Distinction between Deductive and Inductive Argument

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Deductive Argument

Inferences that are certain, where the truth of the supporting evidence (the premises) guarantees the truth of what we've inferred (the conclusion), are called Deductive Inferences or Deductive Arguments. The relationship between the evidence or the grounds for the inference and the inference itself is such that the conclusion cannot be false if the premises are true. Of course, the premises might not actually be true, but even if they're not, the relationship between the evidence and the inference is the same. The inference is Valid, even if the evidence is faulty.

EXAMPLE

For instance, if we observe that:

All dolphins are fish, and that
No fish are mammals, then we would be right to infer that
No dolphins are mammals

even though we'd be wrong about the facts (it's true that no fish are mammals, but it's not true that dolphins are fish).

Arguments or inferences that are certain or intended to be certain are Deductive Arguments or Inferences. The inference is Valid when it is certain and is Invalid when it is meant to be certain but is incomplete.

EXAMPLE

For instance:

All politicians are dirty rotten liars.
So, all politicians are dangerous.

Clearly something is missing, but equally clearly the missing connection can be supplied if we were to add the missing (or implicit) premise

All dirty rotten liars are dangerous.

Before we added this premise, the argument was Invalid (because incomplete), but we can see that the (completed) inference was intended to be certain because we can see quite clearly how to complete it, and we treat the additional premise as "missing" (or ...