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Comment by DeepFriedButter | Hacker News Reader

Learn about the Münchhausen trilemma, even in mathematical logic it is not possible to formulate a proof that is neither, dogmatic, circular or regressive. For this reason I tend to refrain from making any of those objections when people talk about their personal motivations. I even think this was the best part of the blog, the other stuff was talk about cringe mind-maps with weird names like how a cult has special words for mundane stuff. I hate these galaxy brain types trying to escape their linear western way of thinking by employing the complex plane. If you want to read some meandering thought on why you should be a Machiavellian go and read "Politics as wish". A classic.

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I give you the Münchhausen or Agrippa“s trilemma. But in math we start with natural numbers or sets. Starting with „wise“ and „loving“ as primitives is a different thing.

You can even treat mathematics as syntax, that only gets meaning when applied to the world. Then your primitives get meaning by what you can technically construct with it and by what you can predict with it. That together with the no miracles argument let‘s science circumvent the trilemma in my opinion. All that’s needed is a pragmatic semantic, or better practice as a quite weak fundament.

You’ve simple renamed axioms, unprovable assumed truths, to “primitives”. The munchhausen trilemma undermines all truths (at least all truths that anybody’s every tried to prove so far), neither science nor mathematics circumvent it in any way. Any belief that they do is not a scientific or logical position, it’s a faith based position (aka a religious belief).

That was not my main point, but primitives are not axioms. They are objects talked about in axioms. I give you they are close.

My point was that

1. numbers are simpler primitives than wisdom

2. You can treat mathematics purely syntactically, as meaningless games played by rules

3. You can then give them neaning in the elaborate practice of scientific research, technical implementation and prediction, on the background of human language and practice. Mind you, we went to the moon and have mobile phones and penicillin.

4. Since this can other than science grasping something about reality only explained by a big miracle, it does not matter where you started the proof of your worldview. It’s not grounded in rationalistic first philosophy, against which the trilemma argues. It is simple, practical, ongoing and repeatable success - power over nature if you will. That is a basis outside of logic. Ignore at your own peril, but true - I cannot logically prove it so you must believe. That’s all talk and never found a useful truth, like Kant already noticed in his preface to KdrV [1]. It has not changed a bit since then.

Lastly, from what you say I understand that the trilemma „undermines all truths“. Is it itself true? And then what? Is it thus faith based? Or does it undermine itself? You see that this logico-rationalistic approach leads nowhere?

[1] http://www.zeno.org/Philosophie/M/Kant,+Immanuel/Kritik+der+...

Truth in pure mathematics doesn’t really have any meaning, because you simply invent the rules, and then derive further truths from that invented basis (these rules are correctly referred to as axioms btw, not primitives). It’s your leap to somehow deriving a non-axiomatic basis for natural sciences that’s completely in error.

> Lastly, from what you say I understand that the trilemma „undermines all truths“. Is it itself true? And then what? Is it thus faith based? Or does it undermine itself?

I suggest you read the full sentence:

> The munchhausen trilemma undermines all truths (at least all truths that anybody’s every tried to prove so far)

It’s entirely possible that a logical proof may exist that survives the trilemma. However it does seem as though nobody’s ever come up with one, and it’s difficult to imagine how that could ever happen. The usefulness of the trilemma is to undermine arguments that people have elevated above their merits (like your claims about natural sciences). If you could prove anything at all, even the most simple thing, in a way that survives the trilemma, I’d love to hear it. I’m sure it would be the most interesting thing I’ve ever read.

I think we are talking past each other.

> Truth in pure mathematics doesn’t really have any meaning, because you simply invent the rules

Yes, I was saying that you can view mathematics like that. Not everyone does though, so I question that it necessarily is as you say.

I’m further saying that science is not simply belief or faith based, because otherwise all its achievement would look like one big miracle. And that seems contrary to the claim that it would be faith based. Without first philosophy and a logico-metaphysical “foundation”, whatever that could be, to whoch the trilemma could be applied. I think the very idea of something epistemically stronger than practical success that will prove science right is a flawed idea from the outset - what will prove it right? But please try to apply the trilemma - I would be interested. I often learn surprising new things here.

If you read my reply above you will find that I said that primitives are not axioms. These are the things axioms talk about, sometimes also referred to as atoms. But you may refer to them by no matter which word you like if you make it clear. Important is only that we understand reach other, though we will likely not agree. It’s a complex topic, and this medium is not necessarily made for that.

And lastly, my point about the presentation of the trilemma still stands. I did not quote the full sentence to not make this too long, not to make a cheap point against a straw man.

The trilemma is a practical hammer that can be used against first philosophy that tries to prove how everything is from the armchair. But make it a first philosophy itself, and it becomes self defeating.

The natural sciences are, put simply, the study of the natural world via experimentation and the collection of empirical evidence. However none of the empirical evidence you might collect (or any other type of evidence for that matter), can survive the scrutiny of the trilemma. You cannot prove that a chair exists, or an apple, or a pen without relying on circular reasoning, an infinite regression of reasoning, or by inventing some axiomatic foundation. I’m not aware of any scientific knowledge that’s capable of circumventing this trilemma, as you put it.

You might think it’s sensible to believe that apples exist, and that the world you perceive around you is real, but this is strictly a faith based position, no matter how perfectly obvious it might seem to you.

Thanks for your clarification. I really enjoy your arguments.

I reply that I find the idea of from first principles proving the existence of something, e.g. an apple a weird notion. What is the justification of asking for it? That is a rationalistic-philosophic concept I can only chuckle at. What about the human information-processing tract is so special that this would help anything? I completely agree that the trilemma helps against these attempts.

I do not agree that it is a useful or meaningful practice.

I’m not setting out to prove something this way.

I’m saying: you have projects and plans that you want to be successful. Truth found by the scientific method has in general a track record of being repeatably found again, and thus will help you. Religion, philosophy, astrology ideology does not have that track record. That’s what makes science unique and points to that it has found some truths. Otherwise it’s track record would be miraculous.

I’m also saying this is as good as it gets, precisely because of the trilemma.

To try to make myself clear: I’m thinking that this practice of proving from first principles would need to be shown to do anything useful, before I‘ll look into it. I think it’s a failed idea, though I believed it long. It’s often taken for granted, but it’s highly questionable.

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