Contemporary education hates generality. Generalization is meant to be a flawed way of thinking. Do not generalize! Adhere to the aprticular! They tell us. That is a crude generalization. 
But what does it mean, to generalize? What is that function of the mind, generalizing, before we become indocrinated into the vulgarity of the particular? 
We begin generalizing as soon as we begin thinking.
Indeed, perhaps to think simply is to generalize --to find more meaning than the perception of the occasion.
From this x is y, to some x are y, to all x are y.
But what is the final "all" here?
To think this final all means the predication upon all possible and actual individual x's is not adequate to how we think.
A generality always has exceptions.
Thus, the universal quantifier "all" is a perversion of the true manner of how we think generality.
The true thinking of generality is the embracing of the individuals by the concept.
Where the concept is what has been formed by experience.
Thus, to generalize is to return to experience what it itself has given us.
To generalize is to begin the playful process of communicating with reality according to its own content.
Of course, not all generalizations are reality-listening.
Indeed, most of us obtain our generalities not from a direct engagement with reality
but from Education. 
Education or programming.
We learn the correct generalizations, and learn to think against our nature, which is to generalize.
The task to retreive the authentic functions of thinking is to learn to learn from experience once more.
Not to be afraid of the non-exhaustiveness of our generalizing. 
True empiricism is the trust that reality teaches,
and our generalizations, by listening to reality, can be more than fallacies or projections.