In addition, there are two approaches to apologetics. The first is evidential which represents the concept that Jesus died for the whole world. This is what I believe. The other approach is presuppositionalism which exemplifies the concept that Jesus died only for the elect.(source)
Apparently describing the same class, faith_to_move writes:
We also discussed the various approaches to apologetics. I do not agree with the presuppositional view. This approach is often known as the Limited Atonement approach. Believes that Christ only died for the elect, and that only the elect can understand the evidence. They must first agree on certain presuppositions before the Gospel can be effectively presented.(source)
I would definitely agree more closely with the evidential view: which would be commonly defined as a General Atonement approach. Basically, the evidential view says that Christ died for the world (John 3:16, right) and that each living soul has a God-shaped hole that can only be filled by God. Therefore, each person is created in the image of God (imago Dei) and can be shown using evidence that a personal God loves them.
These are not accurate representations of the presuppositional and evidential approaches. The evidential approach attempts to argue that the "majority of the evidence favors my view," (William Lane Craig and many atheists argue this way) whereas the presuppositional approach attempts to show the superiority of the presuppositions associated with Christianity as contrasted with those of opposing views (Greg Bahnsen famously argued this way).
Neither approach has anything directly to do with the atonement or the scope of the atonement. While presuppositional apologetics is dominated by Reformed apologists, there are also Reformed apologists who apply an evidentialist approach, or other approaches, such as the so-called "classical" approach.
The only way to tie presuppositional apologetics to the atonement is to note that the doctrine of the Limited Atonement is the only doctrine that does not lead to self-contradiction. However, I trust that Dr. Caner is not willing to concede that point.
In fact, I did not initially believe that Dr. Caner had really made claims like the ones indicated in the quotations above, because I have seen the entry in The Popular Encyclopedia of Apologetics, a book that Dr. Caner co-edited. That entry (see here and scroll forward to the sub-section on evidential apologetics) would not lead one to the views expressed above, whether or not that entry is itself totally accurate, and that entry is attributed to Ergun Caner himself.
So, I don't know what to say. I understand that the book I've linked to above is also a textbook for the course. If so, may I encourage folks taking the course to read the textbook rather than relying on the lecture?