Deductive Logic is a process of looking at conclusions to see if they flow from their premises. Notice, this is not about truth, an argument can be valid without the premises themselves being true. For example,
A. All men are mortal
B. Socrates is a Man
C. Socrates is mortal
This argument is valid, as well as sound, because its premises happen to be true. A valid, but not sound argument could be,
A. All politicians are secretly reptiles
B. Russ Feingold is the former Junior Senator of Wisconsin
C. Russ Feingold is secretly a reptile
All right, this is all fun and games, but how do we make sense of INDUCTION, that is to say, us looking at the world, and making an argument. The problem with induction is, as David Hume argued, plenty of instances do not confirm whether something is NECESSARILY true. For example, all swans in the UK are white, thus for years people thought all swans are necessarily white. However, as soon as the British found a single black swan in Australia, that necessary connection was destroyed, (for a more contemporary example, the existence of intersex people destroys the idea that biological sex is dyadic).
In the middle of the 20th century, a band of merry philosophers called the Logical Positivists attempted to figure out how all social, intellectual, political, ethical, and ontological issues could be solved in a very specific, definitive, scientific way. One of these individuals, Carl Hempel, attempted to figure out a system of inductive logic that would mirror the certainty of deductive logic. However, he ran into a problem which he highlighted as the Paradox of the Ravens.
So, suppose we make a logical form of a well-confirmed observation, “All Ravens are Black” >> All Ps are Q
In logic, if All Ps are Q, necessarily, than Not-Qs must be not-P. That is, if something is not black, than it necessarily cannot be a raven. This should be uncontroversial, but these two terms are equivalent: “All Ps are Q” is equal to “All not-Ps are not-Q.”
And here lies the issue: when I observe not-black things, my computer for instance, why do I regard this as being a very different act than observing a raven? The paradox of the ravens would suggest that all induction of non-black things would confirm the proposition that all ravens are black, and yet that seems very odd.
As it turns out, induction does not easily reduce to logical forms, and the positivist project turns out to be a dead-end in the history of 20th century philosophy.