The problem of induction is a philosophical question of whether employing induction to validate our assumptions is logical. Hume questions how an anticipation or a conclusion to an inductive reasoning can be justified. According to him, an inductive argument is normal observations. For example (observation) fire is hot, (conclusion) all fires are hot. For Hume, the observation and direct conclusion is a clear indicator that there is a lost premise, confirming his claims that induction argument is not completely clear. Without further reasoning, the argument goes through the observation and directly into conclusion, an indicator that we acknowledge the theory linking the two.
Induction initiates the likelihood that reasonable yet bogus theories may be regarded as scientific knowledge, therefore a logical reason for its use was sought after. If the principle of uniformity of nature could be verified using pure reason, then the application of induction could be reasonable. However, attempt to verify such theory failed. The only way to justify the theory of induction to a considerable extent is observation, that future will always be like the past, but this kind of reasoning must use the type of inference it is deliberated to justify.
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In conclusion, examining the Hume problem of induction from a philosophical and logic approach, induction must provide a technique of selecting which theory to induce from specific observations. Such techniques are provided. So there is no specific process of conducting induction that a researcher could ever do. For this reason, nobody has ever induced a theory because induction is not a properly defined technique of a developing a theory; it is a partial set of procedures hence logically impossible to adhere it to entirety. Therefore, the problem of induction does not have an explicit solution that everybody can agree on and the only resolution may be is to consider what we logically believe in.