Final answer:
The ideas of the Enlightenment philosophers were based on rationalism, empiricism, progressivism, and cosmopolitanism. These ideas laid the foundations for scientific inquiry, government based on popular representation, and economic systems designed to create wealth.
Step-by-step explanation:
The ideas of the Enlightenment philosophers were based on several key concepts. Firstly, rationalism is the idea that humans are capable of using their faculty of reason to gain knowledge. Secondly, empiricism promotes the idea that knowledge comes from experience and observation of the world. Thirdly, progressivism is the belief that humans can make unlimited, linear progress over time through reason and observation. Lastly, cosmopolitanism reflected Enlightenment thinkers' view of themselves as citizens of the world. These ideas laid the foundations for scientific inquiry, government based on popular representation, and economic systems designed to create wealth.