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According to Reichenbach's account, predictive knowledge is not knowledge that one or more event will occur in the future or that a probability (i.e., a frequency or a series of similar events that occur as a certain percentage of a total) will continue to hold for the future. This results from his premise that a statement about the future cannot be uttered with the claim that it is true, because one can imagine that the contrary will happen. I argue that if anything is to count as predictive knowledge, it is the knowledge that frequent repetitions of similar events are subject to numerical regularities (i.e., his inductive posit). This sort of knowledge provides a basis for predicting the future, because it presupposes a regularity in nature, such that what may hold for the future can be inferred from knowledge of the past. The problem of induction counts as the central objection to Reichenbach's account. Induction is unjustified, because his inductive posit, whose justification counts as a justification for induction, is itself justified by induction. In other words, induction is used to justify the claim that induction will continue to be successful in the future, which is a circular form of reasoning. His solution involves the idea of a posit, i.e., a statement which we treat as true although we do not know that it is so. Induction cannot be justified by proving that it will lead to true conclusions, but only that it will lead to good posits. Induction is justified, because it is the best method available for predicting the future, and this is so, because it leads to good posits. Reichenbach's account is open to two criticisms. First, his solution to the problem of induction is either (a) not a justification for induction, but for the use of induction, which is different sort of justification altogether, and thus still leaves his account subject to the problem of induction, or (b) it is circular. For if induction is justified because it leads to good posits, then it must also lead to his inductive posit, whose justification counts as a justification for induction. Second, there is a dilemma that weakens his account. If his inductive posit is particular, then it cannot be used to derive predictive statements. If it is translated as general, then either the result is the same, because it is falsifiable (for frequencies are subject to irregularities within relatively short periods of time), or it applies only to contexts where series of events continue for very long periods of time, in which case the posit is useless for all practical purposes. |
In his book, The Rise of Scientific Philosophy, Hans Reichenbach develops an account of predictive knowledge that is intended to be empirical yet immune to traditional objections to the idea of acquiring knowledge of the future on the basis of knowledge of the past. He gives a number of examples of predictive knowledge. One of them is the traditional example in which the conclusion that all swans are white is derived from the premise that all swans observed in the past have been white. It is possible that this conclusion is false, but, nonetheless, it seems to involve knowledge of a probability, a probability that is supposed to be the basis for saying that the prediction that the next swan will be white is better or more convincing than the contrary. There is also the more precise case, where it is predicted that the probability for tossing heads with a coin is one-half, based upon a series of past trials in which heads turns up nearly the same number of times as tails. Again, it is not known which will turn up, but it may be known that the probability for heads turning up in a future toss of any coin is equal to the probability for tails, namely, one-half. In another example, a detective draws certain inferences regarding the perpetrator of a crime on the basis of the data he has collected. With the data, he attempts to find the most probable explanation. Reichenbach also considers the case in which the predictive conclusion is that there is an 80 per cent probability that it will rain tomorrow, which is based on observations of weather in the past. These examples regarding swans, coins, and so forth have something in common. First, predictive knowledge involves knowledge of the past. The prediction that the next swan will be white is based upon the knowledge that all swans observed in the past have been white. Second, it also involves making a claim about the future. And third, predictive knowledge is used as a guide for our daily actions. We do not plan a trip to the beach just because it is possible that it will not rain on the day we go; rather, we supposedly know that there is a greater probability for it not raining than otherwise. Thus predictive knowledge can be said to be inferential in nature in that it is marked by a sort of move or transition from the domain of experience to, at the time of the inference, somewhere beyond the reef of experience and all possible observation.
But what is it that is inferred from past observations? If it is predictive knowledge, then, it cannot be knowledge that a particular event will occur, such as observing a white swan or the toss of any coin turning up heads. According to Reichenbach, "A statement about the future cannot be uttered with the claim that it is true", because "we can always imagine that the contrary will happen, and we have no guarantee that future experience will not present to us as real what is imagination today." [1] The imagination evidently plays an important role in determining whether a statement about the future can be claimed to be true. If one can imagine that the contrary of a prediction will hold, then it is possible that the contrary will be the case. And this prevents one not only from knowing that the statement about the future is true, but also from knowing that the event or events it makes reference to will occur. So, if predictive knowledge is not knowledge that a single event will occur, then just what is predictive knowledge? Reichenbach offers a clue. He writes,
| ...when we toss a coin and say that the probability of heads turning up is one-half, we say something about future events. What we say is perhaps not easy to formulate; but there must be some reference to thefuture the future contained in the statement, since we employ it as a guide for action. [2] |
He claims that when one makes a prediction, something is being said about future events, which is different than saying that these events will occur in the future. One does not necessarily have to say that a number of events will occur in order to say something about them (one might say that such and such will be the case about these events, given that they occur, which could involve their nature or relationship with other events as opposed to their occurrence). What is also important is that what is said about the future involves more than one event. The question is: What is it that is said about more than one event that may count as predictive knowledge? According to Reichenbach's conception of predictive knowledge, to say that the probability of heads turning up is one-half is not to say that either heads or tails will turn up, nor is it to assign a probability to the single event of heads turning up. Rather, it is to say that in a series of trials of tossing any coin, one-half of those trials will result in heads turning up. The foregoing claim does not imply that a single event, or series of events, will occur, yet it still states something about the future, namely, that if the series is extended into the future, then tossing heads will occur a certain number of times out of the total number of trials. Thus, predictive knowledge at least involves the knowledge that a number of similar events will occur a certain number of times out of a total number of trials. According to Reichenbach, this number of events out of a total (i.e., a complete series of events) is a frequency. His theory of probability (i.e., the frequency theory of probability) contains the assumption that a probability is not some vague degree of credibility or certainty; rather, it is simply a frequency. Thus, part of the idea of predictive knowledge involves knowledge of the foregoing sort of probability, that is, knowledge of frequencies.
In summary, predictive knowledge is in part constituted by past observations, probability (as a frequency), and the inductive inference, which is used to extend a probability into the future. The process that leads to assertions such as, 'All swans are white', can now be explained. Past observations reveal that along with every case in which a swan is observed it is also observed that the swan is white. These cases form a series of events, and the probability or frequency associated with the series is the number of swans observed to be white out of the total number of swans observed. From the foregoing series, it is inferred by means of induction that the probability will continue to hold for the future. In other words, it is inferred that in a future series of cases in which swans are observed, it is probable that every swan will be white. The foregoing still does not indicate what predictive knowledge is, aside from the knowledge that a frequency will continue to hold with a continuation of a series. More importantly, the idea that predictive knowledge is knowledge of a probability is subject to the same problem that rendered it impossible to know whether a single event will occur. It is still possible to imagine that a probability will not hold for the future. Thus, both the idea that predictive knowledge is knowledge of the occurrence of a single event and the idea that it is knowledge of a probability must be set aside for the time being.
There must be something that allows one to predict the future, something that will allow one to infer that a frequency will continue to hold for the future. In clarifying one of the objections to his theory of probability, Reichenbach makes reference to the general assertion that "frequent repetitions of similar events are subject to numerical regularities..." [3] and claims that it can only be established by means of a number of other inductive inferences. A justification of that assertion may very well be what grounds all predictive knowledge and allows one to make predictions. Its generality presupposes a form of regularity in nature, such that when any past frequency of a series of events is observed to be regular, it can be assumed that it will hold with a continuation of that series into the future. In other words, the assertion assumes that, given any series of similar events, if those events repeat frequently, then they are subject to numerical regularities; and if a series of events is subject to numerical regularities, then it follows that the frequency with which they occur will continue to hold for the future. For the general assertion implies more than the numerical regularity of frequencies in the past; it also implies the same regularity in the future. For example, the general probability statement, 'The probability for rolling a six on any die is one-sixth', includes the assumption not only that rolling a six has occurred with a certain frequency in the past and that this frequency has been numerically regular, but also that the frequency will continue to be regular in a future series of trials. However, the foregoing probability statement can be established only if all similar events occurring with a certain frequency occur in a numerically regular fashion. And this is where Reichenbach's general assertion comes in; it grounds all claims that include the assumption that a frequency will continue to hold for the future. The general assertion, then, can be used to derive statements that rest on the assumption that a certain frequency will continue to hold for the future. Thus, if anything is to count as predictive knowledge, it is knowledge that all frequent repetitions of similar events are subject to numerical regularities. To say that a frequent repetition of similar events is subject to numerical regularities is to say that the number of times these events occur out of a total remains consistent in a numerical fashion, and knowledge of this grounds predictions concerning the continuation of frequencies into the future, on the basis of their repetitions in the past.
Reichenbach considers two objections to his account of predictive knowledge. The first objection has to do with the fact that people ordinarily attribute probabilities to single events. He writes that, "It makes no sense to attach a degree of probability to an individual event, because one event is not capable of being measured by degrees", and so, "A statement about the probability of a single event is meaningless." [4] To illustrate the objection, consider the belief that there is a 98 per cent probability that a person with AIDS will die. What could this possibly mean? One appears to be attributing the probability of 98 per cent to a single event. But, if a probability is nothing more than a frequency of events, then this belief will be meaningless; for a victim of the AIDS virus will either die or not die, and so it would be nonsensical to suppose that he or she would die 98 percent of the time. The fact that probability statements about single events are meaningless generates a problem for Reichenbach's account, because many of our inferences concerning what will occur in the future rest upon the assumption that the probability of one event is greater than the probability of another. To deal with the problem, Reichenbach claims that,
| To speak of a meaning of probability for a single event is a harmless or even useful habit, because it leads to a correct evaluation of the future as soon as this language is translated into a statement about a series of events. [5] |
To translate language into a statement about a series of events requires what he calls a transference of meaning. He suggests that "The logician will also allow a man to speak. . .of a probability in a single case, and regard such mode of speech as representing a fictitious meaning. Using a technical term he speaks of a transfer of meaning from the general to the particular." [6] For example, a particular probability statement such as, 'There is a 99 per cent probability that the next swan will be white', is translated into a general probability statement such as, 'Given the class of all swans, the probability for observing white swans from that class is 99 per cent'. But the idea of a transference of meaning is not used just to rescue his account of predictive knowledge from the charge of being inapplicable to single events. There is this "correct evaluation" of the future of which Reichenbach speaks, which is somehow related to translating particular probability statements into general probability statements. It comes in two forms: First, it comes from the general probability statement that is used in the transference. According to Reichenbach, these general statements include the assumption that a frequency observed in the past will hold approximately for the future. This is supposedly one correct evaluation of the future. The other is that a general probability statement will also imply certain things about predictions regarding single events. Consider the general probability statement that expresses a probability of 99% for observing white swans from the entire class of swans. This statement implies that the prediction that the next swan will be white will be successful more often than the prediction that the next swan will not be white. Thus the transference of meaning from the particular to the general results in two correct evaluations of the future: The prediction that a frequency will continue to hold for the future and the assumption that a prediction of any single event (which is a member of a class of similar events, such as observing white swans) will be correct a certain number of times
The truth of a prediction about a single event is dependent upon the truth of a general probability statement, because, on the basis of the transference of meaning, they have the same meaning. Furthermore, a general probability statement can only be established by means of a justification of Reichenbach's general assertion, i.e., that frequent repetitions of similar events are subject to numerical regularities. Thus, this evaluation of the future of which Reichenbach speaks can be considered correct only if his general assertion is justified.
In summary, the first objection to Reichenbach's account is that, according to it, probability statements about single events are meaningless. The problem is solved by means of a transference of meaning from general probability statements to particular probability statements. Furthermore, the transference, according to Reichenbach, is beneficial because it leads to a correct evaluation of the future. The correct evaluation is of two sorts. First, a frequency will continue to hold for the future, and, secondly, the prediction of any single event belonging to a class of similar events will be correct a certain number of times out of a total. However, the correctness of both evaluations depends on a justification of Reichenbach's general assertion, because to justify the claim that a particular prediction will be successful a certain number of times requires knowing the truth of a general probability statement, and the truth of a general probability statement can only be justified by justifying his general assertion. What stands in the way of this sort of justification is the second objection.
The problem of induction, a major obstacle Reichenbach must surmount in order to develop his account of predictive knowledge, generates the second objection. It generates an objection, because making predictions, whether they are about single events, frequencies, or numerical regularities, requires the use of the inductive inference. The method of induction involves an inference from knowledge of the past to a prediction of what will hold for the future. The explanation for the emphasis placed upon Reichenbach's general assertion so far is that its justification is also a justification for induction. For to justify the extension of a frequency into the future, based upon the numerical regularity of that frequency in the past, requires a justification of the general assertion that all frequent repetitions of similar events are subject to numerical regularities. His description of the problem of induction runs as follows:
| It is true that for the frequency interpretation the degree of probability is a matter of experience and not of reason. . . .But the assertion that frequent repetitions of similar events are subject to numerical regularities can only be established by the use of inductive inferences and seems to involve a principle not derivable from experience. [7] |
Given the empiricist's requirement that induction
must be based upon experience, there is only one set of relevant experiences
available for establishing the assertion that frequent repetitions
of similar events are subject to numerical regularities. Those
experiences are past observations of cases where frequencies of
various sorts of events (e.g., those involving dice, coins,
swans, etc.,) were found to be regular. And from observations
of the foregoing sort it is inferred that any frequency
(whether past, present, or future) found to be regular will
continue to be so in the future. There is another way of
understanding the justification: induction has always been
successful in the past, and so one might infer that it will
continue to be successful in the future. The future success of
induction presupposes that frequencies will continue to be
regular. The problem with this justification is that the assertion that similar events are subject to numerical regularities presupposes that all frequencies (as opposed to just one frequency) found to be regular in the past will continue to be regular, and since "all frequencies" includes those in the future, the assertion can be said to contain a prediction. And this prediction is itself established by an inductive inference. Hence, the assertion whose justification would count as a justification of induction is justified by means of induction, which means that the assertion is used to justify itself. And this is a circular form of reasoning, because induction can only be justified by assuming that it is justified.
Reichenbach's way of dealing with the problem of induction rests on the idea of a posit. He maintains that, "The concept of the posit is the key to the understanding of predictive knowledge" [8] and a posit is, as he defines it, "a statement which we treat as true although we do not know whether it is so." [9] It has already been shown that predictive knowledge cannot involve knowing that a single event will occur in the future or that a frequency (or probability) will continue to hold for the future. It is no surprise that Reichenbach's general assertion is subject to the same objection drawn from the imagination. Just because the assertion may be regarded as the foundation of all predictive knowledge does not make it impervious to criticism. One can easily imagine that there is at least one frequent repetition that is not subject to numerical regularities. Consequently, since there is no guarantee for the truth of the general assertion and thus all other statements that make reference to the future, it becomes necessary to employ the idea of a posit and simply treat them as if they were true. The question is: Does the employment of the posit render it possible to solve the problem of induction and acquire knowledge of the future? Since his general assertion or any other predictive statement cannot be demonstrated to be true, and given the impossibility of demonstrating that induction will lead to true conclusions, Reichenbach argues that,
| It is different when the predictive conclusion is regarded as a posit. In this interpretation it does not require a proof that it is true; all that can be asked for is a proof that it is a good posit, or even the best posit available. Such a proof can be given, and the inductive problem can thus be solved. [10] |
Regarding a predictive conclusion as a posit is
definitely a far cry from claiming that it is true; for treating a
posit as if it were true does not require a justification for its truth,
whereas claiming that it is true does. In regarding a prediction as
a posit, and treating it as if it were true, its truth is simply
posited and not justified. However, in order to reap all the benefits
from the prediction a justification of some sort is still required;
the only difference is that it is not a justification for its truth,
but for the claim that it is a good posit. According to
Reichenbach, to prove that induction will lead to good posits,
as opposed to true conclusions, is to supply a justification for
induction. Furthermore, since the justification of induction is
also a justification for his general assertion, his solution to
the problem of induction will show that it is a good posit as well.
With this task ahead of him, he offers an analogy that supposedly
explains how induction is justified.
| The man who makes inductive inferences may be compared to a fisherman who casts a net into an unknown part of the ocean--he does not know whether he will catch fish, but he knows that if he wants to catch fish he has to cast his net. Every inductive prediction is like casting a net into the ocean of the happenings of nature; we do not know whether we shall have a good catch, but we try, at least, and try by the help of the best means available. . . .This justification of induction is simple; it shows that induction is the best means to attain a certain aim. The aim is predicting the future. [11] |
Casting a net into an ocean is analogous
to predicting either the occurrence of single events or the continuation
of a frequency. Just as we do not know whether we shall have a good
catch, we also do not know whether our predictions are or will be true.
Nonetheless, the inductive inference is used to make predictions,
not because there is a justification for the claim that it will lead
to true conclusions, but because it is the best method available.
Reichenbach is certainly correct in saying that his justification of
induction is simple. The justification is merely a pragmatic appeal:
Given, and only given, the goal of predicting the future, induction
is used because it is the best method available. This justification
is just a pragmatic reason for the employment of induction.
The surprising aspect of Reichenbach's solution to the problem of induction, or, for that matter, his entire account of predictive knowledge, is that contrary to what one might expect to result from an account of predictive knowledge, we do not actually have knowledge of future states of affairs. One does not know, for instance, that the next swan will be white or that in the next series of swans observed, ninety-nine per cent of them will be white. Predictive knowledge must be knowledge that induction is the best method a vailable for successfully predicting the future. Thus it must be the best method available for predicting that the next swan will be white or that ninety-nine per cent of the next series of swans observed will be white. Earlier it was assumed that it was the knowledge that frequent repetitions of similar events are subject to numerical regularities (i.e., Reichenbach's general assertion) that grounded all predictive knowledge and thus justified making predictions. It turns out that this knowledge is not attainable; it is the knowledge that induction is the best method available that supposedly justifies or allows the casting of predictions. And if induction is the best method available, then it becomes practical to posit the truth of his general assertion as well. Thus, there are two major results that follow from Reichenbach's account of predictive knowledge: First, there is no actual knowledge of future states of affairs, because there is no proof that induction will lead to true conclusions. And second, there can be no probability of a single event, because a statement about the probability of a single event is meaningless. However, there are two objections to Reichenbach's account.
Part II