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