Ludwig Wittgenstein Quotes

Nothing is more important than the formation of fictional concepts, which teach us at last to understand our own.

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

As one who has taught mathematics at all levels of university instruction, I am well aware of the negative attitude of so many students toward the subject. There are many reasons for this, one of them no doubt being the esoteric, dry way in which we teach the subject. We tend to overwhelm our students with formulas, definitions, theorems, and proofs, but we seldom mention the historical evolution of these facts, leaving the impression that these facts were handed to us, like the Ten Commandments, by some divine authority.

Reading activates and exercises the mind. Reading forces the mind to discriminate. From the beginning, readers have to recognize letters printed on the page, make them into words, the words into sentences, and the sentences into concepts. Reading pushes us to use our imagination and makes us more creatively inclined.

Some persons have contended that mathematics ought to be taught by making the illustrations obvious to the senses. Nothing can be more absurd or injurious: it ought to be our never-ceasing effort to make people think, not feel.

The secret of good teaching is to regard the child's intelligence as a fertile field in which seeds may be sown, to grow under the heat of flaming imagination.

Teaching is, after all, a form of show business.

The task is simple. We will organize children and teach them in a perfect way the things their fathers and mothers are doing in an imperfect way.

Was there a little time between the invention of language and the coming of true and false?

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

Reading is a gymnasium for the imagination where people can work out, get ready for the shocks of existence. [...] For me, the intimate teachers have not only taught me how to make things, they have represented some qualities of mind and mindfulness that I would like to have.

..holding a book but reading the empty spaces.

I'm a shy, nervous person, and I don't like teaching with "terms." I didn't teach them, like, "This is first person, this is second person, this is foreshadowing," or whatever, so no one probably felt like they were learning anything. But I feel like teaching in that way reduces the concept to a term.

Teaching well draws from the same well that writing draws from: the reserves of compassion and ability to listen and concentrate on another. So I have to have fine line between teaching and writing. I try not to ever think of career. I just try to go to the dream world every day.

The eight laws of learning are explanation, demonstration, imitation, repetition, repetition, repetition, repetition, repetition.

If I'm teaching deep things, then I view it as important to make people feel like they're learning deep things, because otherwise, they will still have a hole in their mind for "deep truths" that needs filling, and they will go off and fill their heads with complete nonsense that has been written in a more satisfying style.

In 1847 I gave an address at Newton, Mass., before a Teachers' Institute conducted by Horace Mann. My subject was grasshoppers. I passed around a large jar of these insects, and made every teacher take one and hold it while I was speaking. If any one dropped the insect, I stopped till he picked it up. This was at that time a great innovation, and excited much laughter and derision. There can be no true progress in the teaching of natural science until such methods become general.

I once knew an otherwise excellent teacher who compelled his students to perform all their demonstrations with incorrect figures, on the theory that it was the logical connection of the concepts, not the figure, that was essential.

Teaching for creativity involves teaching creatively. There are three related tasks in teaching for creativity: encouraging, identifying and fostering.

It is nothing short of a miracle that modern methods of teaching have not yet entirely strangled that sacred spirit of curiosity and inquiry, for this delicate plant needs freedom no less than stimulation.

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

So many things that you can ask children hopefully pique their interest and they can design and think for themselves. Having children draw and illustrate what they saw in their minds' eyes during the story is a tremendous teaching aid.

There is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], ... or, like this, seems to raise them, by successive steps of initiation, to higher and higher states of conscious intellectual being.

There is something more important than logic: imagination

Concepts are mental images.