Sunday, July 11, 2010

Scope of Logic & Inductive and Deductive Logic

In logic, "argument" does not have the common connotation of dispute (no shouting or name calling involved!). Argument is simply statements that support a conclusion. Logic does not deal with truth or the persuasive power of argument. Logic is only concerned with an objective relationship between argument and conclusion.

Scope:
An argument is a group of statements standing together.
e.g. From Sherlock Holmes:
1. This is a large hat.
2. Someone is the owner of this hat.
3. Owners of large hat have large heads.
4. People with large head large brains.
5. People with large brains are highly intellectual.
6. Owner of this hat is highly intellectual.

First 5 statements are premises; the sixth one is a conclusion.

Here 2 questions arise:
1) Are the premises correct?
2) Are the premises properly related to the conclusion?
Logic is concerned with the second question only.

Scope of Logic: Logic deals with the relation between premises and conclusion, not with the truth of the premises.

Deductive vs. Inductive Logic
Deductive Logic:
e.g. Every mammal has a heart.
All horses are mammals.
Every horse has a heart.

If all of the premises are true, the conclusion is true.
All of the facts in the conclusion are already contained, at least implicitly, in the premises.
Purpose of deductive logic is to highlight the contents of the premises.
Deductive logic is either entirely conclusive or entirely inconclusive...mathematical arguments are deductive.

Inductive Logic:
e.g. Every horse that has ever been observed has had a heart.
Every horse has a heart.

If all of the premises are true, the conclusion is probably true but not necessarily true.
Conlcusion contains information (facts) not present, even implicitly, in the premises.
Purpose of inductive logic is to extend the range of knowledge.
Inductive logic admits a degree of strength depending upon the level of support premise provides to the conclusion...the relation between a scientific generalization and its supporting observational evidence is inductive logic.

Source: Logic - Wesley C. Salmon. Pub. Prentice Hall Inc. 1963

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