Grayling has been saying that the big web companies should be required to regularly ''send us a report on what they have got on us''.
The top British thinker told the Sydney Morning Herald that this would be a first step in reclaiming privacy thoughtlessly given away in our seduction by social media.
Historically the ''complete anarchy'' surrounding the initial use of revolutionary communication technologies is brought to order by users wanting boundaries.
Humanity is at a crucial phase and the current situation will not be allowed to last for long, he thinks.
Grayling said that people tweet about him walking down the street or in a restaurant or on a bus and he found that a terrible invasion of privacy.
Professor Grayling said that this is the price you have to pay for living in a ''noisy, messy, quarrelsome democracy''. The press should be allowed to ''get away with a few things because it is a price worth paying'' for the ''very crucial, noble'' investigative work it does in the public interest.
But he was a little miffed that the British government plans to extend state surveillance on the internet and to allow secret court hearings at the discretion of politicians in civil cases related to national security.
He said that civil liberties were under attack like never before and it was ''very thought-provoking'' that governments have the capability to hack into people's private digital information.
Grayling said that the challenge is to find an internationally agreed regime for safeguarding people's private information without damaging the ''very worthwhile anarchy'' of the internet and related technologies.