More on Deductive and Inductive Reasoning

Inductive reasoning goes from the specific to the general. Deductive reasoning goes from the general to the specific. Let me elaborate.

Deductive reasoning starts with a general rule, a premise, which we know to be true, or we accept it to be true for the circumstances. Then from that rule, we make a conclusion about something specific. Example:

All turtles have shells

The animal I have captured is a turtle

I conclude that the animal in my bag has a shell

A conclusion reached with deductive reasoning is logically sound, and airtight, assuming the premise is true. Deductive reasoning is fully convincing when it is based on a definition. If *by definition* a shilling is a flat disc, copper in color and has a profile of Nyerere on it, then I can be sure the shilling in my pocket has those qualities.

The obvious strength of deductive reasoning is that conclusions derived with it are fully certain. The weakness, which was illustrated in the most recent example, is that no new information is added. The fact that the shilling in my pocket is a copper disc with Nyerere on it was clear from the initial data, so the conclusion hasn't added any new information.

Inductive reasoning is making a conclusion based on a set of empirical data. If I observe that something is true many times, concluding that it will be true in all instances, is a use of inductive reasoning. Example:

All sheep that I've seen are white

All sheep must be white

This example makes inductive reasoning seem useless, but it is in fact very powerful. Most scientific discoveries are made with use of inductive reasoning. A majority of mathematical discoveries come about from conclusions made with inductive reasoning, or observation. But the key word is "discovery." With induction something can be discovered but not proven.

The general flow of events is like this: a)make observations b)form conclusions from empirical data c)prove conclusions with deductive reasoning. So if I notice that all triangles I come across have 180 degrees, through inductive reasoning I may form a hypothesis that *all* triangles have 180 degrees. But now that inductive reasoning has pointed me in the right direction, deductive reasoning allows me to prove my hypothesis as fact.

There is just too much data out there to gather, to just go around blindly using deductive reasoning. Induction allows us to mine the data, and points out significant bits of information. From there we can prove things and form hard facts.