ABSTRACT
Much of our everyday reasoning deals with probabilities. We observe patterns and conclude that, based on these, such and such a belief is probably true. This is inductive reasoning.
The Appalachian Trail (AT), a 2,160-mile footpath from Georgia to Maine in the eastern US, has a series of lean-to shelters. Suppose we backpack on the AT and plan to spend the night at Rocky Gap Shelter. We’d like to know before-hand whether there’s water (a spring or stream) close by. If we knew that all AT shelters have water, or that none do, we could reason deductively:
Both are deductively valid. Both have a tight connection between premises and conclusion; if the premises are true, the conclusion has to be true. Deductive validity is an all-ornothing affair. Deductive arguments can’t be “half-valid,” nor can one be “more valid” than another.
