A Quote by Hilary Putnam

The physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material world, even if he has to speak of numbers, vectors, tensors, state-functions, or whatever to make the abstraction.
One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?
The idea to have both something that belongs to what we call supernatural and, at the same time, is anchored in the real world, I think it gives more strength to whatever has to do with the real world and whatever has to do with some transcendence of the material world.
The world of physics is essentially the real world construed by mathematical abstractions, and the world of sense is the real world construed by the abstractions which the sense-organs immediately furnish. To suppose that the "material mode" is a primitive and groping attempt at physical conception is a fatal error in epistemology.
Abstraction is real, probably more real than nature.
The seventeenth century witnessed the birth of modern science as we know it today. This science was something new, based on a direct confrontation of nature by experiment and observation. But there was another feature of the new science-a dependence on numbers, on real numbers of actual experience.
Far from being a material world, this is a psychic world, which allows us to make only indirect and hypothetical inferences about the real nature of matter. The psychic, alone has immediate reality, and this includes all forms of the psychic, even
Ordinarily all desires exist in the second state of consciousness, the dreaming state. Desire is a dream and to work for a dream is doomed from the very beginning, because a dream can never become real. Even if sometimes you feel it has become almost real, it never becomes real - a dream by nature is empty. It has no substance in it.
For me, I don't talk about numbers. I've had big contracts my whole career; I just don't like talking about numbers if they're real or not real... whatever offers I've had, I always keep it private.
The physicist may be satisfied when he has the mathematical scheme and knows how to use for the interpretation of the experiments. But he has to speak about his results also to non-physicists who will not be satisfied unless some explanation is given in plain language. Even for the physicist the description in plain language will be the criterion of the degree of understanding that has been reached.
I am a hopeless romantic. A silly, ridiculous, foolish romantic. I live in a fantasy land. I need to get real. And now, for the first time, I want to get real. I want a real relationship with a real man in the real world–-with all the real problems, faults, and whatever comes with it.
The screen is a window through which one sees a virtual world. The challenge is to make that world look real, act real, sound real, feel real.
Numbers instill a feeling for the lie of the land, and furnish grist for the mathematical mill that is the physicist's principal tool.
Everyone in the United States is so intense about maintaining a separation between Church and State when the real concern should be about keeping a separation between Corporations and State--because in America (and most of the rest of the Western World, for that matter) economics is the real religion.
To my mathematical brain, the numbers alone make thinking about aliens perfectly rational. The real challenge is to work out what aliens might actually be like.
An administrator in a bureaucratic world is a man who can feel big by merging his non-entity in an abstraction. A real person in touch with real things inspires terror in him.
States in the world are like individuals in the state of nature. They are neither perfectly good nor are they controlled by law.
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