Theory of science
By
Arve Meisingset
Theory of Science
as Proof theory
• Statements about classes of instances
• Hypothesis: x (xD  P(f(x)))
• For all apples (the apple hangs on a branch of a tree, then it
is true that the apple bends the branch with the force
F=g*m(apple))
• Popper’s falsification
• x (xD  P(x))   x (xD  P(x))
• There exists an apple on a particular branch that both rests
on a table, Hence, it is Not True that For all …
Theory of knowledge
• Statement about individual instances
– This apple exists
– This apple is red, or the redness of this apple exists
System
Nowegian
Phenomena
Data not denoting anything
Isomorphism
Phenomena not being denoted
Arve’s views
• Extreme nominalist; phenomena (both classes and instances) are data in
some observer automaton; ref. the War of Universals
• Phenomenologist; neither the real world nor concepts exist (the way
phenomena exist), repeated observations organise the world of phenomena
• Finitist; real numbers are functions with no stop condition, there exists no
infinity, no continuity, and no sets; ref. Cantor
• Constructivist; equations are just boundary conditions of algoritms; an
equation without an algortm is an incomplete specification
• Relativist; all phenomena must be refered to some observer phenomenon
• Automaton; we cannot claim to more general than the automata we can
•
describe without making claims which do not denote
etc.!