Explore a comprehensive lecture on the formal and functional competence of large language models from a cognitive perspective. Delve into central fallacies, formal linguistic confidence, and the roadmap of cognitive neuroscience and language processing. Examine the language network, verb agreement tasks, and the nature of large neural networks and language models. Investigate formal language confidence, functional competence, and various linguistic constructions. Analyze syntax and semantic coherence, formal competence, and functional confidence across formal reasoning and world knowledge domains. Consider the implications for targeted benchmarks, modularity, and evaluation methods in the field of artificial intelligence and cognitive science.