Logical form is a linguistic formula used for deductive and inductive reasoning, logical analysis, and retroduction. It reduces a statement to its essential components and is attributed to Aristotle. It can determine if an argument is true, but is not foolproof. Logical form is created by transforming statements into variables and is treated as a mathematical statement. Recognized logical forms of argumentation help identify if an argument is valid or invalid, while logical fallacies weaken arguments.
A logical form is essentially a linguistic formula designed to reveal the essentials of a true statement. Methods of thinking that employ logical form include deductive and inductive reasoning, logical analysis, and retroduction. Logical form is achieved by reducing a statement to its essential components, using quantifier variables for the active parts of the sentence. When the statement is an argument, it can be called the form of the argument. The development of this method is attributed to the Greek philosopher Aristotle.
One major advantage of this method is that it is a means of examining the fundamental parts of an argument to determine whether its form allows for the possibility that the argument is true. However, it’s not a foolproof method; a logical form can prove a false argument to be true if one of the argument’s premises is false, so it is not safe to assume that an assertion is true based on the logical form alone. When applying a logical form to a statement, it is important to consider whether the statement should be applied as a whole or only in a particular context, because a statement may be true in some situations even if it is not true in all situations.
Logical form is created by transforming the parts of a statement into components represented by variables. In the statement “All candy is dessert and all dessert is wonderful,” the shape would be represented as “All C is D and all D is W.” Once reduced to variables, it is treated as a mathematical statement. This abbreviation gets out of the way information that is irrelevant to the contextual truth of the claim, allowing conclusions to be drawn from the form of the claim rather than the content. From this statement it can be deduced that C, being D, is also W, therefore all candies are wonderful. The introduction of the statement “All cake is sweet” or “All P is D” to the previous statement would lead to the conclusion that all cake, being a cake, is also wonderful.
The decomposition of arguments into their basic components often reveals that such arguments follow one of the recognized logical forms of argumentation. These shapes help identify whether an argument is valid, valid, or invalid based on how the statements leading to a conclusion are organized. Common valid argument forms include dilemma, proposal mode, and removal mode. The many logical fallacies that create weaknesses in invalid arguments include the use of personal attacks, generalizations, or appeals to authority to make the stated case.
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