Edmund Husserl, the founder of phenomenology, was Heidegger's teacher in Freiburg. His theory was a new version of Cartesianism with the focus on consciousness as 'subjectivity'. Phenomenology is the examination of consciousness in the flow of experience. It is the study of the intentional structure of experiences, which means that consciousness is oriented towards something else.

Husserl's philosophical method is to subtract external knowledge from the external world (putting it into 'parentheses') which is when the philosopher reflects on how a phenomenon appears to consciousness. When looking at a tree, what remains after making the parentheses is a pure tension between the subject and the object. It is an introspective analysis of experience that attempts to go beyond linguistic expressions or a common understanding of the phenomenon.

Husserl was primarily a mathematician who was interested in the nature of truth more than life's problems. His philosophy seeks certainty, just like Descartes, Hume and Kant. He was looking for an 'Archimedean' point from which to establish a foundation for all knowledge. His interest is focused on the form and need for mathematical and philosophical truths.

His method aims to develop a worldview without prejudice that allows a rational exploration of the interconnections between phenomena. Following the Kantian concept of 'transcendental Ego' Husserl develops a 'transcendental phenomenology' as the foundation of all knowledge.

This is a contribution to epistemology, but it is based on questionable assumptions derived from German idealism.

Bertrand Russell explains his epistemological vision in The Problems of Philosophy. He affirms that philosophy is seeking certainty and we assume the certainty of many things that, when we look at them more closely, we realise that they are full of contractions. The more we learn from the world the more we realize that we know little for sure. The question of what our senses tell us lies in the problem of change.

To explain this problem Russell distinguishes between appearance and reality and calls it 'skepticism of the senses'. He gives the example of a table that is perceived based on the light in the room, the distance from the sensor, and how the light reflects from the table to the eyes. The same happens with the texture of the furniture and its shape.

"There is no logical impediment to suppose that life is a dream ..." Bertrand Russell

Thus Russell affirms that these observable facts must lead us to doubt our senses. The 'real' table is an inference, not the thing itself. He praises Descartes for having introduced the method of doubt and showing that the subjective is the most accurate base. According to Russell, trying to prove that there is a reality outside the mind is an argument about probabilities, not certainties.

Ludwig Wittgenstein published his ideas on epistemology in Über Gewissheit (1969) (On Certainty), a reflection on Moore's idea in his book A Defense of Common Sense (1925). Moore argues that common sense allows certain things to be known with certainty.

Wittgenstein distinguishes between knowledge and certainty by claiming that they are two categories, not two mental states and neither implies the other. It is possible to be in a state of knowledge without being sure and to be safe without having knowledge. Certainty is not identified with apprehending but with a form of action. A proposition is true when its truth is presupposed in the various activities of a community. In other words, it is our action that causes us to call something true.

A recurring theme in the book is that there are things that should not be doubted for activities to be possible and this includes the act of doubting.

"A doubt that doubts everything would not be a doubt."  Wittgenstein

An important result is Wittgenstein's assertion that all doubt is grounded in underlying beliefs and therefore the most radical forms of doubt must be rejected because they are contradictory to the very system that expressed them. Philosophical skepticism works within a rational debate, but if one doubts excessively, rationality itself is undermined and thus the basis for doubting.

However, Wittgenstein argues that skepticism only makes sense when we abstract from everyday life. He claims that a proposition is meaningless if it is not placed within a specific context. But once we attribute a context to propositions the doubts of a skeptic will lack the generality that would cast doubts on the external world. It is only by removing the language from all possible contexts, and thus rendering it useless, that skepticism can work.

Martin Heidegger in his book on ontology Sein und Zeit (1927) (Being and time) raises his fundamental question: What is Being? It begins with a critique of Descartes that, according to the author, did not raise the problem of the nature of being that accompanies the existence of the self. This Dasein is a community way of life similar to a shared language. It is Cartesianism in reverse: I exist then I can think.

"The human being is not the lord of beings, but the shepherd of Being." Heidegger

He also wants to reverse the Aristotelianism that proceeds by logic and grammar and is imprisoned in language. He wants to free language from grammar and logic as creation does poetics.

For Aristotle, thinking was a technique, a process of reflection in the service of doing and creating things. For Heidegger, thinking is not a practical task in the service of action. Thus he distances himself from scientific positivism and from Marxists like Sartre. He tries to develop a holistic philosophy that understands existence and thought as two sides of the same coin. He rejects an instrumental interpretation of thought (positivism) and an emphasis on pure theory (idealism, Platonism).

He disagrees with Plato because he was fascinated by the theory that carries an implicit promise of power over nature. For Heidegger, this led us, mistakenly, to believe that thinking is reality. This leads us to imagine that we can build models of everything including human beings and their world and that the way human beings relate to things is to have a theory about them. He wants to teach that there is no theory about what makes possible theories.

Heidegger aims to apply Husserl's method by not asking 'What is in your experience?' but 'What constitutes your experience?' It radicalizes Husserl's method and maintains that concepts like 'mind', 'subject', 'object' and even 'world' have no basis in experience and are thus reifications and not a fundamental analysis that investigates the correlation between thought and experience.

Heidegger's concept Dasein (Being) implies a permanent crisis of identity. We want to know who or what we really are, but what we consider our identity can easily be a false or misinformed concept. This will lead him to an interest in psychiatry.

Alfred Ayer published The Problem of Knowledge in 1956. In it he presents several theories of knowledge that have been proposed as responses to a radical skeptic who argues for a large gap between:

- belief in an external world, the existence of other minds or the reality of the past,

- the evidence on which these beliefs are based.

However, he changes his previous positivism and admits that not everything can be translated into the language of the senses. Instead he argues that constructions made on the basis of experience have their own validity.

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