# informal logic

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). Johnson and Blair[1] define informal logic as "a branch of logic whose task is to develop non-formal standards, criteria, procedures for the analysis, interpretation, evaluation, criticism and construction of argumentation in everyday discourse."

Opinion pieces of newspapers provide illustrative textbook examples of informal logic,[2] usually because these pieces are short and often fallacious. However, informal logic is also used to reason about events in the human and social sciences. In fact, most reasoning from known facts to unknown facts that uses natural language, even if combined with mathematical or statistical reasoning, can be regarded as an application of informal logic so long as it does not rely on additional empirical evidence.

## Mathematics and the natural sciences

In mathematics the reasoning that occurs in proofs, though informal, is often regarded as a close approximation to a formal proof, that is, one which is carried out in a formal system of logic. Note that in practice, however, the separation between an informal mathematical proof and its formal idealization is so large that hardly anyone attempts to bridge that gap. This gap arises because most steps in informal proofs accumulate an enormous number of simple logical inferences, or other proof steps which are straightforward to most readers with enough mathematical experience. Moreover, many mathematical researchers regard proof as something other than a sequence of inference steps. Nevertheless, one of the goals of the Mizar project is to formalize the entire body of informal proofs of mathematics.

In theoretical physics, arguments are used to derive new formulae or physical principles. These arguments often use mathematics, although in many cases the relations between assertions in a derivation contain mathematically serious gaps. Examples of these mathematical gaps are failure to prove convergence of an infinite series or an integral (or worse, rely on an expression whose value is known to be divergent) or ignoring quantities which are small in a limiting sense. Despite mathematical gaps, arguments used in physical derivations are generally considered to be valid arguments.

## Social sciences

In the social sciences many arguments are based on applications of statistics to demonstrate correlation or lack thereof between sets of variables, such as levels of income and education, ethnicity and wealth and so on. Such arguments are based on theories of statistical hypothesis testing together with empirical data accumulated by polling, collection of historical records, long term studies etc. Econometrics is the branch of economics that applies statistics to economics. Besides statistics, economists use a wide variety of analytical tools, for example, calculus, qualitative reasoning about systems of equations, asymptotic analysis (theories of growth), and so on.

## Law and politics

An extremely intricate form of reasoning is legal reasoning since it involves such considerations as legal precedent and existing law. The nature of the propositions used in legal reasoning is one of the concerns of legal theory.

## References

1. ^ Johnson, Ralph H., and Blair, J. Anthony (1987), "The Current State of Informal Logic", Informal Logic, 9(2–3), 147–151.
2. ^ Walton, Douglas N. (1989), Informal Logic, A Handbook for Critical Argumentation, Cambridge University Press, Cambridge, UK.

• Blair, J. Anthony, Hansen, Hans V., Johnson, Ralph H., and Tindale, Christopher (eds.), Informal Logic. (Journal of Record).
• Johnson, Ralph H., Manifest Rationality: A Pragmatic Theory of Argument, Lawrence Erlbaum, 2000.
• Johnson, Ralph H., and Blair, J. Anthony, "Logical Self-Defense", IDEA, 2006. First published, McGraw Hill Ryerson, Toronto, ON, 1997, 1983 (2e), 1993 (3e). Reprinted, McGraw Hill, New York, NY, 1994.

An argument is a statement (premise) or group of statements (premises) offered in support of another statement (conclusion). Argument may refer to:

### General types of argument

• Argument form, a method of logically analyzing sentences

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.
Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. A proof is a logical argument, not an empirical one. That is, one must demonstrate that a proposition is true in all cases before it is considered a theorem of mathematics.
The Mizar system consists of a language for writing strictly formalized mathematical definitions and proofs, a computer program which is able to check proofs written in this language, and a library of definitions and proved theorems which can be referred to and used in new articles.
Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
In mathematics, a series is often represented as the sum of a sequence of terms. That is, a series is represented as a list of numbers with addition operations between them, for example this arithmetic sequence:

1 + 2 + 3 + 4 + 5 + ... + 99 + 100.

INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) is detecting some of the most energetic radiation that comes from space. It is the most sensitive gamma ray observatory ever launched.
Divergence can refer to:

In mathematics:
• Divergence, a function that associates a scalar with every point of a vector field
• The defining property of divergent series; series that have no bounded sum
In science:
• Genetic divergence

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
A statistic (singular) is the result of applying a function (statistical algorithm) to a set of data.
Poll may refer to:
• Opinion poll, a survey of people's opinions. As in ‘a poll of registered voters’ or ‘an opinion poll of regular movie goers.â€™
• Polling station, a place where a voters cast their ballots

Econometrics is concerned with the tasks of developing and applying quantitative or statistical methods to the study and elucidation of economic principles.[1] Econometrics combines economic theory with statistics to analyze and test economic relationships.

In pure mathematics and applications, particularly the analysis of algorithms, real analysis, and engineering,
Economic growth is the increase in value of the goods and services produced by an economy. It is conventionally measured as the percent rate of increase in real gross domestic product, or GDP. Growth is usually calculated in real terms, i.e.
precedent or authority is a legal case establishing a principle or rule that a court or other judicial body adopts when deciding subsequent cases with similar issues or facts.
LAW may refer to:
• Lightweight Anti-tank Weapon, like the M72 LAW (US Army) and the LAW 80 (British Army)
• Palestinian Society for the Protection of Human Rights (also known as LAW)
• League of American Bicyclists, formerly known as the League of American Wheelmen

Argumentation theory, or argumentation, embraces the arts and sciences of civil debate, dialogue, conversation, and persuasion. It studies rules of inference, logic, and procedural rules in both artificial and real world settings.
An Argument map is a visual representation of the structure of an argument in informal logic. It includes the components of an argument such as a main contention, premises, co-premises, objections, rebuttals and lemmas.
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.
Critical thinking consists of mental processes of discernment, analyzing and evaluating. It includes all possible processes of reflecting upon a tangible or intangible item in order to form a solid judgment that reconciles scientific evidence with common sense.
A fallacy is a component of an argument that is demonstrably flawed in its logic or form, thus rendering the argument invalid in whole. In logical arguments, fallacies are either formal or informal.
An informal fallacy is an argument pattern that is wrong due to a mistake in its reasoning. In contrast to a formal fallacy, the error has to do with issues of rational inference that occur in natural language; which are broader than can be represented by the symbols used in formal
In informal logic, an inference objection is an objection to an argument based not on any of its stated premises, but rather on the relationship between premise and contention.
Inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.
In informal logic and argument mapping, a lemma is simultaneously a contention for premises below it and a premise for a contention above it.

• Co-premise
• Objection
• Inference objection
• Lemma (mathematics)
• Lemma (linguistics)