Yes, you are correct. The dominant natural philosophy of the 17th and early 18th centuries, known as catastrophism, was indeed based on the belief in a very short geological history for Earth.

Here's why:

* Biblical Interpretation: The prevailing view was heavily influenced by the biblical account of creation, which implied a relatively recent creation event (around 6,000 years old).

* Catastrophes as Explanations: Catastrophists believed that major geological features (like mountains, canyons, and fossils) were formed by sudden, catastrophic events like floods, volcanic eruptions, and earthquakes. These events were seen as divinely ordained and responsible for shaping the Earth's surface in a short period.

* Lack of Evidence for Gradualism: At the time, there wasn't sufficient evidence to support the idea of slow, gradual geological processes (like erosion and sedimentation) that could take millions of years.

This view was challenged by the rise of uniformitarianism in the late 18th and 19th centuries, which proposed that geological processes observed today are the same as those that occurred in the past. This shift led to the acceptance of a much older Earth and a more gradual understanding of geological history.