[d0mine]

Bayesian approach sounds like a religion (one true way).

There is nothing unusual about different mathematical methods/models producing different results e.g., the number of roots even for the same quadratic equation may depend on "private" thoughts such as whether complex roots are of interest (sometimes they do/sometimes they don't). All models are wrong some are useful.

[lalaithion]

> the number of roots even for the same quadratic equation may depend on "private" thoughts such as whether complex roots are of interest

You are confusing ambiguity in a problem statement due to human language being imprecise with two well-specified identical experimental results having different results due to the intentions of the human carrying them out.

Is arithmetic a religion because there's "one true way" of adding integers?

[d0mine]

It is not about human language being imprecise. I can formulate the questions using the math language precisely with the exact same result (different number of roots are possible for different formulations of the problem for the same "physical" (coefficients of the quadratic equation) setup).

The Map is not the Territory.

Different maps can be useful. No true map.

[kevindamm]

I can think of at least two ways to add integers.. the categorical way that applies a mapping from the set into itself, and the set-theoretic way that deals with unwrapping and rewrapping successor relations. The latter is sometimes resorted to in heavily-relational contexts like Datalog.

[lalaithion]

Yes, this is addressed in the original article... there are multiple "lawful" ways of adding integers which all give the same results, and likewise in probability all "lawful" ways of analyzing data should give the same results. If you have two different ways of adding numbers which give different results, one is not lawful.

[pdonis]

> Bayesian approach sounds like a religion (one true way).

Only about the things that can be mathematically proven. Which is just like any other branch of math.

It is true that some Bayesians (and EY can be argued to be among them) like to talk as though Bayesian computation is a drop-in replacement for your brain. Of course it isn't, and Bayesianism, like any mathematical approach, should be taken with a good-sized dose of humility. As Bertrand Russell said, to the extent that mathematical propositions refer to reality, they are not certain, and to the extent that they are certain, they do not refer to reality.

[pdonis]

> the number of roots even for the same quadratic equation may depend on "private" thoughts such as whether complex roots are of interest

No. The number of roots that you care about might depend on your private thoughts; but the number of roots itself does not. It's a mathematical fact. It just might not be a mathematical fact that you actually care about. But what you care about is not part of math.

[lupire]

Why are you ignoring the quaternion roots? 3x3 matrix roots?

[pdonis]

Normally "quadratic equation" means "over the complex numbers" (and the mention of "complex roots" in the post I responded to bears out that interpretation).

But yes, different mathematical models can give different answers for things like "number of roots of an equation". But that doesn't mean math depends on "private thoughts". It just means you need to specify which mathematical model you are talking about.

[biomcgary]

One of my priors: "a group of people who look like a faith-based community, but claim not to be one, should not be trusted".

[usgroup]

Yeah I’d agree at some depth. We don’t talk enough about integers, rationals and real numbers and what they imply for our “normative rationality” or “epistemological commitment”. But aside from the integers, everything else is totally suspicious.