Formal Reasoning
In formal reasoning we're talking about things like algorithms, systematic methods that allow you to produce a correct solution to a problem, assuming that a solution even exists. As the example in the book states, that astronomers' estimates of the sun's core temperature were based on formal reasoning—this logical reasoning, which has rigorous procedures to reach those valid conclusions; some of those procedures included applications of mathematical formulas. Those formulas are examples of algorithms. Algorithms are sometimes expressed as flowcharts , something you might be fairly familiar with. And a formal reasoning would also include rules of logic, and syllogisms, syllogisms being those logical arguments where you're given two premises with a conclusion and you have to see, "Are the premises and conclusion valid? Does the conclusion logically follow from the premises?" And of course, you know, with any logical reasoning puzzle, we may have certain biases that lead us astray and perhaps cause us to make illogical conclusions or logical fallacies. And these are certainly things you would talk more about if you took a course in logic and reasoning; so for the purposes of this course, we're going to kind of leave it to some of those classes if you want to explore that further. What we really want to focus a bit more on is informal reasoning.