The issue of the advantage or rather dangerousness of redescriptive activities motivated Rorty’s landmark private/public divide, and yet, upon closer inspection, the divide itself needs to be rethought precisely in the light of the possibility that the ironist attitude can jeopardize the quest for public solidarity by frustrating one’s fellow beings in their tentative activities of identities-formation. It is no chance that Rorty eventually recurred to a reconciliation of the private with the public sphere through the figure of the «liberal ironist», for whom redescription is always in the service of social cooperation, rather than getting in the way of it. What is detrimental to moral growth, private and public alike, is then the overlooking of the practical consequences of our own ironic activities, for which no algorithm is indeed possible nor welcome.