# What are the types of non-deductive arguments?

I've been looking for it, but Google leads the search to multiple sort of pages that, although they talk about logic, explain the subject very differently from each other and they don't fix a list with the same and they usually don't list all of them.

So I thought it'd be nice to have this question answered here so that it helps me to clear my doubts now at the same time it helps others in the future as well.

And, in the field of informal logic, what are good examples of the types of non-deductive arguments?

• To start, there's "inductive". If you Google search deductive vs inductive you'll find quite a lot of discussion. – lurker Jun 18 '19 at 16:51
• However, what mathematics calls "induction" is actually a kind of deductive reasoning, so there'll be lots of noise in the results ... – hmakholm left over Monica Jun 18 '19 at 16:51
• There's "reductio ad obsurdium," which is basically proof by contradiction. Also check out "abductive reasoning". Finally, there's "hand-waving" but perhaps that's a little too informal. hehe – lurker Jun 18 '19 at 16:54
• This might be a better question for a philosophy forum. – DanielV Jun 18 '19 at 20:03
• That's true, @DanielV. I'll post there then. – JorgeAmVF Jun 18 '19 at 20:18

All the kinds of arguments you'll find in a mathematical proof aim to be deductive: You start by setting out exactly what it is you're assuming (though this can be partly implicit if you're doing things for the ten thousandth time) and then your reasoning aims to demonstrate that it cannot possibly be otherwise than what you claim, unless one of your assumptions also fail.

For this reason non-deductive reasoning is basically reasoning that falls outside the scope of mathematical proofs, and a site for mathematics is not a good place to get a classification of its forms.

This is not to say that mathematicians don't do non-deductive reasoning at all. For example a logician might say

I believe the axioms of ZFC are consistent because thousands of extremely clever people have tried very hard to find a contradiction among them for better than a hundred years, and all failed.

which is a reasoned belief but fundamentally non-deductive. Mathematicians just are careful not to pretend that such arguments prove stuff.

• Thanks for the answer, Henning, and sorry for bringing a question related to informal logic here because you're right about what you said on the subject. However, considering it could be treated as a definite list and believing they could be known negatively (you know, the "don'ts") made me brought it here even though. Also lists of known non-deductive arguments vary from a source to another so I'm keen to know what could be the more trustworthy (some points prediction, generalization, analogy, authority others reductio or even the difference between "then" and "possibly", for example) – JorgeAmVF Jun 18 '19 at 17:19

I think it's safe to say that deductive reasoning is usually taken to describe types of inference where the truth of the premises guarantees the truth of the conclusion in a robust, or stable way, i.e., in such a way that this doesn't break down upon acquiring new information (provided also, as Henning mentions in his answer, that terms are well defined, unambiguous, the rules of deduction are properly used, etc.).

More concretely, if a conclusion $$\varphi$$ follows from a set of premises $$\Gamma$$, then $$\varphi$$ should also follow if we add more stuff to $$\Gamma$$. In other words, the truth of $$\varphi$$ is firmly established by the truth of $$\Gamma$$, and there's no fear that we'll have to take back $$\varphi$$ if we learn new things (i.e., the inference relation is assumed to be monotonic).

Falling outside the scope of this category there would be types of inference where the truth of the premises by themselves is, in some way, not enough to guarantee the truth of the conclusion. These would be cases where the truth of the premises $$\Gamma$$ supports the truth of the conclusion $$\varphi$$ only up to a certain degree (as in probabilistic reasoning); only in 'typical' (or most) circumstances; or only under special assumptions, e.g., that there is no evidence to the contrary. These are cases where we're likely to change our assessment of $$\varphi$$ as more information comes in.

Many of these patterns of inference can be found in common-sense reasoning: the type of 'imperfect' reasoning humans engage in on a day-to-day basis to navigate the world. And many of these are of interest to computer scientists and AI researchers, and are studied formally under the heading of defeasible reasoning and non-monotonic logic (links are to the Stanford Encyclopedia of Philosophy articles on the topics).