David Hume claimed that it is:
[…] impossible for us to satisfy ourselves by our reason, why we should extend [our experience of cause and effect] beyond those particular instances, which have fallen under our observation. We suppose, but are never able to prove, that there must be a resemblance betwixt those objects, of which we have had experience, and those which lie beyond the reach of our discovery.
This gives rise to the problem of induction: how can we defend assuming the so-called uniformity of nature that we take to exist when we generalize our limited experience to that which lies “beyond the reach of our discovery”? For instance, how can we justify our belief that the world of tomorrow will, at least in many ways, resemble the world of yesterday? Indeed, how can we justify believing that there will be a tomorrow at all?
A point worth highlighting in response to this problem is that, even if we were to assume that we have no justification for believing in such uniformity of nature, this would not imply that we thereby have justification for believing the opposite: that there is no uniformity of nature. After all, to positively state that the patterns we have observed so far do not predict anything about states and events elsewhere would also amount to a claim about that which lies “beyond the reach of our discovery”, and so this claim seems to face the same problem.
The claims 1) “there is (some degree of) uniformity throughout nature” and 2) “there is no uniformity throughout nature” are both hypotheses about the world. And if we look at the limited part of the world about which we do have some knowledge, it is clear that the former hypothesis is true to a large extent: patterns observed at one point in time and space do indeed predict a lot about patterns observed elsewhere.
Does this then mean that the same will hold true of the part of the world that lies beyond the reach of our discovery? One can reasonably argue that we do not have complete certainty that it will (indeed, one can reasonably argue that we should not have complete certainty about any claim our fallible mind happens to entertain). Yet if we reason as scientists — probabilistically, endeavoring to build the picture of the world that seems most plausible in light of all the available evidence — then it does indeed seem justifiable to say that hypothesis 1 seems much more likely to be true of that which lies “beyond the reach of our discovery” than does hypothesis 2. This is not least because hypothesis 2 would imply an extreme uniqueness of the observed compared to the unobserved, whereas hypothesis 1 merely amounts to not assuming such an extreme uniqueness.
If we think in this way — in terms of competing hypotheses to which we assign different levels of plausibility — Hume’s problem of induction no longer seems so compelling or problematic. After all, even if we cannot deductively prove our hypotheses about that which lies beyond our experience, we can still have probabilistic reasons — based on cumulative observations — to consider some hypotheses (much) more likely than others.
The Problem of Induction Relies on Induction
In addition to these points about probabilistic reasons, it is worth noting that one can turn Hume’s skeptical argument on itself. For example, Hume’s argument assumes that there is something that lies “beyond the reach of our discovery”, beyond our known experience. But, in Hume’s spirit, we can ask what justifies this inductive assumption about there being something beyond our known experience. It seems that Hume is here assuming something for which he has no deductive proof. In the very framing of his argument, he is tacitly assuming what he thinks we cannot have satisfying reason to believe. After all, what deductive proof can Hume give for there being anything beyond our known experience?
Relatedly, one can make an argument suggesting that it is impossible to give a coherent argument against (at least some degree of) uniformity in nature. For in order to even raise a doubt or an argument against (some degree of) uniformity in nature, one is bound to rely on the very thing one is trying to question. For example, one must assume that words will still mean the same in the next moment as they did in the previous one, and not least that there will be a next moment to begin with.
Thus, it seems impossible to coherently argue against or doubt at least some degree of uniformity in nature, which itself seems to be a reason to believe in such uniformity. After all, that something cannot be coherently doubted arguably gives us some reason to believe it.
In sum, if one thinks we have good reason to take the problem of induction seriously, or good reason to believe that this problem will persist in the future (since it has in the past), then one also believes that we have good reason to make (at least some) inductive generalizations about that which lies beyond the reach of our discovery.
Magnus Vinding 