logic

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 inference and through the study of arguments in natural language. The field of logic ranges from core topics such as the study of fallacies and paradoxes, to specialized analysis of reasoning using probability and to arguments involving causality. Logic is also commonly used today in argumentation theory.
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(n.)
The science or art of exact reasoning, or of pure and formal thought, or of the laws according to which the processes of pure thinking should be conducted; the science of the formation and application of general notions; the science of generalization, judgment, classification, reasoning, and systematic arrangement; correct reasoning.
  

(n.)
A treatise on logic; as, Mill's Logic.
  

Logic An attempt to formulate the processes of the ratiocinative mind, connecting idea with idea in a causal sequence, leading from predicate to conclusion. When the predicate consists of axioms, the species of logic is called deductive, or reasoning from the general to the particular; when the predicate is facts of experience, the logic is called inductive, or proceeding from particulars to generals. As a means of arriving at truth it alone is quite unreliable, as it is but a body of rules based on human experiences, and hence it is often rather a means of justifying conclusions after they have already been formed. This unreliability arises both from the difficulty of applying the process with rigid precision, and also from the uncertainty of the predicates in both systems. A study of what is written on logic will show that there is no agreement as to what constitutes an axiom -- whether it is an intuitive perception of truth, or whether it is merely an inference from experience. The same uncertainty exists as to the validity of the assumptions from which inductive chains of reasoning are drawn.
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On PMTH, the word "logic" generally refers, not to the colloquial meaning of this term but to the system of formal reasoning introduced by Aristole. Aristotle's logic was based on three principles, the Law of the Excluded Middle, the Law of Contradiction  and the Law of Identity.   In recent times there are symbolic logics which can be more complex.  In Aristotlean, or categorical, logic, a statement can be only true or false, not both at the same time.  In modern logics, there can be alternative valuations of a statement.  In fuzzy logic , we can speak of the proportion of truth in each statement.