“Science fiction makes the implausible possible, while science fantasy makes the impossible plausible.”

The Circus of Dr. Lao Introduction (1956)

It's the art of the possible. Science fiction is the art of the possible. It could happen. It has happened.
A Conversation with Ray Bradbury - Point Loma Nazarene University, Writer's Symposium By The Sea; April, 2001 http://www.cosmolearning.com/videos/a-conversation-with-ray-bradbury-2001-1131/

Interview with Weird Tales (24 May 2007) http://weirdtales.net/wordpress/2007/05/24/george-rr-martin-on-magic-vs-science/
Context: I think that for science fiction, fantasy, and even horror to some extent, the differences are skin-deep. I know there are elements in the field, particularly in science fiction, who feel that the differences are very profound, but I do not agree with that analysis. I think for me it is a matter of the furnishings. An elf or an alien may in some ways fulfill the same function, as a literary trope. It’s almost a matter of flavor. The ice cream can be chocolate or it can be strawberry, but it’s still ice cream. The real difference, to my mind, is between romantic fiction, which all these genres are a part of, and mimetic fiction, or naturalistic fiction.

The Paris Review interview (2010)
Context: Science Fiction is the fiction of ideas. Ideas excite me, and as soon as I get excited, the adrenaline gets going and the next thing I know I’m borrowing energy from the ideas themselves. Science fiction is any idea that occurs in the head and doesn’t exist yet, but soon will, and will change everything for everybody, and nothing will ever be the same again. As soon as you have an idea that changes some small part of the world you are writing science fiction. It is always the art of the possible, never the impossible.

Address at the Conference on Cosmic Design, American Association for the Advancement of Science, Washington, D.C. (April 1999)

In a panel about his work in Comic Con 2010. Quoted in China Miéville Takes Comic Con http://www.tor.com/blogs/2010/08/china-mieville-takes-comic-con.