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Logical reasoning is a form of thinking that is concerned with arriving at a conclusion in a rigorous way. [1] This happens in the form of inferences by transforming the information present in a set of premises to reach a conclusion.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
A function that takes two arguments. In logic and mathematics, this is often a function that combines two values to produce a third value, such as addition or multiplication in arithmetic. binary relation A relation involving two terms or elements, defining a particular relationship between pairs of objects from two sets (or from one set to ...
On this view, the laws of logic are trivial since they are true by definition: they just express the meanings of the logical vocabulary. [178] Some theorists, like Hilary Putnam and Penelope Maddy, object to the view that logic is knowable a priori. They hold instead that logical truths depend on the empirical world. This is usually combined ...
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. As a formal science , logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of ...
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 two of the above illustrations, is the following: Let the letters 'P', 'Q', and 'S' stand, respectively, for the set of men, the set of ...
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science.Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language.
Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the nineteenth century with the aid of an artificial notation and a rigorously deductive method. [5]