Final answer:
The founding belief inspired by salutary neglect is the 'consent of the governed'. Salutary neglect allowed for self-rule and contributed to the colonial emphasis on a government that operates with the consent of its citizens.
Step-by-step explanation:
The founding belief that was inspired by salutary neglect is consent of the governed. Salutary neglect was a period of time when the British government allowed its colonies to self-rule without much interference. This tradition of self-rule contributed to the colonial belief in representative government and the idea that governments are legitimate only if they have the consent of those they govern. This aligns with the philosophy of John Locke who insisted that a social contract existed between the government and the governed, where the government must protect the natural rights of the people. This was also fundamental to the American Revolution and the subsequent creation of the U.S. Constitution, which sought to establish a government based on the consent of the governed and protection of inalienable rights, including life, liberty, and the pursuit of happiness.