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In philosophy, the geometrical method is a way of philosophizing that starts from a small set of self-evident axioms and tries to build a comprehensive logical system using deductive reasoning. Definition
The reasoning in a deduction is by definition cogent. Such reasoning itself, or the chain of intermediates representing it, has also been called an argument, more fully a deductive argument . In many cases, an argument can be known to be valid by means of a deduction of its conclusion from its premises but non-deductive methods such as Venn ...
Deductive reasoning, the mental process of drawing inferences in which the truth of their premises ensures the truth of their conclusion Natural deduction , a class of proof systems based on simple and self-evident rules of inference that aim to closely mirror how reasoning actually occurs
Deductive inference is monotonic: if a conclusion is reached on the basis of a certain set of premises, then that conclusion still holds if more premises are added. By contrast, everyday reasoning is mostly non-monotonic because it involves risk: we jump to conclusions from deductively insufficient premises.
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
A priori ('from the earlier') and a posteriori ('from the later') are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on experience. A priori knowledge is independent from any experience. Examples include mathematics, [i] tautologies and deduction from pure reason.
Philosophy of logic is the philosophical discipline studying the scope and nature of logic. [59] It examines many presuppositions implicit in logic, like how to define its basic concepts or the metaphysical assumptions associated with them. [ 158 ]
In logic and the philosophy of logic, specifically in deductive reasoning, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).