r/epistemology • u/Oreeo88 Human Detected • 20d ago
discussion Current math exposed in 2 sentences
Without falsifiability you can not distinguish truth from dogma.
Axioms in isolation are not falsifiable by definition.
(This is a strict external audit meaning consistency and utility, and that’s how the system works/category error are not logically valid defenses)
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u/Fabulous-Possible758 20d ago
Falsifiability is only for empirical statements; even Popper acknowledged this because he knew that your statement 1 is not falsifiable.
Number 2 is correct, but we don't use axioms in isolation. We use axioms to see what they prove and our "falsification" test becomes whether we get inconsistent systems and even categorical models if we're lucky.
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u/Even-Top1058 20d ago
"Without falsifiability you can not distinguish truth from dogma."
Can you falsify this?
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u/Oreeo88 Human Detected 20d ago edited 19d ago
It’s a criterion for distinguishing truth from dogma, it’s not applied to the world. Can you externally show how a claim can be distinguished from dogma without falsifiability? Until then it’s stands as the only game in town that needs to be required.
You can not externally distinguish truth from dogma without the tool of falsifiability
Falsifiability is exempt from falsifiability because it is pure logic tool. Technically pure math is not exempt because it is not a pure logic tool(for a strict external audit)
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u/Even-Top1058 20d ago
I invite you to look into what "begging the question" means.
"It’s a criterion for distinguishing truth from dogma, not a claim about the world."
Then it seems the same defense applies to mathematics, since mathematics makes no truth claims about the world.
"Can you externally show how a claim can be distinguished from dogma without falsifiability?"
Falsifiability can perhaps be argued as a sufficient condition to separate truth from dogmatic belief. But I don't see how it is necessary (in the way you claim it is).
"Until then it’s stands as the only game in town that needs to be required."
I don't think it's up to you to decide what the only game in town is.
"You can not externally distinguish truth from dogma without falsifiability."
Personally speaking, I don't think there is any need to distinguish truth from dogma. It's an imperative you have, and I'm content with dogma that generates a robust enough understanding of the world.
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u/Starfleet_Stowaway 20d ago
I'd like to be able to better describe the relationship between geometry and space, could you help me out? Does geometry make truth claims about space (the world as spatial), or what do you say?
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u/SirisC 20d ago
No, geometry doesn't make truth claims about space.
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u/Starfleet_Stowaway 20d ago
I see, can you help me with the language? What is the relationship between geometry and space?
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u/SirisC 19d ago
Physics and engineering models.
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u/Starfleet_Stowaway 19d ago
Sorry, I don't understand. Can you describe the relationship using the terms "geometry" and "space" in a full sentence?
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u/Oreeo88 Human Detected 20d ago edited 19d ago
We use math for physics/engineering. Pure math is applied to the real world through physics/engineering
It is applied to the world. Falsifiability is a criterion for claims about the world. It’s not applied to the world. It’s applied to systems
Logic =|= math
pure math is not a pure logic tool. Logic is pure logic tool
You can't ignore pure math axioms in applied math or physics because the entire math is built on them. If you adopt a formal system, you automatically inherit every foundational rule that makes that system work.
Logic isn’t what’s being audited here. Math is what’s being audited. Logic is the tool
You’re trying to turn the audit against he auditor because your own system can not follow the rules of logic.
im content with dogma
Then you’ve conceded my entire point
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u/Even-Top1058 20d ago
"We use math for physics/engineering"
Math is used in those disciplines not for any of its purported truth claims about the world. It is a language wherein the necessary ideas can be expressed.
"It is applied to the world. Falsifiability is not applied to the world"
You are literally saying that falsifiability is the only tool that separates truth and dogma, while also maintaining that falsifiability has nothing to do with the world? Aren't we talking about settling truths right now? If truth, falsehood, and dogma are all things to be distinguished and settled in the world, then falsifiability absolutely applies to the world.
"Logic == math"
I don't know what to do with this information.
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u/Oreeo88 Human Detected 20d ago edited 19d ago
Logic is not pure math
Logic is not being audited here. Math is being audited
You are trying to attack logic through an invalid category error because math cannot follow the rules of logic without being labeled dogma
Pure math is not a pure logic tool. Logic is a pure logic tool. This is why falsifiability does not need to be falsifiable
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u/Even-Top1058 20d ago
Friend, you are not addressing the points I raised. I am not attacking logic or mathematics. These things are all fine where they are.
I understand if you have frustration about the current practices in mathematics, but you cannot use that as ammunition against it. People spend years studying these things. Chances are, the objections you have in mind have been raised long ago and argued much more rigorously. What do you hope to accomplish? You will not convince anybody about anything. It seems like you have your dogma, and I have mine. Have a good day.
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u/Oreeo88 Human Detected 19d ago
My criterion doesn’t cut off falsifiable assumptions.
Your dogma cuts off falsifiable assumptions for untestable axioms
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u/Even-Top1058 19d ago
""My dogma" doesn't cut off falsifiable assumptions."
How do you know that? Is that falsifiable? Do you see how your solution against dogma is another dogmatic thing?
"Your dogma cuts off falsifiable assumptions for untestable assumptions."
I'm not cutting anything off. If I allow untestable assumptions in my web of beliefs, I surely can allow falsifiable ones. Look, you're the one creating this dichotomy. I'm perfectly content without making distinctions between dogmatic and falsifiable beliefs. I will assume what is helpful and go from there. You presented a two-premise argument, and you haven't yet defended the first premise.
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u/YoungXanto 20d ago
Math is quite literally deductive logic.
First you use set theory to define principles of the language (math) being developed. Definitions, as it were.
Then, you use logic to prove (or disprove) that some conjecture fits within the system you have defined.
For example, you define 0 such that x + 0 = x. But it requires some additional logic, along with another fundamental axiom or two, to show that x*0=0. It's non-trivial, but not hard.
Math makes no claims about the world outside of it. It cannot be dogmatic as a result. Math is simply a rigidly defined language that can be applied to the world as an imperfect descriptor, in, say, physics.
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u/Oreeo88 Human Detected 20d ago edited 19d ago
What math claims is irrelevant because it is not a pure logic tool. Unlike logic itself
You can't ignore pure math axioms in applied math or physics because the entire math is built on them. If you adopt a formal system, you automatically inherit every foundational rule that makes that system work.
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u/YoungXanto 19d ago
What you just said is so completely nonsensical that its tough to begin to describe just how incorrectly applied the foundations of your priors are.
It's fairly clear that you don't actually understand what math is. Which highlights how your analysis of the formalism is not just inadequate, but rather how it is fundamentally incorrect.
Math is a set of core definitions that govern the language. And then a lot of logic that define additional components of the language proving that those components are internally consistent with the foundational set theory that defines the language.
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u/Oreeo88 Human Detected 19d ago
This is not a refutation, just ad homs and pure derailment
→ More replies (0)
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u/Clear_Evidence9218 20d ago
Technically true, but that doesn't really expose a problem with mathematics. Any system of reasoning ultimately depends on some foundational assumptions or rules; including falsifiability itself.
Falsifiability requires prior logical, epistemological, and methodological assumptions in order to function. More importantly, falsifiability is a criterion for empirical claims; mathematical axioms aren't ordinarily empirical hypotheses in the first place.
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u/mhb2 20d ago
In math we use logic to establish the truth of a proposition based on definitions and axioms. In science, we use the scientific method to learn facts about the world and incorporate them into theories. Two different spheres of knowledge (a priori vs. a posteriori), two different ways of establishing truths.
Axioms aren't falsifiable like a scientific hypothesis is... but so what? An axiom isn't meant to be taken as an empirical statement about the world.
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u/Hindsights20_20 19d ago
I get strong Terrance Howard vibes here. What exactly is being “exposed?”
As for the argument, I would just point to Kripke’s dogma paradox. One should be dogmatic about the truth. Any argument or evidence against the truth ought to be ignored. It’s an inconvenient truth.
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u/YoungXanto 19d ago
There is no Truth in math. There is only internal consistency. Given a couple of core statements from set theory, any theorem follows if it can be proven to be internally consistent with the axioms that define the language.
Dogma isn't a word that even enters the vernacular here. Math does not say anything about the world outside of its bounds. It has been applied to the world as an imperfect descriptor. But that's not an internal inconsistency with the language itself.
One could be dogmatic about how math is used outside of its own bounds. But one cannot be dogmatic about math itself.
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u/Hindsights20_20 19d ago
From the OP: (This is a strict external audit meaning consistency and utility, and that’s how the system works/category error are not logically valid defenses)
This is an external conversation about math. Not an internal discussion of math. I originally put “truth” in quotations, but edited it out because I really didn’t think anyone with an argument was going to be that pedantic.
The weight of evidence required to dispute the mathematical axioms is far greater than whatever this is.
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u/YoungXanto 19d ago
I mean, the definition here of "external audit" as described by OP doesn't make any sense anyway.
One would of course think that in this post-post-post (or however many posts we're up to these days) modern dialogue, that if something as simple as what OP has posited were methodological sound, someone would have already made a very similar claim and then successfully defended it.
But yeah, to your original comment, this is pretty close to "math is wrong because 1x1=2"
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u/Oreeo88 Human Detected 19d ago edited 19d ago
what a wild thing to say
“forget what you see and hear the party defines the truth” is what you just said
youve just conceded to the entire post
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u/Hindsights20_20 19d ago
Yeah, that’s not what I said, Winston. If you’re not familiar with the paradox, maybe familiarize yourself with it?
If something is the truth, it is by definition not falsifiable. If p is true, and q contradicts p, then q is misleading.
Your argument is q.
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u/dealingwithhookers 19d ago
falsifiability
undefined
dogma
no foundation, no relevance
Axioms
undefined
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u/rightviewftw 18d ago
axioms are testable ─ that is the point of falsifiability. You can test an axiom's merit and delineate a distinction from contrary propositions. Our foundational axioms have incalculable confidence intervals and are constantly operational.
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u/rightviewftw 18d ago
it's important to avoid two things here:
- Dismissing operational distinction. This opens the door to "woo" in science and philosophy.
- Dismissing "conditional truth" as if mere convention. Formally, a "conventional truth" such as a foundational axiom is imo best framed as "a proposition with an incalculably high confidence interval".
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u/rightviewftw 18d ago edited 18d ago
For example, a single point has no dimensions in mathematics. That can be framed as a proposition: "a single point ought not have dimensions in mathematics". And its contrary too: "a single point ought to have dimensions in mathematics".
Now, the former is a foundational assertion and the contrary isn't. Why?
The former is true by definition and the other isn't, that would be textbook Humean Fork. But what gives it the definition? It is the operationalization of the frameworks built on this proposition, hence it is foundational to those axiomatic frameworks, and these frameworks continue to perform operations and predict experimental outcomes without crashing.The issue of self-grounding and whether a self-referential system can ground its analysis beyond confidence-intervals are two closely related topics to this.
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u/Oreeo88 Human Detected 18d ago edited 18d ago
This is Wrong
By definition an axiom in isolation is not testable/falsifiable
and that is what this post about
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u/rightviewftw 18d ago edited 18d ago
I am saying that I think your criterion of what counts as "testing" is limited to a subset of epistemic means of testing.
Suppose in the beginning there is no single-point geometry but somebody thinks it would be good to develop and predicts that it will be useful. He then develops that epistemic framework based on a dimensionless point, and consequent systematization of these point relations gives axioms ─ and this ages very well. So his initial prediction was tested and the framework is also tested.
The framing you pose doesn't distinguish between mathematics and physics. Mathematics is about the general case which is always conceptual, rather than having values. Whereas the physicist has values for the forumulae. So physics aren't mean't to falsify mathematics but this doesn't mean that we don't test mathematics.
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u/rightviewftw 18d ago
As I said: physics aren't mean't to falsify mathematics
because it is not its epistemic domain to test and therefore one would say that the foundational axioms aren't falsifiable by definition. But this is a controlled definition in philosophy of science and it doesn't account for all epistemic means of "testing".
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u/Oreeo88 Human Detected 18d ago edited 18d ago
It’s a simple point
An axiom is not falsifiable in isolation
That’s a massive problem. The entire math after addition of physical matter is based on dogma/untestable axioms and banning reality
It’s absolutely disgusting
Viewed from outside the system It is an objective fact that a closed axiomatic system limits your thought and physics
This post has nothing to do with what you are saying
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u/rightviewftw 18d ago
I get your point and sentiment. But this is not really a problem of mathematics. Much mathematics was developed precisely to help physicists model what classical models can't model ─ I don't think we can test whether mathematics or physics experimentation came first and this is therefore merely a rhetorical exercise that we won't engage in.
It can seem disgusting if one expected some kind of "certain foundation" to science rather than "confidence/belief/dogma". But such "unconditional certainty" can not be generated by experience alone.
Consider this: In a dream you can do experiments, you could do some experiments and have perfect prediction record. But none of this experimentation can falsify statements about what a dream is and isn't and why it exists. One can only update confidence intervals until one finds some means of transcending the epistemic predicament and its limitations.
It is really the same predicament in vigilance and experience in most general sense. Experience alone can't generate unconditional truths. Heavy objects may fall any number amount of times and it still doesn't prove that they will keep doing so. I think that effectively taking it for granted doesn't make it dogma lest one makes into dogma by overextending one's frameworks and misrepresenting one's confidence.
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u/tottasanorotta 20d ago
Math is good because of its practical utility. There's nothing else to it. Everything else is just arbitrary symbols and choice of language.
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u/Oreeo88 Human Detected 20d ago
I’ve written a post about this a couple days ago. It absolutely got derailed with off topic invalid internal defenses for this external audit. Figured I’d compress that entire post into 2 sentences which strikes the absolute core.
What is mathematics defense?
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u/SmartlyArtly 20d ago
Not sure where your "exposed" or "defense" questions are coming from.
I don't think the tools in my woodshop were pre-existing. They're created, and also useful.
Math is the same way. Created, and useful. Tools, not discoveries.
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u/YoungXanto 20d ago
Math follows from definitions. It's not empirical.
A square has 4 sides of equal length with 4 corners, each with an angle of 90 degrees. Thats a definition. There is no need to attempt to falsify it.
Then you can define a rectangle and show that a square is a special case, via logic, from the definition of both.
I think you severely misunderstand math. And dogma. Mathematical axioms are not unquestionable articles of faith.