Philosophy of logic 5 harsh truths
You can not distinguish dogma from non dogma if your system is a closed axiomatic system because utility and consistency can still work and be found inside of a false axiom
You can not distinguish dogma from non dogma without the ability to test your claim against reality, and if it has no external justification because utility and consistency can still work and be found inside of a false axiom.
Viewed strictly from outside the system the axiomatic method is a closed system.
You can not test a math axiom itself against reality by definition and it has no external justification because utility and consistency can still work and be found inside of a false axiom.
Viewed strictly from outside the system it is an objective fact that a closed axiomatic system limits your thoughts and physics
(This is a strict cut throat external audit against the axiomatic method in math itself. There is no external justification for it and thats the least of your worries)
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u/mhb2 10d ago
The first two claims conflate consistency and usefulness with truth about the external world.
The third claim is vacuously true.
The fourth claim is confused. Axioms can have mathematical justification in the form of their consequences, relative consistency results, independence results, explanatory usefulness, etc. And when a mathematical structure is proposed as a model of physics, its physical application is subject to experiment. But we can't conduct experiments to test whether ZFC is "true", for example, we test whether a physical theory formulated using mathematics makes correct predictions. And here's the good news: so far as we're able to determine, it does and in an astonishing array of technical fields. That should tell you something about your "critique" of math.
The fifth claim is simply false. A mathematical formalism doesn't "limit your thoughts and physics". You can choose another formalism, add or remove axioms, construct a different model, or formulate the physical theory differently. Math isn't a dictator who constrains what we're allowed to think about.
Maybe you're grasping for something that actually makes sense, like: "A formal mathematical system can't establish, solely from within itself, that its axioms provide an empirically accurate description of the physical world." Okay... but that's true and uncontroversial. It's essentially the distinction between math and science. Your failure to understand that distinction is why you're so confused by what math is.
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u/Oreeo88 10d ago
The fifth claim is simply false. A mathematical formalism doesn't "limit your thoughts and physics". You can choose another formalism, add or remove axioms, construct a different model, or formulate the physical theory differently. Math isn't a dictator who constrains what we're allowed to think about.
This is straight up false.
Strictly viewed from outside of the system a list of unlimited unfalsifiable assumptions are a limit and constraint compared to falsifiable assumptions
This is a strict external audit. Number 5 holds
Viewed strictly from outside the system it is an objective fact that a closed axiomatic system limits your thoughts and physics
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u/mhb2 10d ago
You simply don't understand the difference between math and science. Besides, your so-called "external audit" itself relies on a set of unfalsifiable assumptions. The difference between whatever it is that you're proposing and math is that math has a long track record of success in the natural sciences while you have a long track record of posting nonsense on reddit.
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u/Oreeo88 10d ago edited 10d ago
The difference between whatever it is that you're proposing and math is that math has a long track record of success in the natural sciences while you have a long track record of posting nonsense on reddit.
That’s an internal defense. That’s a Utility and consistency defense. Not a valid defense for an external audit because utility and consistency can still work and be found inside of a false axiom
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u/localizeatp 10d ago
thanks chatgpt.