Inductive arguments

[eastbaymu...@gmail.com]

Are ampliative and inductive arguments the same thing?

[G. Randolph Mayes]

For our purposes, it is close enough. An ampliative argument is one in which the conclusion contains more information than the premises. However, probabilistic reasoning, such as in Bayesian or frequentist statistics, is also typically called inductive, and these arguments are not ampliative because the conclusion is is asserted only with the probability conferred on it by the premises. Strictly speaking this form of induction is actually deductive.

[eastbaymu...@gmail.com]

Thank you for helping me clear that up!  Also, I'm having some difficulty making a distinction between alternative hypotheses and counter examples.  My mind is wanting to conflate the 2 and I worry that they are actually different things.

[G. Randolph Mayes]

Right, those are kind of in the same semantic cloud, but there are important differences.

Regarding hypotheses, an alternative hypothesis is just a different way of explaining a set of observations. My hypothesis is that the restaurant is closed because it is a holiday, yours is because they are out of business. In this class we will speak of auxiliary hypotheses, and these are hypotheses we adopt, often without evidence, for the purpose of maintaining the current hypothesis in the face of evidence against it. Ptolemy's epicycles were constructed as auxiliary hypotheses in this sense. If I tell you that it's unlikely they are out of business because they were open yesterday, you might adopt the auxiliary hypothesis that the owner died..

The word 'counterexample' is used in a lot of different ways in ordinary English, but in philosophy and logic it doesn't have anything especially to do with explanatory contexts. A counterexample to an argument is an imagined state of affairs in which the premises hold true, but the conclusion is false. If someone argues:  Poodles are dogs, Fifi is a dog, so Fifi is a poodle, we would say this is invalid, because counterexamples exist. It could, e.g, be that Fifi is a labrador, since this is consistent with the truth of the premises.