Strictly speaking, all of our knowledge outside of mathematics consists of conje
ID: 3194868 • Letter: S
Question
Strictly speaking, all of our knowledge outside of mathematics consists of conjectures. Some of these conjectures, like those found in physics or court rooms or history books are considered forthright and reliable. There are other conjectures all around us that may not be respected or reliable, such as opinions or broadcaster commentary. Mathematical knowledge is secured with deductive reasoning but we all, mathematicians and non-mathematicians alike, support our intuitions with inductive reasoning. The difference between the two types of reasoning is great and manifold. Give a description in this difference of reasoning. Then comment on how each type of reasoning is important to the study of logic.
Explanation / Answer
Induction is usually described as moving from the specific to the general, while deduction begins with the general and ends with the specific; arguments based on experience or observation are best expressed inductively, while arguments based on laws, rules, or other widely accepted principles are best expressed deductively.
Consider the following example:
Adham: I've noticed previously that every time I kick a ball up, it comes back down, so I guess this next time when I kick it up, it will come back down, too.
Rizik: That's Newton's Law. Everything that goes up must come down. And so, if you kick the ball up, it must come down.
Adham is using inductive reasoning, arguing from observation, while Rizik is using deductive reasoning, arguing from the law of gravity. Rizik's argument is clearly from the general (the law of gravity) to the specific (this kick); Adham's argument may be less obviously from the specific (each individual instance in which he has observed balls being kicked up and coming back down) to the general (the prediction that a similar event will result in a similar outcome in the future) because he has stated it in terms only of the next similar event--the next time he kicks the ball.
As you can see, the difference between inductive and deducative reasoning is mostly in the way the arguments are expressed. Any inductive argument can also be expressed deductively, and any deductive argument can also be expressed inductively. Even so, it is important to recognize whether the form of an argument is inductive or deductive, because each requires different sorts of support. Adham's inductive argument, above, is supported by his previous observations, while Rizik's deductive argument is supported by his reference to the law of gravity.
Thus, Adham could provide additional support by detailing those observations, without any recourse to books or theories of physics, while Rizik could provide additional support by discussing Newton's law, even if Rizik himself had never seen a ball kicked. The appropriate selection of an inductive or deductive format for a specific first steps toward sound argumentation.