Steve3007 wrote: ↑July 20th, 2020, 3:05 amOne of the core problems--maybe the single core problem--lies in what we take mathematics to be. If one is a mathematical platonist, and one tends to think that we've more or less correctly figured out "real" mathematics, then one is far ore likely to take mathematical manipulations that lead to predictive success to be telling us something about what the world is really like.Palumboism wrote:That's how science works. When you see something that doesn't make sense, you come up with a hypothesis for the reason why. In this case calculations for many galaxies show they should fly apart based on the amount of matter they have. The math indicates dark matter should be there.So, putting it more generally, we observe patterns in our observations. We use mathematics as the language to describe those patterns; like English but more precise and quantitative. That then helps us to extrapolate from those patterns and make predictions of future observations. In some cases, the predictions lead to the hypothesis that the best way to describe those future observations would be to propose the existence of some thing. In this case, that something is "dark matter", but in principle it could be anything.
The issue that some people seem to have with this process is that last part. There appears to be a view that jumping from patterns in observations to proposing the ontological existence of "things" whose proposed existence fits the patterns in the observations is going too far. It seems almost like a form of dualism - i.e. a fundamental separation into two parts - between ontology and utility; between what is and what is useful for predicting the results of experiments. In some ways ( but certainly not all ways) it reminds me of the disdain for experimentation that is often traced back to the likes of Pythagoras, and which led, for a thousand years or more (at least in Western Science/Natural Philosophy), to the view that if you want to understand the way that the world is, the one thing you don't do is look at it!
Similar comments go for physical law realism and the like.
Re instrumentalism, if we're taking our theories to be telling us what the world is really like, then we're no longer in the world of instrumentalism. Per the Wikipedia article on instrumentalism, for example (and there's a very extensive citation for this), "According to instrumentalists, a successful scientific theory reveals nothing known either true or false about nature's unobservable objects, properties or processes."