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For the certainty of the truth of a proposition like '2 + 2 = 4', one rather appeals "to the coherence of [one's] proposition with an enormous mass of others" whose truth must stand or fall with it. [5] Coherentism is a view either about the structure and system of knowledge and truth, or else justified belief.
The argument from reason is a transcendental argument against metaphysical naturalism and for the existence of God (or at least a supernatural being that is the source of human reason). The best-known defender of the argument is C. S. Lewis .
In the most general terms, a reason is a consideration in an argument which justifies or explains an action, a belief, an attitude, or a fact. [1] Normative reasons are what people appeal to when making arguments about what people should do or believe. For example, that a doctor's patient is grimacing is a reason to believe the patient is in pain.
An argument is formally valid if and only if the denial of the conclusion is incompatible with accepting all the premises. In formal logic, the validity of an argument depends not on the actual truth or falsity of its premises and conclusion, but on whether the argument has a valid logical form.
Logic and rationality have each been taken as fundamental concepts in philosophy. They are not the same thing. Philosophical rationalism in its most extreme form is the doctrine that knowledge can ultimately be founded on pure reason, while logicism is the doctrine that mathematical concepts, among others, are reducible to pure logic.
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.
A logical or mathematical argument that demonstrates the truth of a statement or theorem, based on axioms, definitions, and previously established theorems. proof by cases A proof technique that divides the proof into several cases, showing that the statement to be proved holds in each case. proof by induction
In any area of mathematics defined by its assumptions or axioms, a proof is an argument establishing a theorem of that area via accepted rules of inference starting from those axioms and from other previously established theorems. [7] The subject of logic, in particular proof theory, formalizes and studies the notion of formal proof. [8]