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I'm well aware of all the discussion in the field of philosophy of science spurred by Hume's formulation of the problem of induction: https://plato.stanford.edu/entries/induction-problem/

My question is: what were the reactions among scientists working in the field and doing experiments? In the second half of the 18th century there were already scientists applying the scientific method in different fields, like physics, astronomy, chemistry...

How was Hume's criticism of induction received? Was it dismissed right away? Was it taken seriously?

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    None, because none was needed. Hume did not find any problem with induction itself, he found a problem with justifying induction from facts and reason. But he also suggested that it is justified instead by a higher authority, nature that "has implanted in us an instinct, which carries forward the thought in a correspondent course to that which she has established among external objects". Thus, it was a 'problem' for philosophers only, scientists and laymen alike could safely proceed as they always did.
    – Conifold
    Commented May 13 at 4:12
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    See e.g. Hume, The Philosophy of Science and the Scientific Tradition: no significant connections, not only with practicing physics (that can be quite obvious), but neither with "emprical" scientists like Darwin. Commented May 13 at 6:37
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    You might be interested in this (which I personally consider a little gem), at least in so far as it adds to the perspective: The Evils of Inductive Skepticism, D.C. Williams, from The Ground of Induction, 1947. Commented May 13 at 17:31

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I can't speak for people in the 18th century, but there isn't really much for scientists to do about it.

The principle of induction has proven to be exceedingly useful for predicting things, and for improving our lives through technological development (and every time the future does resemble the past arguably serves as evidence of induction). So it doesn't matter that much if there isn't strict deductive proof or whatever to justify it.

I wouldn't be surprised if the response was similar to how modern scientists seem to respond: Oh, okay. Well, you do your philosophy and we'll get back to doing useful things based on induction.

Your options are somewhere between: (1) throw out everything that's based on induction, until the problem of induction is "properly" solved (which seems likely to never happen, but that conclusion in itself may require induction) and (2) disregard the problem and keep building off of the principle of induction. Given how many useful things that have been built on top of induction, #2 seems like the obvious choice.

Of course, we should keep in mind that future events may not always exactly resemble the past, but this is itself something we can apply induction to, by e.g. looking at how long and how consistently some event has happened, by considering the unpredictability of dependent factors or inductively reasoning about A to conclude that B will cease at some point (e.g. the Earth orbits the Sun, but there are other physical forces that will result in it no longer doing that in a few billion years). All of this is basically just part of doing good science.


My preferred "solution" to the problem of induction is some sort of model of coherence, and saying that induction being a thing is just a better explanation for the evidence than it not being a thing.

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The claim that science was not actually based on induction, but actually on falsifiability, was not first brought up by Karl Popper. It dates back at least to Blaise Pascal:

In order to show that a hypothesis is evident, it does not suffice that all the phenomena follow from it; instead, if it leads to something contrary to a single one of the phenomena, that suffices to establish its falsity.
https://en.wikipedia.org/wiki/Blaise_Pascal#First_atmospheric_pressure_vs._altitude_experiment

So, my guess is that it's how scientists would respond to the Hume's problem of induction.

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    This only makes sense if science can only be based on one thing, or if induction and falsifiability are mutually exclusive, but they aren't. Science is built on both. One can also say the idea of falsifying some hypothesis is itself based on induction, because if you reject the idea that the future resembles the past, then you wouldn't be able to create hypotheses about future events based on past events, and you wouldn't be able to test any hypotheses.
    – NotThatGuy
    Commented May 13 at 22:40

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