Jean Piaget Quotes

You'd be surprised how hard it can often be to translate an action into an idea.

Awareness of universals is called conceiving, and a universal of which we are aware is called a concept.

Two elements are needed to form a truth - a fact and an abstraction.

All human knowledge thus begins with intuitions, proceeds thence to concepts, and ends with ideas.

An absolute can only be given in an intuition, while all the rest has to do with analysis.

Intuition and concepts constitute... the elements of all our knowledge, so that neither concepts without an intuition in some way corresponding to them, nor intuition without concepts, can yield knowledge.

I have an unusual type of thinking. I have no visual memory whatsoever. Everything is conceptual to me.

Abstraction is real, probably more real than nature.

By object is meant some element in the complex whole that is defined in abstraction from the whole of which it is a distinction.

Abstraction is a mental process we use when trying to discern what is essential or relevant to a problem; it does not require a belief in abstract entities.

Abstraction is everybody's zero but nobody's nought.

An idea is always a generalization, and generalization is a property of thinking. To generalize means to think.

One can imagine that the ultimate mathematician is one who can see analogies between analogies.

The analysis of the thing is not the thing itself.

From a drop of water a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other.

Pure mathematics is, in its way, the poetry of logical ideas.

Logicians may reason about abstractions. But the great mass of men must have images.

I am never satisfied until I can make a mathematical model of what I am studying. If I succeed in making one, I understand. If I cannot, I do not understand.

I've always been interested in visualizing something, whether it's a memory or an idea you want to be true. I am a big believer in that. I'm constantly thinking of that. If I can't picture something, then it doesn't make sense to me.

I became interested in structure when I was in graduate school. How is it that the brain perceives structure in a sometimes disorganized and chaotic world? How and why do we categorize things? Why can things be categorized in so many different ways, all of which can seem equally valid?

I can see that, without being excited, mathematics can look pointless and cold.

A thought functions only as a fragmentary part in the formulation of an idea.

Ideas are information taking shape.

Far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures images and processes by intuition.

By speaking, by thinking, we undertake to clarify things, and that forces us to exacerbate them, dislocate them, schematize them. Every concept is in itself an exaggeration.