Generalization Fallacy

The Generalization Fallacy is a logical fallacy that is commonly applied by laymen when making predictions, and is a formal fallacy in Mathematical Logic.  The act of applying a  universal quantifier OVER a term when that term is existential. 

For example:  This car is blue, therefore all cars are blue.
For example:  Some people hate flowers, therefore all people hate flowers.
For example:  Suppose function h maps to z in integers, for z less than 5, h is less than 5, then h is less than 5 everywhere.

Generalization fallacy cannot be applied to terms which are existential. 'Some', 'Particular', 'Almost', 'Probably' are keywords for existential quantifiers.  If one states 'some' and use that as a conclusion over terms, it is invalid to state a fallacy occurred.  The way in that instance to dismiss the case is to show ALL instances cannot be attributed to that conclusion.

The act of generalization is a formal fallacy unless the terms being applied are well defined (means you know everything about the object).  The act of induction is a useful term to properly spread the quantifier through an induction hypothesis, that allows one to conclude things about infinitely many instances over a single case.  This is the effective cure for a statement that holds informally, but must be shown formally.

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