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In epistemology, the Münchhausen trilemma is a thought experiment used to demonstrate the impossibility of proving any truth, even in the fields of logic and mathematics. If it is asked how any given proposition is known to be true, proof may be provided. Yet that same question can be asked of the proof, and any subsequent proof. The Münchhausen trilemma is that there are only three options when providing further proof in response to further questioning:

• The circular argument, in which the proof of some proposition is supported only by that proposition
• The regressive argument, in which each proof requires a further proof, ad infinitum
• The axiomatic argument, which rests on accepted precepts which are merely asserted rather than defended

The trilemma, then, is the decision among the three equally unsatisfying options.

The name Münchhausen-Trilemma was coined by the German philosopher Hans Albert in 1968 in reference to a trilemma of "dogmatism versus infinite regress versus psychologism" used by Karl Popper. It is a reference to the problem of "bootstrapping", based on the story of Baron Munchausen (in German, "Münchhausen") pulling himself and the horse on which he was sitting out of a mire by his own hair.

It is also known as Agrippa's trilemma or the Agrippan trilemma after a similar argument reported by Sextus Empiricus, which was attributed to Agrippa the Skeptic by Diogenes Laërtius, as well as Fries's trilemma after German philosopher Jakob Friedrich Fries. Sextus' argument, however, consists of five (not three) "modes". Popper in his original 1935 publication mentions neither Sextus nor Agrippa, but attributes his trilemma to Fries.

In contemporary epistemology, advocates of coherentism are supposed to accept the "circular" horn of the trilemma; foundationalists rely on the axiomatic argument. The view that accepts infinite regress is called infinitism.

In philosophy and psychology, an alief is an automatic or habitual belief-like attitude, particularly one that is in tension with a person's explicit beliefs.

For example, a person standing on a transparent balcony may believe that they are safe, but alieve that they are in danger. A person watching a sad movie may believe that the characters are completely fictional, but their aliefs may lead them to cry nonetheless. A person who is hesitant to eat fudge that has been formed into the shape of feces, or who exhibits reluctance in drinking from a sterilized bedpan may believe that the substances are safe to eat and drink, but may alieve that they are not.

The term alief was introduced by Tamar Gendler, a professor of philosophy and cognitive science at Yale University, in a pair of influential articles published in 2008. Since the publication of these original articles, the notion of alief has been utilized by Gendler and others — including Paul Bloom and Daniel Dennett — to explain a range of psychological phenomena in addition to those listed above, including the pleasure of stories, the persistence of positive illusions, certain religious beliefs, and certain psychiatric disturbances, such as phobias and obsessive–compulsive disorder.

In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality.

Molyneux's problem is a thought experiment in philosophy concerning immediate recovery from blindness. It was first formulated by William Molyneux, and notably referred to in John Locke's An Essay Concerning Human Understanding (1689). The problem can be stated in brief, "if a man born blind can feel the differences between shapes such as spheres and cubes, could he, if given the ability to see, distinguish those objects by sight alone, in reference to the tactile schemata he already possessed?"

Sturgeon's revelation (as expounded by Theodore Sturgeon), referred to as Sturgeon's law, is an adage cited as "ninety percent of everything is crap." The sentence derives from quotations by Sturgeon, an American science fiction author and critic; although Sturgeon coined another adage he termed "Sturgeon's law", the "ninety percent crap" remark became Sturgeon's law.

The phrase was derived from Sturgeon's observation while science fiction was often derided for its low quality by critics, the majority of examples of works in other fields could equally be seen to be of low quality, and science fiction was thus no different in that regard from other art forms.

The unexpected hanging paradox or hangman paradox is a paradox about a person's expectations about the timing of a future event which they are told will occur at an unexpected time. The paradox is variously applied to a prisoner's hanging, or a surprise school test. It could be reduced to be Moore's paradox.

Despite significant academic interest, there is no consensus on its precise nature and consequently a final correct resolution has not yet been established. Logical analysis suggests that the problem arises in a self-contradictory self-referencing statement at the heart of the judge's sentence. Epistemological studies of the paradox have suggested that it turns on our concept of knowledge. Even though it is apparently simple, the paradox's underlying complexities have even led to its being called a "significant problem" for philosophy.

Michel Eyquem, Seigneur de Montaigne ( mon-TAYN; French: [miʃɛl ekɛm də mɔ̃tɛɲ]; 28 February 1533 – 13 September 1592), known as Michel de Montaigne, was one of the most significant philosophers of the French Renaissance. He is known for popularizing the essay as a literary genre. His work is noted for its merging of casual anecdotes and autobiography with intellectual insight. Montaigne had a direct influence on numerous Western writers; his massive volume Essais contains some of the most influential essays ever written.

During his lifetime, Montaigne was admired more as a statesman than as an author. The tendency in his essays to digress into anecdotes and personal ruminations was seen as detrimental to proper style rather than as an innovation, and his declaration that "I am myself the matter of my book" was viewed by his contemporaries as self-indulgent. In time, however, Montaigne came to be recognized as embodying, perhaps better than any other author of his time, the spirit of freely entertaining doubt that began to emerge at that time. He is most famously known for his skeptical remark, ''Que sçay-je?" ("What do I know?", in Middle French; now rendered as "Que sais-je?" in modern French).

Pyrrhonism is an Ancient Greek school of philosophical skepticism which rejects dogma and advocates the suspension of judgement over the truth of all beliefs. It was founded by Aenesidemus in the first century BCE, and said to have been inspired by the teachings of Pyrrho and Timon of Phlius in the fourth century BCE. Pyrrhonism is best known today through the surviving works of Sextus Empiricus, writing in the late second century or early third century CE. The publication of Sextus' works in the Renaissance ignited a revival of interest in Skepticism and played a major role in Reformation thought and the development of early modern philosophy.

The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. First introduced by Arthur P. Dempster in the context of statistical inference, the theory was later developed by Glenn Shafer into a general framework for modeling epistemic uncertainty—a mathematical theory of evidence. The theory allows one to combine evidence from different sources and arrive at a degree of belief (represented by a mathematical object called belief function) that takes into account all the available evidence.

In a narrow sense, the term Dempster–Shafer theory refers to the original conception of the theory by Dempster and Shafer. However, it is more common to use the term in the wider sense of the same general approach, as adapted to specific kinds of situations. In particular, many authors have proposed different rules for combining evidence, often with a view to handling conflicts in evidence better. The early contributions have also been the starting points of many important developments, including the transferable belief model and the theory of hints.

Social facilitation is defined as improvement or decrease in individual performance when working with other people rather than alone.

In addition to working together with other people, social facilitation also occurs in the mere presence of other people. Previous research has found that individual performance is improved by coaction, performing a task in the presence of others who are performing a similar task, and having an audience while performing a certain task. An example of coaction triggering social facilitation can be seen in instances where a cyclist's performance is improved when cycling along with other cyclists as compared to cycling alone. An instance where having an audience triggers social facilitation can be observed where a weightlifter lifts heavier weight in the presence of an audience. Social facilitation has occasionally been attributed to the fact that certain people are more susceptible to social influence, with the argument that personality factors can make these people more aware of evaluation.

The Yerkes-Dodson law, when applied to social facilitation, states that "the mere presence of other people will enhance the performance in speed and accuracy of well-practiced tasks, but will degrade in the performance of less familiar tasks." Compared to their performance when alone, when in the presence of others they tend to perform better on simple or well-rehearsed tasks and worse on complex or new ones.

The audience effect attempts to explain psychologically why the presence of an audience leads to people performing tasks better in some cases and worse in others. This idea was further explored when some studies showed that the presence of a passive audience facilitated the better performance of a simple task, while other studies showed that the presence of a passive audience inhibited the performance of a more difficult task or one that was not well practiced, possibly due to psychological pressure or stress. (See Yerkes–Dodson law.)