1. Week 5: INTERNAL CRISIS Armahedi Mahzar ICAS Jacarta 2010
PHILOSOPHY
of SCIENCE
Week 5: INTERNAL CRISIS
Armahedi Mahzar
ICAS Jacarta 2010

2. Internal Crisis of Science
Physics
Mathematics

3. Internal Crisis of Science
Empirical Objectivism
Theory of Relativity
Quantum Theory
Mathematical Rationalism
Meta-mathematics
Computationalism

4. Internal Crisis of Science Principle of Relativity (Einstein)
Relativity of Space Time
Matter Energy Equivalence

5. Special Theory of Relativity
1905, Albert Einstein resolved the Michelson-Morley crisis by
discarding the ether concept and
asserting the principle of relativity —that the laws of physics are the same for all observers in uniform motion.
Shortly after publishing his 1905 paper on special relativity, Einstein realized that his theory required a fundamental equivalence between mass and energy, which he expressed in the equation E=mc2.

6. Special Theory of Relativity
As the consequence of his theory, we have to admit the relativity of space and time
Accordingly, two twins would age at different rates if one left on a high-speed journey to a distant star and then returned.
This experiment has actually been done, not with twins, but with an atomic clock flown around the world.
time slows as speed increases comes from measuring muons at the top and bottom of mountains.

7. General Theory of Relativity
Historically, the path to general relativity followed Einstein's attempt to incorporate gravity into relativity theory
gravity is not a force, but a local curvature manifestation of space-time geometry.

8. General Theory of Relativity
the expansion of the universe predicted by the theory of general relativity is now a known rate.
the existence of black holes, objects that warp space and time so that not even light can escape.

9. Indeterminacy of Observation
Quantum Theory
Indeterminacy of Observation
Wave Particle Duality

10. Heisenberg Principle of Uncertainty
Indeterminacy of Observation
We can not observe both the position and the momentum of a particle with the same accuracy

11. Wave-Particle Duality
Photo-electric Effect of Light as photon
Electron diffraction
Diffraction of Light as wave
Electron as Particle

12. Foundation of Mathematics
Logicism
Intuitionism
Formalism

13. Locicism Bertrand Russel
mathematics is an extension of logic and therefore some or all mathematics is reducible to logic

14. Intuitionism Brouwer
Mathematics as the constructive mental activity of humans.
Mathematics does not consist of analytic activities wherein deep properties of existence are revealed and applied.
logic and mathematics are the application of internally consistent methods to realize more complex mental constructs.

15. Formalism Hilbert
statements of mathematics and logic can be thought of as statements about the consequences of certain string manipulation rules.

16. Criticism of Mathematical Reductionism
Kurt Godel Theorem of Incompleteness
Alan Turing Theorem of Indecidability

17. Theorem of Incompleteness (Godel)
Incompleteness of Consistent Axiom System
Inconsistency of Complete Axiom System

18. Undecidability Theorem
there is no algorithm which can be applied to any arbitrary program and input to decide whether the program stops when run with that input

19. Conclusion Objects can not be separated from subject
Mathematical rationality can not be reduced