Let us start with a passage:
"He (Newton) had just been graduated from college...In the long summer afternoons he sits in the orchard which still stands near the old gray stone house; on one memorable day, an apple falls with a slight thud at his feet. It was a trifling incident which has been idly noticed thousands of times; but now, like the click of some small switch which starts a great machine in operation, it proved to be the job which awoke his mind to action. As in a vision, he saw that if the mysterious pull of the earth can act through space as far as the top of a tree, a mountain, and even to a bird soaring high in the air or to the clouds, so it might even reach so far as the moon..."
(from L.T. More, Isaac Newton: A biography. New York: Scribner's, 1934)
This story about the development of Newton's Theory of Gravitation is a classic example of inductive reasoning. Inductive reasoning is a method used to discover new information or to supply missing information. When we use inductive reasoning, we observe, test, and check things out in some systematic fashion.
Besides inductive reasoning another method of logic is deductive reasoning. Deductive reasoning is a method of developing the consequences of a law, as we studied in geometry, where we state the axioms and then make all sorts of deductions.
This act of reasoning, drawing of conclusions, judgements, or inferences is the methods of logic. Logic is the science of inference. Here we will try to find about how these disciplines work, why they are important, and how they are used.
The principle of science is the following: The test of all knowledge is experiment. But what is the source of knowledge? Experiment, itself, helps to formulate the laws that summarize the required knowledge. Experiment gives us hints, in this sense; experiment is sole judge of scientific truth. But also needed is imagination to perceive the patterns of observed results and derive generalizations. After generalization, it is again experimented to verify whether our hypothesis is correct. Hence science is all about experiment, imagination, deduction, inference and hypothesis.
All scientific theories are either deduced from experimental findings or generalized from previous works. For instance, classical Newtonian physics is the generalization of laws governing motion of rigid bodies and Cartesian space concept. Quantum Mechanics arose from the inference of Uncertainty Principle and experiments with electron. Darwin’s the theory of Evolution developed from the concept s of random variation and natural selection that he inferred from the work of Robert Malthus: An Essay on the Principle of Population (1798).
Science is the study of nature and the correlation between cause and effect of natural process. The elements of nature under investigation are the entities of formal logic invented because of their use in describing and systematizing facts of experience or observations.