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An inductive inference is a logical inference that is not definitely true, given the truth of its premises. This makes it different from deductive inferences, which must be true if their premises are true. To account for this discrepancy, inductive inferences are traditionally preceded by the word “probably.” Deductive inferences tend to draw specific conclusions from general rules, and inductive inferences typically draw general rules from specific instances.
The study of logic is essentially the study of arguments. It aims to break down points made in debates so that they can objectively be measured for validity. Arguments are generally broken down into premises, which are the facts upon which the inference is being built.
For example, a classic deductive argument begins with the two premises, “All men are mortal” and “Socrates is a man.” From these premises, the inference “Socrates is mortal” can be drawn with deductive validity. In other words, if the two premises are true, then the conclusion will also be true. This is what is considered a valid argument.
An inference is something that can be drawn from a premise or several premises. A very simplistic inference is simply the negative version of a premise. For example, from the premise “All men are mortal” a person can also infer that “No men are non-mortal.” Based on that premise, it is possible to infer that if something is not mortal, it is not a man.
An inductive inference is one where the premises could be true but the conclusion false. For example, if Jane were to be seen walking her dog outside the market at seven o' clock on Monday, and then seen again at the same time the following Monday, it could be inductively inferred that she will be there again the following week. It is possible that the two premises, which are the sightings, could be true, and yet she doesn’t show up the following week. Still, an inductive inference could be made to state that she probably will be.
An inductive inference is also assigned a “strength” based on how likely it is. If Jane had been seen for ten weeks in a row, the inductive inference would be much stronger. If she'd only been seen once so far, however, the inductive inference would be rather weak.
An inductive inference seems to me to be very similar to a prediction - rather like weather forecasts, actually.
Given known weather patterns (dark clouds mean rain, the meeting of high and low pressure systems usually lead to storms), we can try and predict what will happen next, but we have no certainty that it will actually happen.
This is exactly opposite to mathematics, which is deductive. Two plus two will equal four - always, no exceptions.