The first problem has to do with his justification of induction. According to his argument, induction is justified because it is the best means available for predicting the future. Furthermore, he claims that the inductive method is unjustifiable given the rationalist postulate that all knowledge must be demonstrable as true, because "there exists no proof that it will lead to true conclusions." [12]  Thus he resorts to a justification of induction that proves, not that it will lead to true conclusions, but that it will lead to good posits. It is therefore apparent that for Reichenbach induction is justified because it is the best means available, and it is the best means available, because it leads to good posits. However, the question of how one is to determine whether or not a posit is good raises some difficulties for his justification. Although general probability statements and predictions about the occurrence of single events can both be regarded as posits, the key posit upon which to focus is Reichenbach's general assertion that frequent repetitions of similar events are subject to numerical regularities. The justification of this assertion may also count as a justification for induction, because inferring the future from the past presupposes that all frequent repetitions of similar events are subject to numerical regularities, that is, that the regularity of events in the past will continue to hold for similar events in the future. In fact, the justification of induction requires a justification of the general assertion, which will henceforth be referred to as his inductive posit. But if induction is justified because it leads to good posits, then it must be demonstrated that induction will lead to Reichenbach's inductive posit, thus making it a good posit. And the problem with this is that both the posit whose justification is counted as a justification for induction and one of the posits to which induction leads are one and the same, which means that induction is used to justify itself. Is this not the type of circularity that Reichenbach wished to avoid in the first place? The problem is that if induction is justified because it leads to good posits, then it must also lead to the posit whose justification counts as its own justification. This obviously cannot be counted as a justification without the implication of circularity. Reichenbach is left with three alternatives. The first is that his inductive posit must not be regarded as a good posit. The second is that his inductive posit must be shown to be good by some method besides induction. And the last alternative, which is similar to the second, is that induction must be shown to be the best method available for predicting the future by some means other than that of showing that it leads to good posits. The first alternative leaves induction unjustified. As for the second alternative, it is by no means clear what sort of method could be used to show that Reichenbach's inductive posit is a good posit without simply accepting it as so and leaving it at that, which is, from an epistemological standpoint, an unacceptable form of justification.

Thus, the last alternative seems to be Reichenbach's only recourse. Supposing that this is the case, it still remains questionable whether the claim that induction is the best means available entails the claim that induction is justified. Reichenbach certainly does not clarify what being the best means available has to do with the justification of induction; he only suggests that, "This justification of induction is very simple; it shows that induction is the best means to attain a certain aim." [14]  A justification for induction must involve at least one premise supporting a conclusion. However, there is a problem in determining what this conclusion may be. According to Reichenbach, it cannot be the claim that induction will lead to true conclusions. Furthermore, following from the discussion that led to the three alternatives, the conclusion cannot be the claim that induction will lead to good posits; for induction would then lead to the conclusion (viz., Reichenbach's inductive posit) whose truth justifies induction. If anything, the conclusion would be the claim that one is justified in using induction to predict the future, which follows, in part, from the premise that induction is the best means available. But this is not a justification for induction; rather, it is a justification for using induction to predict the future. There is definitely a difference between these two foregoing forms of justification. One may be justified in using induction to predict the future, because it is the best means available; but this does not justify induction itself. A justification for induction requires supporting either the claim that it will lead to true conclusions or the claim that it will lead to good posits. According to Reichenbach, there is no proof that establishes the former claim. Thus, since a justification of the latter claim leads to circularity, Reichenbach's justification must not be a justification for induction, but for the use of the inductive method as a means to predict the future. One may be justified in using, or even resorting to the use of induction to predict the future, regardless of whether induction itself is justified, that is, whether there is actually a justification for induction independent of our using it.

In summary, Reichenbach's attempt to justify induction rests on the assumption that it is the best means available to predict the future, and it is the best means available because it leads to good, or even the best posits. However, this justification is inadequate, because induction leads to a posit (i.e., his inductive posit) whose justification counts as a justification for induction. Out of three alternatives, Reichenbach is left with only one; namely, that induction is justified, only because it is the best means available for predicting the future, and not because it leads to good posits. This justification is also inadequate, because it only justifies the use of the inductive method, and not induction itself. A justification of induction must establish either the claim that induction will lead to true conclusions or the claim that it will lead to good posits, and since Reichenbach is not in a position to establish either of these claims, his justification for induction is unsatisfactory.

The second problem with Reichenbach's account has to do with how his inductive posit is to be interpreted. Up to this point the assertion that frequent repetitions of similar events are subject to numerical regularities has been treated as a general assertion so it can be used to derive probability statements and make predictions. However, there is a dilemma that severely weakens Reichenbach's account, which generates a problem that requires leaving open the question of whether the assertion is general. In brief, it can be explained as follows: The assertion that frequent repetitions of similar events are subject to numerical regularities is either particular or general. If the assertion is particular, then it cannot be used to derive general probability statements and thus predictions of single events. If the assertion is general, then it is falsifiable, which also means that it cannot be used derive general probability statements and predictions about single events. Both horns of the dilemma have the same result: Reichenbach's inductive posit no longer allows one to make predictions, and the rock bottom upon which predictive knowledge rests turns to sand.

To establish the dilemma in greater detail, suppose that Reichenbach's inductive posit is interpreted as particular. It could then be translated as, 'Some frequent repetitions of similar events are subject to numerical regularities'. This version of the posit is inadequate, because it cannot be used to derive predictive statements. Consider the following statement: 'Repeated trials of playing Russian Roulette reveal that players frequently kill themselves one-sixth of the time'. Reichenbach's posit, according to the first interpretation, only implies that some frequent repetitions of similar events are subject to numerical regularities. Consequently, although there is the frequent repetition of Russian Roulette players killing themselves one-sixth of the time, one cannot use his inductive posit to infer that this frequent repetition will continue to hold for the future. For the term, 'some', allows for at least one case in which a frequent repetition is not subject to numerical regularities, and the frequent repetition of Russian Roulette players killing themselves one-sixth of the time may very well be that one case. To state the problem in other words, from two particular premises, one being the assertion that some frequent repetitions of similar events are subject to numerical regularities, and the other being the claim there is an instance of numerical regularity in a frequent repetition, the conclusion that the particular instance of regularity will continue to hold for the future does not follow. For the instance of regularity expressed by the second premise is not necessarily comprised by what is expressed by the first premise. It follows, then, that Reichenbach's inductive posit, interpreted as particular, cannot be used to derive predictions.

Now suppose that Reichenbach's inductive posit is general, in which case it would be translated as, 'All frequent repetitions of similar events are subject to numerical regularities'. Interpreted this way, the posit appears to be too strong. Is it not possible that there is at least one frequent repetition that is not subject to numerical regularities? Consider the following example: For some time, all those who contracted AIDS have also tested HIV positive--this seems to exhibit a frequent repetition--but recently it was found that some individuals with AIDS do not test HIV positive. So much for nature's regularity. Of course, one might object that given the right amount of time (perhaps a very long amount of time), even apparent irregularities will turn up consistently, thus preserving the regularity of nature presupposed by Reichenbach's inductive posit. But Reichenbach does not clarify how often a repetition of similar events must occur before it can be regarded as "frequent". And so long as this remains unclear, past instances of the irregularity of nature will count against his inductive posit. Perhaps his posit applies only to very long periods of time during which similar events are found to repeat frequently. The problem with this is that it makes Reichenbach's theory of probability very limited--enough so that it may be rendered useless for all cases except those that involve repetitions of similar events that continue for very long periods of time. And in most cases, one cannot afford to wait around for long periods of time in order make predictions. In short, if Reichenbach's inductive posit is applied to series of events that do not continue for long periods of time, is most certainly falsifiable. And so it becomes pointless to treat the posit as true, when in fact it can be shown to be false, which means that it can very easily lead to false predictions. On the other hand, if the posit is applied to series of events that do continue for long periods of time, it is rendered useless for all practical purposes. For in everyday cases in which we are required to predict what will hold for the future, we do not have the time to conduct a series of trials for a long period of time before there is sufficient basis for our inferences.

In conclusion, although Reichenbach's account of predictive knowledge has merit on account of the uniqueness of employing the idea of the posit, it is subject to two difficulties. The first is that his justification for induction carries with it the implication of circularity, unless it is justified simply because it is the best means available for predicting the future, and not because it leads to good posits, in which case it only justifies the use of induction and not induction itself. The second difficulty is the dilemma that arises once one attempts to get clear on the logical character of what is posited with Reichenbach's inductive posit. If his inductive posit is interpreted as particular, then it cannot be used to derive probability statements and make predictions. If it is interpreted as general, then it is either falsifiable, which also means that it cannot be used to derive probability s tatements and make predictions, or it applies only to cases where similar events continue for very long periods of time, in which case it is useless for all practical purposes. In light of these difficulties, it remains to be seen whether an account of predictive knowledge can be developed which is immune to traditional objections to the idea of acquiring knowledge of the future on the basis of knowledge of the past.