Formal reasoning is used to make a precise explanation of certain phenomena, such as: the laws of physics or the atomic and molecular structures, and the relationship of the behavior of matter. Formal reasoning is also used in scientific and mathematical calculations and to support arguments in court cases and in politics, as well as in the classroom in various disciplines, for instance the philosophy of science and the history of science.
Induction is commonly used in logic reasoning. An example of inductive reasoning can be the following: let us say there is a theory that states, “Birds do not sleep”. This theory may not have evidence to support it, but we can still infer from its general assumptions, “No birds do sleep”, as we can with many other general assumptions. Another example would be: if we assume, “All men are mortal”, it will follow, “Men cannot fly”men can only fly when they want to” and the like. These are inductive reasoning, where the hypothesis (generalization) is derived from evidence that supports it.
Another way to describe inductive reasoning is the following: “A given set of facts is assumed in order to infer the truth of a general proposition, then an argument is made from the given set of facts to the general proposition and then the inductive reasoning makes a claim about the conclusion of the argument.” The premise of the argument used in inductive reasoning, or the premise used in an inductive inference, must first be considered: “is there really any evidence to support a particular set of facts”. Then, an inductive argument is made: “there is a possibility that there is some evidence to support the existence of a fact, and that this evidence is consistent with that particular set of facts.” Finally, the conclusion of the inductive argument is “that this evidence is consistent with the existence of that particular set of facts.” All of these are considered as premises in the inductive reasoning, where as a result of the deduction of the premises the inductive argument leads to a certain conclusion.
Inductive reasoning has a number of limitations. It does not help with proving theories or falsifying theories. It cannot prove or disprove things beyond reasonable doubt. There are too many possibilities to test the premises or theories that are used to construct inductive reasoning, such as: all physical objects are physical; all persons are human beings; all physical objects possess a definite essence; or all physical objects are identical. This is called the’many worlds’ problem.
Inductive reasoning can be used in conjunction with deductive reasoning, in order to support an argument. For instance, an inductive argument may be used to support the fact that: “The law of gravity is real.”
However, it cannot be used to prove, “The law of gravity is unreal.” (An inductive inference will not prove or disprove anything, unless it is supported by a series of inductive inferences.) Therefore, we cannot prove “The law of gravity is real” from “The law of gravity exists.”
Another limitation of inductive reasoning is the fact that it is a very scientific process. It is not based on anything other than “the principle of parsimony” and the evidence of its use. This is because a belief may be supported only if there are enough strong grounds for it to be believed. This is where logic comes in, because it can be used to establish both the existence and the falsity of the theory/hypothesis used to support the belief.