Science is based on induction. In general, induction can be seen as reasoning from particulars to general statements. The problem of induction is that there does not seem to be any way to justify induction logically. Indeed, induction is seen as the opposite of deduction (the basis of logic). The classic issue of justification for induction was spawned by Hume’s skeptical challenge: just because we have seen or heard of the sun rising every morning during recorded history, what justification do we have for expecting it to happen tomorrow? How do we make this “inductive leap,” and what grounds do we have for believing the conclusions thus drawn?
This is the essence of scientific theory-building. We use induction to build scientific theories; if induction is shown to be invalid, we run the risk of showing all of science as invalid. The possibility that science is not the Holy Grail many think it is results in a frantic pursuit for its logical justification.
The logical positivists sought to systematize all of science using logical notation and deductive principles. They wanted to reduce science to a series of axioms from which deductions could be made as in Euclidean geometry (a notion which we can trace back to Descartes). For example, Carnap presents axiomatic systems for physics and biology. Since science rests on inductions, the positivists thought they needed to develop a logical (deductive) justification for induction.
Circularity is an aspect of deductive logic and many people fall into the trap of trying to apply deductive logic criteria to induction. Some say that all arguments for induction rests on induction itself and this makes the argument invalid. This is why Wittgenstein’s argument is that the positivist approach falls in on itself – which is the very point of the Tractatus. Wittgenstein was not suffering from the delusion that induction could be justified by logic.
The process of induction is the process of assuming the simplest law that can be made to harmonize with our experience. This process, however, has not logical foundation but only a psychological one.
Ludwig Wittgenstein, TLP, 6.363-6.3631
Nelson Goodman presented a further wrinkle to this problem: consider the statement that “all emeralds are green.” Now consider the definition of a new word “grue” – this word means “green up to and including today, but blue afterwards.” It seems that all evidence collected for the statement “all emeralds are green” also supports the statement that “all emeralds are grue.” Thus the “problem of induction” can also be extended to the problem of how to compare two (different) inductive conclusions. What criteria can be used to compare and select between competing statements?
Another approach to the problem is the “pragmatic” argument. This view can be summarized as follows: Given that we don’t have full knowledge of the situation and can’t generate a deductive conclusion, we utilize induction when we are forced to make a decision – that is, when we have nothing to lose by employing it. This argument escapes the bonds of trying to justify induction logically, but doesn’t really “satisfy” if you’re trying to legitimatize the entire scientific enterprise.
The next step can be seen as the acceptance of the inherent conventional nature of any “scientific” statement. Even such statements as (using Popper’s example) “this is a glass of water” are fraught with assumption. Wittgenstein tackled similar statements as only meaningful within the language-game being played. Following Wittgenstein and Foucault, if we are to claim that, e.g., my hands disappear when I am not paying attention to them, we will be opening ourselves up for a compelled trip to an institution. We will simply not be making sense; certain shared aspects of human existence and language require that certain statements can be made unequivocally. Thus Wittgenstein points out that if a lion could speak we still would still not be able to understand him (because we do not sufficiently share his experience).
Some statements are obvious from a linguistic standpoint; to deny that dogs are mammals is to misunderstand the use of the words “dog” and “mammal.” At some point we simply agree to a certain set of basic “furniture” for a discussion. It is this agreement that avoids the reductio ad absurdum into which the positivists fell.
But the philosophy of science is not interested in the process (or psychology) of induction; it is interested in how knowledge is accumulated and legitimatized in science. Given that someone has made an induction, how do we confirm it? We don’t – we can only attempt to dis-confirm it. Failing in our best effort to do so, we can use it as a working hypothesis until further evidence presents itself. This is a variation on the pragmatic defense.
Thus we arrive at Kuhn’s argument: certain statements are “obvious” when thinking within a system; and not, when not. Breaking out of the system – taking systematic assumptions as not-given – is fodder for a revolution, scientific or otherwise. Thus Kuhn’s solution to the problem of justifying induction is that, since all knowledge is built on shifting sand, induction does not need to be justified. And thus, I suppose, neither does science. But, if we don’t have to justify science, why do we have to justify mysticism?
Kuhn’s solution to the problem of justifying induction is that, since all knowledge is built on shifting sand, induction does not need to be justified. And thus, I suppose, neither does science. But, if we don’t have to justify science, why do we have to justify mysticism?