Reasoning is broadly defined as the process of drawing conclusions. It is related to psychology, philosophy, linguistics, cognitive science, logic, probability theory and artificial intelligence.
There are several theories of reasoning. The most commonly used is that people rely on mental logic, which includes inference rules. There are several theories of cognitive process that are the underpinnings of understanding human reasoning. One idea is that people rely on a logic using formal inference rules much like logicians use in propositional calculus. Another theory is that people use domain-specific or content specific rules of inference. The last idea is that people rely on mental models. And finally it may be that people compute probabilities.
Research on deductive reasoning has frequently compared human reasoning with eh prescriptions of a logical system. A logical system consists of rules of inference that produce true conclusion to be derived from true beliefs. This is the rule of modus ponens. It looks like this:
1. If it rains tomorrow, then the game will be canceled.
2. If the game is canceled, then our team will surely lose the pennant.
3. It will rain tomorrow.
The idea is that given the proposition A implies B. And given A we can infer B. So from 1 and 3 we can infer 4 by modus ponens
4. The game will be canceled.
From 2 and 4 we can infer 5
5. Our team will surely lose the pennant.
Conditional reasoning is reasoning by conditional statements
Example: If the maid hid the gun, then the butler was not at the scene of the crime.
It is easy to make a mistake with this kind of reasoning. Example:
1. If the ball rolls left, the green light comes on.
2. The ball rolls left,
3. Therefore, the green lamp comes on.
Also an error in reasoning:
1. If God exists, life will be beautiful
2. God does not exist.
3. Therefore, life is not beautiful
Reasoning about qualifiers
We have to be careful about reasoning with words like all or some. There must always be a qualifier in a categorical statement such as, All doctors are rich or No politicians trustworthy. This is where it is important to remember that your brain does not understand sarcasm. It takes what you tell it at face value. So when qualifiers are present the brain must be taught to process it skeptically. Many people make errors when dealing with categorical syllogisms, particularly errors that involve the acceptance of invalid conclusions. This pattern of errors is partially described by atmosphere hypothesis, which asserts that people are inclined to accept conclusions similar to the premises.
The components of the inductive reasoning process are hypotheses formation and hypotheses evaluation. For an agreement to be inductively valid. The conclusion must be probable if the premises are true. This criterion contrasts with that for deductive valid argument, in which the conclusion must be certain if the premises are true.
Bonnefon, J-F. & Hilton, D. (2002). The suppression of modus ponens as a case of pragmatic preconditional reasoning. Thinking and Reasoning, 8, 21-40.
Byrne, R.M.J., Espino, O. & Santamaria, C. (1999). Counterexamples and the suppression of inferences.” Journal of Memory & Language”, 40, 347-373.
Johnson-Laird, P.N. and Byrne, R.M.J. (1991). Deduction. Hillsdale: Erlbaum