Morning Comrade. Axioms in Euclids Geometry. Gödel's two theorems - Uncertainty and I think the other one was certainty, or what you could call in the understanding of certainty that a system can't prove it's consistency from within its own rules. IE you can't be your own judge and jury.
Subjective, when we use the word objective should we attach the meanings in the words useful. Axioms are well considered subjective gueses they are the basis of mathematics . If you follow the agreed upon rules the answer will be right but not necesssarily true. Does mathematics have a context in the way that language does, do we think of it as an objective understanding within the rules of mathematics game. Does this mean that Objective is a subset of Subjective and meanings in objective should include usefulness rather than truth?
Yes. What we call "Objective" is best understood as intersubjective consistency within a chosen language game.
Mathematics does not deliver metaphysical "Truth" with a capital T; it delivers internal correctness relative to its starting axioms. The value of those axioms isn't their absolute truth, but their usefulness—their ability to help us build bridges, predict orbits, or write algorithms.
Objectivity is a specialized tool invented by subjective beings to produce reliable, testable outcomes. It is a subset of the subjective, bounded entirely by human purpose.
As Kant pointed out, we never experience the "thing-in-itself" (das Ding an sich). We only ever experience reality filtered through our perceptive apparatus and symbolic systems. Our tools are not mirrors reflecting the universe—they are navigational instruments helping us steer through it.
Ivan Ivanovich wants to know whether there is pudding other than pears tonight?
The answer is no.
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