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Given that Ayers believes in education reform as the motor-force in a revolution whose goal is to eliminate capitalism; and given that Ayers created the CAC as a means of bringing education reform to Chicago, and given that Ayers specifically links the revolutionary struggle, political organizing, and pedagogy; and given that Barack Obama (a pedagogue and political organizer) was chosen to be CAC's chairman and executive leader, this raises serious questions about Obama.
Non-partisan Politifact explores the matter.

Regardless of Ayer's views however, it seems the CAC was not exactly out of the mainstream when it came to education reform, at least when you compare it to other education programs. It was rather conventional, in fact.

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The programs the foundation funded were designed to allow individuals from the "external partners" – whether the musicians in the symphony or the business leaders in the commercial club – to help improve student achievement. They were along the lines of mentoring by artists, literacy instruction, professional development for teachers and administrators, and training for parents in everything from computer skills to helping their children with homework to advocating for their children at school.
Also, it was not only founded by a Republican as Vicki mentions, but Ayers was one of a diverse group of people involved in the project. People like Stanley Ikenberry, former president of the University of Illinois; Arnold Weber, former president of Northwestern University and assistant secretary of labor in the Nixon administration; Scott Smith, then publisher of the Chicago Tribune; venture capitalist Edward Bottum; John McCarter, president of the Field Museum; Patricia Albjerg Graham, former dean of the Harvard University Graduate School of Journalism. I'm not sure you can count all of these people as like-minded or even sympathetic to the views elaborated above on anti-capitalist revolution.

Further, although Ayers was one of three activists that got the Annenberg grant, when it came to the day-to-day of the CAC, according to the executive director, Ayers himself "never made a decision programmatically or had a vote." He was part of an advisory group to the board. Politifact states:

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[...] there was a long list of individuals involved with the Chicago Annenberg Challenge whose positions provided them far more authority over its direction than Ayers' advisory role gave him.
There is little evidence to indicate the CAC was proposing education reform that purports anything that is not to improve public schools in Chicago, despite Ayer's participation and whatever views he might have on revolution, education and capitalism.

Also, not that this was mentioned in the post, but Obama was recruited by Deborah Leff, who had worked with Obama before in another foundation. There is no evidence to indicate that his appointment there had anything to do with Ayers.

So it seems to me like another round of the guilt by association claim where because Ayers had certain views on education, this somehow bears on Obama. But this is all based on circumstancial evidence and tenous connections. It entails disregarding a large amount of evidence to the contrary by people in a better position to know than those disseminating these insinuations (such as conservative commentator Stanley Kurtz, who suggests the nefariousness of CAC).

The NYT had a good quote:

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“I saw no evidence of a radical streak, either overt or covert, when we were together at Harvard Law School,” said Bradford A. Berenson, who worked on the Harvard Law Review with Mr. Obama and who served as associate White House counsel under President Bush. Mr. Berenson, who is backing Mr. McCain, described his fellow student as “a pragmatic liberal” whose moderation frustrated others at the law review whose views were much farther to the left.
alcyone


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