# Are all non-deductive arguments inductive?

I am having troubles with understanding this question. Can someone give me an example/insight about where to go from here?

• It might be bi-directional! – OmG Apr 19 '20 at 17:24
• Not if like Perice you believe there is a third type of argument - abduction. Of if like Gil Harman you believe that inference to the best explanation is neither deductive nor inductive. – Geoffrey Thomas Apr 19 '20 at 17:45
• I don't think there is a standard here. The distinction is drawn in different ways by different philosophers. Some consider abduction and inference to the best explanation as a subset of induction, others define them as distinct from induction. It's best to ask your interlocutor how they're using their terms. – Adam Sharpe Apr 19 '20 at 18:00
• Not only; see Argument: "There are several kinds of arguments in logic, the best-known of which are "deductive" and "inductive." – Mauro ALLEGRANZA Apr 19 '20 at 18:07
• Does this answer your question? Are "if smoke then fire" arguments deductive or inductive? – Conifold Apr 20 '20 at 6:38

Not all non-deductive arguments are inductive. There are also abductive arguments, bayesian inferences...etc.

As you know, this is a deductive argument, it goes from a universal (e.i : all) to a particular.

1) All Unicorns have a horn
2) Mua is a Unicorn
3) Therefore, Mua has a horn


Maybe we would need an inductive argument to support the first premise for example , here is what an inductive argument would look like :

1) Zoe is a Unicorn and has a horn
2) Boone is a Unicorn and has a horn
3) Chong is a Unicorn and has a horn
..
..
n) Probably, all Unicorns have a horn


The inductive argument is the opposite, it goes from many particulars to one generalization, and because a Unicorn can possibly give birth to baby mutated Unicorn with 2 horns instead, we use Probably .

Because inductive conclusions are not as certain as deductive ones.

Now, to Abductive Reasoning , suppose that you were walking by the beach, and stumbled upon C-shaped footprints that look like a horse's

Argument

1) All C-Shaped footprints are either horses, mules, donkeys...etc or Unicorns.
2) These are C-Shaped footprints
3) Therefore, this is either a horse, mule, donkeys...etc or a unicorn.


Of course given the size of the footprints, you can safely say it is very unlikely that it is a mule or donkey. Let's just ignore them.

We are left with horse and unicorn.

What kind of reasoning makes you prefer horse over unicorn?

This is Abduction in action : You always go with the answer that needs less explanation, the simplest answer here is horse.

For one reason : You already are familiar with horses, a unicorn would be quite a stretch.

Why is it that the image is not an evidence that Unicorns exist?

Simply because there are other species that we already know exist that offer simpler explanations , an abductive argument would look like this :

Abductive Argument

1) All C-Shaped footprints are either horses or Unicorns.
2) These are C-Shaped footprints
3) And, a horse is a simpler explanation (since horses are already known to exist)
4) Therefore, this is probably a horse, (it could be a unicorn, but that would make things more complicated).


Other types of reasoning (not in the same sense as the previous three )

There is yet other types of reasoning, which are not always reliable.

• Teleological Reaoning : from x, conclude the purpose / goal from the fact that x is true. (this type of reasoning is often misleading, although sometimes useful).
• Analogical Reasoning : from the fact that x is similar to y in some respect r, conclude that what is true for x is also true for y . This type of reasoning is often useful, but sometimes it may lead to informal fallacies and false analogies.
• Causal Reasoning : Attempts to establish a causal relationship between x and y , given a set of facts. Keep in mind that often this conclusion is false, and that correlation does not imply causation. (it can be that y causes x, or x causes y, or x and y both are correlated and caused by another hidden variable z).

As for bayesian inferences, It is not exactly a reasoning in the same respect, and is not normally included with the three types of reasoning (deductive, inductive and abductive), but this link may be of use :

https://plato.stanford.edu/entries/epistemology-bayesian/

• Regarding abductive reasoning, you can think "Occam's razor" – SmootQ Apr 21 '20 at 21:37

You may have a look at Peirce's Paper in Chance, Love and Logic ( available at archive.org). Also: Baldwin's Dictionay Of Philosophy ( in which Peirce wrote logic entries).

https://plato.stanford.edu/entries/peirce/#dia

Here Peirce establishes a trichotomy that is ( I believe) standard nowadays :

(1) analytic reasoning --> deduction

(2) synthetic reasoning --> a) induction and b) abduction ( or " hypothetical reasoning")

Hence, Peice's point is that not all ampliative reasoning is inductive.

• Abduction has the following form :

Result

Rule

Case

That is: you infer that a given phenomenon should probably be explained as an instance of a given rule ( that you already know) ; abduction is an " inference to the best explanation".

Inducton has the structure :

Case

Result

Rule

And deduction the structure :

Rule

Case

Result