It has recently been suggested that heterodox economics can benefit from an engagement with classical surplus theory. However, caution is often recommended due to the ideological concepts that are embedded in classical political economy. This article argues that many of the ideological concepts that are often attributed to classical political economy are actually not part of classical political economy, but rather of a “vulgar” form of political economy, a project that emerged after Ricardo. This vulgar project, often termed as “Ricardian economics,” is often mistakenly taken to be a development of classical political economy, but it is actually a rupture with the classical political economy of Petty, Smith, and Ricardo, as Marx, and later Sraffa, argued. Once this is acknowledged, the relationship between classical political economy and heterodox economics becomes clearer.