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6: Inductive Logic II - Probability and Statistics

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  • Inductive arguments, recall, are arguments whose premises support their conclusions insofar as they make them more probable. The more probable the conclusion in light of the premises, the stronger the argument; the less probable, the weaker. As we saw in the last chapter, it is often impossible to say with any precision exactly how probable the conclusion of a given inductive argument is in light of its premises; often, we can only make relative judgments, noting that one argument is stronger than another, because the conclusion is more probable, without being able to specify just how much more probable it is.

    • 6.1: The Probability of Calculus
      Sometimes, however, it is possible to specify precisely how probable the conclusion of an inductive argument is in light of its premises. To do that, we must learn something about how to calculate probabilities; we must learn the basics of the probability calculus. This is the branch of mathematics dealing with probability computations. We will cover its most fundamental rules and learn to perform simple calculations.
    • 6.2: Probability and Decision Making - Value and Utility
      Faced with uncertainty, we do not merely throw up our hands and guess randomly about what to do; instead, we assess the potential risks and benefits of a variety of options, and choose to act in a way that maximizes the probability of a beneficial outcome. Things won’t always turn out for the best, but we have to try to increase the chances that they will. To do so, we use our knowledge—or at least our best estimates—of the probabilities of future events to guide our decisions.
    • 6.3: Probability and Belief - Bayesian Reasoning
      Here we have a reasoning process—adjusting beliefs in light of evidence—which can be done well or badly. We need a way to distinguish good instances of this kind of reasoning from bad ones. We need a logic. As it happens, the tools for constructing such a logic are ready to hand: we can use the probability calculus to evaluate this kind of reasoning.
    • 6.4: Basic Statistical Concepts and Techniques
      In this section and the next, the goal is equip ourselves to understand, analyze, and criticize arguments using statistics. Such arguments are extremely common; they’re also frequently manipulative and/or fallacious. It is possible, with a minimal understanding of some basic statistical concepts and techniques, along with an awareness of the various ways these are commonly misused (intentionally or not), to see the “lies” for what they are: bad arguments that shouldn’t persuade us.
    • 6.5: How to Lie with Statistics
      The basic grounding in fundamental statistical concepts and techniques provided in the last section gives us the ability to understand and analyze statistical arguments. Since real-life examples of such arguments are so often manipulative and misleading, our aim in this section is to build on the foundation of the last by examining some of the most common statistical fallacies—the bad arguments and deceptive techniques used to try to bamboozle us with numbers.

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