Transcript A Filosofie II

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
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“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“:
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it is summation 3+2
1.
2.
„evening star“ or „morning star“:
1.
2.
planet Venus
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.
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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.
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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.
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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.
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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
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
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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
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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.
The next level will consist of sentences about sets of 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? …)
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“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.”
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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.
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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.
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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
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