Final answer:
The statement is true, as H. erectus, appearing around 1.8 million years ago, had a brain size close to modern humans and demonstrated advances in tool-making, usage of fire, hunting, and social behavior indicative of increased cognitive complexity.
Step-by-step explanation:
The statement that H. erectus was the first species with a cranial capacity approaching H. sapiens is true. H. erectus appeared approximately 1.8 million years ago and is known to have had a brain size ranging from 775 to 1,100 cubic centimeters, which is quite large compared to earlier hominins but still smaller than the average brain size of modern humans (H. sapiens), which ranges from 1,130 to 1,260 cubic centimeters. The significant increase in brain size in H. erectus showcases a clear trend of encephalization in human evolution, correlating with increased behavioral, cognitive, and cultural complexity.
Moreover, the adaptations and behaviors associated with H. erectus, such as the production of advanced stone tools, use of fire, and evidence of hunting and having a home base, provide strong evidence for its advanced cognitive capabilities that were more similar to those of modern humans than its predecessors. Ultimately, the evolutionary developments in H. erectus such as increased brain size, upright walking, and cultural sophistication, are important aspects in understanding the trajectory of human evolution towards the emergence of H. sapiens.