In epistemology (theory of knowledge), a self-evident proposition is a proposition that is known to be true by understanding its meaning without proof, and/or by ordinary human reason.
Some epistemologists deny that any proposition can be self-evident. For most others, one's belief that oneself is conscious and possesses free will are offered as examples of self-evidence. However, one's belief that someone else is conscious or has free will are not epistemically self-evident.
Philosophical methodology encompasses the methods used to philosophize and the study of these methods. Methods of philosophy are procedures for conducting research, creating new theories, and selecting between competing theories. In addition to the description of methods, philosophical methodology also compares and evaluates them.
Philosophers have employed a great variety of methods. Methodological skepticism tries to find principles that cannot be doubted. The geometrical method deduces theorems from self-evident axioms. The phenomenological method describes first-person experience. Verificationists study the conditions of empirical verification of sentences to determine their meaning. Conceptual analysis decomposes concepts into fundamental constituents. Common-sense philosophers use widely held beliefs as their starting point of inquiry, whereas ordinary language philosophers extract philosophical insights from ordinary language. Intuition-based methods, like thought experiments, rely on non-inferential impressions. The method of reflective equilibrium seeks coherence among beliefs, while the pragmatist method assesses theories by their practical consequences. The transcendental method studies the conditions without which an entity could not exist. Experimental philosophers use empirical methods.
In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously defined concepts. It is often motivated informally, usually by an appeal to intuition or taken to be self-evident. In an axiomatic theory, relations between primitive notions are restricted by axioms. Some authors refer to the latter as "defining" primitive notions by one or more axioms, but this can be misleading. Formal theories cannot dispense with primitive notions, under pain of infinite regress (per the regress problem).
For example, in contemporary geometry, point, line, and contains are some primitive notions.
In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text. Such proofs can be considered more elegant than formal or mathematically rigorous proofs due to their self-evident nature. When the diagram demonstrates a particular case of a general statement, to be a proof, it must be generalisable.
A proof without words is not the same as a mathematical proof, because it omits the details of the logical argument it illustrates. However, it can provide valuable intuitions to the viewer that can help them formulate or better understand a true proof.