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Our second assignment was entitled "Problems with Induction", and we were required to answer a number of questions related to the philosophical view known as inductivism, which holds that scientific laws and theories can be derived from facts or observational evidence using inductive reasoning. The questions make specific reference to the work of David Hume1 and Henry Goodman2 (see notes at the end of this article). I have also provided the answers to two of the questions originally posed in assignment 1 concerning naïve inductivism and teleological explanations, because I feel they are both more relevant to this article. I list each of the questions below, followed by my answers:
Why did Hume think that belief in a causal relation was the basis of induction?
"Hume was essentially saying that there is no logical reason to suppose that two events are connected. For example, we can observe an effect that always seems to occur at the same time some other event is taking place. So (for example) we experience the fact that the Earth and objects on it warm up during periods when the Sun is out. We also experience the fact that the opposite also occurs, i.e. that the Earth and objects on it cool down when the Sun goes in.
Hume says that there is no logical reason to assume that this will happen. In other words, had we not experienced these warming and cooling effects, there would be logical reason to suppose that the presence of the Sun in the sky would have any effect at all on the temperature of the Earth and the objects on it.
Hume distinguishes between propositions that concern relations of ideas and those that concern matters of fact. For example, the statement 'bachelors are unmarried' defines one aspect of the relationship between two states - being married, and being single. A bachelor is, by definition, unmarried of course. This statement tells us nothing, however, about the real world. We can derive the fact that a bachelor is not married by applying logic, because we understand the concepts of marriage and bachelorhood. The same cannot be said for the 'matters of fact' Hume refers to, which tell us something about the world, like 'snow is white'.
The assumption we made above (that the Sun warms the Earth) is based upon observation only. It does not arise as the result of logical deduction. The ideas involved (of the sun being in the sky and the Earth warming up) are not logically related, and therefore the proposition (that the Sun warms the Earth) is not logically provable through deduction. The only basis for our belief that the Sun warms the Earth is that we have observed that warming occurs when the Sun is in the sky. This is what Hume calls a causal connection because it relates the appearance of the Sun (the cause) with the warming of the Earth (the effect).
We believe, based on our observations, that when the Sun is in the sky, it will cause the Earth to warm up. Since induction is based upon observing things that occur under defined circumstances (i.e. associating some effect with one or more causal factors), and then forming conclusions based upon those observations, it is our belief in a causal relationship (according to Hume) that is the basis of induction."
State the Humean analysis of causation, making sure to define any relevant terms.
"Hume feels that we must examine our experience of the relationship between cause and effect in order to understand its nature and thereby determine whether it justifies our use of inductive practices. He argues (perhaps rather stating the obvious, I would have said) that our knowledge of cause and effect is based on a process of extrapolating from past experience. In other words, because we have always seen a particular effect occurring in the past when a particular causal factor (or set of factors) has existed, we assume that this pattern will be repeated in the future. Causation, according to Hume, becomes a matter of constant conjunction.
This means that, in our experience, some particular effect is constantly conjoined with (i.e. has always been associated with) some specific cause. There is an assumption here that this causality will hold for future events, of which of course we can have no experience. We believe, essentially, that things will continue to follow the same pattern in the future that they have done up until the present (a potentially dangerous assumption, I suppose, especially for turkeys during the festive season).
Hume associates this notion with that of contiguity, i.e. that cause and effect are usually close together in either space or time (or both). Alternatively, that there is some chain of events connecting the cause-and-effect events of interest, in which any two adjacent links will be contiguous in either space or time (or both). Ladyman gives, as an example of the latter, the case where someone types words into a computer, and following some chain of related and contiguous events comprising causes and effects, someone else reads those words on a page. My understanding is that Hume does not claim this contiguity as an absolute imperative.
The Ladyman text states that a cause usually precedes an effect in time, although an example is given of the two occurring simultaneously (the oak beam being the cause of the roof staying up) and there is even mention that some philosophers believe in the possibility of a cause bringing about an effect in the past (well, I suppose our understanding of space-time is still extremely limited, after all). The last component of the Humean analysis of causation is our expectation that the occurrence of some event (the cause) will trigger some other event (the effect).
Hume argues that causation does not imply what he calls a necessary connection between cause and effect, despite what some philosophers have claimed. We may see the conjoined events, but we do not see the necessary connection between them. There are, he says, two competing views of causation that produce the same conclusion. One view (the necessitarian view) insists on the existence of a necessary connection (a metaphysical view, if you like).
His own view is that there is no evidence of such a connection, and he appeals to the 'Occam’s razor' principle that essentially says that if we have two competing hypotheses, and all other considerations are equal, we should choose the simpler of the two. Hume argues that, since his own view of causation does not complicate things by involving metaphysical implications, it should therefore, as the simpler of the two hypotheses, be the accepted one."
Explain, in your own terms, Hume’s problem of induction. What does it show?
"Hume’s problem with induction is that the conclusions reached through the adoption of an inductive argument could be false regardless of the number of observations on which they are based. There are even historical examples that show that this can be the case, as with the belief that prevailed among Europeans at one time that all swans are white based on their observations, whereas we now know that there are also black swans (these being indigenous to Australia and New Zealand). There is also, of course, the case of the turkey who assumed it would continue be fed as usual during the Christmas holidays.
The principles of induction upon which much of our scientific knowledge is based are, on the face of it, fairly sound. They rely on making a large number of observations under different circumstances, and getting the same result every time. The weakness of induction, as Hume pointed out, is that it relies on some crucial assumptions. First of all, we assume that the future will be like the past. In other words, exactly the same effects will be observed in the future, in a given set of circumstances, as have always been observed hitherto. Furthermore, we assume that the laws of nature will be the same in different places.
On this last point, we can say with some certainty that the laws of physics would appear to be the same for those parts of the known universe that we have observed to date, but is that really saying very much? We are only just beginning to explore the secrets of 'dark matter', for example. Until fairly recently, its existence was only hinted at, now we are investigating the possibility that it may well comprise a significant proportion of the total mass of the universe.
Hume has a point, really. We cannot know the future. We assume that the future will be like the past because in the past, the future has always turned out to be like the past (a question that also arises for me, however, is how much do we really know about the past, since according to Carl Sagan’s cosmic calendar we have only arrived on the planet in the last few minutes of the cosmic year?). We have no real evidence to suppose that the future will be like the past other than that our experience tells us so. In cosmic terms, our experience is just as limited as that of the turkey at Christmas.
We can, in defence of induction, apply the argument that its conclusions have nearly always been correct in the past – itself an inductive argument and thus (Hume argues) a circular one. Hume appears to accept, however, that in the absence of some more compelling scientific method, we will continue to use inductive reasoning, if for no other reason than because it is necessary for our survival, although he also seems to feel that we have a psychological disposition towards inductive reasoning that is more powerful than the need to justify or rationalise its use.
In a nutshell, he is saying that the only justification we have for induction is our belief that the future will resemble the past, but that this belief is itself based on our past experience, i.e. it is arrived at using induction, and it is of course the justification of induction itself which is being questioned. Therefore we have no justification for our inductive practices, which he says are the product of 'animal instinct and habit rather than reason'. This implies that all our scientific knowledge has no rational foundation."
Why can we not solve Hume’s problem by appeal to the uniformity of nature?
"Numerous approaches have been taken in the attempt to resolve Hume’s problem with inductive reasoning. The problem, Hume stated, is that inductive reasoning is not reasoning at all but ‘a habit or a psychological tendency to form beliefs about what has not yet been observed on the basis of what has already been observed’, and that it can’t be justified on rational grounds.
Arguments refuting this have included the notion that it is widely accepted as being rational and therefore it is rational according to accepted norms; a more subtle version of this argument is that induction is more rational than any argument Hume can raise against it. Yet another approach is to argue that Hume is demanding a deductive defence of induction, based on the assumption that deduction is the only possible source of justification, and that this is unreasonable; and so it goes on.
One of the commonly adopted arguments for induction depends on the assumption that nature is uniform. The argument essentially say that if a sufficient number (let’s call it N) of observations are made under differing circumstances, and yet unfailingly lead to the same conclusion, i.e. that a particular causal relationship exists, then we can justifiably expect that all future observations will lead us to the same conclusion. In other words, the causal relationship that we have observed in the past will always hold in future, because its occurrence depends upon the existence of some natural law, and that law will not change.
The problem that immediately arises is the question of what constitutes an acceptable value for N. Even assuming we establish such a value, the inference is that before we have made the required number of observations, the conclusion evidenced by our observations cannot be considered valid, and yet once we have made N observations, all of a sudden those conclusions are justified.
This problem can be mitigated somewhat by saying that the more observations we make, the more certain we can be of our conclusions. To this end, one can point to the numerous applications of Newtonian mechanics. The principles embodied therein are ubiquitous in just about every branch of engineering, for example. And yet these same principles, at one time thought to be sacrosanct, do not hold once we start looking at objects that move at near light speeds.
Indeed, the boundary between classical and modern physics is generally acknowledged to be that between the investigation of things we can observe and measure directly (such as the motion of the planets) and that of things we can neither observe directly nor measure in a traditional sense (such as the orbit of an electron around the nucleus of an atom). The laws that have been established by classical physics still apply to the things that we can see, hear and touch, but we must adopt a completely different set of laws to describe (for example) interactions that occur at the subatomic level. It would appear that, in this respect at least, Hume’s scepticism may be justified."
What is Goodman’s new riddle of induction? What does it show?
"Goodman states that only a hypothesis of a ‘lawlike’ nature can be confirmed by an instance of itself. He uses the example of a piece of copper that is shown to conduct electricity, thereby confirming the hypotheses that all pieces of copper will conduct electricity. He contrasts this to an ‘accidental’ occurrence such as the occurrence that a particular man in a lecture hall happens to be a third son. This, he says, cannot be taken to confirm a hypothesis that all men in a lecture hall must be third sons.
The problem according to Goodman is that it is not always easy to differentiate between hypotheses that are lawlike and those that are not. He takes the position that confirmation of a hypothesis (which is after all what we are trying to achieve) depends more on the characteristics of the hypothesis than upon how it is formed syntactically.
He illustrates this using the following scenario: Suppose we have a rule that says that all objects in a population (emeralds for example) are green. Another rule says that all objects in some other population (say sapphires) are blue. So far so good, you might think. Goodman then introduces some new terms. An object is ‘grue’ if it is green and was first observed before time t, or if it is blue and was not observed before time t. At the same time, an object is ‘bleen’ if it is blue and was first observed before time t, or if it is green and was not observed before time t.
Note that grue and bleen are not colours. Two things can be the same colour (i.e. either both blue or both green) and yet one can be grue and the other bleen, depending on when each was first observed (i.e. before or after time t). Furthermore, no physical change occurs at time t. Something that was green remains green, and something that was blue remains blue.
Up until time t, all our observations support the hypothesis that all emeralds are green. They also support the parallel hypothesis that all emeralds are grue. The first hypothesis will be supported by observations that occur after time t, because emeralds observed will still be green. The second hypothesis, however, will not.
After time t, all emeralds observed will be bleen, and not grue as predicted by our second hypothesis. If they were observed to be grue after this time, then by definition they would also have to be blue, which is a contradiction of our first hypothesis. My understanding of Goodman’s point is that observations that confirm the first hypothesis would negate the second hypothesis, and vice versa, despite the fact that they both rely on the same set of observations (although I freely admit to still being a tad confused by this scenario).
Of course, we can intuitively determine which of the two hypotheses is legitimate. Goodman’s scenario is obviously contrived in order to demonstrate a point, which is that we have no real criteria for determining what constitutes a lawlike hypothesis. Goodman says that accidental (i.e. non-lawlike) hypotheses are often characterised by reference to some particular individual, or through the involvement of some spatial or temporal restriction (the latter, of course, being a crucial factor in our emerald conundrum).
Complete generality, then, would appear to be a requirement, but successfully defining it is not so easy. He argues that being able to avoid non-lawlike predicates in practice is not enough from a philosophical point of view. We are still unable to unambiguously define what distinguishes lawlike (confirmable) hypotheses from accidental (non-confirmable) ones. This, Goodman says, is the new riddle of induction."
How would you respond to Goodman’s new riddle? Critically evaluate your response.
"To an extent I can see where both Hume and Goodman are coming from. Hume has questioned the very basis of inductive reasoning because it depends completely on our assumption that the laws of nature remain constant, are the same everywhere, and that the future will be like the past. Philosophers have painstakingly ground out a solution set for Hume’s problem, only to be faced with Goodman’s ‘new riddle’.
The riddle he poses is that of how to determine, once and for all, whether a hypothesis is truly lawlike or not. He does not accept, he says, the simple device of avoiding non-lawlike predicates in practice, since this relies on the application of (what – instinct? common sense?) some arbitrary criteria based on experience or intuition, rather than on some defining theory of confirmation.
Like Hume, however, he poses the question, but does not offer an acceptable solution. I would argue that the very nature of knowledge itself means that we can never attain absolute certainty, and that the search for such certainty, whilst certainly worthwhile, is somewhat akin to the way in which an artisan strives for perfection.
My own feeling is that, in the struggle to understand the very nature of scientific knowledge itself, Goodman’s contribution has been an extension of Hume’s. It pushes the boundaries, and if nothing else prevents the philosophical community at large from becoming complacent by posing new questions.
I come to this subject from the standpoint of someone directly involved in the practice of science, albeit computer science, and as a former teacher in the field of computing. I also come to it as someone who has a lifelong interest in science generally, particularly in the fields of astrophysics and cosmology.
My response to Goodman’s riddle is thus coloured somewhat by the fact that, whilst I can appreciate the philosophical point of view he postulates, and whilst I also believe that a philosophy of science should strive towards some form of justification for our scientific beliefs, it will not impact on the day-to-day activities of the scientific community – a view Hume seems to concur with. I further have to confess that I sometimes struggle with the finer points of the concepts described by Goodman, but then I do not consider myself to be a philosopher as such; merely a scientific practitioner seeking a philosophical perspective that will hopefully inform my writing in the future."
Characterize, in your own terms, naïve inductivism. In doing so, clearly state (a) what question it is meant to answer; (b) how it does so; and (c) what it proposes as the scientific method.
"Naïve inductivism describes the process of arriving at a conclusion based on having made a large number of observations. It is conditional upon all of the observations having supported the conclusion, and none of the observations having contradicted it. It is also conditional upon there having been a sufficient number of observations, made under a sufficiently broad range of circumstances, so that the adoption of the conclusion can be considered to be justified and reasonable.
Suppose we carry out a study of the effects of exposure to a lethal dose of radiation on the human body. We cannot directly observe either the radiation itself or the effect it has on individual cells in a subject exposed to radiation while that subject is still alive. We can however reasonably accurately estimate the level of exposure that has occurred, and record the resulting physiological symptoms over a period of time, starting from the time at which the subject is exposed.
When the subject dies, tissue samples will give us very accurate figures for the actual dosage received, and the physiological effects can be assessed. A final analysis can therefore be made using measurable and quantifiable data. If we have studied a sufficient number of cases, we can reasonably infer from our observations that radiation doses above a certain level are invariably lethal.
A less quantifiable (and over the years quite controversial) group of scientific studies involves the effects of smoking tobacco cigarettes. Based on the observations of medical practitioners and various study groups, it has been claimed that smoking causes a number of serious respiratory ailments, including COPD and lung cancer, as well as contributing to heart disease and other medical conditions.
The evidence comes from numerous studies, carried out over many years, involving both smokers and non-smokers. The conclusions (that smoking is a major causal factor in a number of serious medical conditions) are supported by statistical analysis of those observations.
What the studies cannot do, however, is prove beyond reasonable doubt that smoking is the sole cause, or even the major contributing factor, of any one disease. Lung cancer, for example, occurs in non-smokers as well, perhaps due to exposure to carcinogens through other means.
There are also plenty of examples of smokers – even heavy smokers - who never contract one of the diseases normally associated with smoking. Nevertheless, there is sufficient observational evidence to be able to reasonably claim that smokers are more likely, statistically, to contract these same diseases, and that both the length of time a person has smoked and the average number of cigarettes they have smoked will impact on their statistical chances of suffering such a fate."
Provide an example of a bad teleological ‘explanation’; be sure to make it clear why such the purported explanation is bad!
"A teleological explanation is one that proposes that something is the way it is as a result of some defined ultimate purpose. This generally works out for items that are designed and manufactured by humans. A hammer, for example, has a certain weight and hardness because it is designed for the express purpose of driving a nail into a piece of wood. Attempting to apply the same kind of argument to naturally occurring phenomena often fails because it implies a purpose that simply does not exist, reflecting, perhaps, a human need to assign purpose to all things.
An example of a bad teleological ‘explanation’ could be that ‘the sun radiates warmth in order to nurture life on Earth’. This is implausible for a number of reasons. First of all, it implies that the sun has a purpose, i.e. to nurture life. Consider the fact that the sun is a star, and that there are something like two billion stars in our galaxy alone. We can be fairly certain that many of these stars – probably the majority – do not have planets orbiting them that will support life. What, then, is their purpose?
We also know that the sun radiates heat because of the nuclear fusion reaction that is occurring within it, and that this reaction is occurring because the sun has, at some point in its past, acquired sufficient mass to trigger this type of reaction (the critical requirement is estimated to be roughly thirteen times the mass of Jupiter – about 2.5 × 1028 kilograms).
Furthermore, thanks to the work of scientific researchers like Clair Patterson, we now know that the Earth has been around for something like four and a half billion years (and the Sun presumably much longer). It is also estimated that life did not exist on the Earth for the first billion years, so what was the ‘purpose’ of the Sun during this period? Hardly to warm the Earth up, since it began its existence in a largely molten state."
Notes: