## Are all non-deductive arguments inductive?

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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 – 2020-04-19T17:24:19.833

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 – 2020-04-19T17:45:57.537

1I 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 – 2020-04-19T18:00:45.353

Not only; see Argument: "There are several kinds of arguments in logic, the best-known of which are "deductive" and "inductive."

– Mauro ALLEGRANZA – 2020-04-19T18:07:03.370

– Mauro ALLEGRANZA – 2020-04-19T18:08:39.220

For two arguments to be inductive or deductive, the predicate domain of one should be contained within the other (leaving entities grow, plants grow). Without containment, they have not necessarily an inductive or deductive quality (birds grow, apples are red). Moreover, such classification is quite subjective, it all depends on the nuances of language (does the fact that multiple samples are useful is a deduction or an induction of the fact that multiple cases are worthwhile?). Therefore... yes. Or no. – RodolfoAP – 2020-04-19T21:27:38.343

There’s also abduction and analogy. – William – 2020-04-20T03:31:37.490

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Does this answer your question? Are "if smoke then fire" arguments deductive or inductive?

– Conifold – 2020-04-20T06:38:14.363

Actually, it is a matter of definition. But it is clearer than noted above. 'Inductive' can just mean 'capturing more information than you started with', or it can mean 'distilling a pattern from the relationships between multiple examples'. In the latter sense, mathematical 'complete' induction is both deductive and inductive and there are a lot of forms of discovery that are neither. In the former sense, there is a bright line separating induction from deduction: deduction only elaborates or exposes information that was implicit in what you started from, and everything else is induction. – hide_in_plain_sight – 2020-05-07T14:27:23.010

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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/

1Regarding abductive reasoning, you can think "Occam's razor" – SmootQ – 2020-04-21T21:37:11.250

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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