Logic in a narrow sense is equivalent to deductive logic. By definition , such reasoning cannot produce any information in the form of a conclusion that is not already contained in the premises. In a wider sense, which is close to ordinary usage, logic also includes the study of inferences that may produce conclusions that contain genuinely new information. Such inferences are called ampliative or inductive , and their formal study is known as inductive logic.
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They are illustrated by the inferences drawn by clever detectives, such as the fictional Sherlock Holmes. The contrast between deductive and ampliative inferences may be illustrated in the following examples. However, when a forensic scientist infers from certain properties of a set of human bones the approximate age, height, and sundry other characteristics of the deceased person, the reasoning used is ampliative, because it is at least conceivable that the conclusions yielded by it are mistaken. The most important logical constants are quantifiers , propositional connectives, and identity.
Logical form can also be thought of as the result of replacing all of the nonlogical concepts in a proposition by logical constants or by general logical symbols known as variables. The formulas in 3 and 4 above are explicit representations of the logical forms of the corresponding English propositions. The study of the relations between such uninterpreted formulas is called formal logic. It should be noted that logical constants have the same meaning in logical formulas, such as 3 and 4 , as they do in propositions that also contain nonlogical concepts, such as 1 and 2.
Valid logical inferences are made possible by the fact that the logical constants, in combination with nonlogical concepts, enable a proposition to represent reality. Indeed, this representational function may be considered their most fundamental feature. Build a bridge to get the car onto the ferry. Help Robo fix everything!
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