deductive and inductive arguments

PREMISE:

A premise is a reason given.

ARGUMENT:

An argument is a set of premises and a conclusion.

DEDUCTIVE ARGUMENTS

An argument is a set of premises and a conclusion. Look at this argument:

"Socrates is a man"  first premise
"Men are mortal"    second premise
________
"Socrates is mortal" conclusion

Now, there are deductive and inductive arguments.

Deductive argument are “truth preserving”, because the truth of its premises guarantees the truth of its conclusion.

Deductive arguments can be valid or invalid. If VALID, then the conclusion necessarily follows from the premises (even if the premises were false).

"Socrates is a man" (T)
"Men are mortal"    (T)
________
"Socrates is mortal"  (T)

the above argument is valid. in addition the premises are true. if the argument is VALID and its premises true, the conclusion must be true. we call this kind of argument SOUND. 

now let's play a bit with truth values:

"Socrates is a man"  (T)
"Men are immortal" (F)
__________
"Socrates is immortal" (F)

the above argument IS VALID, i.e, though the conclusion follows from the premises, though one premise is false. We have a false premise and a false conclusion, yet the above argument is VALID, but UNSOUND

See that deduction is independent from experience beause the reasoning is self contained in the premises. Remember that the premises could be false and the argument still be valid. 

DEDUCTION IS APRIORISTIC. MATHEMATICS IS AN EXAMPLE OF AN APRIORISTIC DISCIPLINE. 

______________

INDUCTIVE ARGUMENTS:

An inductive argument establishes a conclusion with high degree of probability. Here the truth of their premises does not guarantee the truth of their conclusion.

Every windstorm observed so far in this area comes from the north. We can see a big cloud of dust in the distance. So, probably a new windstorm is coming from the north.

Analysis: The above argument is a strong inductive argument. The "so far" in the premise is simple and cautious, and the conclusion uses "probably."  Strong inductive arguments establish the conclusion with high probability IF the premises were true.

 

There are three kinds of inductive arguments: 

Inductive generalization: It goes from a premise about a sample to a conclusion about the population, or it derives general principles from specific observations.  

Analogical Induction: The process of analogical inference involves noting the shared properties of two or more things and from this basis inferring that they also share some further property:

Example:
 

Athenians and spartans are similar with respect to speaking the same language & being Pantheists
An Athenian has been observed to have further property X
Therefore, a Spartan probably also has property X.

Enumerative Induction: It reasons from particular instances to all instances. 

Example: If one observes 100 swans, and all 100 are white, one might infer "All swans are white." 

 

(As you can see, even if the premises are true, it does not entail the conclusion's truth. The conclusion might be true, and might be thought probably true, yet it can be false).

Inference to the best explanation IBE: 

Phenomenon Q.

E provides the best explanation for Q.

Therefore, it is probable that E is true.

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As you can see, a big difference between deduction and induction is that the latter depends from experience. 

INDUCTION IS BASICALLY A POSTERIORI. 

SO, WE CAN SAY THAT SCIENTIFIC THEORIES ARE A POSTERIORI, NEVER ABSOLUTELY CERTAIN.