I had to look up Sproul on Presuppositional apologetics. I have learned long ago that Sproul was a Thomist, whose approach is classicism.
It is good that there is a direct source:
From what I could fathom, Sproul's argument against Presuppositionalism is merely based on defending his classical apologetics. He threw in petitio principii (circular logic flaw), equivocation fallacy (misuse of definition) and a "tie" (like kissing your sister which is uninteresting/unnecessary).
What Sproul failed to realize is that the presuppositional apologetics essentially calls the prove of the existence of God irrelevant, unnecessary and is beneath God. In this sense, God's existence cannot be proven. This is not to say that God can be disproved.
It must be clear that presuppositional apologetics does not nullify other forms of apologetics. It merely stands on to of them in importance and forms a foundation for the rest of them in methodology. Presuppositional apologetics is not to tell someone he/she is lying about his/her disbelief in God, but to help the evangelist to understand and build efficient means of doing apologetics in any particular circumstances.
Therefore, Sproul has already disqualified classical apologetics from presuppositionalism point of view when he was fixated on proving the existence of God, which is secondary in apologetics. This is not to say that Sproul is unaware of Romans 1:18-20, which is the strong pillar of presuppositional apologetics. However, by not considering the importance of presuppositional apologetics, Sproul made evangelism less enthusiastic, less personal for the energy for it have shifted to the scholastic dissection of apologetics. Though it is unfortunate that after Van Til, Westminster is facing tough financial dilemma; The Ligonier method of fundraising is very disturbing, in fact the very nature of fundraising is disturbing for any church. There is no differentiation between that and offering anymore, which is a problem. The only reason Ligonier or RTS could survive Westminster is because they do more outreach. Not evangelism, but books and talks. Westminster somehow could do only very little of it. The brain has become too heavy for the legs to move the preacher.
Ultimately, even a great weapon could still be rendered ineffective because the last of its imperfection is its user.
Lesson 2: Why Apologetics
Apologetics is both positive and negative (offensive and defensive). I don't see it matters as to if offensive is positive or negative, either ways seem to work.
Calvin: There's distinction of proof vs. persuasion. The task of the apologists is to prove, not persuade because people denies the truth unless the Holy Spirit works on them. Sproul's illustration: Dead people don't bleed...so when Charle's thumb got poked by the psychologist and bled, his consistent believe that he's dead made him reply: Oh, so dead people bleed too!
Apologetics though do not persuade, but it is useful in many ways, ie. assures young Christians who are challenged by all kinds.
Lesson 3 - Pre-Evangelism
Assensus (assent = agreement): firmitas (by authority), certitude (by testimony, evidential (by evidence). By saying Apologetics seeks the third type of assent - evidential, I think this is why they call Sproul a Thomist.
Saving Faith: Notitia/Notae (content of faith), Assensus (acceptance of facts), Fiducia
Only fiducia (faith involving affection for Christ) is engendered by the Holy Spirit.
Lesson 4 - Lesson 4: Four Steps Backward
Sproul's 4 non-negotiable assumptions (Sproul's presupposition):
1. The Law of Non-Contradiction
2. The Law of Causality
3. Basic reliability of the senses
4. Analogy
Sproul: Never negotiate these!
Lesson 5: Law of Contradiction
Modern Americans closed to objective truth. But no one could escape from it and they all live in deliberate denial (by force and temporarily).
Aristotelian logic = Organon of science.
Karl Barth & Emil Brunner advanced relativism. Barth in his "Der Römerbrief" (Commentary on Romans), mentioned "Unless a Christian affirm both poles of contradiction, he is yet mature." Brunner in "Wahrheit als Begegnung" (True as encountered): Contradiction is the hallmark of truth!
Lesson 6: Law of Causality
Proper definition: Every effect must have an antecedent cause.
Bertrand Russell embraced this law and claimed he believed in God initially but after reading John Stuart Mill, who asked Who made God, Russell's worldview changed.
His problem was that he got the definition wrong "Everything" must have a cause.
This is an formally/analytically true law/statement. Analytically = formally = true by definition, not additional information.
Lesson 7: Reliability of Sense Perception
Hume's Customary relationship/Contiguity (assumption of causality)
Sproul: It's one thing to say I don't know what's the cause, it's another to say there is no cause.
Hume went too far in skepticism: All sciences reduced to skepticism. Kant awaken by Hume from his dogmatic slumber and "rescue" science.
Dr. Gerstner: What is mind? No matter. What is matter then? Never "Mind".