What is the relation between Belief and one's Axioms?

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Suppose Person A believes in [Fact 1]. Is this equivalent to Person A 'operating' with the axiom: "Fact 1 is true" (and any axioms necessitated by Fact 1).

Similarly if Person A states their belief in [Fact 1], Would this be shorthand for Person A stating that they operate on all axioms necessitated by Fact 1 and the axiom "Fact 1 exists"? Is then the purpose of the word 'belief' to be a convenient shorthand for communicating either to oneself or to others what axioms one operates with? (Note: When I say 'operate' what I'm referring to is any mental process of Person A (Reasoning, Algorithmic processes et cetera).

Is recognising/stating belief purposed to reflect objective reality? If not is it meant to reflect the intentions of the 'believer'? What if neither, is the function of recognising/stating belief?

TomDot Com

Posted 2020-09-24T17:15:16.517

Reputation: 157

People don't often differentiate between beliefs in this way, sometimes they believe in general principles (axioms), or in conclusions they have come to, or even perceived particulars ("I believe the sky is blue today"). – Kristian Berry – 2020-09-24T18:45:37.230

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No, not really. Facts do not function as axioms, not in common practice and not in science. Facts are concrete and specific, "axioms", to be of use, have to be general, so they are not "necessitated" by facts nor derivable from them. They are generated by other means (creative, subject to values like simplicity, coherence, unification, etc.) and then kept or discarded according to their compatibility with facts. In science this is loosely called "hypothetico-deductive method".

– Conifold – 2020-09-24T19:55:33.697

@Conifold Sorry for bungling terminology, so then if I instead rephrased all instances of 'axioms' with 'knowledge', would this then imply that Person A in the act of communicating belief to themself or others, agrees to an informal mental contract between all parties aware, that they will act in all future scenario's with the implicit assumption that 'Fact 1' is the case and that Person B + Person C + ... can reliably interpret that to mean that they intend to do this? – TomDot Com – 2020-09-25T01:43:30.283

I do not think people have any such contracts in mind, but communicating a belief can be reasonably interpreted as intention to act on it (when it is actionable, can be trusted as truthful, and is not light-hearted). However, beliefs do not comprise facts, they are abductive surmises that depend on facts, habits, stereotypes, biases, values, etc., in very complicated and roundabout ways.

– Conifold – 2020-09-25T04:40:59.650

@Conifold So from the POV of Person B, implicit within the action of Person A recognising/stating a belief is that Person A has conducted abductive reasoning and the end result of this reasoning was the objective claim of 'Fact 1'.So after recognizing this would Person A 's stating belief in 'Fact 1' be purposed to indicate this? – TomDot Com – 2020-09-25T05:43:30.690

@Conifold As a slightly unrelated question, what is the difference between stating belief in 'Fact 1'; and stating intention to act, knowing 'Fact 1' is true? – TomDot Com – 2020-09-25T05:50:06.480

The output of abduction typically is not a fact, even in loose colloquial sense it needs to be well-confirmed to become one. And it needs to be broadly accepted to get to objective. Stating belief need not apply to any specific action, only vague intention to take it into account when acting. Stating intention to act is something much more concrete. – Conifold – 2020-09-25T06:24:21.377

No answers