On the subject of belief, I’m instinctively drawn to logical systems that demand consistency, closure, and introspection. And the KD45 system among them exerts a special pull. It consists of the following axioms:

• K (closure): If you believe an implication and you believe the antecedent, then you believe the consequent. E.g. if you believe “if X then Y” and you believe X, then you also believe Y.
• D (consistency): If you believe X, you don’t also believe not-X (i.e. X’s negation).
• 4 (positive introspection): If you believe X, then you also believe that you believe X, i.e. you’re aware of your own beliefs.
• 5 (negative introspection): If you don’t believe X, then you believe that you don’t believe X, i.e. you know what you don’t believe.

Thus, KD45 pictures a believer who never embraces contradictions, who always sees the consequences of what they believe, and who is perfectly aware of their own commitments. It’s the portrait of a mind that’s transparent to itself, free from error in structure, and entirely coherent. There’s something admirable in this picture. In moments of near-perfect clarity, it seems to me to describe the kind of believer I’d like to be.

Yet the attraction itself throws up a paradox. KD45 is appealing precisely because it abstracts away from the conditions in which real human beings actually think. In other words, its consistency is pristine because it’s idealised. It eliminates the compromises, distractions, and biases that animate everyday life. To aspire to KD45 is therefore to aspire to something constantly unattainable: a mind that’s rational at every step, free of contradiction, and immune to the fog of human psychology.

My attraction to KD45 is tempered by an equal admiration for Bayesian belief systems. The Bayesian approach allows for degrees of confidence and recognises that belief is often graded rather than binary. To me, this reflects the world as we encounter it — a realm of incomplete evidence, partial understanding, and evolving perspectives.

I admire Bayesianism because it doesn’t demand that we ignore uncertainty. It compels us to face it directly. Where KD45 insists on consistency, Bayesian thinking insists on responsiveness. I update beliefs not because they were previously incoherent but because new evidence has altered the balance of probabilities. This system thus embodies humility, my admission that no matter how strongly I believe today, tomorrow may bring evidence that forces me to change my mind.

The world, however, isn’t simply uncertain: it’s often contradictory. People hold opposing views, traditions preserve inconsistencies, and institutions are riddled with tensions. This is why I’m also drawn to paraconsistent logics, which allow contradictions to exist without collapsing. If I stick to classical logic, I’ll have to accept everything if I also accept a contradiction. One inconsistency causes the entire system to explode. Paraconsistent theories reject that explosion and instead allow me to live with contradictions without being consumed by them.

This isn’t an endorsement of confusion for its own sake but a recognition that practical thought must often proceed even when the data is messy. I can accept, provisionally, both “this practice is harmful” and “this practice is necessary”, and work through the tension without pretending I can neatly resolve the contradiction in advance. To deny myself this capacity is not to be rational — it’s to risk paralysis.

Finally, if Bayesianism teaches humility and paraconsistency teaches tolerance, the AGM theory of belief revision teaches discipline. Its core idea is that beliefs must be revised when confronted by new evidence, and that there are rational ways of choosing what to retract, what to retain, and what to alter. AGM speaks to me because it bridges the gap between the ideal and the real. It allows me to acknowledge that belief systems can be disrupted by facts while also maintaining that I can manage disruptions in a principled way.

That is to say, I don’t aspire to avoid the shock of revision but to absorb it intelligently.

Taken together, my position isn’t a choice of one system over another. It’s an attempt to weave their virtues together while recognising their limits. KD45 represents the ideal that belief should be consistent, closed under reasoning, and introspectively clear. Bayesianism represents the reality that belief is probabilistic and always open to revision. Paraconsistent logic represents the need to live with contradictions without succumbing to incoherence. AGM represents the discipline of revising beliefs rationally when evidence compels change.

A final point about aspiration itself. To aspire to KD45 isn’t to believe I will ever achieve it. In fact, I acknowledge I’m unlikely to desire complete consistency at every turn. There are cases where contradictions are useful, where I’ll need to tolerate ambiguity, and where the cost of absolute closure is too high. If I deny this, I’ll only end up misrepresenting myself.

However, I’m not going to be complacent either. I believe it’s important to aspire even if what I’m trying to achieve is going to be perpetually out of reach. By holding KD45 as a guiding ideal, I hope to give shape to my desire for rationality even as I expect to deviate from it. The value lies in the direction, not the destination.

Therefore, I state plainly (he said pompously):

• I admire the clarity of KD45 and treat it as the horizon of rational belief
• I embrace the flexibility of Bayesianism as the method of navigating uncertainty
• I acknowledge the need for paraconsistency as the condition of living in a world of contradictions
• I uphold the discipline of AGM belief revision as the art of managing disruption
• I aspire to coherence but accept that my path will involve noise, contradiction, and compromise

In the end, the point isn’t to model myself after one system but to recognise the world demands several. KD45 will always represent the perfection of rational belief but I doubt I’ll ever get there in practice — not because I think I can’t but because I know I will choose not to in many matters. To be rational is not to be pure. It is to balance ideals with realities, to aspire without illusion, and to reason without denying the contradictions of life.