1. Here are two features of scientific reasoning that might initially have struck you as surprising, but which we have found to be unavoidable. Explain why they are unavoidable.
(a) A scientist may be justified in believing a theory to be false even if every observation that has been made so far is exactly as the theory predicts. (It might be helpful for you to think about two different curves that run through the same data points.)
(b) It is possible for a scientist to be justified in continuing to believe in a theory’s truth even if scientists have made some observations that they haven't yet found a way to fit with the theory. (To illustrate your points, give an example from the history of science.)

2. Identify several differences between laws and accidents. Give examples to illustrate those differences. How do these differences motivate Hempel’s D-N model of scientific explanation? Explain that model, and then give ONE counterexample to it. Explain carefully exactly why it counts as a counterexample.

3. The principle of energy conservation says that energy is neither created nor destroyed. It follows from this principle that the energy powering some phenomenon cannot have been created out of nothing but must have come from somewhere.
Radioactivity is the apparently spontaneous emission of energetic sub-atomic particles from atoms. That is, a radioactive atom suddenly ejects a particle at tremendous velocity. When radioactivity was discovered (in 1896), it seemed to conflict with the principle of energy conservation, which was accepted by all physicists and chemists. That is because according to energy conservation, the energy that powers the emission of particles from radioactive atoms must come from somewhere. But from where? The energy powering those particles seemed to have no source.
In 1898, Marie Curie (who became one of the most famous 20th-century physicists and a two-time Nobel Prize winner) investigated the origin of radioactive energy. She considered the possibility that the energy powering the emission of sub-atomic particles from a radioactive atom comes from some unknown source outside of that atom. She wrote:
One might imagine that all of space is constantly traversed by rays similar to X-rays [that is to say, invisible to our naked eyes], only much more penetrating [that is, having greater energy] and being able to be absorbed only by certain elements [namely, only by the radioactive atoms], where the absorbed energy of the rays powers the emission of particles from the atoms.
Regarding this “ray theory” regarding the origin of the energy powering radioactivity (a term that she was the first to use), Curie commented:
Any exception to [the law of energy conservation] can be evaded by the intervention of an unknown energy which comes to us from space. To adopt such an explanation or to put in doubt the generality of the [law of energy conservation] are in fact two points of view which to us amount to one and the same thing as long as the nature of the energy [source] here invoked is entirely arbitrary.
What is Curie saying? Explain her point in your own words. As you should expect, one or more of the concepts that we have discussed sometime in this course is relevant to your answer. Please explain the relevant concept(s) fully. Do you believe that Curie is correct in her view – not her scientific view about the origin of the energy powering radioactivity, but her view about the justification of the “ray theory” regarding this energy’s origin?

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One way to understand the possibility of a scientist having justification to believe that a theory is false in the face of putatively confirmatory observations is by recognizing that “the” theory in question is not some monolithic thing. That is, a theory’s predictions, with which observations may or may not match, are in fact the predictions of a particular hypothesis plus a host of implicit auxiliary assumptions and hypotheses. Under the Hypothetico-Deductive (HD) model of theory confirmation, the idea is that, if observations turn out to match a theory’s predictions, then the theory is (likely) confirmed; if observations fail to match a theory’s predictions, then the theory is (likely) falsified. The problem for this model, however, is that, because the test of “a” theory is actually the testing of the theory plus its auxiliary assumptions, then, if observations fail to match the theory’s predictions, it is not clear whether it is due to the falsity of the hypothesis of interest or of one or more of the auxiliary assumptions...

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