> The best that we can do is probably say something along the lines of "these are the best methods of getting closer to the truth that we have available - if anyone claims to have better methods, they are very likely wrong", but you still need to have the humility to accept that even the best models that we have to date are not infallible.
This last sentence slightly conflates the scientific method with the models they produce. I am not claiming that the models are "true", I am claiming that the scientific method is the only reasonable means of gaining a reliable understanding of the objective nature of reality, assuming it exists; and that you cannot pick and choose what you believe in based on your intuition.
Quantum principles have been proven in experiments that have as tight a margin of error as measuring the width of the United States to one human hair, producing shockingly consistent and effective models that were absolutely critical to the development of modern technology. Yet some people somehow refuse to accept these models as an "accurate" reflection of reality, whereas they'll take, at face value, psych/sociological/economic studies that are frankly nothing short of pathetic in comparison.
In regards to science, I am saying that there is a hierarchy of belief. You can draw the line wherever you like in terms of what you think is "true", but you cannot reorder this hierarchy and believe these sorts of psych studies while at the same time questioning the physical models that power the technology that is used to publish them.
And this isn't speaking about math, which is a particularly special case given that it is not scientific but still produces shockingly effective results.