Ghost Writer
7th May 2003, 09:41
Below is a paper I wrote regarding the problem of scientific induction, and how I believe it can be resolved. I happen to think that Marxists should listen closely when I discuss how a theory should be discarded in the presence of evidence that disconfirms the very theory that they continue to cling to, like a child who loves their blanky. Anyway, I thought someone might want to read my paper. By the way, I hold the copywrite, as I do with all my works. Don't get any ideas, James.
Abstract:
Hume’s problem of induction has raised some significant questions regarding the use of the scientific method to make general inferences about the world. The problem exists largely because Hume is applying deductive rules to a matter of induction. In any case, the problem exists because the scientist is assigning more information to the conclusion than is specifically stated in the problem. We must show that deduction applies to this type of argument, or that something warrants the inductive inference.
To apply the rules of deduction we must have one of two scenarios. First, we can either obtain perfect knowledge by gathering an infinite amount of evidence, which is obviously impossible. Secondly, we can assume that there are fundamental principles that dictate how the universe works, and then work to obtain the meaning behind those laws. If this can be done perhaps it is possible to use those postulates to fill in the holes of the argument to make it valid. The problem Hume has with the latter method is the imaginative nature of creating the assumptions and applying them as if they are true. Since this is the case, we must show these laws to be true. Only then will our inferences leave the realm of induction and achieve the level of deductive reasoning sought by Hume.
To answer this perplexing problem, I advance a theory of infinite regression that will allow our inferences to become less inductive in nature as the degree of certainty increases over time. To exemplify my theory, also shared by Laurence Bonjour, I use the analogy of mathematical modeling of specific systems to science as a model of the reality. Just as our models are refined to become more accurate at describing the systems we are interested in, science also shares this characteristic, as it becomes more accurate with time and constant data input.
I suggest that as the scientific process continues to improve with new discoveries, it has been demonstrated to yield spectacular results. If an excellent approximation of the truth is established, we may be close enough to the truth to extrapolate without a large margin of error. Perhaps we could even use empiricism to prove the truth of the propositions being used in the ampliative argument. When this happens the propositions will no longer be a matter on induction, we will have achieved deduction. More likely, is the discovery of the laws that govern the behavior of our universe. With these axioms we can then apply them to the logical structure, where before they were assumed. The effect will be to achieve a deterministic theory of science that allows us to leave behind the induction needed for current science to exist.
Background: The Problem of Induction as Proposed by David Hume
Clearly, all ideas that humanity believes with respect to the distant past, or the near future, are based on inductive arguments. What we have not directly experienced, we have no absolute way of knowing. These concepts of past and future must be based on inferences that can be drawn from our present experience, or on a general principle. Making broad generalizations based on our limited scope of knowledge is most definitely inductive in nature. Hume asks; what is the justification for scientific induction?
A problem arises out of Hume’s question, since arguments must be either inductive or deductive. Valid arguments only contain as much information in the conclusion, as was stated in the premises. Thus, to make generalizations about the future is invalid, since we can only draw from past or present experiences and observations to describe the future. Therefore, in making scientific predictions about the future, we must rely on the inductive argument. To warrant the use of an inductive argument in making scientific predictions, we must then rely on an inductive argument to describe the strength of the inference. This is often done by using the following argument:
Induction has worked in the past.
So, it will also work in the future.
The use of induction to describe induction is fallacious and begs the question. In fact, this was a specific attempt made by Max Black, among others. However, induction to justify induction has been criticized by many, as it avoids the very question proposed by Hume. This is where the dilemma comes into play, as we must look for better justification. This task has proven to be difficult for even the greatest scientists and philosophers in recent history.
Obviously, we use induction on a day to day basis. A common analogy used to describe the problem inherent in its use is laid out in the following form. By comparing man’s belief that past experience of the sun rising and setting warrants the belief that the sun will continue perform in this manner, to that of a turkey who has been fed by the farmer everyday in his life. The question is raised about whether or not the turkey is justified in believing that the farmer is coming to feed him on Thanksgiving Day. Although scientific induction requires more than a common sense approach, the same type of problem persists when employing it to arrive at general conclusions about the universe.
Hume believed that there were only two distinct ways to justify inductive reasoning, demonstrative and empiricism. In fact, Hume was a staunch advocate of empiricism. Hume thought that the demonstrative, or logic reasoning, method could only establish the truth of the premises. Similarly, experimental induction also fails to establish the truth about a conclusion, since the conclusion can never be observed indefinitely. Hence, the problem of the turkey still persists in scientific induction. If we care about the answer to Hume’s Problem of Induction, it seems that we have a serious problem in employing the many methods of science, because none of them can solve this perplexing paradox generated by a skeptic.
To shed further light on the problem Hume brought to the realm of scientific thinking, we must look at his view of the law of causality, which is one of the very axioms the all science is based on. Hume made the argument that no connection need exist between the cause and effect. As an empiricist he was inclined to believe that the relations between cause and effect could really only be justified empirically, and because of the problem of induction these relations could not justifiably be inferred. However, Hume thought the only connection that man has with knowledge rests in mathematics, that matters of fact are only ascribed to knowledge through the imagination. In other words, if using empiricism cannot warrant causal relations, our account of these causal connections rest on nothing more than a belief. Thus, Hume rejected the law of causality.
Thesis:
My answer to Hume includes aspects of coherence, and correspondence theories tied together in an effort to justify scientific induction through the use of infinite regression.
Outline of Procedure:
The paper will proceed as follows:
First, I discuss how Hume’s problem has been dismissed by many, as a pseudo-problem, and as an unfair question. Then I assert the importance of this question to those who believe in fundamental truths. I explain why the uniformity of nature argument breaks down, and why further explanation is needed to rectify the issues raised by Hume. Then the paper delves into similar arguments that rely on assumptions about the universe.
From there, I suggest that science is concerned with arriving at a deterministic view, a theory of everything. Hume’s rejection of the law of causality is discussed, as it pertains to the axiomatic truths sought after by scientists. The significance that these truths could have to achieving deterministic science is discussed. In addition, I include a discussion of how the current method has enabled us to derive many of the laws used in the scientific field.
An analogy of mathematical modeling is used to explain my theory of infinite regression. I discuss the idea of convergence, and state that science as a model allows us to get closer to the truth. Furthermore, I discuss the similarities between my thinking and Bonjour’s coherence and correspondence theory as an answer to Hume. I explain the three main parts outlined by Bonjour’s theory, especially the importance that new observations play the scientific model of the truth. This feedback and improvement cycle allows us to revise our approximation of the truth. Then, I offer my own interpretation, explaining how good science will yield approximations, which can be used to model outcomes that are not present in the original data. If this can be applied to reality, then it may not be fully necessary to obtain perfect information.
Finally, I argue that if our theory converges close to the actual truth, it may be possible to empirically arrive at axioms that can then be plugged back into the arguments, where before the premises have been hidden and assumed. The argument will then be deductively valid, and satisfy skeptics like Hume. Even if we never achieve the deductive argument sought by Hume, it can be shown that our use of induction will, in fact, make our science less inductive, as we arrive at new postulates that can be applied to further refine humanities version of the truth.
Argument:
Most people treat Hume’s problem as a non-issue, a pseudo-problem, not even deserving a second thought. They say that the rational basis of a belief is enough to warrant its use. To act otherwise would be to act irrationally. Most disturbing about this evasive answer to Hume is that many scientists subscribe to this school of thought. Many scientists do not care to concern themselves with this kind of epistemological problem, as they get paid either way, and their assumptions have led to many practical applications. This is troubling because good scientists should not pull their theories out of thin air. They should have reasons for the conclusions, as should everybody. In fact, often times their reasoning is sound, even though they do not explain the basis for their inductive leap. Perhaps they have been indoctrinated with a contemporary view that has worked well enough for their purposes, and the result of their work leaves them satisfied.
There have been many people who have tried to explain the very tenants needed to make induction valid in a deductive sense. Since inductive inferences remain ampliative, meaning the conclusion carries more information than the premises, a presupposition must be assumed in order to validate the inferential argument. This method requires that we make certain assumptions about nature. The most popular version of this is the uniformity of nature, promoted by John Stuart Mill. The argument then takes the following form:
All observable samples take the form X
Future will follow past observations
Therefore, all future sample will take the form X
This answer requires some sweeping assumptions, as there is no reason to assume that because something behaves a certain way in the past it will continue to behave that way in the future. The problem with this implied premise rests in its dogmatic nature. Nothing more than a belief holds this argument together. A belief in nature’s uniformity does not prove the merit of the argument. In order to use uniformity of nature as the basis for induction, we must prove its truth or accept it solely on belief. Thus, the uniformity of nature is not sufficient to answer Hume’s problem of induction. We need further explanation.
Perhaps we could get around the problems inherent within the uniformity of nature by discovering the nature of the laws that govern the behavior of the universe. If we knew what created this apparent uniformity, then we could plug these axioms back into the formerly inductive argument to create a new argument that is both valid and true. In addition, we would also know where this behavior deviated, and we could then avoid the dilemma that the turkey finds himself in on Thanksgiving Day.
Surely, it is the goal of the pure scientist to derive truths that will clarify our view of reality. In fact, the very nature of science has been to provide a fundamental “theory of everything”. Quoting Dewey B. Larson:
“In a significant sense the ideal of science is a single set of principles, or perhaps a set of mathematical equations, from which all the vast process and structure of nature could be deduced.”
For example, the search for a unified field theory, and work on the super-string theory are testaments to this goal. It is believed, by many, that such universal principles do exist, whether it is the Law of Causality or Scientific Materialism. The sooner we describe all the necessary axioms for such a theory, the sooner skeptics like David Hume can be silenced.
Hume rejected probably one of the most important postulates relied upon by all scientists. He rejected the Law of Causality. The rejection of such a fundamental postulate of science seems to defy the very idea of an objective reality. Common sense tells us that there are laws that govern the behavior of the universe. Many philosophers think that objective reality is independent of man’s conception, although it can be arrived at through the rational operations of the mind. Is this idea reasonable? Sure. Is there reason to believe that humans might reason their way to the wrong answer? Absolutely. It is the job of science to verify the degree to which these rational assumptions hold true to in the real world.
Prior to taking An Introduction to Logic and The Scientific Method, I was discussing the concept of infinity with one of my peers. I wrote the following:
There is an upward limit on the amount of truth that man is able to obtain over the course of its existence in the universe. That much I concede. However, infinite truth is hardly something that can be derived, simply because the possibilities seem endless to a species with our intellectual capacity.
I submit that the level of attainable knowledge in the universe is such that if a numerical value could be placed on it, that number would appear very large. With this you must look at man's ability to derive truths and make discoveries when it comes to the universe. This is the rate-limiting step that disables man for reaching that bound. So you see the amount of knowledge that our limited minds can compile or store will never achieve the amount of truth or knowledge that the universe holds. Even if our civilization did progress to a higher order species, the absolute value of the knowledge achievable would remain an asymptote. We could get closer and closer to that value without truly achieving it.
Although I had never heard of the problem of induction at that time, it seems that I came rather close to the one of the better answers to Hume’s challenge. There exist two ways to answer Hume’s problem. The choices remain to either gather all possible knowledge in the universe, or to find the assumed premises that allowed the conclusion to be made in a manner consistent with deductive logic. My argument of infinite regression provides the best compromise of the two possible answers.
If by employing scientific induction we can generate the axioms that account for the missing premises needed to take a previously ampliative argument to the level of a deductive argument, is their not evidence enough to justify scientific induction? What about the utility of being able to take empirical data, reason to a theory that provides some outcome, which is independent of the original evidence, and the derive knew knowledge? Isn’t induction then justified, as it has provided a new approximation of the truth?
In fact, the method of scientific inference that we currently use has brought us laws of nature, physics, astronomy, and chemistry, which explain certain phenomenon with a large degree of accuracy. Do these laws always account for the behavior of systems in all cases? No, they do not. Surely, scientists have not found all the laws of nature that exist in the world. In fact, our view is still rather limited, and these laws must be applied to the various fields separately, in many cases. The search for the theory that will allow us to tie it all together continues.
The beautiful symmetry that the universe exhibits is too large of a coincidence for any argument against regularity of the universe, the law of causality, or scientific materialism to be seriously applied. After all, it would be ludicrous to deny the existence of this reality, as it would fly in the face of our experience of the world. If reality exists, there must be some framework for it. The purpose of science is to discover the rules that govern our universe, so we can more accurately describe it, and predict outcomes.
Assume that a belief in fundamental truth and the law of nature is a reasonable assumption to make. If this is true, it can be said that there are mathematical functions that represents the behavior of the universe, given these fundamental constraints. In calculus, we use many methods of approximating functions. For example, a very complicated function, or unknown function that represents some behavior can be approximated using sequences and series, namely Taylor and Maclaurin series. These sequences and series are represented in polynomial forms since they are relatively easy to work with. The higher order the degree of polynomial used, the more closely it will approximate the function. When the Taylor series approaches the functions with a reasonably small margin of error, the series is said to converge with the function. Our formation of the truth through scientific induction follows the same pattern of convergence, as the mathematical model to the behavior of a specific system. This is the basis of my argument, which agrees with Laurence Bonjour’s theory. My answer to Hume includes aspects of coherence, and correspondence theories tied together in an effort to justify scientific induction through the use of infinite regression.
To continue, Bonjour’s theory has three parts to it. He believes that an infinite regression of human knowledge can lead to a good approximation of reality, and that those sets of values that fail to converge in reality should be discarded. Thus, Bonjour subscribed to a correspondence theory. This is evident, because of his stipulation that belief systems can only be defended in as far as they begin to converge with ultimate reality over time. This is similar to the type of behavior described in the preceding paragraph.
In addition to his view that theories should converge with the real world observations, Bonjour had another important rule for inductive reasoning. Theory must remain coherent over the long run. That is, the likelihood of convergence is increased with coherence over time.
However, there remains a third condition. There is an observation requirement placed on belief systems that demonstrate the first two characteristics. This requirement states that it is necessary for theories that converge and are coherent to be based on empirical data. The data will have a stabilizing effect. The stabilization is achieved by continuously feeding data to the theory. More data will produce anomalies that will require one to rethink their theories. The picture will become clearer, and a more refined version of the truth can be obtained. As this process continues over time, the belief system will begin converging with the real world account of what is happening. Figure 1 exemplifies the real world application of this observational requirement.
Figure 1
A marvelous account of this very type of regression, of fitting models to more accurately represent the truth of the situation is seen in the development the cubic equations of state. In thermodynamics, Boyle’s and others produced a useful method of keeping one or more variables constant while measuring the effects of changing just one of the variables. This was applied to gasses and led to a very important relationship between temperature, pressure, and volume, known as the ideal gas law. From this relationship the kinetic theory of gasses was developed, which describes how kinetic energy relates to the absolute temperature of the system. From the assumptions made by this theory an explanation for the phenomenon observed by Boyles was developed. Finally, deviations from ideal gas behavior could be predicted, and new models that more accurately describe gasses at higher temperatures and higher pressures could be developed. Primitive equations of state were again revised when chemical engineers ran into trouble with those models. Hence cubic equations of state were developed, and are used in many of the applications that better humanities outlook in the world. Certainly, the advances in processing, and the new technologies that have been derived from their application, will lead to new problems that must be dealt with. When these situations are encountered, the data will be used to produce an even better model. This same sort of regression is happening in all of the physical sciences. The justification can also be measured in the result it has had on our prospects of the world.
In general, scientists collect data. Those pieces of information are plotted on a graph as points. A linear or logarithmic plot can then be fitted to the data. This is used as a model. The less data a person has the less likely they are to produce a model that will allow them to interpolate and extrapolate. If a person has gathered a large amount of data, and have used appropriate methods to collect that information, the more accurate they will be when they try to estimate values not specifically given by the data.
The degree to which a scientist is warranted in making inferences from their model rests in the accuracy, amount, and usefulness of their data. The same can be said for scientific induction, in a general sense.
Suppose we were to apply a very similar example to science in general. Clearly, the more we know the better our approximation of the truth will become. Ultimately, we may reach a point where our approximation converges so well, that we can say that we have arrived at the truth, although this process must be carried off infinitely in order to achieve that actual state. This is precisely the asymptotic behavior that was discussed by me when I was addressing infinite knowledge with my friend, and it accounts for my reasons in developing a theory that agrees heavily with Laurence Bonjour’s coherence justification for induction. Although we may never actually achieve perfect knowledge, the faith scientists have in science may lead us to those very axioms that have made science less inductive in the past.
Conclusion:
In conclusion, think of humanity's current view of the world as the fuzzy picture a sleeping person experiences as he first awakens from a slumber. Over time consciousness is elevated and the person’s sight becomes more enhanced. I would argue that this is precisely the sort of awakening that science has enable humanity to undergo through the use of science. Since the scientific method was first advanced we have seen a constant regression of the data, and the theories, which result from the manipulation of the data. Old theories have given way to better explanations of reality. As a result, we have benefited from a wider range of view throughout the universe, both on a macro scale and on a micro scale. Reality has become less fuzzy, as we clarify the lens through which we view the world. Therefore, the regression process discussed in this paper is shown to work.
If this process is allowed to repeat infinitely, it could lead to a close approximation of the truth, where the fundamental axioms previously assumed can be proven empirically. Such knowledge would make scientific induction, scientific deduction. Does this mean that we have answered Hume’s problem of induction? No, because we are still dependent upon induction for scientific logic. Only time will tell, whether or not our theories will ultimately converge with reality. From the exponential rate which humanities ability to derive truths grows, all indications point to the possibility of we will one day unlock the secrets of the universe.
Even if we never complete the entire picture, there exists a very pragmatic use for the scientific method of knowledge seeking. The results in the past four centuries alone can attest to this fact. Should we be bothered by what seems to be a critical paradox within our modern epistemology? Yes, in fact, this very problem constitutes the driving force behind science. We long for perfect knowledge; therefore we must use the current means in an effort to achieve that ideal state. If this state is ever achieved, Hume’s problem will have been solved, because there will no longer any need for induction. We will then be able to define all the logical premises necessary to arrive at a certain conclusion, without making any assumptions. Furthermore, it will have been demonstrated that induction was warranted because through it we were able to achieve the deductive arguments that Hume seemed unreasonable for demanding of the scientific method.
Scientists are hot on the trail of the fundamental postulates that could provide the sought after deterministic framework of our reality, at least as it applies to matter and the make-up of the universe. As far as the soft sciences (fields like history, sociology, political science) go, there is much work to be done. Perhaps it will never be possible to fully account for all behaviors in all cases, especially when that tricky free-will variable plays a role in the system. However, I would argue that the utility of this theory alone provides its own justification for its use.
Summary:
David Hume’s problem of induction is a difficult paradox to resolve. Various attempts to shrug him off have failed, as the problem persists to this day. I believe that I have found a way to rectify the issues created by Hume’s skepticism. In searching for the answer to one of life’s conundrums, I came across a man whose thinking closely resembled mine. Laurence Bonjour developed a system of coherence and correspondence that compliments what I call the infinite regression model of truth. This theory explains how induction can lead to continually updating the basic framework of science, and over time it will essentially converge with the reality that exists independent of human senses. In this occurrence, our approximation of the truth will be so close to reality, that it should be possible to derive the axioms needed for a deterministic scientific theory that will avoid all the problems of induction. Through this cycle of infinite regression we may arrive at deduction, though an inductive process. This can only happen through an extremely large amount of time and effort, so the problem has not been successfully solved. However, the pragmatic justification alone is enough reason to continue using the various tools generated through the past use of the scientific method. It would be absurd to scrap something that has worked so well.
References:
1.) Goodman, Lenn E. In Defense of Truth: A Pluralistic Approach. Humanity Books, 2002
2.) Giancoli Douglas C. Physics for Scientists and Engineers. 3rd Ed, Prentice Hall, 2000
3.) Smith, Ness, and Abbott. Chemical Engineering Thermodynamics. 6th Ed, McGraw-Hill, 2001
4.) Kitchner, Richard F. The Conduct of Inquiry: An Introduction to Logic and Scientific Method. University Press of America, 1999
5.) Larson, Dewey B. Reciprical System of Theory. http.//www.reciprocalsystem.com/spu/spums2.htm
6.) The Problem of Induction. http.//www.cs.okstate.edu/~marcin/kp/phil151_f98/notes/10Induction.html
7.) Bonjour’s Metajustificatory Argument. http.//members.primary.net/~gmarshals/bonjour.htm
(Edited by Ghost Writer at 9:53 am on May 7, 2003)
Abstract:
Hume’s problem of induction has raised some significant questions regarding the use of the scientific method to make general inferences about the world. The problem exists largely because Hume is applying deductive rules to a matter of induction. In any case, the problem exists because the scientist is assigning more information to the conclusion than is specifically stated in the problem. We must show that deduction applies to this type of argument, or that something warrants the inductive inference.
To apply the rules of deduction we must have one of two scenarios. First, we can either obtain perfect knowledge by gathering an infinite amount of evidence, which is obviously impossible. Secondly, we can assume that there are fundamental principles that dictate how the universe works, and then work to obtain the meaning behind those laws. If this can be done perhaps it is possible to use those postulates to fill in the holes of the argument to make it valid. The problem Hume has with the latter method is the imaginative nature of creating the assumptions and applying them as if they are true. Since this is the case, we must show these laws to be true. Only then will our inferences leave the realm of induction and achieve the level of deductive reasoning sought by Hume.
To answer this perplexing problem, I advance a theory of infinite regression that will allow our inferences to become less inductive in nature as the degree of certainty increases over time. To exemplify my theory, also shared by Laurence Bonjour, I use the analogy of mathematical modeling of specific systems to science as a model of the reality. Just as our models are refined to become more accurate at describing the systems we are interested in, science also shares this characteristic, as it becomes more accurate with time and constant data input.
I suggest that as the scientific process continues to improve with new discoveries, it has been demonstrated to yield spectacular results. If an excellent approximation of the truth is established, we may be close enough to the truth to extrapolate without a large margin of error. Perhaps we could even use empiricism to prove the truth of the propositions being used in the ampliative argument. When this happens the propositions will no longer be a matter on induction, we will have achieved deduction. More likely, is the discovery of the laws that govern the behavior of our universe. With these axioms we can then apply them to the logical structure, where before they were assumed. The effect will be to achieve a deterministic theory of science that allows us to leave behind the induction needed for current science to exist.
Background: The Problem of Induction as Proposed by David Hume
Clearly, all ideas that humanity believes with respect to the distant past, or the near future, are based on inductive arguments. What we have not directly experienced, we have no absolute way of knowing. These concepts of past and future must be based on inferences that can be drawn from our present experience, or on a general principle. Making broad generalizations based on our limited scope of knowledge is most definitely inductive in nature. Hume asks; what is the justification for scientific induction?
A problem arises out of Hume’s question, since arguments must be either inductive or deductive. Valid arguments only contain as much information in the conclusion, as was stated in the premises. Thus, to make generalizations about the future is invalid, since we can only draw from past or present experiences and observations to describe the future. Therefore, in making scientific predictions about the future, we must rely on the inductive argument. To warrant the use of an inductive argument in making scientific predictions, we must then rely on an inductive argument to describe the strength of the inference. This is often done by using the following argument:
Induction has worked in the past.
So, it will also work in the future.
The use of induction to describe induction is fallacious and begs the question. In fact, this was a specific attempt made by Max Black, among others. However, induction to justify induction has been criticized by many, as it avoids the very question proposed by Hume. This is where the dilemma comes into play, as we must look for better justification. This task has proven to be difficult for even the greatest scientists and philosophers in recent history.
Obviously, we use induction on a day to day basis. A common analogy used to describe the problem inherent in its use is laid out in the following form. By comparing man’s belief that past experience of the sun rising and setting warrants the belief that the sun will continue perform in this manner, to that of a turkey who has been fed by the farmer everyday in his life. The question is raised about whether or not the turkey is justified in believing that the farmer is coming to feed him on Thanksgiving Day. Although scientific induction requires more than a common sense approach, the same type of problem persists when employing it to arrive at general conclusions about the universe.
Hume believed that there were only two distinct ways to justify inductive reasoning, demonstrative and empiricism. In fact, Hume was a staunch advocate of empiricism. Hume thought that the demonstrative, or logic reasoning, method could only establish the truth of the premises. Similarly, experimental induction also fails to establish the truth about a conclusion, since the conclusion can never be observed indefinitely. Hence, the problem of the turkey still persists in scientific induction. If we care about the answer to Hume’s Problem of Induction, it seems that we have a serious problem in employing the many methods of science, because none of them can solve this perplexing paradox generated by a skeptic.
To shed further light on the problem Hume brought to the realm of scientific thinking, we must look at his view of the law of causality, which is one of the very axioms the all science is based on. Hume made the argument that no connection need exist between the cause and effect. As an empiricist he was inclined to believe that the relations between cause and effect could really only be justified empirically, and because of the problem of induction these relations could not justifiably be inferred. However, Hume thought the only connection that man has with knowledge rests in mathematics, that matters of fact are only ascribed to knowledge through the imagination. In other words, if using empiricism cannot warrant causal relations, our account of these causal connections rest on nothing more than a belief. Thus, Hume rejected the law of causality.
Thesis:
My answer to Hume includes aspects of coherence, and correspondence theories tied together in an effort to justify scientific induction through the use of infinite regression.
Outline of Procedure:
The paper will proceed as follows:
First, I discuss how Hume’s problem has been dismissed by many, as a pseudo-problem, and as an unfair question. Then I assert the importance of this question to those who believe in fundamental truths. I explain why the uniformity of nature argument breaks down, and why further explanation is needed to rectify the issues raised by Hume. Then the paper delves into similar arguments that rely on assumptions about the universe.
From there, I suggest that science is concerned with arriving at a deterministic view, a theory of everything. Hume’s rejection of the law of causality is discussed, as it pertains to the axiomatic truths sought after by scientists. The significance that these truths could have to achieving deterministic science is discussed. In addition, I include a discussion of how the current method has enabled us to derive many of the laws used in the scientific field.
An analogy of mathematical modeling is used to explain my theory of infinite regression. I discuss the idea of convergence, and state that science as a model allows us to get closer to the truth. Furthermore, I discuss the similarities between my thinking and Bonjour’s coherence and correspondence theory as an answer to Hume. I explain the three main parts outlined by Bonjour’s theory, especially the importance that new observations play the scientific model of the truth. This feedback and improvement cycle allows us to revise our approximation of the truth. Then, I offer my own interpretation, explaining how good science will yield approximations, which can be used to model outcomes that are not present in the original data. If this can be applied to reality, then it may not be fully necessary to obtain perfect information.
Finally, I argue that if our theory converges close to the actual truth, it may be possible to empirically arrive at axioms that can then be plugged back into the arguments, where before the premises have been hidden and assumed. The argument will then be deductively valid, and satisfy skeptics like Hume. Even if we never achieve the deductive argument sought by Hume, it can be shown that our use of induction will, in fact, make our science less inductive, as we arrive at new postulates that can be applied to further refine humanities version of the truth.
Argument:
Most people treat Hume’s problem as a non-issue, a pseudo-problem, not even deserving a second thought. They say that the rational basis of a belief is enough to warrant its use. To act otherwise would be to act irrationally. Most disturbing about this evasive answer to Hume is that many scientists subscribe to this school of thought. Many scientists do not care to concern themselves with this kind of epistemological problem, as they get paid either way, and their assumptions have led to many practical applications. This is troubling because good scientists should not pull their theories out of thin air. They should have reasons for the conclusions, as should everybody. In fact, often times their reasoning is sound, even though they do not explain the basis for their inductive leap. Perhaps they have been indoctrinated with a contemporary view that has worked well enough for their purposes, and the result of their work leaves them satisfied.
There have been many people who have tried to explain the very tenants needed to make induction valid in a deductive sense. Since inductive inferences remain ampliative, meaning the conclusion carries more information than the premises, a presupposition must be assumed in order to validate the inferential argument. This method requires that we make certain assumptions about nature. The most popular version of this is the uniformity of nature, promoted by John Stuart Mill. The argument then takes the following form:
All observable samples take the form X
Future will follow past observations
Therefore, all future sample will take the form X
This answer requires some sweeping assumptions, as there is no reason to assume that because something behaves a certain way in the past it will continue to behave that way in the future. The problem with this implied premise rests in its dogmatic nature. Nothing more than a belief holds this argument together. A belief in nature’s uniformity does not prove the merit of the argument. In order to use uniformity of nature as the basis for induction, we must prove its truth or accept it solely on belief. Thus, the uniformity of nature is not sufficient to answer Hume’s problem of induction. We need further explanation.
Perhaps we could get around the problems inherent within the uniformity of nature by discovering the nature of the laws that govern the behavior of the universe. If we knew what created this apparent uniformity, then we could plug these axioms back into the formerly inductive argument to create a new argument that is both valid and true. In addition, we would also know where this behavior deviated, and we could then avoid the dilemma that the turkey finds himself in on Thanksgiving Day.
Surely, it is the goal of the pure scientist to derive truths that will clarify our view of reality. In fact, the very nature of science has been to provide a fundamental “theory of everything”. Quoting Dewey B. Larson:
“In a significant sense the ideal of science is a single set of principles, or perhaps a set of mathematical equations, from which all the vast process and structure of nature could be deduced.”
For example, the search for a unified field theory, and work on the super-string theory are testaments to this goal. It is believed, by many, that such universal principles do exist, whether it is the Law of Causality or Scientific Materialism. The sooner we describe all the necessary axioms for such a theory, the sooner skeptics like David Hume can be silenced.
Hume rejected probably one of the most important postulates relied upon by all scientists. He rejected the Law of Causality. The rejection of such a fundamental postulate of science seems to defy the very idea of an objective reality. Common sense tells us that there are laws that govern the behavior of the universe. Many philosophers think that objective reality is independent of man’s conception, although it can be arrived at through the rational operations of the mind. Is this idea reasonable? Sure. Is there reason to believe that humans might reason their way to the wrong answer? Absolutely. It is the job of science to verify the degree to which these rational assumptions hold true to in the real world.
Prior to taking An Introduction to Logic and The Scientific Method, I was discussing the concept of infinity with one of my peers. I wrote the following:
There is an upward limit on the amount of truth that man is able to obtain over the course of its existence in the universe. That much I concede. However, infinite truth is hardly something that can be derived, simply because the possibilities seem endless to a species with our intellectual capacity.
I submit that the level of attainable knowledge in the universe is such that if a numerical value could be placed on it, that number would appear very large. With this you must look at man's ability to derive truths and make discoveries when it comes to the universe. This is the rate-limiting step that disables man for reaching that bound. So you see the amount of knowledge that our limited minds can compile or store will never achieve the amount of truth or knowledge that the universe holds. Even if our civilization did progress to a higher order species, the absolute value of the knowledge achievable would remain an asymptote. We could get closer and closer to that value without truly achieving it.
Although I had never heard of the problem of induction at that time, it seems that I came rather close to the one of the better answers to Hume’s challenge. There exist two ways to answer Hume’s problem. The choices remain to either gather all possible knowledge in the universe, or to find the assumed premises that allowed the conclusion to be made in a manner consistent with deductive logic. My argument of infinite regression provides the best compromise of the two possible answers.
If by employing scientific induction we can generate the axioms that account for the missing premises needed to take a previously ampliative argument to the level of a deductive argument, is their not evidence enough to justify scientific induction? What about the utility of being able to take empirical data, reason to a theory that provides some outcome, which is independent of the original evidence, and the derive knew knowledge? Isn’t induction then justified, as it has provided a new approximation of the truth?
In fact, the method of scientific inference that we currently use has brought us laws of nature, physics, astronomy, and chemistry, which explain certain phenomenon with a large degree of accuracy. Do these laws always account for the behavior of systems in all cases? No, they do not. Surely, scientists have not found all the laws of nature that exist in the world. In fact, our view is still rather limited, and these laws must be applied to the various fields separately, in many cases. The search for the theory that will allow us to tie it all together continues.
The beautiful symmetry that the universe exhibits is too large of a coincidence for any argument against regularity of the universe, the law of causality, or scientific materialism to be seriously applied. After all, it would be ludicrous to deny the existence of this reality, as it would fly in the face of our experience of the world. If reality exists, there must be some framework for it. The purpose of science is to discover the rules that govern our universe, so we can more accurately describe it, and predict outcomes.
Assume that a belief in fundamental truth and the law of nature is a reasonable assumption to make. If this is true, it can be said that there are mathematical functions that represents the behavior of the universe, given these fundamental constraints. In calculus, we use many methods of approximating functions. For example, a very complicated function, or unknown function that represents some behavior can be approximated using sequences and series, namely Taylor and Maclaurin series. These sequences and series are represented in polynomial forms since they are relatively easy to work with. The higher order the degree of polynomial used, the more closely it will approximate the function. When the Taylor series approaches the functions with a reasonably small margin of error, the series is said to converge with the function. Our formation of the truth through scientific induction follows the same pattern of convergence, as the mathematical model to the behavior of a specific system. This is the basis of my argument, which agrees with Laurence Bonjour’s theory. My answer to Hume includes aspects of coherence, and correspondence theories tied together in an effort to justify scientific induction through the use of infinite regression.
To continue, Bonjour’s theory has three parts to it. He believes that an infinite regression of human knowledge can lead to a good approximation of reality, and that those sets of values that fail to converge in reality should be discarded. Thus, Bonjour subscribed to a correspondence theory. This is evident, because of his stipulation that belief systems can only be defended in as far as they begin to converge with ultimate reality over time. This is similar to the type of behavior described in the preceding paragraph.
In addition to his view that theories should converge with the real world observations, Bonjour had another important rule for inductive reasoning. Theory must remain coherent over the long run. That is, the likelihood of convergence is increased with coherence over time.
However, there remains a third condition. There is an observation requirement placed on belief systems that demonstrate the first two characteristics. This requirement states that it is necessary for theories that converge and are coherent to be based on empirical data. The data will have a stabilizing effect. The stabilization is achieved by continuously feeding data to the theory. More data will produce anomalies that will require one to rethink their theories. The picture will become clearer, and a more refined version of the truth can be obtained. As this process continues over time, the belief system will begin converging with the real world account of what is happening. Figure 1 exemplifies the real world application of this observational requirement.
Figure 1
A marvelous account of this very type of regression, of fitting models to more accurately represent the truth of the situation is seen in the development the cubic equations of state. In thermodynamics, Boyle’s and others produced a useful method of keeping one or more variables constant while measuring the effects of changing just one of the variables. This was applied to gasses and led to a very important relationship between temperature, pressure, and volume, known as the ideal gas law. From this relationship the kinetic theory of gasses was developed, which describes how kinetic energy relates to the absolute temperature of the system. From the assumptions made by this theory an explanation for the phenomenon observed by Boyles was developed. Finally, deviations from ideal gas behavior could be predicted, and new models that more accurately describe gasses at higher temperatures and higher pressures could be developed. Primitive equations of state were again revised when chemical engineers ran into trouble with those models. Hence cubic equations of state were developed, and are used in many of the applications that better humanities outlook in the world. Certainly, the advances in processing, and the new technologies that have been derived from their application, will lead to new problems that must be dealt with. When these situations are encountered, the data will be used to produce an even better model. This same sort of regression is happening in all of the physical sciences. The justification can also be measured in the result it has had on our prospects of the world.
In general, scientists collect data. Those pieces of information are plotted on a graph as points. A linear or logarithmic plot can then be fitted to the data. This is used as a model. The less data a person has the less likely they are to produce a model that will allow them to interpolate and extrapolate. If a person has gathered a large amount of data, and have used appropriate methods to collect that information, the more accurate they will be when they try to estimate values not specifically given by the data.
The degree to which a scientist is warranted in making inferences from their model rests in the accuracy, amount, and usefulness of their data. The same can be said for scientific induction, in a general sense.
Suppose we were to apply a very similar example to science in general. Clearly, the more we know the better our approximation of the truth will become. Ultimately, we may reach a point where our approximation converges so well, that we can say that we have arrived at the truth, although this process must be carried off infinitely in order to achieve that actual state. This is precisely the asymptotic behavior that was discussed by me when I was addressing infinite knowledge with my friend, and it accounts for my reasons in developing a theory that agrees heavily with Laurence Bonjour’s coherence justification for induction. Although we may never actually achieve perfect knowledge, the faith scientists have in science may lead us to those very axioms that have made science less inductive in the past.
Conclusion:
In conclusion, think of humanity's current view of the world as the fuzzy picture a sleeping person experiences as he first awakens from a slumber. Over time consciousness is elevated and the person’s sight becomes more enhanced. I would argue that this is precisely the sort of awakening that science has enable humanity to undergo through the use of science. Since the scientific method was first advanced we have seen a constant regression of the data, and the theories, which result from the manipulation of the data. Old theories have given way to better explanations of reality. As a result, we have benefited from a wider range of view throughout the universe, both on a macro scale and on a micro scale. Reality has become less fuzzy, as we clarify the lens through which we view the world. Therefore, the regression process discussed in this paper is shown to work.
If this process is allowed to repeat infinitely, it could lead to a close approximation of the truth, where the fundamental axioms previously assumed can be proven empirically. Such knowledge would make scientific induction, scientific deduction. Does this mean that we have answered Hume’s problem of induction? No, because we are still dependent upon induction for scientific logic. Only time will tell, whether or not our theories will ultimately converge with reality. From the exponential rate which humanities ability to derive truths grows, all indications point to the possibility of we will one day unlock the secrets of the universe.
Even if we never complete the entire picture, there exists a very pragmatic use for the scientific method of knowledge seeking. The results in the past four centuries alone can attest to this fact. Should we be bothered by what seems to be a critical paradox within our modern epistemology? Yes, in fact, this very problem constitutes the driving force behind science. We long for perfect knowledge; therefore we must use the current means in an effort to achieve that ideal state. If this state is ever achieved, Hume’s problem will have been solved, because there will no longer any need for induction. We will then be able to define all the logical premises necessary to arrive at a certain conclusion, without making any assumptions. Furthermore, it will have been demonstrated that induction was warranted because through it we were able to achieve the deductive arguments that Hume seemed unreasonable for demanding of the scientific method.
Scientists are hot on the trail of the fundamental postulates that could provide the sought after deterministic framework of our reality, at least as it applies to matter and the make-up of the universe. As far as the soft sciences (fields like history, sociology, political science) go, there is much work to be done. Perhaps it will never be possible to fully account for all behaviors in all cases, especially when that tricky free-will variable plays a role in the system. However, I would argue that the utility of this theory alone provides its own justification for its use.
Summary:
David Hume’s problem of induction is a difficult paradox to resolve. Various attempts to shrug him off have failed, as the problem persists to this day. I believe that I have found a way to rectify the issues created by Hume’s skepticism. In searching for the answer to one of life’s conundrums, I came across a man whose thinking closely resembled mine. Laurence Bonjour developed a system of coherence and correspondence that compliments what I call the infinite regression model of truth. This theory explains how induction can lead to continually updating the basic framework of science, and over time it will essentially converge with the reality that exists independent of human senses. In this occurrence, our approximation of the truth will be so close to reality, that it should be possible to derive the axioms needed for a deterministic scientific theory that will avoid all the problems of induction. Through this cycle of infinite regression we may arrive at deduction, though an inductive process. This can only happen through an extremely large amount of time and effort, so the problem has not been successfully solved. However, the pragmatic justification alone is enough reason to continue using the various tools generated through the past use of the scientific method. It would be absurd to scrap something that has worked so well.
References:
1.) Goodman, Lenn E. In Defense of Truth: A Pluralistic Approach. Humanity Books, 2002
2.) Giancoli Douglas C. Physics for Scientists and Engineers. 3rd Ed, Prentice Hall, 2000
3.) Smith, Ness, and Abbott. Chemical Engineering Thermodynamics. 6th Ed, McGraw-Hill, 2001
4.) Kitchner, Richard F. The Conduct of Inquiry: An Introduction to Logic and Scientific Method. University Press of America, 1999
5.) Larson, Dewey B. Reciprical System of Theory. http.//www.reciprocalsystem.com/spu/spums2.htm
6.) The Problem of Induction. http.//www.cs.okstate.edu/~marcin/kp/phil151_f98/notes/10Induction.html
7.) Bonjour’s Metajustificatory Argument. http.//members.primary.net/~gmarshals/bonjour.htm
(Edited by Ghost Writer at 9:53 am on May 7, 2003)