion, hence demonstrating its invalidity.

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Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration.
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The social sciences are a group of academic disciplines that study human aspects of the world. They diverge from the arts and humanities in that the social sciences tend to emphasize the use of the scientific method in the study of humanity, including quantitative and qualitative
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Please help recruit one or [ improve this article] yourself. See the talk page for details.
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Deductive reasoning, according to many dictionaries^[1]^[2]^[3]^[4], is the type of reasoning that proceeds from general principles or premises to derive particular information.
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Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not ensure it. It is used to ascribe properties or relations to types based on tokens (i.
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In discourse, a premise (also "premiss" in British usage) is a claim that is a reason (or element of a set of reasons) for, or objection against, some other claim. In other words, it is a statement presumed true within the context of the discourse for the purposes of arguing
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logical form of an argument is the representation of its sentences using the formal grammar and symbolism of a logical system to display its similarity with all other arguments of the same type.
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Logical consequence, arguably the most fundamental concept in logic, is the relation that holds between a set of sentences (or propositions) and a sentence (proposition) when the latter "follows from" the former.
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This article is about the soundness notion of informal logic. For soundness in mathematical logic, see soundness theorem.

A logical argument is sound if and only if

the argument is valid

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In propositional logic, a tautology (from the Greek word ταυτολογία) is a sentence that is true in every valuation (also called interpretation) of its propositional variables, independent of the truth values assigned to these
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A validator is a computer program used to check the validity or syntactical correctness of a fragment of code or document. The term is commonly used in the context of validating HTML, CSS and XML documents or RSS feeds though it can be used for any defined format or language.
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In western philosophy, reason has had a twofold history. On the one hand, it has been taken to be objective and so to be fixed and discoverable by dialectic, analysis or study.
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The history of logic documents the development of logic as it occurs in various cultures and traditions in history. While many cultures have employed intricate systems of reasoning, logic as an explicit analysis of the methods of reasoning received sustained development originally
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Philosophical logic is the study of the more specifically philosophical aspects of logic. The term contrasts with mathematical logic, and since the development of mathematical logic in the late nineteenth century, it has come to include most of those topics traditionally
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Philosophy of logic is the branch of philosophy that is concerned with the nature and justification of systems of logic. Some fundamental questions with which it is concerned are:

Is there only one "true" logic, or are many logics equally correct?

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Mathematical logic is a branch of mathematics, which grew out of symbolic logic. Subfields include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic has contributed to, and been motivated by, the study of foundations of mathematics, but
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The metalogic of a system of logic is the formal theory of the formal logic. Results in metalogic will consist of such things as formal proofs demonstrating the soundness of the logic.
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Logic in computer science describes topics where logic is applied to computer science and artificial intelligence. These include:

Investigations into logic that are guided by applications in computer science.

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Reasoning is the mental (cognitive) process of looking for reasons for beliefs, conclusions, actions or feelings.^[1] Humans have the ability to engage in reasoning about their own reasoning using introspection.
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Abduction, or inference to the best explanation, is a method of reasoning in which one chooses the hypothesis that would, if true, best explain the relevant evidence.
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Informal logic or non-formal logic is the study of arguments as presented in ordinary language, as contrasted with the presentations of arguments in an artificial, formal, or technical language (see formal logic).
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proposition is the content of an assertion, that is, it is true-or-false and defined by the meaning of a particular piece of language. The proposition is independent of the of communication.
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Inference is the act or process of deriving a conclusion based solely on what one already knows.

Inference is studied within several different fields.

Human inference (i.e. how humans draw conclusions) is traditionally studied within the field of cognitive psychology.

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Only a valid argument with true premises must have a true conclusion.
The validity of an argument depends on its form, not on the truth or falsity of its premises and conclusions. Logic seeks to discover the forms of valid arguments.
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An argument is cogent if and only if the truth of the argument's premises would render the truth of the conclusion probable (i.e., the argument is strong), and the argument's premises are, in fact, true.
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Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived until the advent of modern predicate logic in the late nineteenth century.
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Validity

See also