Logical Inferences: Induction & Deduction

There are two types of logical inferences; induction and deduction.

Inductive reasoning aims at developing a theory while deductive reasoning aims at testing an existing theory.

1. Inductive Reasoning 

a) From specific sample to the general principle
- Generalisation 

'My older brother is good at math. My friend's older brother is good at math. My neighbour's big brother is a math tutor. Therefore, all older brothers are good at math.'

Rule: Greater the sample; the stronger the argument.

b) Effect to Cause 

Modus Ponens: if p THEN q, p THEREFORE q 

[ Premises THEREFORE Conclusion= Argument] 

When it rains (cause) THEN the street gets wet (effect), the street is wet (effect), THEREFORE it must have rained (cause).

Note: There can be other causes to specific effect, maybe they have washed the streets. 

Therefore inductive argument can be called a strong argument. 

2. Deductive Reasoning 

a) From general principles to a specific conclusion

For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid.

b) Cause to effect 

[ Premises THEREFORE Conclusion= Argument] 

Modus Ponens: If p THEN q, p THEREFORE q

When it rains (cause) THEN the street gets wet (effect), it is raining (cause) THEREFORE the street will be wet ( effect). 

"Cause" has determined "effect or effects" therefore deductive arguments are valid. 

Rule: If all premises are true, then the conclusion is also "true" in the case of a deductive argument. 

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