It's fun to realize how deeply ingrained the current scientific process is in our way of thinking.
All of these ideas that you tacitly take for granted are itself mutable parts of the scientific process:
* That iterative improvement and hill-climbing is an effective process for improving results.
* That replication of experiments and convergence is a truth-generating enterprise.
* That truth can be expressed numerically.
* That there are some values that are "known good". By what process? According to whom?
To be clear, I don't disagree with those. However, these rules aren't baked into the firmament of the universe. They are processes we humans have chosen to apply in our social process of reaching conensus on truth. In other words, this list here isn't physics, it's technology.
It's entirely possible to imagine a culture whose truth finding bodies don't take for granted one or more of these rules at all. That culture might be more or less effective (again, according to what metrics?), but it would still be well-defined.
> That iterative improvement and hill-climbing is an effective process for improving results.
Not essential to science; in fact, there’d a major viewpoint within metascience that explicitly rejects this as popular mythology of how science works in practice, holding that models change by revolution more than evolution.
> That replication of experiments and convergence is a truth-generating enterprise.
Not part of science, in the same way that your use of “truth” later is not.
> That truth can be expressed numerically
No. While scientism may make essential connections between science and truth, science itself only depends on useful predictive models being expressable, not about truth being expressable, numerically or otherwise, or even being a coherent, meaningful concept.
> That there are some values that are "known good"
That's not only not essential to the scientific process, but contrary to something that is: that all results are contingent.
> That culture might be more or less effective (again, according to what metrics?)
Isn't this the idea of "free will". That you get to choose for yourself the metrics you want to optimize your life for?
Now I think that you'll use a combination of learned and inherited desires for it. But the idea here is that each individual can express those desires, and then the "success" of a society is thus to maximize each individuals success, even when they differ in their metrics.
That's a made up concept as well, but I think it still stems from individual desires. We've just mostly all individually observed that an organized society that compromises with each other to maximize each and everyone's individual desires has less risk to our own desires being squandered.
The alternative would be to try to achieve power over others to maximize your desires, and maybe from history and life experience, people have found that to be not sustainable or only achievable for a few, thus your chances at it are lower.
In essence, I think I'm saying that it seems over time people know their desires, but don't know how to beat fulfill them, and this is the metric.
I don't think this is what is held by those-who-do-science-and-philosophy-at-large (though it may be a generally accepted hand-wave, I don't know). See, for example Category Theory for a branch of what-I-believe-would-generally-be-called-science that doesn't use numbers, but instead expresses things with sets and relations.
The logician is the intersection of the set of all scientists and the set of all philosophers.
That article says that mathematics is ill-founded, not that math has something inexpressible by logic. Mathematics can be reduced to logic that is ill-founded.
Isn't the basic point of quantum physics that this isn't true? We can only make guesses with probabilities, but we can't know the actual truth, and therefore can't express it numerically.
Sure, but the probabilities are numbers too. Which is again sort of acknowledging the need to fit quantum mechanics into a numeric framework.
Imagine you were studying ice cream flavors. You might design a study like, "We'll ask a lot of people and the flavor that the most people prefer is the best." In other words, the metaprocess you use to design your experiment itself tacitly assumes you need a numeric result. The presumption of comparison and quantifying frames the questions you even think to ask.
But you can imagine an alternate culture that when studying ice cream flavors doesn't even ask questions with numeric answers. It could be, "We'll ask a lot of people to try flavors and write poems about the experience."
We wouldn't even call this "science". Because there is a hidden border around even the term that affects how we are able to evolve the scientific process.
Funny thing about quantum mechanics... we use numbers to describe probabilities and functions to describe probability distributions. But the mathematical models we use are incomplete (and, looking at neutron decay, incompatible) so can we really conclude that numbers are the right abstraction?
And no, not poems. Elements of finite groups are not numbers, but they crop up in physics frequently. Topologies are not numbers, but they're also significant in physics.
All of these ideas that you tacitly take for granted are itself mutable parts of the scientific process:
* That iterative improvement and hill-climbing is an effective process for improving results.
* That replication of experiments and convergence is a truth-generating enterprise.
* That truth can be expressed numerically.
* That there are some values that are "known good". By what process? According to whom?
To be clear, I don't disagree with those. However, these rules aren't baked into the firmament of the universe. They are processes we humans have chosen to apply in our social process of reaching conensus on truth. In other words, this list here isn't physics, it's technology.
It's entirely possible to imagine a culture whose truth finding bodies don't take for granted one or more of these rules at all. That culture might be more or less effective (again, according to what metrics?), but it would still be well-defined.