It may appear to many that there is no problem at all here. If we see the same thing happen in a number of cases, it appears to be perfectly correct that we should claim that the next such case will result in what has been observed previously in such cases. However, one of the things philosophy does is to question what appears to be obvious. Philosophers of Science, for example, originally saw inductivist logic at the heart of the scientific method. It seemed obvious that science worked by collecting data (the observations) and then drawing a general law from an examination of the observations. Yet when the history of science was examined, it was found that many of the greatest scientific discoveries did not exactly conform to this model. Other difficulties also arose as the question was investigated more closely. For example, we might state the principle of induction as follows: "If a large number of As have been observed and found to possess the property B, without exception, under all conditions, then all As possess the property B". However, there are two questions which any holder of such a view must deal with. First, how many observed cases constitute enough for the General claim to come into effect? (To use a famous example from Russell, how many observations of white swans can logically guarantee that the next swan seen will not be black). Second, can the principle of induction be logically justified? It would appear that logical justification can only arise byway of induction. The principle can only claim justification based upon its successful applications (a number of As observed and found to possess the property B).
Induction is like writing "Gold" on a box into which I then place a nugget of gold, and then another, and then another, and so on, until the observer of my actions is challenged to predict the material of the next nugget to go into the box. The observer cannot claim knowledge based upon his observations. The next rock to go into the box could be gold, or any other substance. The label on the box (so to speak) is simply a mental one, with no power to influence events in the real world. This then, is the logical flaw in induction.
Induction is logically inconsistent in that the number of possible cases which might be observed is infinite and no number of observed cases which give the same result can therefore increase the probability of that result occurring in the next observed case, because no number can make a dent on infinity. Probability remains zero.
Proposed Solution [Top of the page]
The
solution I would like to offer for consideration came to me as a result of
long contemplation of Zeno's paradoxes,
in particular, the paradox known as The
Stadium. In attempting to resolve the paradox, I found an approach
which I believe may be useful in tackling the problem of induction. As a precursor
to my own examination of a possible answer, perhaps you would care to examine
Aristotle's solution to
Zeno's paradox?
Zeno's logical paradox is derived from the artificial nature of measuring distance based on number. Numbers are infinite, but that does not mean that there are an infinite number of discrete points in space. Just because our number-based measurement systems can go on to ever-finer divisions of scale infinitely, it does not follow that what is measured goes on dividing into ever-finer divisions infinitely also. The mistake arises from an erroneous belief in the actuality of logical fictions, invented to help us to deal with the world. "Twoness" has no actual existence, as an entity, in the real world. It is a concept which we apply to reality to help us to deal with it - so is any other number. So is anything else we apply to the real world, when it is built upon number (comparison and identity).
The breaking down of reality into individual, defined, discrete events, is a human invention. The world is viewed in this way in order to better handle it. We are confronted by a mass of undifferentiated data, which we order (the ordering promoting a feeling of control and security).
Take an example: the act of consuming food. The food is chewed and then swallowed. But in this very act of describing the event I am artificially separating it from its context within a continuing process, breaking Reality down into parts. Our language is theory-laden, abstracting and analytical. Similarly, the act of chewing the food can be separated from the act of swallowing it. But why? The division is arbitrary. It is made: but any number of other, equally artificial and equally valid divisions could be made. The starting and ending points we pick as the limits of the event are arbitrary (we can extend the event or we can shorten it, as we choose). We could say that the consuming of food involves the capture of prey, or the growing of crops; the mastication of the food involves the cutting up by certain teeth, involves the crushing of the food between certain other teeth, powered by the clamping together of the jaws, the mixing of the food with saliva - we can become more particular or more general, as we wish. And we could trace this even further back, mentioning the absorption of energy from the sun, or even right back to the formation of the universe. The point is, the dividing up of the observed event is as artificial as the separation of the event itself from its context within reality. The event itself does not have the artificially imposed "Beginning" which we give it, nor the artificially imposed "Ending". It is part of a continuum. It is only our pattern-seeking brain which divides it up.
The logical gap arises from a logical fiction. The event observed is treated as one of a series of discrete entities. But no such entities exist in reality. The human observer, the human mind, with its intended observation, forms an artificial mental framework, and the event observed has no discreteness beyond that framework, for the framework defines the entity and the entity (an event) is not discrete, but is part of an ongoing process (the process of Reality, which is still working itself out). The human brain concentrates on this artificial framework, separating the event from its surroundings and comparing it with other separated events which are taken to be identical. This concentrative and focusing process separates the phenomena we wish to examine, and by making them eminent, patterns them into a coherent and consistent series of likenesses. It is rather like reconstructing a carpet by picking out two strands of thread from the weave.
Conclusion [Top of the page]
This, I propose, is how the problem concerning the principle of induction arises. We say that we "observe a number of As", when there are no two events which can be classed together as identical, and therefore there is no "number of" to consider, if we acknowledge the validity of the argument proposed above. There is only the continuing observation of a continuing process; from the examination of a mentally abstracted part of the process, we can guess at the trends which may lie within it.
If the events which Science examines are not actually separated within the continuous process of Reality, how is it possible to derive predictive knowledge from our examination of only a part of that process? A possible reply would be to say that the part of the process examined has both a pattern and a "direction", so to speak. The process is itself too complicated to deal with as a whole, but this does not mean that we can learn nothing from an examination of some of its parts and detect some of the process's tendencies. Because we examine a part, and the whole is greater than its parts, this means that our knowledge will necessarily be flawed. However, such examinations do lead to at least some knowledge. We assume that the parts which interest us are signs that the whole of the process has patterning, because we discern causality in the parts we examine (the events we observe). We string together our "Events" with causal links, and the causal links are the threads within the carpet of Reality, enabling Science to gain an impression of the pattern, which allows for prediction.
It is quite possible, I believe, that Zeno and Paramenides were correct in refusing to accept the reality of empty space. The more we discover, the more likely it appears that there is no such thing as space, in the sense of, a container which holds things but which is itself utterly empty. Everywhere we look, there are the fields and energies that hold atoms apart, the same fields and energies which created the universe as we now perceive it. The same fields and energies which perhaps take the form of matter in the right context.
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