Unlike deductive arguments, inductive reasoning allows for the possibility that the conclusion is false, even if all of the premises are true. Instead of being valid or invalid, inductive arguments are either strong or weak, which describes how probable it is that the conclusion is true. Another crucial difference is that deductive certainty is impossible in non-axiomatic systems, such as reality, leaving inductive reasoning as the primary route to (probabilistic) knowledge of such systems.
- 5.2: Cogency and Strong Arguments
- Inductive arguments are said to be either strong or weak. There’s no absolute cut-off between strength and weakness, but some arguments will be very strong and others very weak, so the distinction is still useful even if it is not precise. A strong argument is one where, if the premises were true, the conclusion would be very likely to be true. A weak argument is one where the conclusion does not follow from the premises.
- 5.5: Statistical Reasoning- Bayes’ Theorem
- Bayesian reasoning is about how to revise our beliefs in the light of evidence. We'll start by considering one scenario in which the strength of the evidence has clear numbers attached.
- 5.6: Legal Reasoning and Moral Reasoning
- In this discussion of moral reasoning, we will learn how to decide what to do. In this sense, moral reasoning is the most practical part of the process. When we reason about morality we build arguments, just like when we reason about anything else. But arguments involving moral propositions have to be constructed in a special way. This is partly to help us avoid the Naturalistic Fallacy. But it is also to help ensure that our arguments about morality are consistent.