Presuppositionalism is a blanket term for a broad spectrum of beliefs that are self-described by their adherents as axiomatic: in the relevant sense here, that belief in the existence of a god is as properly basic as an adoption of logical laws. These sorts of positions immediately call a few questions to my mind -- questions I would like to answer (if I can, or to wrangle with if I might) here: must we all, in fact, presuppose at least something? Is there a difference between some presuppositions and others in terms of epistemic strength and value?
The answer to the first question (must we all presuppose something?) is, without question, and somewhat counter-intuitively -- yes. There are no epistemic foundations that are free of presupposition; and ironically this very fact undermines a few theistic presuppositional epistemologies which claim access to direct divine knowledge of an absolute sort. So what is it that any epistemology must presuppose such that there is no justification possible in principle which could provide a foundation for the belief?
The belief I'm referring to -- which all epistemes presuppose in lieu of primary justification (recursive justification does not count) -- is the belief that our mental and cognitive faculties are capable of (and geared towards) producing true beliefs while avoiding false ones. After all, how can we possibly justify that belief without presupposing it? It's not possible, and so the presuppositionalist is vindicated on at least one minor point: we are all, to some degree, presuppositionalists.
However, what presuppositionalist arguments for the rationality of theistic beliefs often fail to do is to ask the question of whether some presuppositions have more epistemic merit than others in an objective sense. Is there an epistemic difference between presupposing our cogntive faculties are efficacious -- as opposed to presupposing the existence of a deity? Yes, and I'd like to point to the principle of parsimony here, an epistemic incarnation of Occam's Razor.
All I must do is point out that everyone must presuppose their mental faculties are reliable in order to have an episteme at all in the first place -- we are transcendentally bound to that presupposition: we can't even disagree with it without at the same time calling upon it! It is therefore safe from criticism from even the most worried skeptic.
However, the same can't be said for theistic presuppositions: there is no transcendental force urging its acceptance to us; we are quite free to doubt theistic presuppositions in our epistemic methods without invoking an immediate, explicit contradiction. Thus there is an objective and fundamental difference between the two presuppositions: one is universal, transcendental, and so required of us; the other is subjectively adopted, open to skepticism without contradiction, and in comparison to the other -- extraneous.
There I call attention to a sort of epistemic principle of parsimony: why carry more presuppositions than are absolutely necessary, particularly when there exist alternative epistemologies with fewer presuppositions?
Anyone?
I think this is all true as it is stated.
I would question the use of the word 'carry' as it relates to presuppositions, though. How do you define the word in this context? Does it mean to hold those presuppositions as certainly true, or does it mean to merely entertain them as possibly true? I think the definition of this term has a large impact on the conclusion of this argument.
I agree with Aristotle's statement that the mark of an educated mind is the ability to entertain a thought without accepting it. In this case, the thoughts are presuppositions.
In other words, if some says "If A, therefore B", and another person says, "If X, therefore Y", and we don't accept A or X as valid axioms, then we likely do not accept B or Y. However, we may agree that B follows from A and Y follows from X, if A and X are indeed true in some world.
Strict avoidance of too many presuppositions can result in stagnation of advancements in knowledge. It seems important to make jumps of logic, treating statements as true, in order to follow the paths and see where they lead. That doesn't mean the worlds described by that series of logical steps would be held as true; it merely means that this becomes yet one more possible world that we can imagine and describe. It becomes one more source of inspiration in our armory of how things could be, how things might be, in order to propose possible solutions to current or future problems.
I do agree that certain axioms are more fundamental or valuable. For example, without the law of identity or the law of non-contradiction, it's not really possible to use language in any intelligent manner. Every argument presupposes these laws as true.
An example of yours where mental faculties are assumed to be reliable is an assumption we must accept on some basic level but not necessarily in its entirety, because it's not clearly defined. Reliable to what extent? I could assert that my mental abilities to follow logic are reliable, but I could also assert that there appear to be some truths that cannot be converted into knowledge without direct experience. Logic alone is insufficient in such cases. For example, if a person is born blind and has never seen color, there is no logical argument to describe what Red looks like. We could use logic to explain its existence as a frequency band of electromagnetic radiation that is perceived by the eye, but we cannot use logic to explain how it subjectively appears. There is an as-of-yet insurmountable barrier between logic and it's ability to know that without direct experience.
It seems prudent to weigh arguments that rely on fewer or more fundamental presuppositions more heavily than ones that rely on a greater number of presuppositions or more abstract presuppositions that are not immediately able to be demonstrated as false or shown to render a discussion impossible, without necessarily asserting that those arguments with fewer and more fundamental presuppositions are certainly true. They're just easier to defend, and more humble, because generally a smaller subset of Truth is claimed to be converted into knowledge in comparison to worldviews that require more numerous and complex presuppositions.
In short, it's a useful skill to be able to entertain a multitude of possible worlds, and this requires making use of various presuppositions. The most important thing in this context is not the number or type of presuppositions for any given argument, but instead it's the ability of the person to identify and understand which presuppositions they're relying on in their own arguments or in the arguments of others.