Logic > Umar Iqbal

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INFERENCE

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INDUCTIVE AND DEDUCTIVE INFERENCE

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VALID INFERENCE

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REASONING

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FORM OF AUGUMENT

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DEDUCTIVE REASONING

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INDUCTIVE REASONING

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ABSTRUCTIVE REASONING

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FALLACIOUS REASONING

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FORMAL FALLACIS

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REFRENCES

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INFERENCE 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. Logic studies the laws of valid inference.

The accuracy of inductive and deductive inferences The conclusion inferred from multiple observations is made by the process of inductive reasoning. The conclusion may be correct or incorrect, and may be tested by additional observations. In contrast, the conclusion of a valid deductive inference is true if the premises are true. The conclusion is inferred using the process of deductive reasoning. A valid deductive inference is never false. This is because the validity of a deductive inference is formal. The inferred conclusion of a valid deductive inference is necessarily true if the premises it is based on are true. The field of half-truths as they relate to the truth of observations, is another area of concern impacting inference based on observations.

Valid inferences Inferences are either valid or invalid, but not both. Philosophical logic has attempted to define the rules of proper inference, i.e. the formal rules that, when correctly applied to true premises, lead to true conclusions. Aristotle has given one of the most famous statements of those rules in his Organon.

An example: the classic syllogism Greek philosophers defined a number of syllogisms, correct three-part inferences, that can be used as building blocks for more complex reasoning. We'll begin with the most famous of them all: All men are mortal Socrates is a man -----------------Therefore Socrates is mortal.

The reader can check that the premises and conclusion are true. The validity of the inference may not be true. The validity of the inference depends on the form of the inference. That is, a valid inference does not depend on the truth of the

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premises and conclusion, but on the formal rules of inference being used. In traditional logic, the form of the syllogism is: All A is B All C is A ---------All C is B

Since the syllogism fits this form, then the inference is valid. And if the premises are true, then the conclusion is necessarily true.

REASONING Reasoning is the process of looking for reasons on which to base one's beliefs or actions. In philosophy, the study of reasoning typically focuses on what makes reasoning good or bad, appropriate or inappropriate. Philosophers do this by either examining the form or structure of the reasoning within arguments, or by considering the broader methods used to reach particular goals of reasoning, such as beliefs or actions. Psychologists, in contrast, tend to study how people actually reason, and how those methods of reasoning help or hinder people.

Reasoning and forms of argument One approach to the study of reasoning is to identify various forms of reasoning that may be used to support or justify conclusions. The main division between forms of reasoning that is made in philosophy is between deductive reasoning and inductive reasoning. Formal logic has been described as 'the science of deduction' (Jeffrey, 1991, 1). The study of inductive reasoning is generally called either 'informal logic' or 'critical thinking'.

Deductive reasoning Deductive arguments are intended to have reasoning that is valid. Reasoning in an argument is valid if the argument's conclusion must be true when the premises (the reasons given to support that conclusion) are true. One classic example of deductive reasoning is that found in syllogisms like the following: 1. All humans are mortal. 2. Socrates is a human. 3. Therefore, Socrates is mortal. The reasoning in this argument is valid, because there is no way in which the premises, 1 and 2, could be true and the conclusion, 3, be false.

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Validity is a property of the reasoning in the argument, not a property of the premises in the argument or the argument as a whole. In fact, the truth or falsity of the premises and the conclusion is irrelevant to the validity of the reasoning in the argument. The following argument, with a false premise and a false conclusion, is also valid, (it has the form of reasoning known as modus ponens). 1. If green is a colour, then grass poisons cows. 2. Green is a colour. 3. So, grass poisons cows. Again, if the premises in this argument were true, the reasoning is such that the conclusion would also have to be true. In a deductive argument with valid reasoning the conclusion contains no more information than is contained in the premises. Therefore, deductive reasoning does not increase one's knowledge base, and so is said to be non-ampliative. Within the field of formal logic, a variety of different forms of deductive reasoning have been developed. These involve abstract reasoning using symbols, logical operators and a set of rules that specify what processes may be followed to arrive at a conclusion. These forms of reasoning include Aristotelian logic, also known as syllogistic logic, propositional logic, predicate logic, and modal logic.

Inductive reasoning Inductive reasoning contrasts strongly with deductive reasoning. Even in the best, or strongest, cases of inductive reasoning, the truth of the premises does not guarantee the truth of the conlusion. Instead, the conclusion of an inductive argument follows with some degree of probability. Relatedly, the conclusion of an inductive argument contains more information than is already contained in the premises. Thus, this method of reasoning is ampliative. A classical example of inductive reasoning comes from the empiricist David Hume: 1. The sun has risen in the east every morning up until now. 2. So, the sun will also rise in the east tomorrow.

Abductive reasoning , or argument to the best explanation often involves both inductive and deductive arguments. However, as the conclusion in an abductive argument does not follow with certainty from its premises it is best thought of as a form of inductive reasoning. What separates abduction from the other forms of reasoning is an attempt to favor one conclusion above others, by attempting to falsify alternative

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explanations or by demonstrating the likelihood of the favored conclusion, given a set of more or less disputable assumptions.

Fallacious reasoning Flawed reasoning in arguments is known as fallacious reasoning. Reasoning within arguments can be bad because it commits either a formal fallacy or an informal fallacy.

Formal Fallacies Formal fallacies occur when there is a problem with the form, or structure, of the argument, and, for this reason, always make an argument invalid. Consider, for example, the following argument: 1. If a drink is made with boiling water, it will be hot. 2. This drink was not made with boiling water. 3. This drink is not hot. The reasoning in this argument is bad, because the antecedent (first part) of the conditional (the 'if..., then...' statement) can be false without the consequent (second half) of the conditional being true. In this example, the drink could have been made with boiling milk, or heated in the microwave, and so be hot in spite of the truth of statement 2. This particular formal fallacy is known as denying the antecedent.

References • • •

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Jeffrey, Richard. 1991. Formal logic: its scope and limits, (3rd ed.). New York: McGraw-Hill. Vincent F. Hendricks, Thought 2 Talk: A Crash Course in Reflection and Expression, New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8 Scriven, Michael. 1976. Reasoning. New York: McGraw-Hill. ISBN 0-07055882-5 Ian Hacking. An Introduction to Probability and Inductive Logic. Cambridge University Press, (2000). Edwin Thompson Jaynes. Probability Theory: The Logic of Science. Cambridge University Press, (2003). ISBN 0-521-59271-2. David J.C. McKay. Information Theory, Inference, and Learning Algorithms. Cambridge University Press, (2003). Stuart Russell, Peter Norvig. Artificial Intelligence: A Modern Approach. Prentice Hall, (2002). Henk Tijms. Understanding Probability. Cambridge University Press, (2004). André Fuhrmann: Nonmonotonic Logic. 5

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