The Intractable Problem Revised: is ought gap

In previous discussions I've shown the on naturalism delivers an undercutting defeater for naturalism on evolution is low or inscrutable and that naturalism has a normative force issue. 

I seek to describe these issues further, integrating previous studies to justify my claims and to challenge the naturalistic framework conclusively. 

The Intractable Problem revised:

As noted before, I showed that even given generous assumptions like P (probability a single belief is correct) =0.7 or 70% with 8 auxiliary hypotheses at 100% efficacy only yields P(R|N&E)=22.5% requiring an unreasonable K boost of 333.3% to get above 75%. Meaning, the best case scenario on naturalism and evolution we shouldn't expect our reliable cognition faculties above 23%, which means if any of these auxiliary hypotheses are lower, it will never be above 22.5%. 

In fact I show based on reasonable assumptions; "I will maintain H1&H4 are relatively high, and I generously assume a 0.9 probability to these. 

Additionally, I place 0.2 probability to the remaining 6 hypotheses. 

In way of defence; remember Churchland's "four F's", H1 and H4 are directly involved in these expected evolutionary pressures to select for survivability. H2, H3,H5,H6,H7 and H8 are not clearly processes or mechanisms that can have clear and effective survival mechanisms to select for reliable cognitive faculties" I show P(R|N&E)=0.0000015552%,. Even at 10 auxiliary hypotheses, where H9 and H10 at 0.2 or 20% only yields P(R|N&E)=0.0001821%" (this included a slight boost, to ensure the additional hypotheses add to the overall probability, not hinder.), note: I showed only with 10 auxiliary hypotheses all at 100% efficacy does P(R|N&E) =89.4%, but as noted before, this is unreasonable.

In otherwords, at no point, based on reasonable assumptions, is P(R|N&E) ever above 22.5%. This undermines and underscores the intractable problem, the naturalist can't say I've dismissed the strength of these additional hypotheses, as even at 100% it doesn't get above 22.5%.

The problem:

David Hume famously elucidated the "is-ought gap" showing that any moral truths, like "one ought tell the truth" only describes an 'is', what is the fact, not an 'ought' without presupposing additionally hidden assumptions, like telling the truth is a good. 

In otherwords, moral truth claims devolves into circular reasoning upon further exploration. 

For example:

Descriptive: People generally want to live in harmonious societies.

Prescriptive: Therefore, we ought to act in ways that promote harmony.

Hume pointed out that the transition from the descriptive fact "people want harmony" to the prescriptive conclusion "we ought to promote it" is not self-evident. Something more must be added like a moral principle stating that what people want is morally good.

Why this is uniquely an issue for naturalism?

Even if we agree (on a naturalistic worldview) a set of moral duties, they lack any normative force, that is to say, what binds a person, that they ought to do X, rather than ~X, even if no one is there to see or know? It seems to me, that on naturalism, we can agree a set of principles, yet if another culture, society or individual disagrees, they have only done something we disagree with, not necessarily done anything truly wrong.

However, I think the issue goes deeper at every level, I believe there is an Is-Ought bridge issue all the way down.

At every point, the naturalist can only describe how a thing 'is', not why or why it ought to be that way. For example, the naturalist can describe gravity is 9.8m/s² but it cannot justify why it ought to be the way it is, or why gravity is so uniformly distributed in the universe. For instance there is no brute fact gravity must be 9.8m/s² or that it must be perpetual throughout the universe, it could have been higher or lower in strength, or gravity could be fluctuating in strength. 

This issue filters deeper; for instance, the claim that engineers ought to make strong bridges, makes the following 'is' statements; 

1. That gravity is such a value.

2. That gravity is predictable.

3. It is a good to promote human flourishing.

4. Bridges that fail, break and injur or kill is bad.

As I highlighted, gravity didn't need to be the way it actually is, nor is there any necessity to its predictability. Additionally, the moral dimension is assumed not proven. 

Connecting the dots:

• Churchland’s View: Reasoning reduces to neural processes selected for survival (the “four F’s”: feeding, fleeing, fighting, reproducing), not truth. This suggests beliefs are adaptive but not necessarily true, casting doubt on reasoning’s reliability.

• Nagel’s Critique: Naturalism can’t explain why we ought to trust our reasoning for objective truths, as it’s just a product of contingent evolutionary processes.

• General Problem: Reasoning is an is (a set of neural mechanisms), with no normative ought ensuring its truth-tracking. This aligns with the is-ought gap “all the way down”: naturalism lacks a normative anchor for why reasoning should produce true beliefs.

These points directly support the EAAN’s premise that P(R∣N&E) is low, as they suggest naturalism provides no reason to expect our cognitive faculties to be reliable for truth, especially for abstract or philosophical beliefs like naturalism itself.

Connecting to my Calculations for P(R∣N&E)

My calculations estimate P(R∣N&E), the probability that cognitive faculties are reliable (producing at least 75% true beliefs) given naturalism and unguided evolution. 

Using a binomial distribution, assuming:

( p ): Probability a single belief is true (baseline p=0.5, generous upper bound p=0.7).

( n ): Number of beliefs (100 or 1000).

( k ): Number of true beliefs needed for reliability (e.g., k≥75% for n=1000.

Reliability threshold: At least 75% true beliefs (or 60% in an objection).

The results:

For n=1000, p=0.7, k≥75%: 

P(R∣N&E)≈0.03%.

For p=0.5: 

P(R∣N&E)is even lower 0.0000000136%

The “Is-Ought Gap and Reasoning” points that P(R∣N&E)is low and likely decrease it further by highlighting naturalism’s normative deficit. Let’s explore how.

How the Is-Ought Gap Impacts P(R∣N&E)

The is-ought gap, as applied to reasoning, strengthens the EAAN by providing philosophical and epistemic reasons to doubt that naturalism and evolution select for truth-tracking cognitive faculties. Here’s how it ties into my calculations and affects P(R∣N&E):

No Normative Ought for Truth-Tracking:

• Point from Section: Naturalism describes reasoning as a contingent is—neural processes shaped by evolution for survival, not truth. There’s no ought ensuring these processes align with truth, as Churchland’s “four F’s” emphasize (survival over truth).

• Impact on P(R∣N&E): This supports my baseline p=0.5 (50% chance a belief is true). If evolution optimizes for survival, not truth, a belief’s truth-value is as likely as its falsity, provided it’s adaptive. For example, in my hypothetical species’ false belief (e.g., predators play hide-and-seek) could be as adaptive as a true one (e.g., predators are dangerous). This justifies assigning p=0.5, or at most p=0.7, as I argue, since there’s no normative mechanism in N&E to favor truth.

• Decrease in Probability: The lack of a normative ought makes it less likely that evolution would produce faculties where p>0.5. If reasoning’s purpose is survival, not truth, the probability of reliability (75% true beliefs) is closer to my lower estimates (e.g., 10^−58 for p=0.5) than optimistic ones (e.g., p=0.75, yielding 51.46%).

Churchland’s “Four F’s” and Survival Over Truth:

• Churchland’s claim that cognitive faculties prioritize survival (feeding, fleeing, fighting, reproducing) over truth directly undermines confidence in ( R ). Truth “takes the hindmost” unless it serves survival.

• Impact on P(R∣N&E): This reinforces the zebra example and hypothetical species scenario. Adaptive behaviors (e.g., running from a lion) don’t require true beliefs, only effective ones. My calculation assumes p=0.5 because false beliefs can be as adaptive as true ones (e.g., washing vegetables for “joy” vs. cleanliness). Churchland’s view suggests evolution is indifferent to truth unless it correlates with survival, lowering ( p ) toward 0.5 rather than 0.7 or higher.

• Decrease in Probability: By emphasizing survival over truth, Churchland’s perspective makes the generous p=0.7 less plausible. If truth is secondary, the probability of achieving 75% true beliefs (k≥75%) is closer to my lower-bound estimates (e.g., 0.0000000136% for p=0.5 where k = 60%).

Nagel’s Skepticism About Objective Truth:

• Nagel argues that naturalism can’t explain why we ought to trust our reasoning for objective truths (e.g., about naturalism itself). Reasoning’s evolutionary origins make it suspect for abstract or philosophical beliefs.

• Impact on P(R∣N&E): This directly supports the focus on higher cognitive faculties in the hypothetical species. Beliefs about food or predators might align with survival, but abstract beliefs (e.g., “naturalism is true”) are less likely to be selected for truth. Nagel’s point suggests that ( p ) for such beliefs is low, as they’re not directly tied to the “four F’s.” My calculations for n=1000 beliefs include abstract ones, where p=0.5 is reasonable, as false philosophical beliefs (e.g., “the universe is indifferent”) could be adaptive if they motivate survival behaviors.

• Decrease in Probability: Nagel’s skepticism lowers ( p ) for complex beliefs, reducing P(R∣N&E). Even based on my generous p=0.7 on n=1000, yields only 0.03%, this assumes some truth-tracking, but Nagel suggests abstract reasoning is less reliable, pushing ( p ) closer to 0.5.

The Is-Ought Gap as a General Defeater:

• The is-ought gap “all the way down” means naturalism can’t justify why reasoning ought to be reliable. This epistemic weakness undermines trust in any belief, including naturalism.

• Impact on P(R∣N&E): This aligns with EAAN’s Premises 2–4: if P(R∣N&E) is low, this becomes a defeater for ( R ), which defeats all beliefs, including N&E. My calculations quantify this; the is-ought gap amplifies this by showing naturalism lacks a normative framework to expect reliable cognitive faculties. 

• Decrease in Probability: The is-ought gap reinforces the argument that P(R∣N&E)is low by highlighting naturalism’s inability to provide a reason for p is greater than 0.5.This makes makes the baseline p=0.5 more plausible than p=0.7 P(R|N\&E) further.

The problem deepens 

The issue then becomes, the descriptive we ought to promote human flourishing, only describes an is, but if another culture disagrees, they haven't done anything wrong, they just have a differing descriptive moral framework. 

In other words, the culture rejecting flourishing violates no objective ought; it merely faces reduced survival prospects, underscoring naturalism’s normative scope.

This then builds on my argument, if our cognitive faculties are unreliable, this means any descriptive facts we might have becomes under scrutiny, including moral claims.

The bridge may well be well built if we assume gravity is uniform and it may well be beneficial that the bridge stays up, but it remains the fact that the naturalist cannot adequately justify or bridge the 'is-ought' gap it tries to bridge when naturalist try to explain the world. 

Additionally, as it pertains to reasoning for the naturalist who accepts evolution. Foundational principles of logic, like the laws of non-contradiction, identity or the principles of sufficient reasoning becomes problematic at best.

The first principles of logic carry a normative force: we ought to reason according to the Law of Non-Contradiction to avoid incoherence. However, the argument suggests that naturalism cannot ground this “ought.” If reasoning is just a contingent product of evolution, there’s no objective reason to trust that it aligns with truth or that we ought to follow logical principles. For example:

• A naturalist might describe the Law of Identity as a useful heuristic for survival, but they cannot explain why we ought to accept it as universally true.

• If another individual or culture rejects logical principles (e.g., embracing contradictions), naturalism can only say they are acting inconsistently with survival-enhancing norms, not that they are objectively wrong.

This normative deficit strengthens the EAAN’s defeater: if naturalism cannot justify why we ought to trust our reasoning, it undermines confidence in all beliefs, including the first principles of logic.

Moreover, even if the naturalist wants to insist pragmatic truths are adaptive behaviors, thus are more likely to foster more true than false beliefs. I address this head on in my probabilistic calculations, my H1 hypotheses (Pragmatic Truth) even granting P=70%(more likely true than false) and assuming all 8 hypotheses are 100% efficacious, only yields P(R|N&E)= 22.5%! The naturalist has to prove why P is higher than 75%? Which I maintain is unwarranted. 

Theism’s explanatory power 

Theism on the other hand doesn't face similar issues. God as a maximally great being, having omnipotence (the ability to do anything logically possible), omniscience (knowing all true facts, including moral facts) and omnibenevolence (being perfect) grounds moral and nomological facts.

I've argued elsewhere that once God instanciates nomological laws, like gravity, it has some objective discoverable and comprehensible facts. The laws may each be contingent facts about the universe, but God creating the universe at the big bang, creating the universe to unfold naturally. Allowing chemically light elements, to create stars that would eventually explode to create heavier elements, to eventually allow for complex life, like ourselves to develop in a seemingly privileged spot in the galaxy with unique properties making earth a seemingly rare planet.

In my defence of the teleological argument, I show that even based on generous assumptions of a 1 in 10 probability for each of the 21 revised Drake's equation parameters needed for a habitable planet, it yields a 1 in 10^21, even NASA's exoplanet website suggests based on the original Drake Equation it's only 1 in 10^22 and in the book ‘The Privileged Planet’ Guillermo Gonzalez and Jay W. Richards states "we are able to determine that the probability, even in our fine-tuned universe, of getting just one Earth-like planet, with its Solar System and all its requisite conditions, is less than one chance in 10^180."

This along with the growing body of evidence for the fine-tuning of the universe gives credence to the reasonable assumption, based on the evidence, the inference to the best explanation is the begining of the universe and the fine-tuning of the universe is best described by design. 

Similarly, moral facts and imperatives are best explained by the omniscient mind of God, who knowing all true facts including moral truths, knows what acts and thoughts are conducive to the flourishing of creatures like ourselves and His omnipotence means he is able to instantiate it and has the power to force its normative weight.

Under theism, the first principles of logic are grounded in God’s rational nature. The Law of Identity reflects the consistency of God’s being; the Law of Non-Contradiction aligns with divine truth; and the Law of Excluded Middle corresponds to God’s omniscience, which admits no ambiguity. The normative force of these principles is rooted in God’s command to reason truthfully, giving theists a reason to trust their cognitive faculties and adhere to logic. This avoids the naturalist’s problems of low P(R|N&E) and the is-ought gap.

This leads to probability that cognitive faculties would be reliable under theism and evolution. P(R|T&E) is extremely high, where P=0.80 n=1000 and K=75% this yields a probability of 99.99%.

Possible Objections 

Objection: Naturalists, such as Daniel Dennett or Steven Pinker, argue that evolution likely selects for truth-tracking cognitive faculties because true beliefs are generally more adaptive than false ones. For example, accurately perceiving a predator’s location or correctly reasoning about food sources enhances survival, suggesting ( p ) is higher than p=0.5 or p=0.7:

• Survival requires accurate representations of the environment (e.g., “there’s a lion” vs. “there’s no lion”). False beliefs, like your “predators play hide-and-seek” example, may occasionally be adaptive but are less reliable across diverse contexts.

• Natural selection optimizes cognitive mechanisms (e.g., perception, memory) for truth, as errors are costly. This supports a higher ( p ), perhaps p=0.9, making P(R∣N&E) almost certain.

• Critics might argue my auxiliary hypotheses (H2, H3, H5–H8 at 0.2) underestimate evolutionary pressures on complex cognition, as abstract reasoning (e.g., planning, social coordination) also enhances fitness.

Response:

In my original argument and here, I show that even granting all 8 hypotheses with 100% efficacy, it only increases it to 22.5%, which is low. Arguing that 0.2 for the other 6 hypotheses might be higher is an irrelevant objection as even based on 100% the ceiling is 22.5%. The objection is just arguing how low the probability is, not that my calculation is unfair. 

H1 and H4 are survival enhancing, thus I give these hypotheses a suitably high probability, but as I reason, a false belief, like the zebra that sees an object in the middle distance and runs can be adaptive, even if it’s false, or the hypothetical species that thinks the predator wants to play hide and seek all gets the individual in the right place.

So, I do not see why P is greater than 0.7 on N&E, as this is already suitably high enough to give more true beliefs than false, steelmanning the argument as far as I'm allowed.

Objection: Naturalistic moral realists, like Sam Harris or Peter Railton, argue that moral facts can be grounded in objective natural properties (e.g., well-being, flourishing) without invoking a normative “ought” beyond empirical facts. This challenges the claim that naturalism cannot bridge the is-ought gap or provide normative force for moral duties.

• Harris (The Moral Landscape) argues that moral “oughts” reduce to facts about maximizing well-being, measurable via neuroscience and psychology. For example, “we ought to promote harmony” follows from the descriptive fact that harmony enhances flourishing, with no hidden moral principle needed.

• Railton’s reductive naturalism posits that moral norms emerge from evolutionary and social processes, giving them normative force through reciprocal altruism and social contracts. If a culture rejects flourishing, it faces objective harm (reduced survival), which naturalists argue is sufficient to ground morality.

• This extends to the bridge example: engineers “ought” to build strong bridges because collapse harms well-being, a fact grounded in biology and sociology, not requiring a non-natural “ought.”

Response:

Even granting all of this is correct, those facts are 'is' statements, not objectively binding 'ought's' the society like North Korea or ISIS that doesn't promote wellbeing of its citizens has merely foregone the benefits of a society that promotes such wellbeing. In otherwords, a Western society can merely suggest their disapproval, but it would be more like a social faux pas, like forgetting a guests name or breaking wind at the table, than anything objectively wrong on a naturalistic framework. 

Objection: Naturalists like W.V.O. Quine or Gilbert Harman argue that logical principles (e.g., Law of Non-Contradiction, Identity) are empirical generalisations or heuristics shaped by evolution, not requiring normative grounding. This challenges the claim that naturalism cannot justify the normative force of logical principles.

• Quine’s naturalised epistemology treats logic as part of our “web of belief,” revised based on experience. The Law of Non-Contradiction is useful because it aligns with observed reality, not because it’s universally true.

• If a culture embraces contradictions, they face practical incoherence (e.g., failed predictions), which evolution penalises. This pragmatic utility grounds logic’s “ought” without needing an objective normative force.

• My EAAN critique (low P(R∣N&E)) is countered by arguing that logic’s reliability is tested through survival, not philosophical certainty, raising confidence in reasoning.

Response:

In my defence of the EAAN (Naturalism Intractable Problem), I discuss the 'general rule', which on evaluation, shows that every animal (except humans) do not have reliable cognitive faculties, their beliefs (if they have beliefs analogous to human beliefs) are adaptive to survival, not necessarily truth. If N&E were true, our cognitive faculties shouldn't be much above that of the apes, we are the exception not the rule. 

At best, we can agree they have pragmatic truth, but the culture or individual that didn't adhere to the law of non-contradiction isn't doing anything wrong, they merely act against the social norms.

In conclusion.

I believe I have shown that the person that holds N&E has an intractable problem and an is-ought bridging gap all the way down in all spheres of logic (moral, physical and metaphysical). In conjunction to this, this undercuts any reliability of their cognitive faculties, wielding the EAAN’s probabilistic calculations to support my claims. 

Additionally, I show theism superiority and show that on P(R|N&E) is low but P(R|T&E) is extremely high. Theism, provides reasons why first principles of logic, reason in general and moral normative force is grounded in the maximally great being, best described as God.