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.
Some further comments gathered from the facebook presuppositional apologetics group: I take exception with the idea that a precondition requires an ONTOLOGICAL presupposition (that God exists) but that it does NOT require it EPISTEMOLOGICAL one. I understand the point that they are making and the distinction between the two. I just don’t think that it works. I just don’t think that the two are as easily separable as is often claimed. It comes off as naive to think so. One’s idea of ontology will necessarily have ramifications for his epistemology, and vice versa.. same with his ethic. The two simply are not separable in practice. This notion of starting with epistemology, and from there moving to a metaphysic, as far as I understand, is a relatively contemporary thought. Older schools thought in terms of entire worldviews where one entailed the other. So, basically I think this bifurcation between epistemology and ontology is unjustified. At the very least the person must provide some argument for why they think such a bifurcation could and should be made.
Classical guys separate ontology and epistemology to the point where they are not even related when in fact they are related although distinct metaphysical discussions.
In addition to the excellent comments and points already mentioned, an elaboration on some of them can be found in Bahnsen's lecture "The Myth of Neutrality" (available on YouTube). His "apple sorting machine" thought experiment is very helpful.
Bahsen on the topic -- Metaphysics is the doctrine of being, what is real, what is true, what is the structure of and what does actually exist in the universe. Those things which have existence: metaphysics. And the doctrine of God is a metaphysical doctrine because we are talking about there being a God, especially a trans-physical being, be it God or laws of logic, whatever it is. Metaphysics.
Epistemology asks, “how do you know what you know, what are the criteria of knowing, what is the belief state and the questions having to do with knowing and the knowing process.”
Now RC is saying that he wants to start with epistemology and move to ontology, or metaphysics. Let’s just start with the law of non-contradiction, the basic reliability of sense perception and the law of causality. And from those epistemological platforms, from that platform, move to the existence of God.
What I want to say is you can’t begin even with that platform if you don’t already have the existence of God and that’s not an ontological statement because we have agreed ontologically that there wouldn’t be any logic or sense experience if God hadn’t created the world unless there is a coherent God. I am making an epistemological point that it doesn’t even make sense to use mathematics or empiricism or natural science of any sort without already knowing that there is a God that is the context in which interpretation and predication is possible. That’s the transcendental argument, saying that the precondition of intelligibility and knowledge is already… the existence of God. And that does not purport to be a probable argument for God’s existence but a certain argument, a necessary argument, an inescapable argument.
James Anderson on the "Presups confuse ontology and epistemology" objection: https://www.proginosko.com/2020/07/does-presuppositionalism-confuse-ontology-and-epistemology/?fbclid=IwAR2jJPs8l-FPKwM5DsmKXKOzoUAkSuTBWST2ZuzCjhmooD49jhoZUjbixVc