Limits of Science?. John E. Beerbower
the molecular theories. Even if that reduction were to be achieved, the question of whether the genetic theory is true would still present itself.
One might say that the question is not important or that it is not really meaningful. The macro theory “explains” what happens (that is, what occurs) and enables action based upon reliable predictions, even if it does not “describe” the details of how, or even why, it occurs.
More on deduction
The common view has been that a theory of scope can achieve something that mere inductive inferences cannot.10 Such a theory can enable one with logical certainty to make predictions about or to foresee consequences of certain actions beyond the immediate relationship that gives rise to the inductive inference of causality. That ability would seem to offer the promise of a statement of causality that has real content, even if certain aspects of the theory may more appropriately be called fictions (like the “gene”). For example, instead of the relative primitive understanding that fire burns (or is hot), one could achieve a theory of what causes combustion, what the process of fire actually is, what the impact on living cells caused by fire is and why we feel pain following contact with fire.
Of course, one would not need or expect to generate theories sufficient to explain the entire chain of events at one time. Pieces of the chain can be examined and theories propounded for each piece. In part, the success of each such theory will ultimately be judged by whether that theory fits into the theories that are tentatively accepted for the other pieces. If it all works when the pieces are put together, one feels more confident that each piece is right.
Let me suggest that an interesting question is whether we can say that a theory can ever be expected to be true or reflect reality. Cf. Paul Feyerabend, The Tyranny of Science (2011) (original published in Italian in 1996), p.66. Many scientific theories consist of a substantial edifice of theoretical (or mathematical) propositions that touches the physical world only occasionally and may, in some of those places, do so only incidentally. As we shall see later, much of modern physics consists of abstract mathematical models, many parts of which have no currently known or even imagined counterparts in the physical world. Great excitement is generated in the broader scientific community when a researcher is able to identify an empirically testable proposition and then find that the prediction of the theory is “confirmed” by the empirical test. The excitement arises even when the testable hypothesis is in no sense central or at the core of the theory; it can be a remote and quite technical implication of the theoretical construct. The scientific community views the lack of falsification as a partial confirmation that the theory is true. But what does true mean in this context? Do we expect that the theory might, can or even should correspond to reality in the sense of resembling or modeling the details of reality?
The “Problem” of Induction
Philosophers of science have devoted considerable attention to what has been called the “problem of induction.” The problem is interesting, because the process which philosophers call induction reflects the principle means by which man has made sense of the external world.
The issue arises from the difficulties in articulating a reason why it is logical to conclude that event B will occur subsequent to an occurrence of event A, based upon the fact that on occasions in the past, B has been observed to follow A, or, in another formulation, how we can justify inferring from a particular event or series of events a rule that applies generally in other cases or will apply to future events.
The process of induction essentially assumes that apparent patterns that are observed in the course of natural events are likely to reoccur. At a minimum, induction assumes that there are patterns or regularities in the physical world.
The question for philosophers is whether there is a logical or philosophical “principle of induction.” To take the classic example, just because the Sun has come up every morning for all of recorded history (as far as we know) is there a sound logical or philosophical basis (or argument) to believe that it will come up tomorrow morning? Clearly, the fact of regular occurrences in the past in and of itself does not prove that the same thing will occur in the future; indeed, one could speculate that in some contexts it could be more likely that something different will happen, at least, eventually. I can grant the philosopher these points, on their own limited terms; but, I would not be willing to conclude that we are not justified in believing that the Sun will come up tomorrow. The logical fact that historical patterns do not guarantee future repetition does not make the expectation of such repetition unreasonable (or, unscientific).
Inferences and predictions
Philosophers have struggled with the question of why such an assumption is philosophically justifiable (as opposed to practically or pragmatically justifiable: e.g., the fact that the assumption has worked in the past has proven to be a good practical reason to assume that it will work again). The question is underscored, or perhaps generated, by the comparison of induction with deductive reasoning, in which the conclusions are compelled as a matter of logical necessity given the premises and rules of deduction. The simple philosophical argument is that if induction could be reformulated so that you could deduce the conclusions being drawn, then it would no longer have the characteristics of induction (i.e., it would have become deduction), but if the demonstration of validity of inductive reasoning is through some other level of inductive reasoning, then the proof is necessarily circular—you cannot prove that induction is valid by means of induction.
I have two concerns about this argument. First, it is constructed on the assumption that there are two and only two types of inference: deductive and inductive. If that assumption is correct, then the dilemma inevitably arises—if you can justify induction by deduction, then it is no longer induction; if you can only justify it by induction, then your proof is necessarily circular. So, one must necessarily look beyond deduction and induction to find a principle of induction.
Interestingly, the same point can be made about deduction. If deduction can be justified only by deductive inference, then deduction is also circular. Of course, as previously discussed, we already recognized that deduction essentially is circular, that is, valid by definition.
That segue brings us to my second concern. The “problem” arises because of the application of the standards of deduction, that is, logical necessity—the way in which a conclusion is “guaranteed” or mandated in a deductive system. Induction cannot and should not be judged by the standards of deduction. In fact, it is interesting to ask what it means that some conclusion is “guaranteed” in the sense of this argument. As we discussed above, there are serious limitations in how deductive reasoning relates to real world events. The reason that deduction is so compelling is that the conclusions are necessarily incorporated in the premises. As a result, deductive reasoning cannot lead to conclusions that contain anything “new.” Now such reasoning may (and often does) lead to conclusions that had not previously been noticed or “seen.” They may not have been obvious, but they are not “new.” (This subject is discussed further in the next chapter on Mathematics.) Deduction, unlike induction, is not ampliative—it does not and cannot lead to something new and additional.
Indeed, the power of induction is that it necessarily leads to conclusions or predictions that extend beyond the known or existing premises and observations. That is why induction is not, and inevitably cannot be, as logically “certain” as deduction. That is also why induction is far more interesting and relevant to our day-to-day lives. If one rejects the idea that the external world is made up of elements that have direct correspondence to innate mental images with real world relationships accurately reflected by human mental processes, so that man can know the world through a priori reasoning; then for any understanding of the external world, there must be some means of access by the mind to the external phenomena. Such access is presumably gained through the senses. One can speculate that the initial tool that the mind uses to gain understanding from the sensory perceptions is induction, based upon the identification of apparent patterns.
It also seems that mankind made an important leap when man began to formulate models and theories that