Television may have the capacity to wipe out human intelligence, but why give up without a fight? The producers of "Reading Rainbow" hit on the idea of fighting television with television. The show is designed to encourage kids to read so that when they grow up, they won't be content with just watching TV until their brains shrivel into raisins.

In its attempt to excite young viewers about the worlds and realms awaiting them on printed pages, "Reading Rainbow" proved a world-class champ. Then the funding rug was pulled out from under it, and now project director Twila Liggett roams the earth like Diogenes, looking not for an honest man, just a generous and public-spirited corporation.

She is learning it might actually be easier to find an honest man. It might even be easier to find an honest man at Leavenworth.

Can a TV show encourage kids to read? Research on "Reading Rainbow" indicates a walloping degree of effectiveness at that. In a survey, booksellers reported average sales increases of from 200 to 780 percent on titles that were featured on the program. Indeed, the publisher of "Three Days on a River in a Red Canoe" reported a 976 percent jump. And librarians responding reported overwhelmingly that children were asking for the books on "Reading Rainbow" in great numbers and by name, which is unusual behavior for young readers. Ratings were good -- as good as for "Mister Rogers' Neighborhood" -- response was great, and "Reading Rainbow" was clearly a success.

Then, it was canceled. Or rather, Kellogg's, the cereal company, which had given grants totaling just over $1 million to help produce the first 20 shows in the series, decided to drop out as corporate sponsor. Since the Reagan administration is busily bankrupting public TV by cutting government support, "Reading Rainbow" can count on only limited funds from the Corporation for Public Broadcasting, the Scroogey federal money-giver. The kind of government support that launched the glamoroso "Sesame Street" now seems out of the question. That leaves the vivacious and tenacious Liggett seeking the pot of gold to keep "Rainbow" going.

"We are hopeful. I'm the eternal optimist," Liggett says. "Four years ago, before we found Kellogg's, I looked for underwriters and didn't find anyone and had lots of people tell me, 'Give it up, Twila.' You know, 'It's a great idea, but give it up.' And I couldn't. It was the kind of thing I knew would work. And that's how I feel now. I just feel that we will find somebody who will come in and see the value of being connected with this."

But Liggett has knocked on many doors and received innumerable no-thank-you's. Have corporations turned unusually cheap in this age of alleged prosperity? Liggett says that even those companies traditionally inclined to support public TV are reluctant to fund children's programming. They feel it's less visible than the stuff adults watch, but she thinks attention is paid by parents to the companies that underwrite good programming for their children.

"People notice," she says. "I notice when somebody has done something positive, qualitative, on television. I make a note of who did that, and I think a lot of people do. I think that companies have the potential of reaping some genuine good will from a whole lot of people out there."

Cereal companies, which push sugary breakfast treats on kids seven days a week in commercial kiddie fare, might support a show like "Rainbow" as a way of making amends. It's never been done, but any of the three TV networks that make fortunes from their Saturday morning cartoon ghettos could underwrite a program like this for a relative pittance, and it would be a tax write-off besides.

On "Reading Rainbow," the intensely personable LeVar Burton, an ideal host who makes great eye contact, guides young viewers through illustrations, adaptations and reviews of currently available books. There's nothing dry or dull. The programs might include a ride in a balloon, a visit to a school for firefighters, a full-fledged musical production number. And there are guest book readers like Bill Cosby, Lorne Greene and Madeline Kahn, reading from books with titles that have included "Hot-Air Henry" and "Gila Monsters Meet You at the Airport." The show is aimed at kids from 5 to 8, but picks up viewers older and younger.

Why did Kellogg's desert such a worthwhile program? Celeste Clark, director of corporate publicity for the company, says from Battle Creek, Mich., that "Rainbow" was "everything that we thought it would be" and notes of those who produced it, "When they started out, I don't think even they really conceived of how successful the program would be."

But Kellogg's had made a commitment to lend financial support to the Statue of Liberty restoration project, Clark says, and so the company bailed out of "Rainbow." There wasn't enough money to support both, it is claimed. Hmmm. In 1983, Kellogg's reported earnings of $242.7 million, up from $227.8 million the year before, on sales of $2.38 billion. Bernice Kanner reports in New York magazine that Kellogg's, Post and the other big cereal companies spent $287 million in 1983 on advertising alone.

The first 20 programs that Kellogg's helped finance are still in reruns on public TV stations throughout the country, but Liggett needs a few million dollars in order to begin production of a new set, or just $1 million to produce 10 for next summer. She would like to make a total of 60 shows. They don't date so they could play for years.

For now, though she hasn't got her grant, she can bolster the morale of those who work on the show with the response of teachers, librarians and the kids themselves. One letter was from a 4-year-old who wrote how much he loved "Rainbow" and sent along a drawing that could be sold in order to raise cash for production costs. "We get real nifty kinds of things," Liggett says.

Liggett, who says she grew up in a house where everyone read, thinks a show like "Rainbow" can help counter TV's tendency to discourage reading, and is also particularly valuable in an age when kids are getting the impression the only kind of literacy they'll need in life is computer literacy (the lowliest kind, surely). "Well I'll tell you what," says Liggett in her firmest schoolmarm tone, "I don't think there's a parent or a person alive who doesn't want their children to become well educated and do well, and I don't care what happens with computers, you still have to learn how to read. And I think even more important than learning, is loving to read, because you don't do stuff you don't like to do.

"And that is what 'Reading Rainbow' is about: not teaching kids how to read, but getting them to love to read. If you love to read, you'll read all the time, and the more you read, the better you get at it, and then you'll stick with stuff that maybe isn't so interesting when you hit those kinds of things later."

"I can go anywhere . . . I can be anything, Take a look, it's in a book," sings the "Reading Rainbow" title tune. "I don't think that television has to be an enemy," Liggett says. "I'm not too crazy about everything on television, but television is there. We know kids watch a lot of it. Why not use it for something really positive?"