A long-standing paradigmatic debate in artificial intelligence is between the so-called symbolic and connectionist (or ‘sub-symbolic’) approaches to knowledge representation. Both approaches aim for uncovering the principles of how general, domain-independent knowledge is structured, generated, and handled by autonomous intelligent agents. Yet each seems to work only for certain kinds of information. The approaches spring from disjoint methodological beginnings; the former is inspired by human introspection (“top-down”), the latter by brain substrates (“bottom-up”). Neither approach has led to a unified theory of general intelligence. Few researchers are fluent in both methodologies, as using either approach calls for significant time and effort easily spanning decades. As a result, progress towards theories of general intelligence have been held hostage. We propose to brake this deadlock with a third approach: Concept-Centered Knowledge Representation (CCKR). Based around situated dynamic knowledge graph generation and management, CCKR captures latent features inherent in conceptual graphs that prior approaches do not address and adds capabilities that we argue are necessary for, and offer a path to, general machine intelligence. Here we explain CCKR and present arguments for its claims, resting in part on the results from two implemented experimental systems, the Non-Axiomatic Reasoning System (NARS) and the Autonomous Empirical Reasoning Architecture (AERA).