Reasoning is a very important part of the scientific method. Reasoning involves how we use observations of the natural world and combine them to form structures or theories that explain a large range of phenomena. Humans are unusual in their powers of reasoning. Perhaps we're not unique. I'm confident there are other sentient animals with fairly high degrees of intelligence, but humans have taken reasoning to an entirely new level. Notice that although science is only a few thousand years old and civilization only 10,000 years old. Humans have had the power of reasoning for longer than that. The last detectable anatomical changes in humans or in their brain chemistry date back about 40,000 years when we had hunter-gatherers and nomads in Africa, even before we ventured into the other continents. A human alive then has exactly the same capability that we do now, and yet they lived in a primitive and simple world with no tools of technology or tools of science. What did they imagine about the world using the same brain they had then that we have now? The formal ideas of reasoning started with the Greek philosophers, an Aristotle, a profoundly influential philosopher who affected physics astronomy mathematics and many other fields. Aristotle develop the rules of deductive logic that still hold today. They were further codified by Bertrand Russell in 20th century. Aristotle's rules of deductive logic or how we define science as it combines statements of the natural world to draw conclusions and inferences. We can look at examples where deductive reasoning fails, and it's important to look at these examples and see if you can see why they fail. Sometimes deductive reasoning fails dramatically in in an obvious way, and sometimes the failure is a little subtle. Often when we miss the failure of logic, it's because we don't question the premises. Logic combines statements of the natural world, or observations, or theories to draw a conclusion. But if those premises or assumptions are faulty or not justified by data or observation, then the combination in logic fails. Logic is just a tool. It can't define the veracity of the statements that go into it. There are two fundamentally different kinds of logic that apply in science in any field of science; deductive and inductive logic. Deduction is the theory put together by Aristotle and burnished over the centuries since then. An example of deductive logic involves arithmetic. This statement two plus two equals four is completely and self-consistently true. It doesn't matter in your opinion, on your point of view, whether there's a why in the month, it's always true. In that way, deductive logic always produces reliable conclusions if the premises are valid. A simple example in astronomy would be this observation say, demonstrates that the earth is larger than the moon. A second observation demonstrates that the sun is larger than the Earth. We can deductively combine these two statements to say that the sun is larger than the moon. In this example, you can of course see the power and the limitation of deductive logic. It's a very reliable conclusion, but in a sense you're not getting out more than was there in the first place and the two separate statements. So deductive reasoning alone cannot guide and drive science. The second form of scientific reason is called induction. Induction was most powerful and first used by Isaac Newton in his theory of gravity. Induction in simple terms is generalizing to a broad theory from a specific or limited set of observations. This generalization is something that happens in science all the time. Because when we develop theories, we can never have tested them in all possible situations. So we're making an inference and we're projecting our conclusion into a broader set of situations, and that's how we test the theory. In Newton's case, he developed a universal law of gravity to explain the orbits of objects in the solar system. At that time, it was just the sun, the earth, the moon, and the planets observable with the naked eye. A very limited set of objects. His theory of gravity explained their orbits extremely well, but he was confident enough in the power of the theory to project and imagine that it would apply to as yet unobserved situations. The great example was Halley's Comet. Before he died, Newton made a prediction of when Halley's comet would reappear. It was named for his friend Halley when it did reappear as predicted by his theory. More profoundly, Newton made his observations and did his theory in a time when we only knew of one set of stars, approximate stars of the Milky Way. But Newton's Universal Law of Gravity turns out to explain the motions of stars in other galaxies, and the motion of other galaxies in a universe with 100 billion galaxies. These as yet unobserved phenomena were perfectly explained by his theory. A dramatic example of induction or generalization from a very limited set of tests of his theory during his lifetime. An example from another field of science might be the Darwinian theory of natural selection and evolution. Darwin of course only was able to make a limited set of observations over a few decades of life forms and how they evolved in response to natural selection in the environment. But the mechanisms he proposed in his book of 1859 were imputed to apply to all species and all forms of evolution over time in the history of the Earth. They've proven to be valid for those larger situations, another example of induction at work. Science is based on reasoning, which we think is a particularly human attribute that we have above all the other animals. This attribute has been present in our brains for tens of thousands of years, even though science is a lot younger. The formal application of reasoning comes in logic, and in particular in two forms of reasoning; deduction, where we deduce principles from a specific set of observations combining them to draw a reliable conclusion, and induction, which involves generalization from a finite set of observations to a much larger set of potential situations. Both forms of reasoning are used in all scientific fields to gain new knowledge.
