### The Logic Forum Discussion Area Logic
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My logic text says that a deductive argument is one where if the premises are all true, then the conclusion must be true, in which case the argument is valid. An inductive argument, on the other hand, is one where the conclusion doesn't necessarily follow from the premises (assuming they're true) but is only true with some degree of probability.

That being the case, is an invalid argument always an inductive argument? I don't think it is, but I'm having trouble distinguishing between inductive and deductive arguments.

Thanks for any help.

Re: Confused about deduction / induction

Hi Greg,

I have written a lot about induction. If you want to study the matter seriously, you can read these three chapters for a start:

http://www.thelogician.net/2_future_logic/2_chapter_46.htm

http://www.thelogician.net/2_future_logic/2_chapter_50.htm

http://www.thelogician.net/7_fortiori/7_chapter_03.htm#_Toc370305854

In this last chapter, which is part of my most recent book, read the part entitled Induction In General.

There you see that there are several forms of induction, including factorial induction (or more commonly generalization and particularization), adduction (the scientific method of hypothesizing and confirming or rejecting), induction based on deduction, and inductive inference that relies on a doubtful deductive process.

To answer your question very briefly, scientific inductive arguments are more conditional than deductive ones. Effectively some information is missing that inhibits deduction. The argument is not wrong in the sense that the conclusion is contradictory to the premises, of course; but it is not fully reliable insofar as the missing information leaves some uncertainty. Some 'induction' is, of course, more guesswork or fantasy than scientific induction (this refers to the fourth category).

I should add that most reasoning is in fact inductive, even when it is thought to be deductive. Studying this matter is of the utmost importance if you want to understand human reasoning and knowledge - so it is really worth the effort.

Something about you (optional) Logician, philosopher

Re: Confused about deduction / induction

Hi Avi,

I have just read an interesting and helpful article which views probability as logic extended to handle cases where results are uncertain, so if TRUE is 1 and FALSE is 0, then in this system deduction is just the special case of these limits, with other values (corresponding to induction) denoting the strength of the argument.

In other words, if P denotes probability,

Valid deduction: P = 1,
Invalid deduction: P = 0,
Induction: 0 < P < 1

You might like to read it if you have the time; I'd be interested in your comments.