This is the problem of induction in a nutshell, and it is something that has alternatively been seen as one of the most severe limitations on true knowledge about the world or as a non-issue in any practical terms. If inductive reasoning cannot be trusted, then all past experience and even experimental data is essentially meaningless in predicting the future and there is no logical reason to assume things should occur one way simply because they have occurred that way before. Many have pointed out how silly it would be to go through the world without inductive reasoning -- not being sure if the door would open when the handle is turned, etc. -- but this does not actually address the logical problem of induction.
Edwards Attempted Answer
There have been attempts to address the problem of induction at the fundamental logical level, some of them seeming to come closer to success than others, but ultimately no one has been able to definitively demonstrate in a logically consistent manner (i.e., without a reliance on inductive reasoning) that inductive reasoning is a valid source of knowledge. One attempt, and a very good attempt, is made by Paul Edwards in his answer to Bertrand Russell's restatement of the problem of induction, and this answer seems to combine both practical and logical arguments against the supposed problem of induction. In response to the basic question, "if a has always led to b in the past, is there a reason to believe that this will be the case in the future?" Edwards attempts to frame this as an issue of semantics, asserting that such a question is to misuse the word "reason," ascribing a much higher-order and restrictive meaning to it than common sense and usage would imply.
Edwards essentially acknowledges that there is no way to supply a reason for believing that a will lead to b as long as "reason" has the definition of an observable fact or something on the level of a relation of ideas -- such...
The context in which the question is posed, according to Edwards, inherently defines "reason" as something that cannot exist for belief in future events, and therefore makes it necessarily true that the answer to the question posed above is "no." The problem of induction, then, is disingenuous.
Edwards' approach to the problem of induction is essentially a logical argument regarding the practicality of the issue, and though he attempts to assert that inductive reasoning is a valid way to derive knowledge because of the semantic issues involved in the definition of the problem itself. This "solution" to the problem of induction is really just a means of sidestepping the issue, however, and not of actually addressing (let alone refuting or countering) the logic of the problem itself. Perhaps the question Edwards addresses does assume a definition for "reason" that automatically and inherently denies its application to suppositions about future events, but the fact that such a definition for "reason" could exist is itself the problem of induction. There is no class of knowledge other than that supplied by inductive reasoning itself to support the use of inductive reasoning in the derivation of knowledge. Though this might be construed as a semantic argument, it is nonetheless a true one, and unless these semantic terms have no relevance in the world of human ideas then this issue must be resolved or be acknowledged as un-resolvable.
Conclusion
It is unquestionably true that to go through life without the use of inductive reasoning would be foolish on a practical level. It is equally foolish, however, to assume that inductive reasoning leads to knowledge in the same way that observation and direct logical reflection can. Semantic or no, the problem of induction will remain a part of the philosophical dialogue for centuries to come.
