The Internet has evolved through successive architectural abstractions that enabled unprecedented scale, interoperability, and innovation. Packet-based networking enabled the reliable transport of bits; cloud-native systems enabled the orchestration of distributed computation. Today, the emergence of autonomous, learning-based systems introduces a new architectural challenge: intelligence is increasingly embedded directly into network control, computation, and decision-making, yet the Internet lacks a structural foundation for representing and exchanging meaning. In this paper, we argue that cognition alone: pattern recognition, prediction, and optimization, is insufficient for the next generation of networked systems. As autonomous agents act across safety-critical and socio-technical domains, systems must not only compute and communicate, but also comprehend intent, context, and consequence. We introduce the concept of a Semantic Layer: a new architectural stratum that treats meaning as a first-class construct, enabling interpretive alignment, semantic accountability, and intelligible autonomous behavior. We show that this evolution leads naturally to a Syntactic-Semantic Internet. The syntactic stack continues to transport bits, packets, and workloads with speed and reliability, while a parallel semantic stack transports meaning, grounding, and consequence. We describe the structure of this semantic stack-semantic communication, a semantic substrate, and an emerging Agentic Web, and draw explicit architectural parallels to TCP/IP and the World Wide Web. Finally, we examine current industry efforts, identify critical architectural gaps, and outline the engineering challenges required to make semantic interoperability a global, interoperable infrastructure.