 Most accounts of truthlikeness satisfy the principle that among true theories truthlikeness covaries with logical strength (for an exception, see Oddie, 1986). So accumulation of knowledge is a special case of increasing verisimilitude, but it does not cover the case of progress by successive false theories. In his attempt to rehabilitate the cumulative knowledge model of scientific progress, Bird admits that there are historical sequences of theories none of which are “fully true” (e.g. Ptolemy—Copernicus—Kepler or Galileo—Newton—Einstein). As knowledge entails truth, Bird tries to save his epistemic account by reformulating past false theories as true ones. He proposes that if \(g\) is approximately true, then the proposition “approximately \(g\)” is true, so that “the improving precision of approximations can be an object of knowledge”. One problem with this treatment is that scientists typically formulate their theories as exact statements, and at the time of their proposal it is not known how large margins of errors would be needed to transform them into true theories. With reference to Barrett (2008), Saatsi (2019) argues that the approximate truth of Newtonian mechanics can be assessed only from the vantage point of General Theory of Relativity, so that this knowledge was not epistemically accessible to Newton at his time. Further, many past theories were radically false rather than approximately true or truthlike, but still they could be improved by more truthlike successors. Ptolemy’s geocentric theory was rejected in the Copernican revolution, not retained in the form “approximately Ptolemy”. Indeed, the progressive steps from Ptolemy to Copernicus or from Newton to Einstein are not only matters of improved precision but involve changes in theoretical postulates and laws. A further problem for Bird’s proposal is the question whether his approximation propositions are able to distinguish between progress and regress in science (Niiniluoto, 2014).