Types of reasoning in the Quran

From: http://www.quran-miracle.info/Quran-Reasoning.htm

Reasoning within an argument gives the rationale behind why one choice, for example should be selected over another. Types of reasoning include:
Abduction: the process of creating explanatory hypotheses.
Analogical reasoning: relating things to novel other situations.
Cause-and-effect reasoning: showing causes and resulting effect.
Comparative reasoning: comparing one thing against another.
Conditional reasoning: using if...then...
Criteria reasoning: comparing against established criteria.
Decompositional reasoning: understand the parts to understand the whole.
Deductive reasoning: starting from the general rule and moving to specifics.
Inductive reasoning: starting from specifics and deriving a general rule.
Modal logic: arguing about necessity and possibility.
Traditional logic: assuming premises are correct.
Pros-vs-cons reasoning: using arguments both for and against a case.
Set-based reasoning: based on categories and membership relationships.
Systemic reasoning: the whole is greater than the sum of its parts.
Syllogistic reasoning: drawing conclusions from premises.
Note that these are not all mutually exclusive methods and several give different lenses onto overlapping areas. In classical argument, for example, all arguments are framed as either inductive or deductive.

Types of reasoning in Quran

Abduction
Description
A is observed. If B were true, then A would be true. Therefore B may be true.
Abductive reasoning, or abduction, is the process of explaining something that is experienced or observed in some way and where there is no existing knowledge to explain the phenomenon. It creates a hypothesis that may or may not be true and which may require further work to verify.
Example
A doctor, meeting a set of symptoms not met before, considers diseases that have similar symptoms and wonders if the presented condition is something similar.
Example from Quran
Bakara/85 (A.Yusuf Ali)After this it is ye, the same people, who slay among yourselves, and banish a party of you from their homes; assist (their enemies) against them, in guilt and transgression; and if they come to you as captives, ye ransom them, though it was not lawful for you to banish them. Then is it only a part of the Book that ye believe in, and do ye reject the rest? but what is the reward for those among you who behave like this but disgrace in this life?- and on the Day of Judgment they shall be consigned to the most grievous penalty. For Allah is not unmindful of what ye do.

Analogical reasoning
Description
A is like B. M is in A. N is in B. So M is like N.
In analogical reasoning, an analogy for a given thing or situation is found, where the analogy is like the given thing in some way. Other attributes of the analogical situation are then taken to also represent other attributes of the given thing.
To use an analogy:
Start with a target domain where you want to create new understanding.
Find a general matching domain where some things are similar to the target domain.
Find specific items from the matching domain.
Find related items in the target domain.
Transfer attributes from the matching domain to the target domain.
Example
This company is like a racehorse. It's run fast and won the race, and now it needs feed and rest for a while.
Dating of it like flying. At some point, your feet are going to leave the ground.
Example from Quran
Bakara/223Your wives are as a tilth unto you; so approach your tilth when or how ye will; but do some good act for your souls beforehand; and fear Allah. And know that ye are to meet Him (in the Hereafter), and give (these) good tidings to those who believe.

Cause-and-effect reasoning
Description
When you are presenting an argument, show the cause-and-effect that is in operation. Help the other person see why things have happened or will happen as they do.
Show purpose. Link things to higher values. Show the inevitable linkage between what happens first and what happens next. Go beyond correlation (that may show coincidence) to giving
irrefutable evidence of causality.

If you cannot show causal linkage, then you may be successful just by asserting it, because few people will challenge a cause-and-effect assertion.
Example
Say this
Not this
If I help you, you will be more successful.
I will help you.
When the moon is high, things are abroad.
Things are sometimes abroad.
The new additive to fuel makes your car go so much further.
Add our new fuel additive to your car.
Example from Quran
Al-i Imran/160If Allah helps you, none can overcome you: If He forsakes you, who is there, after that, that can help you? In Allah, then, let believers put their trust.

Comparative reasoning
Description
Comparative reasoning establishes the importance of something by comparing it against something else.
The size of the gap between the things compared indicates importance. Compare against a high standard to make something look undesirable. Compare it against a weak example to make it look good.
To create a logical argument, first establish the validity of the comparison benchmark. For less logic, the benchmark may be assumed.
There are many ways to compare, for example:
Compare what people have got (or not got) against what others have.
Compare the past with the future.
Compare what is actual with what is ideal.
Compare words and actions against values.
Example

Say this
Not this
I guess your wife will want something good-looking. How about this one?
This is the right one for you!
How will we know when we have succeeded? Let's discuss this first...
Success means maximum profits.
Our manifesto says we must help those who cannot help themselves. Now, can this person help himself?
We should not help this man.

Example(s) from Quran
Enam/122Can he who was dead, to whom We gave life, and a Light whereby he can walk amongst men, be like him who is in the depths of darkness, from which he can never come out? Thus to those without faith their own deeds seem pleasing.
Nahl/75Allah sets forth the Parable (of two men: one) a slave under the dominion of another; He has no power of any sort; and (the other) a man on whom We have bestowed goodly favors from Ourselves, and he spends thereof (freely), privately and publicly: are the two equal? (By no means;) praise be to Allah. But most of them know not.

Conditional Reasoning

If...then...
Conditional reasoning is based on an 'if A then B' construct that posits B to be true if A is true.
Note that this leaves open the question of what happens when A is false, which means that in this case, B can logically be either true or false.
A classic form of conditional reasoning is in using syllogisms, where a general major premise is combined with a more specific minor premise to form a conclusion. Syllogisms are easy to get wrong and there are many fallacies.
Example from Quran
Sebe/14
Then, when We decreed (Solomon's) death, nothing showed them his death except a little worm of the earth, which kept (slowly) gnawing away at his staff: so when he fell down, the Jinns saw plainly that if they had known the unseen, they would not have tarried in the humiliating Chastisement (of their Task).

Criteria reasoning
Description
Start by defining the criteria by which the outcome of a decision will be judged, and then identify the best decision, given these constraints.
In a logical argument, you will spend much time establishing the criteria as valid first. In a less logical situation, you may assume the criteria are correct, minimizing the time spent on any discussion about them.
Criteria which appeal to common values are likely to be easily accepted.
Example

Say this
Not this
I guess your wife will want something good-looking. How about this one?
This is the right one for you!
How will we know when we have succeeded? Let's discuss this first...
Success means maximum profits.
Our manifesto says we must help those who cannot help themselves. Now, can this person help himself?
We should not help this man.

Example from Quran
Bakara/258Hast thou not turned thy vision to one who disputed with Abraham about his Lord, because Allah had granted him power? Abraham said: "My Lord is He Who Giveth life and death." He said: "I give life and death". Said Abraham: "But it is Allah that causeth the sun to rise from the east: Do thou then cause it to rise from the west." Thus was he confounded who (in arrogance) rejected faith. Nor doth Allah Give guidance to a people unjust.

Deductive reasoning
Description
Deductive reasoning, or deduction, starts with a general case and deduces specific instances.
Deduction is used by scientists who take a general scientific law and apply it to a certain case.
Sherlock Holmes used deduction when he took some general indicators and deduced the specific details of a rather knotty case.
Example

Say this
Not this
Gravity makes things fall. The apple that hit my head was due to gravity.
The apple hit my head. Gravity works!
They are all like that -- just look at him!
Look at him. They are all like that.
Toyota make wonderful cars. Let me show you this one.
These cars are all wonderful. They are made by Toyota, it seems.
There is a law against smoking. Stop it now.
Stop smoking, please.
Example from Quran
Al-i Imran/110Ye are the best of peoples, evolved for mankind, enjoining what is right, forbidding what is wrong, and believing in Allah. If only the People of the Book had faith, it were best for them: among them are some who have faith, but most of them are perverted transgressors.

Inductive reasoning
Description
Inductive reasoning, or induction, is reasoning from a specific case or cases and deriving a general rule.
Derive a general rule in an accepted area and then apply the rule in the area where you want the person to behave.
Give them lots of detail, then explain what it all means.
Talk about the benefits of all the parts and only get to the overall benefits later.
Take what has happened and give a plausible explanation for why it has happened.
Inductive arguments can include:
Part-to-whole: where the whole is assumed to be like individual parts (only bigger).
Extrapolations: where areas beyond the area of study are assumed to be like the studied area.
Predictions: where the future is assumed to be like the past.
Example

Say this
Not this
Look at how those people are behaving. They must be mad.
Those people are all mad.
All of your friends are good. You can be good, too.
Be good.
The base costs is XXX. The extras are XXX, plus tax at XXX. Overall, it is great deal at YYY.
It will cost YYY. This includes XXX for base costs, XXX for extras and XXX for tax.
Heating was XXX, lighting was YYY, parts were ZZZ, which adds up to NNN. Yet revenue was RRR. This means we must cut costs!
We need to cut costs, as our expenditure is greater than our revenue.

Example from Quran
Maide/43
But why do they come to thee for decision, when they have (their own) Torah before them?- therein is the (plain) command of Allah; yet even after that, they would turn away. For they are not (really) People of Faith.

Modal logic
Description
Describe things in terms of possibility and necessity. Also explore how there intertwine.
Do not state things in terms of absolute truth, but say how likely it is.
For necessity, talk about how necessary something is. Thus use words like can, may, should, ought, must, have to.
Talking about how true or necessary something is gives you more potential in arguments as you now have an analogue continuity of alternatives, rather than the black-and-white binary decision of simply whether something is true or false, necessary or unnecessary.
Example

Say this
Not this
The door might be open.
The door is open.
You must do it.
You do it.
They could come here.
They will come here.
Example from Quran
Araf/130
We punished the people of Pharaoh with years (of droughts) and shortness of crops; that they might receive admonition.
Pros-vs-cons reasoning
Description
Pros-vs-cons reasoning seeks to weigh up the arguments for a case (pros) against the arguments against the case (cons).
The argument will usually end up with a conclusion of whether the pros or cons are stronger, thus precipitating a 'reasonable' conclusion. Things that will make a 'pro' stronger (and vice versa) include:
More logical arguments.
More evidence being displayed (including actions and perceptions of other people).
Greater emphasis being put on key words.
More arguments for the case.
Starting with the favored side allows you to fill the other person's mind with the key points, such that the second list becomes less easy to absorb. Starting with the disfavored side allows you to make it sound reasonable, then knock down each of the disfavored arguments with stronger arguments for the contrary case.
You can also choose between giving all of one side and all of another or alternating between each side (the latter is good for comparing related for-and-against arguments).
Example

Say this
Not this
It is useful and cheap, but on the other hand it won't last long and will make you look ungenerous.
It won't last long and will make you look ungenerous.
James likes it, Jan likes it, Bill likes it, Fred likes it. Only Sam and Alice don't like it.
Most people like it.
Look at the list of features on this...But when you try it at home, you may find that...
When you try it at home, you may find that...
Example from Quran
Bakara/219
They ask thee concerning wine and gambling. Say: "In them is great sin, and some profit, for men; but the sin is greater than the profit." They ask thee how much they are to spend; Say: "What is beyond your needs." Thus doth Allah make clear to you His Signs: In order that ye may consider-

Set-based reasoning
Description
Set-based reasoning is founded on Set Theory. Its arguments range around whether things are members of named groups or not, thus 'A dog is an animal but not a vegetable'.
The basic assumption is one of membership, that an item can be categorized into a given group or set. This also assumes that both the item and the set exist in the first place. The following argument then may include consideration of the overlap between sets and the implications of this.
Set reasoning often thus includes statements along the lines of:
A is a B
If A is a B then...
A is not a B, but it is a C
A is both C and D, therefore...
Example

Say this
Not this
He works for Microsoft. Microsoft people are intelligent. Therefore he is intelligent.
He works for Microsoft and is intelligent.
If this is an international standard CD then it will use ISO standard encryption coding.
ISO encryption will be used here.
If he is both Italian and lives in New York, then he is likely to be fond of pizza.
He probably likes pizza.

Example from Quran
Enbiya/98-99
Verily ye, (unbelievers), and the (false) gods that ye worship besides Allah, are (but) fuel for Hell! to it will ye (surely) come!
If these had been gods, they would not have got there! But each one will abide therein.

Decomposition
Description
Break the item in question down into its component parts. Analyze those parts and how they fit together. And then draw conclusions about the whole.
Example
I want to find out how a rubic cube operates. I pull it apart to see its hidden workings. By reassembling it slowly, I am able to explain its apparently magical cohesion as a whole in terms of three-dimensional geometry.
I listen to your argument and take note of each element. I then argue against each element in turn. Having destroyed the parts, I then assume I have destroyed the whole argument.
Example from Quran
Muminun/78
It is He Who has created for you (the faculties of) hearing, sight, feeling and understanding: little thanks it is ye give!

Systemic reasoning
Description
Understand something by considering it as a whole system. Analyze not just the parts but also the relationships between the parts.
You can use decompositional reasoning to identify parts, but go beyond this in considering the additional things beyond just the parts.
Example
I argue for a new square in the middle of town by considering the aesthetics of space and the relationships between the empty square and the tall buildings around it. I also consider the dynamics of movement and pauses of people during parts of the day and weekend.
Example from Quran
Yasin/40
It is not permitted to the Sun to catch up the Moon, nor can the Night outstrip the Day: each (just) swims along in (its own) orbit (according to Law).

Decomposition & Induction used together
Example from Quran
Araf/179
Many are the Jinns and men we have made for Hell: They have hearts wherewith they understand not, eyes wherewith they see not, and ears wherewith they hear not. They are like cattle,- nay more misguided: for they are heedless (of warning).