#### Contents

- Hypothetico-deductive Support
- Huygens’ Preface to Treatise on Light
- Probability and Statistics
- Approximate Predictions
- Hempel’s Argument against H-D Support

#### Hypothetico-deductive Support

- A scientific theory is supported by its confirmed predictions.
- The more
*unexpected*the truth of prediction (apart from the theory), the greater the H-D support.- Unexpected predictions:
- Electromagnetism’s prediction of Radio Waves
- Special Relativity’s prediction of Time Dilation
- Relativistic Quantum Mechanics’ prediction of Antimatter
- Big Bang Theory’s prediction of CMB Radiation
- General Relativity’s prediction of Gravitational Waves

- Unexpected predictions:
- The greater the
*variety*of confirmed predictions, the greater the H-D support.- General Relativity’s prediction of:
- Orbits of Heavenly Bodies, Motion of Falling Bodies, Time Dilation, Gravitational Redshift, Gravity Waves, Deflection of Light

- General Relativity’s prediction of:

**Christiaan Huygens **(CHRIS-tee-awn HI-goons)

**Preface to ***Treatise on Light* (1690)

*Treatise on Light*(1690)

“There is to be found here a kind of demonstration which does not produce a certainty as great as that of geometry and is, indeed, very different from that used by geometers, since they prove their propositions by certain and incontestable principles, whereas here *principles are tested by the consequences derived from them.* The nature of the subject permits no other treatment. It is possible nevertheless to attain in this way a degree of probability which is little short of complete certainty. *This happens when the consequences of our assumed principles agree perfectly with the observed phenomena, and especially when such verifications are numerous, but above all when we conceive in advance new phenomena which should follow from the hypotheses we employ and then find our expectations fulfilled*.”

#### Probability and Statistics

- H-D support extends to scientific theories and statistical hypotheses that predict probabilities
- Quantum Mechanics
- In the Stern Gerlach Experiment a beam of silver atoms is passed through a Stern-Gerlach magnet. Quantum Mechanics predicts that the probability of a silver atom being deflected upwards is ½. The prediction is confirmed statistically, by shooting billions of silver atoms through the apparatus.

- Statistical Estimation
- The hypothesis that 60% of voters approve of the president’s job performance predicts that there’s a 95% probability that between 57 and 63 percent of a 1000-member random poll approve of the president’s performance. Polls in that range support the hypothesis.

- Quantum Mechanics

#### Approximate Predictions

- Some predictions can’t be derived precisely.
- britannica.com/science/quantum-mechanics-physics
- “The Schrödinger equation cannot be solved precisely for atoms with more than one electron, because of the number of particles and the variety of forces involved.”
- “Despite these difficulties, approximation methods introduced by the English physicist Douglas R. Hartree, the Russian physicist Vladimir Fock, and others in the 1920s and 1930s have achieved considerable success.”

- Hence, much chemistry and some physics use models that make simplifying assumptions and yield only approximate results.

#### Hempel’s Argument against H-D Support

**Consider two theories of gravitation:***Newton’s Theory*- For every two objects
*there’s a force*on each, in the direction of the other, whose magnitude is**Gm**_{1}m_{2}/r^{2} **F = MA**

- For every two objects
*Angel Theory*- For every two objects
*angels exert a force*on each, in the direction of the other, whose magnitude is**Gm**_{1}m_{2}/r^{2} **F = MA**

- For every two objects

- Hempel’s Argument:
- Newton’s Theory is supported by its confirmed predictions of planetary orbits and the motion of falling bodies.
- Making the same predictions, the Angel Theory is equally supported.
- Therefore, there is empirical evidence for the existence of angels.

- H-D support can be defended against Hemple’s argument by appealing to the concept of simplicity.
- Newton’s theory is simpler than the Angel Theory because it doesn’t postulate needless entities.

- Only the simplest theories are supported by their confirmed predictions.

- Newton’s Theory is thus supported by its predictions; the Angel Theory is not.

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