His style is called syllogism, when you make a conclusion based on a set of premises. He introduced the deductive argument: All men have beards, Michael is a man, Michael has a beard. As you can see based on the shape of the reasoning, a person can deduct something that is false, but have sound logical form. He also introduced the inductive argument, which can take some particular premises and draw a universal conclusion. Again, this can be distorted to state a false conclusion. Induction cannot determine validity, but neither can deduction so what is the point? The point is mankind has to think in order to create and make sense out of the world they live in. Logic and philosophy helps them to do that in an orderly fashion.
After Aristotle comes the Stoics in Athens, and they added propositional logic and predicate logic. Each major addition builds on the contributions of the ones before them. Francis Bacon comes around in the 17th century when scientific advances that were happening at the time needed a new logic. They wanted a rational way to organize their statements, and Bacon stated the importance of inductive reasoning. In the 19th century Moore created the algebra of logic, and added mathematic equations to the logical statements. Then we got “If A + B, then C + D”. Modern propositional logic evolved from this. Frege made the logic axiomatic; he refined Aristotle’s work in his important work called Foundations of Arithmetic. He decided the consequence can be true even if the antecedent is false.
Russell introduced the Principia Mathematica based, again, on the work of those before him. I would study him further because he addresses the issue that I always have with the rules of logic, and that is the paradox. He acknowledges the issue and gives name to the Liar’s Paradox. After him comes Tarski, who introduces semantic logic. This is a good name because the whole thing seems like semantics or a play on words. Hilbert’s program follows and brings mathematic language to logic. He is followed by Gödel, part of the Vienna Circle, which was like a think tank of the time. He states that probability is not the same as truth, which makes me ask again- then what use is it?
The answer is the same. Mankind’s thinking and creativity advances and so does the language we use to express those thoughts. Gödel developed logical positivism, which is empirically verifiable or mathematically true. This train of thought led to the creation of the binary code, which is computer language still used today. So all this thinking, beginning with Aristotle, has led to the creation of different branches of logic. There are: extensional, epistemic, deviant, multi-varied and fuzzy logic, among others, and the dialogue is still going on as we progress. This would be a great job, to sit around and think with other thinkers. It is time for 21st century theories to be developed and introduced. We are still looking for truth.