Ontology Quotes

It is the faithfulness of God that allows epistemology to model ontology.

There are no solved problems; there are only problems that are more or less solved.

I have forced myself to contradict myself in order to avoid conforming to my own taste.

Gods have bloody hands.

When I consider this carefully,
I find not a single property which with certainty separates the waking state from the dream.
How can you be certain that your whole life is not a dream?

The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.

Thought that accepts reality as given is no thought at all.

The ontology of materialism rested upon the illusion that the kind of existence, the direct "actuality" of the world around us, can be extrapolated into the atomic range. This extrapolation is impossible, however.

Absence of evidence is not evidence of absence.

You get what you expect. Expect to heal. Expect victory.

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.

All sentences of the type 'deconstruction is X' or 'deconstruction is not X', a priori miss the point, which is to say that they are at least false. As you know, one of the principal things at stake in what is called in my texts 'deconstruction', is precisely the delimiting of ontology and above all of the third-person present indicative: S is P.

Neither the true nor the false roots are always real;
sometimes they are imaginary;
that is,
while we can always imagine as many roots for each equation as I have assigned,
yet there is not always a definite quantity corresponding to each root we have imagined.

"I see it, but I don't believe it."

The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it.

All gods are tricksters, and war gods worst of any.

If, as you teach, the universe has no beginning and no end, why should we?

Calculus works by making visible the infinitesimally small.

Utopia would seem to offer the spectacle of one of those rare phenomena whose concept is indistinguishable from its reality, whose ontology coincides with its representation.

This view [of the infinite], which I consider to be the sole correct one, is held by only a few. While possibly I am the very first in history to take this position so explicitly, with all of its logical consequences, I know for sure that I shall not be the last!

It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.

We admit, in geometry, not only infinite magnitudes, that is to say, magnitudes greater than any assignable magnitude, but infinite magnitudes infinitely greater, the one than the other. This astonishes our dimension of brains, which is only about six inches long, five broad, and six in depth, in the largest heads.

No mercy goes unpunished by the angry gods.

Our acceptance of an ontology is, I think, similar in principle to our acceptance of a scientific theory, say a system of physics;we adopt, at least insofar as we are reasonable, the simplest conceptual scheme into which the disordered fragments of raw experience can be fitted and arranged.

Mathematics is purely hypothetical: it produces nothing but conditional propositions.

Although my knowledge grows more and more,
nevertheless I do not for that reason believe that it can ever be actually infinite,
since it can never reach a point so high that it will be unable to attain any greater increase.

I survive. I survived it all then and I'll survive the rest of it. Without your help.

We must revisit the idea that science is a methodology and not an ontology.

We call infinite that thing whose limits we have not perceived,
and so by that word we do not signify what we understand about a thing,
but rather what we do not understand.

There's something in the Western mind that gets very nervous when you try to talk about the bedrock of ontology.

The line has magnitude in one way, the plane in two ways, and the solid in three ways, and beyond these there is no other magnitude because the three are all.

ALGEBRA is a general Method of Computation by certain Signs and Symbols which have been contrived for this Purpose, and found convenient.

Infinity is a fathomless gulf, into which all things vanish.

Today the major reason for our interest in Flatland is that for the first time we can achieve some of the dreams of our ancestors a century ago and obtain direct visual experience of phenomena in a dimension higher than our own.

In my paper the fact the XY was not equal to YX was very disagreeable to me. I felt this was the only point of difficulty in the whole scheme...and I was not able to solve it.

A good proof is one that makes us wiser.

How dreadful knowledge of the truth can be when there's no help in truth!

Every man heals himself.

To see what is general in what is particular, and what is permanent in what is transitory, is the aim of scientific thought.

What is needed is never to be had without price.

I'm reverent from a distance.

He who does not understand the supreme certainty of mathematics is wallowing in confusion.

Only so much can be borne from men, so much from gods

No human investigation can claim to be scientific if it doesn't pass the test of mathematical proof.

Time is so...fluid where I live

A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?

Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.

My opinion of mankind is founded upon the mournful fact that, so far as I can see, they find within themselves the means of believing in a thousand times as much as there is to believe in.

The world is too big and too intricate to conform to our ideas of what it should be like... Just because we invent myths and theories to explain away the chaos we're still going to live in a world that's older and more complicated than we'll ever understand.

The final philosophy is the ontology of God.