That rule is based on a huge accumulation of data points, not on a mathematical “proof” or derivation from other abstract rules.This is a common feature of inductions, but it isn’t always present (for example, #2 is not deriving a general rule).
Notice that this scene has both of the classic attributes of an inductive reasoning: it’s based on probability, not certainty; and it uses specific past experiences to work out a general rule for the future.“Here is a gentleman of the medical type, but with the air of a military man. He has just come from the tropics, for his face is dark, and that is not the natural tint of his skin, for his wrists are fair.
He has undergone hardship and sickness, as his haggard face says clearly.
His left arm has been injured: He holds it in a stiff and unnatural manner.
Where in the tropics could an English army doctor have seen much hardship and got his arm wounded?
In each of these examples, the conclusion is already contained in the premises; the conclusion is just the premise.
Thus, inductive reasoning is often more useful in science and everyday life because they allow us to generate new ideas about the world, even if those ideas are based on probability rather than certainty.Like Chalmers in the first quote, Jevons here is arguing that perfect certainty is impossible in the real world.We can only have logical certainty when it comes to abstractions, and therefore deductive reasoning will only get us so far — at a certain point, we have to rely on induction to tell us what’s For as long as living things have had brains, they have been making inductive inferences: mice learn to avoid the electrified corner of their cage, inferring probable future events from painful past experience; zebrafish detect small fluctuations in the water and infer (consciously or not) the likely size of an approaching fish through murky water.In this quote, he argues that science is based on inductive reasoning rather than logical “proofs.” Although math is all deductive, science has to depart from pure mathematics when it looks out at the world around us.Because that world is messy and complicated, it may be impossible to “Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities.But the Scottish philosopher David Hume pointed out that this was an impossible way to live.Hume demonstrated that some of our most basic beliefs are based on inductive reasoning: it’s only by induction that we believe the sun will rise tomorrow, or that we have a personal identity that lasts from day to day.Unlike inductive reasoning, deductive reasoning, or deduction, is based on absolute logical certainty.If the premise is true, there’s no way for the conclusion not to be true.In cases like these, the animal’s brain is making an inductive inference.If we couldn’t use inductive reasoning, we wouldn’t survive a single day.