The following is from Dr Jason Lisle's response to Howe's objection in a written debate they had in 2013.
Ontology is the study of the nature of something, It addresses what kinds of things exist.
Epistemology is the study of knowledge - how we know what we know.
Howe is concerned about "'whether Presuppositionalism is making an epistemological point or an ontological point". Perhaps his confusion can be alleviated by recognising that presuppositionalism deals with both epistemology and ontology.
These two things, while different, are inextricably linked.
The kinds of things that exist will come to bear on how we know what we know. And our theory of knowledge will have a profound influence on what we believe to exist. For example, if our epistemology endorses the use of laws of logic in reasoning, then it would be ridiculous for our position on ontology to reject the existence of laws of logic.
Ontology cannot be divorced from epistemology. The transcendental argument points out that if knowledge is possible (an epistemological premise), then God must exist (an ontological claim) since the biblical God is the basis for knowledge (a Scriptural claim). Howe states, "Greg Bahnsen was adamant that Presuppositionalism is making an epistemological and not merely an ontological point".
Bahnsen is quite correct. The presuppositional method deals with both issues. Howe continues, "Obviously, if God is the Creator, then, if the Creator did not exist the creation would not exist. Making this ontological point is saying nothing that distinguishes Presuppositionalism from Classical Apologetics .."
This reveals a profound misunderstanding of the transcendental argument. The secularist denies that God is the Creator, and hence he denies that God is necessary for the universe to exist. In responding to this position, the presuppositionalist asks how the unbeliever's epistemology (e.g., that laws of logic are a useful standard for truth) can possibly comport with the unbeliever's ontology (that the universe is a godless accident).
No unbeliever is able to account for the existence and properties of laws of logic, nor morality, nor uniformity in nature on his own professed worldview. His epistemology is rationally unjustified and in tension with his position of ontology. This is necessarily the case since all knowledge is deposited in Christ (Col. 2:3). And so when Howe says, "Bahnsen's position collapses back into ontology or metaphysics. which ends up making his method Classical", this cannot be defended.
Presuppositionalists deal with ontology too. But the presuppositionalist does not depart from biblical authority as his ultimate standard. Howe says that "to argue that God's existence is necessary for something (in this case, argument) is to make a cosmological argument".
No. this is not a cosmological argument at all, but rather the transcendental argument. The cosmological argument deals with cause and effect; usually it is presented that the universe has a beginning and therefore requires a cause, and only God is a sufficient cause. But the transcendental argument has nothing to do with cause and effect. Rather, it deals with rational justification. It argues that the existence of God is the necessary precondition for knowledge.
Howe states, "If I construct a simple Modus Ponens argument. it can be entirely sound without any of the premises being 'God exists.' To be sure, the Modus Ponens could not exist without God, but, again, this ontological point is not Presuppositionalism" .
It's not that Modus Ponens could not exist apart from God (though indeed it could not), but rather, Modus Ponens cannot be rationally justified as a universal, invariant, exception-less rule of inference apart from God. We could not know that Modus Ponens is legitimate (an epistemological issue), or universal and invariant unless God exists (an ontological issue).
I hope this resolves any confusion on the matter.