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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 .
These two definitions of formal logic are not identical, but they are closely related. For example, if the inference from p to q is deductively valid then the claim "if p then q" is a logical truth. [16] Formal logic needs to translate natural language arguments into a formal language, like first-order logic, to assess whether they are valid.
Association fallacy (guilt by association and honor by association) – arguing that because two things share (or are implied to share) some property, they are the same. [94] Logic chopping fallacy (nit-picking, trivial objections) – Focusing on trivial details of an argument, rather than the main point of the argumentation. [95] [96]
The Banach–Tarski paradox: A ball can be decomposed and reassembled into two balls the same size as the original. Banach–Tarski paradox: A ball can be cut into a finite number of pieces and re-assembling the pieces will get two balls, each of equal size to the first. The von Neumann paradox is a two-dimensional version.
A statement in logic that is formed by combining two or more statements with logical connectives, allowing for the construction of more complex statements from simpler ones. [67] [68] comprehension schema A principle in set theory and logic allowing for the formation of sets based on a defining property or condition. computable function
The philosophy of logic can be understood in analogy to other discipline-specific branches of philosophy: just like the philosophy of science investigates philosophical problems raised by science, so the philosophy of logic investigates philosophical problems raised by logic. [4] An important question studied by the philosophy of logic is how ...
Distinct types of logical reasoning differ from each other concerning the norms they employ and the certainty of the conclusion they arrive at. Deductive reasoning offers the strongest support: the premises ensure the conclusion, meaning that it is impossible for the conclusion to be false if all the premises are true.
Logic (from the Greek "logos", which has a variety of meanings including word, thought, idea, argument, account, reason or principle) is the study of reasoning, or the study of the principles and criteria of valid inference and demonstration.