John asked:

Does Descartes believe that there is not an external world?

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On the contrary: the biggest book he wrote was largely about the external world, about cosmology,
physics and science altogether. You seem to be confusing something elementary here. He said, he
can conceive of his mind independently of having a body; but he never extends this to say, that in this
world,it was possible to have a mind without a body or that the world is an illusion as such. What it
boils down to is an incompatibility between mind stuff and matter stuff. But that's not tantamount to a
denial of the latter.

Jürgen Lawrenz

Sydney

No. In Meditation 6 Descartes argues that there is an external world, although it isn't at all the way it
appears to us.

In Meditation 1 he presents the traditional skeptical arguments for thinking we do not know for certain
whether there is an external world. He never argues that there is no external world, and, in fact, writes
in his Preface that he believes there is an external world.

Ken Stern