… however useful the words may have been in the past, they have now become handicaps to the further development of knowledge. Words like botany and zoology imply that plants and animals are quite different things. … But the differences rapidly become blurred when we start looking at the world through a microscope. … The similarities between plants and animals became more important than their differences with the discoveries that both were built up of cells, had sexual reproduction,… nutrition and respiration … and with the development of evolutionary theory.

Agreeing that plants and animals were produced by Omnipotent fiat does not exclude the idea of natural order and what we call secondary causes. The record of the fiat—“Let the earth bring forth grass, the herb yielding seed,” etc., “and it was so;” “let the earth bring forth the living creature after his kind” — seems even to imply them.

An ever-green revolution implies the enhancement of productivity in perpetuity without associated ecological harm.

And yet I think that the Full House model does teach us to treasure variety for its own sake–for tough reasons of evolutionary theory and nature’s ontology, and not from a lamentable failure of thought that accepts all beliefs on the absurd rationale that disagreement must imply disrespect. Excellence is a range of differences, not a spot. Each location on the range can be occupied by an excellent or an inadequate representative– and we must struggle for excellence at each of these varied locations. In a society driven, of ten unconsciously, to impose a uniform mediocrity upon a former richness of excellence–where McDonald’s drives out the local diner, and the mega-Stop & Shop eliminates the corner Mom and Pop–an understanding and defense of full ranges as natural reality might help to stem the tide and preserve the rich raw material of any evolving system: variation itself.

As was the case for Nobel's own invention of dynamite, the uses that are made of increased knowledge can serve both beneficial and potentially harmful ends. Increased knowledge clearly implies increased responsibility. We reject the notion advocated in some quarters that man should stop eating from the tree of knowledge, as if that were humanly possible.

Every definition implies an axiom, since it asserts the existence of the object defined. The definition then will not be justified, from the purely logical point of view, until we have ‘proved’ that it involves no contradiction either in its terms or with the truths previously admitted.

Evolution is a theory of organic change, but it does not imply, as many people assume, that ceaseless flux is the irreducible state of nature and that structure is but a temporary incarnation of the moment. Change is more often a rapid transition between stable states than a continuous transformation at slow and steady rates. We live in a world of structure and legitimate distinction. Species are the units of nature’s morphology.

First of all, we ought to observe, that mathematical propositions, properly so called, are always judgments a priori, and not empirical, because they carry along with them necessity, which can never be deduced from experience. If people should object to this, I am quite willing to confine my statements to pure mathematics, the very concept of which implies that it does not contain empirical, but only pure knowledge a priori.

For Linnaeus, Homo sapiens was both special and not special ... Special and not special have come to mean nonbiological and biological, or nurture and nature. These later polarizations are nonsensical. Humans are animals and everything we do lies within our biological potential ... the statement that humans are animals does not imply that our specific patterns of behavior and social arrangements are in any way directly determined by our genes. Potentiality and determination are different concepts.

For the same energy output as from coal or oil, methane combustion releases only half as much carbon dioxide. This implies that powering a nation entirely by gas reduces emissions of carbon dioxide by half. … The problem with [production leaks and other escapes of] … methane is that this substance is twenty-four times more potent a greenhouse gas than carbon dioxide.

In general, we look for a new law by the following process. First, we guess it. Then we—don’t laugh, that’s really true. Then we compute the consequences of the guess to see if this is right—if this law that we guessed is right—we see what it would imply. And then we compare those computation results to nature—or, we say compare to experiment or experience—compare it directly with observation to see if it works. If it disagrees with experiment, it’s wrong.

Nothing got him angrier than when people implied he was paranoid. It made him feel persecuted.

The critical mathematician has abandoned the search for truth. He no longer flatters himself that his propositions are or can be known to him or to any other human being to be true; and he contents himself with aiming at the correct, or the consistent. The distinction is not annulled nor even blurred by the reflection that consistency contains immanently a kind of truth. He is not absolutely certain, but he believes profoundly that it is possible to find various sets of a few propositions each such that the propositions of each set are compatible, that the propositions of each such set imply other propositions, and that the latter can be deduced from the former with certainty. That is to say, he believes that there are systems of coherent or consistent propositions, and he regards it his business to discover such systems. Any such system is a branch of mathematics.

The great thing [about Kant’s philosophy] was to form the idea that this one thing—mind or world—may well be capable of other forms of appearance that we cannot grasp and that do not imply the notions of space and time. This means an imposing liberation from our inveterate prejudice.

There are hidden contradictions in the minds of people who “love Nature” while deploring the “artificialities” with which “Man has spoiled ‘Nature.’” The obvious contradiction lies in their choice of words, which imply that Man and his artifacts are not part of “Nature”—but beavers and their dams are.

There are no physicists in the hottest parts of hell, because the existence of a ‘‘hottest part’’ implies a temperature difference, and any marginally competent physicist would immediately use this to run a heat engine and make some other part of hell comfortably cool. This is obviously impossible.

There are pessimists who hold that such a state of affairs is necessarily inherent in human nature; it is those who propound such views that are the enemies of true religion, for they imply thereby that religious teachings are utopian ideals and unsuited to afford guidance in human affairs. The study of the social patterns in certain so-called primitive cultures, however, seems to have made it sufficiently evident that such a defeatist view is wholly unwarranted.

There is an integration of the present impressions with such past ones as they resemble, and a differentiation of them from such past ones as they do not resemble; and this comparison of present with past impressions, dependent on memory, implies classification, and is the germ of what we call Perception and Reasoning.

This relation logical implication is probably the most rigorous and powerful of all the intellectual enterprises of man. From a properly selected set of the vast number of prepositional functions a set can be selected from which an infinitude of prepositional functions can be implied. In this sense all postulational thinking is mathematics. It can be shown that doctrines in the sciences, natural and social, in history, in jurisprudence and in ethics are constructed on the postulational thinking scheme and to that extent are mathematical. Together the proper enterprise of Science and the enterprise of Mathematics embrace the whole knowledge-seeking activity of mankind, whereby “knowledge” is meant the kind of knowledge that admits of being made articulate in the form of propositions.

What is the meaning of human life, or of organic life altogether? To answer this question at all implies a religion. Is there any sense then, you ask, in putting it? I answer, the man who regards his own life and that of his fellow creatures as meaningless is not merely unfortunate but almost disqualified for life.