Although I am aware of the distinction between deduction and induction in logic,

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Although I am aware of the distinction between deduction and induction in logic, which relies on the strength of the link between premises and conclusion, with deduction a matter of necessity and induction a matter of probability, I find the distinction problematic. For instance, the argument "All men are mortal. Socrates is a man. So, Socrates is a mortal" is a classic example of a deductive argument. But the first premise is based on particular cases, so it cannot be universally guaranteed that it would be always true. But the fact that it may not always be true makes it one of probability and not necessity. Would this consideration make a difference as to the argument is deductive or inductive?