Analytical philosophy Gottlob Frege 1848 Wismar 1925 Strengthening

Analytical philosophy Gottlob Frege (1848 Wismar – 1925) • Strengthening of foundations of mathematics • What is the “proof”? “Demonstratio” • Developed „Conceptual script“ – suppression of irrelevant elements of language, emancipation from psychology • Fundaments of arithmetics (what is number? - mistake (Russell)) • Program of logicism – mathematics founded on logic 1

“Über Sinn und Bedeutung” „On Sense and Reference“ (1892) Distinguished two kinds o „meaning“ or „sense“ (of word, indicative sentence). (Not all meaningful sentences express or contain thoughts, e. g. , commands, questions, but only indicative sentences. ) 1. „Reference“ (meaning, Bedeutung) concrete subject in the case of name, truth value in the case of sentence – (extension) 2. Sense (Sinn) haw the subject is given to us (intension). Senses (of words or sentences) are not in the mind, they are not part of the sensible material world. They are public, objective – intersubjective - accessible by more than one person, they are immaterial and imperceptible. E. g. , „ 3+2“: 1. 5 2. it is summation 3+2 „evening star“ or „morning star“: 1. planet Venus 2. Bright star that appears at evening or in the morning An expression is said to express its sense, and denote or refer to its reference. 2

Verity (truthfulness) – is no subject, is not concerning perception but thoughts (propositions) in logical space What sort of thing are the senses expressed by indicative sentences? What sort of thing are thoughts? Frege´s three Realms: The First Realm (things) This is the outer world, the world of material, perceptible things. Things in this world can exist without being perceived or thought. A person who is still untouched by philosophy knows first of all things which he can perceive with the senses, and he/she is convinced that another person equally can perceive the same things. 3

The Second Realm (inner world, „inner thoughts“) (inner – ideas) Sensations, feelings, moods, inclinations, wishes, etc. 1. Ideas cannot be seen or touched, cannot be smelled, nor tasted, nor heard. You do not see your mental image of a tree; you see the tree. That is to have a mental image of a tree. 2. Ideas do not objectively „exist“ but are had. One has sensations, feelings, moods, inclinations, wishes. An idea which someone has belongs to the content of his consciousness. 3. Ideas need a bearer. An experience is impossible without an somebody who has the experience. The inner world presupposes the person whose inner world it is. In this way ideas are unlike objects in the First Realm, which are independent of anyone. 4. Every idea has only one bearer; no two men have the same idea. Idea can be “had” by only one bearer - thoughts are not ideas. If thoughts were ideas, then there would not be e. g. , a single Pythagorean Theorem, but my Pythagorean Theorem, your Pythagorean, … There would be no science common to many, on which many could work. 4

The Third Realm („objective“ thoughts) The Third Realm is the world of „objective“ thoughts (propositions). Like ideas, thoughts cannot be seen, heard, etc. But like things in the First Realm, they do not need a bearer. They are true (or false) whether or not anyone thinks they are. A given thought can be apprehended by more than one person. 5

Analytical philosophy Bertrand Russell (1872 – 1970 Wales) British philosopher, logician, essayist and social critic (pacifism), education, history, political history, religious studies – atheism, advocated „common sense“ defence of logicism - the view that mathematics is reducible to logic - refining the predicate calculus introduced by Frege (which still forms the basis of most contemporary logic), Suspicious basic concepts: spirit, matter, consciousness, experience, causality, time Logical atomism – fundamental fact directly perceived Along with Kurt Godel, Russell is one of the most important logicians of the twentieth century. Nobel Prize for Literature in 1950, many anti-war and anti-nuclear protests 6

Russell's paradox (in reality contradiction!) 1901 R. P. arises within naive set theory (in which any coherent condition may be used to determine a set). Consider the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox. (E. g. , the set of all non-teacups, are members of themselves. ) Self-refering paradox (like the liar paradox) From a contradiction follow all sentences. Set theory underlies all branches of mathematics, if set theory was inconsistent, no mathematical proof could be trusted completely. – crisis of mathematics 7

Russell´s theory of types arranging all sentences into a hierarchy: The lowest level of this hierarchy will consist of sentences about individuals. The next level will consist of sentences about sets of individuals, and so on. Etc. It is then possible to refer to all objects for which a given condition (or predicate) holds only if they are all at the same level or of the same “type”. vicious circle („circular object“ in Frege description, fractals) statements about “all propositions” are meaningless - illegitimate totalities (E. g. , omnipotent God – can he create so heavy stone he cannot lift? …) 8

“Neutral monism” opposed to idealistic monism and materialistic monism The things commonly regarded as mental and the things regarded as physical differ only in respect of arrangement and context. Comparison with a postal directory, in which the same names comes twice over, once in alphabetical and once in geographical order; we may compare the alphabetical order to the mental, and the geographical order to the physical. Just as every man in the directory has two kinds of neighbours, namely alphabetical neighbours and geographical neighbours, so every object will lie at the intersection of two causal series with different laws, namely the mental series and the physical series. “The whole duality of mind and matter is a mistake; there is only one kind of stuff out of which the world is made, and this stuff is called mental in one arrangement, physical in the other. ” 9

Ludwig Wittgenstein 1889 Vienna – 1951 Austrian-Born British philosopher logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. Realschule in Linz (Hitler) Jewish background, loss of faith, study of aircraft engineering (Berlin), met Russell and Frege, study of philosophy in Cambridge, Norway, voluntier in Austian army , italian capcure Tractatus logico-philosophicus (1918, published 1921) crisis, gardener, teacher, 1929 back in Cambridge. Did not publish. 10

The Structure of Tractatus There are seven main propositions in the text: 1 The world is everything that is the case. 2 What is the case (a fact) is the existence of states of affairs. 3 A logical picture of facts is a thought. 4 A thought is a proposition with a sense. (An elementary proposition is a truth-function of itself. ) 5 A proposition is a truth-function of elementary propositions. 6 The general form of a proposition is the general form of a truth function. 7 Where of one cannot speak, thereof one must be silent. Wittgenstein concluded that with the Tractatus he had resolved all philosophical problems. 11

Philosophical Investigations 1953 (Philosophische Untersuchungen) is one of the most influential philosophical work. Wittgenstein discusses numerous problems and puzzles in the fields of semantics, logic, philosophy, mathematics, psychology, mind. He puts forth the view that conceptual confusions surrounding language use are at the root of most philosophical problems, contradicting or discarding much of that which was argued in his earlier work, the Tractatus Logico-Philosophicus. • Language is rather some kind of game 12