Elaborating on Induction and the Inappropriateness of Presuppositions

{The following is a post I made on a thread on the Facebook group Unbelievable.}

As I mentioned earlier, induction is assessing what works. I’m not merely claiming induction includes assessing what works, it IS assessing what works. And rationality is positioning one’s degree of belief to a degree that maps to the degree that something has been assessed to work.
So you have the following apparent paradox: what would it mean for the assessment of what works to fail an assessment that it works? :) This is nonsensical.
Let’s apply some rigor and tease out some of these concepts.
What do we mean by “what works”. This is essentially noting regularities in our experience. These regularities allow us assess to what degree we are warranted in believing event X will occur in the future given its regularity in the past.
And there is what we might call a meta-regularity: the observation of regularity in the success of assessing regularities. Herein lies the apparent paradox: Is it possible for our assessment of regularities become irregular? As fallible minds we can not dismiss this possibility even though we can not fathom what this could ever mean. If this assessment of regularities ever becomes irregular, would there be something else that provide us with the power of predictability? In this remote scenario, I would simple back away from my confidence in this inductive process, and explore whether there was something else that would make my reality more predictable. We are warranted in following whatever works to make our realities predictable. We place non-absolute confidence in what appears to work to the degree that it appears to work, and for as long as it appears to work. No presumptions are required.
(This is parenthetical to some degree, but if I were to discover that I was a brain in a vat, I would not protest, but simply think “Well, this is interesting.”  It appears others who have decided they are somehow warranted in absolute certainty in logic, mathematics or other axiomatic notions would feel the need to protest the violation of the impossibility of this new revealed reality…or so it seems from some of the comments claiming some absolute presumptions are warranted.)
Now let’s deal with the notion of rationality. I want to start with the concept and then find an appropriate linguistic tag rather than start with a linguistic tag and subsequently try to force a concept into that tag. The concept is following what works, and includes the connotation of value or praise being placed on following what works. This is made most salient with its converse. We all consider following what we perceive to not work to be irrational. (This is a critical point, so if you disagree, make that clear.) This is a gradient concept, so we can add nuance by restating this as, “to the degree that someone knowingly follows what they perceive to not work, to that degree they are irrational”. The converse of this produces what I, for a couple decades, have been calling “rationality”. The inverse correlative would be “to the degree that someone knowingly follows what they perceive to work, to that degree they are rational”.
Now, this is important. For this concept, I’ve assigned the linguistic tag “rationality”. Words belong to convention and are not bound by my stipulations, but it appears that most conventional uses of the word “rationality” at least intersect with this concept. If you are in disagreement and have a better linguistic term that will better convey the concept, please let me know. If you feel that the term “rationality” does not adequately convey this concept, provide a term that will more effectively convey the concept. It is the concept I want to convey rather than promote a linguistic tag since concepts are logically prior to the terms employed to convey those concepts.
It is essential to this project that we use terms for which we share identical referents. I’m going to assume you are, at this point, with me on this definition of “rationality”.
Now, note that throughout this discussion I have not treated belief as binary. Nor should I. Because rational belief (in propositions other than immediate perception) is a degree of belief commensurate to the perceive balance of evidence, and because evidence is inductively assessed, all rational beliefs are sub-absolute and subject to revision. There is no need to carry presuppositions, nor is there warrant for this. If by “presupposition” you actually mean a sub-absolute degree of belief wholly based on the degree of the perceived evidence, make that clear now. I would suggest that the etymology of the term “presupposition” implies it is the action of irrationally accepting without any degree of doubt something prior to its assessment, and suggest that it would be confusing to suggest a presupposition is a rigorous mapping of the degree of belief to the degree of the evidence.
(When I say evidence, I don’t only mean only empirical evidence, but also the evidence provided by logical assessments of the proposition in question.)
With this foundation, I think I’m now ready to introduce an argument why you are not rational in holding any presupposition.
P1: For any presupposition X, there was a time in your existence when you did not believe X.
P2: If there was a time where you did not believe X, there was necessarily a point at which you mentally acquired a belief in X.
P3: Human mental acquisition is fallible.
P4: Anything mentally acquired by a human may be wrong.
C1: Your human presupposition X may be wrong.
P5: All presuppositions are believed with absolute certainty.
P6: Presupposition X is held with absolute certainty.
C2: Presupposition X may be wrong, yet is believed with absolute certainty.
P7: Whenever the degree of belief in a presupposition does not map to the degree of perceived evidence for a presupposition, that presupposition is held irrationally.
C3: Presupposition X is held irrationally.
Here’s a more pictorial description of this logical relation. Deduction is subsumed within induction. Deduction necessarily lies within the logical space induction, and can never, for fallible human minds, violate that constraint. All the axiomatic foundations of our deductive games and tools have been acquired at some point in our lives through inductive processes.
Now for the reiteration of my conclusion. I hold no presuppositions. I know my degree of certainty for everything I believe, and there is nothing that I hold with absolute certainty. (I think we agree that it would be absurd for person A to inform person B that they are mistaken about the degree to which they believe something.) Not only do I hold no presuppositions, I have argued that, holding presuppositions is intrinsically irrational.
Let me introduce one more salient example that may clarify some things.
Imagine you are being chased by a bear, and you come to an old suspended walk-bridge across a valley that would allow you to escape…if the walk-bridge does not snap. You assess the frayed ropes of the walk-bridge, and conclude that there is perhaps a 50% chance that you’ll make it across the walk-bridge. You assess there is a 1% chance you’ll survive if you turn to fight the bear. So you decide to cross the bridge. This choice is binary. Either you attempt to cross the walk-bridge or you don’t. You have chosen to attempt to cross the walk-bridge.
Now, does this decision to attempt to cross the walk-bridge require you to change your assessment that the walk-bridge has a 50% chance of snapping? Of course not. If you did, you would be irrational. Yet, I have actually heard it suggested, often in the context of a religious proposition, that it is both rational an necessary to abandon your honest assessment, and to believe the walk-bridge will not snap (or whatever the proposition is) with absolute certainty. This is wrong. Rationality is mapping our degree of belief in X to the degree of the perceived evidence for X. And decisions don’t affect nor should affect that honest assessment of your proper degree of belief.
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{The following is an earlier post, and might add some clarity.}
 The crux of your misunderstanding is found in your notion that induction may not be reliable.
What would it mean for induction to suddenly become unreliable?
Induction is simply identifying regularities.  It doesn’t just involve that, but is equivalent to that. What could it ever mean to identify irregularities in a project of identifying regularities? What could it ever mean, in other words, to find induction irregular?
If there was something that worked better than induction to make sense of the world around me I would abandon induction for whatever is more reliable. (I hope you get the joke here.) (Also note that induction is not cause-and-effect. Readers of Hume may be confused in this respect.)
Rationality is following what appears regular to the degree that it appears regular and for the duration it appears regular. There is no commitment to the persistence of the regularity.
My confidence in any notion about the world around me is grounded in its regularity as I perceive it. When that falters, my confidence falters. When it rises, my confidence rises. I need not absolutely believe any axiom. Axioms are useful only within a system that you, if you are to be rational and epistemically humble as a fallible mind, have not accepted with absolute certainty.
So, no. I’m not required to presuppose anything. Nor do I. This is what epistemic humility requires.
(Note that the type of presuming/presupposing I’m rejecting is one of absolute certainty and does not include ‘assuming for the sake of argument’ or ‘for the sake of testing’ scenarios.)
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Comments are much appreciated.
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