On today’s lecture:
Quick review All knowledge is conditional on evidence, which eventually leads back to our intuitions. The steps in an argument that make it valid are also assumed to be true. Probability and statistics are ultimately about making arguments to support certain propositions or statements.
Logic and arguments Probability is a matter of logic, so we review some simple logical arguments of the “All men are mortal” kind. We move from arguments that produce conclusions that are true to arguments that produce conclusions that might be true.
Arguments begin with a list of premises that are true, or are assumed to be true. A conclusion, which is related to these premises, is said to be “conditional on” or “given” or “based on this evidence” of the premises.
The simplest probabilistic argument is this: Premises “A die will be rolled; it has just six sides, only one of which will show, and only one of which is labeled ‘6’.” The Conclusion of interest: “A ‘6’ will show” has, conditional on, or given, or based on this evidence, the probability of 1/6 of being true.
Next time Other schools of probability and why I think they are insufficient or misleading. What “randomness” means.
These notes are not meant to be complete. See the class notes to the left (“Breaking the Law”), or search this site for “Chapter”, where you can find an early (somewhat crude) version.