I should hope that you would forgive my poor philosophy humor in regards to the above title, but I promise throughout the rest of this post I won’t be making anymore jokes. I will however, be resorting to the topic that I have been quite interested in expositing over the last few weeks: the philosophy of science (I have even had to add another tag in order to categorize them). The reoccurring theme in these posts is dealing in particular with the nature and limitations of scientific methodology; often associated interchangeably among scientists and philosophers by the term induction.
Though I will not go at any grave length in explaining what induction is here, I will make a few passing comments in regards to the language associated with it (particulars, singular statements, etc.) and David Hume’s (1711-1776) interpretation of induction. For the moment, I would like to provide a slightly abridged version of my thoughts before providing a more detailed explanation later.
Basically, I would have to say that Hume’s conclusion is ultimately leading towards the right direction. I mean that particularly on his point regarding the idea that inductively we cannot hold coherently that nature is uniform [as surely as it cannot be accounted for empirically] and will be consistent today, tomorrow, or in the extended future. The problem with Hume’s ideas is due to his matter of skepticism towards reality.
The heart of Hume’s skepticism is motivated by his attack on the foundations of empirical knowledge – i.e., that no generalization about experience is ever rationally justified. Hume writes in his Enquiry of Human Understanding (1748):
What is meant by a sceptic?… scepticism… recommends a universal doubt, not only of all former opinions and principles, but also of our very faculties; of whose veracity, say they, we must assure ourselves, by a chain of reasoning, deduced from original principle, which cannot possibly be fallacious or deceitful. But neither is there any such original principle, which has a prerogative above others, that are self-evident and convincing… no reasoning could ever bring us to a state of assurance and conviction upon any subject. 
Upon examining this passage, the reader is thus introduced in a crude but fair manner to Hume’s skepticism. Though Hume’s conclusion (about induction) is admittedly a strong argument against the claim to know with certainty , the common response to Hume is of a weaker thesis regarding probabilities rather than certainties. According to Geisler’s comment on Hume, we show that our epistemic percentile is amounted to mere probabilities regarding inductive thinking; therefore, “[i]n this way we show that our conclusion is relative to any body of evidence” .
In this post, I intend to deal with Hume’s problem of induction as a matter of considerable merit, but his skepticism is another factor that doesn’t necessarily have to follow to the conclusion of seeing scientific methodologies as probabilistic. In other words, Hume’s skepticism “against induction does not succeed in denying the soundness of induction” .
Francis Bacon and René Descartes were of interesting importance to the rise of modern science later found in the work of Galileo Galilee. Interestingly however, Galileo’s discourse was his similarity to Plato in regards to his reverence for the underlying “mathematical language inherent within nature”. For Galileo, the phenomena of nature must be subject to careful observation and intensive measurement – indeed, his discovery of the laws of motion were due in part to his examination of mathematical regularities in conducted experiments.
Galileo during the time of the philosopher Francis Bacon (1561-1626), had adopted his methodology of preforming experiments and then generalizing the experimental results in order to come to a natural law (i.e., induction). Unfortunately, some problems of induction do happen to emerge. In contrast to deduction (as used by Descartes), where the truth of the conclusion follows from the truth of the premises given; induction does not have this luxury. According to Harold Himsworth (1986), inductive “generalizations may be at fault” in a [particular] way. “They may be correct in a limited context but incorrect in a larger” . He writes an example:
At one time, for instance, the generalization that swans are white birds of a particular shape and size that swim on water was perfectly acceptable to the inhabitants of Western Europe. When some of them discovered Australia, however, they saw birds with all the appearances of swans save that they were black. Consequently, they were driven to amend their previous generalization by eliminating color from the combination of attributes they had hitherto regarded as characteristic of this family of birds. (pp. 35-36)
Therefore, the truth of the supporting claims does not logically guarantee the truth of the conclusion in an inductive system (or syllogism). This is where Hume would ultimately step in and suggest that our use of induction is completely unjustifiable. By virtue of my Microsoft Paint skills (thanks to Google’s lack of model resources), consider the following:
From hence forth, we can call this Hume’s Fork. Essentially, Hume’s argument can be schematized as such:
- (1) If an inductive rule is to be justified, it must be justified by either a deductive rule or an inductive rule.
- (2) It cannot be justified by a deductive rule (or else the principle would not be inductive).
- (3) It cannot be justified by an inductive rule (that would be circular).
- (4) But any justification has to be either via a deductive rule or via an inductive rule – from (1).
- (5) Hence, no inductive rule can be justified – from (1), (2), (3), and (4).
According to Hume in respect to (1), in order to justify induction we must use either induction or deduction. However, if you notice the diagram, to take the induction route is to essentially argue in a circle, because the justification would not guarantee our use of induction. The deduction route on the other hand won’t work either because the truth-hood of induction cannot be deduced from the axioms of logic . Therefore, we are not justified in our use of induction.
Contrary though, is the nature of our experience to induction. For example, though we are not rationally permitted to justify induction, we are psychologically permitted to justify it (fire burns my hand, therefore I will cease from putting my hand in fire). The 20th century then came along and dealt questionably with whether or not science was truly inductive in methodology. Starting with J. S. Mill (1806-1873), the nomological method dealt with scientific pursuits in an interestingly deductive manner:
We see a phenomenon, then come up with a law that may explain it causally. We then deduce what else follows from this law and seek empirical confirmation and falsification. 
Mill’s accusations against Hume are interesting. Hume suggests that we can neither use deduction or induction to justify inductive rules, but Mill’s position on the contrary was that deduction standing alone is thought to work because of inducing generalizations from our experience. In a more direct response, Hume cannot use deductive reasoning to undermine induction (that argument itself hinges off of induction). Mill’s nomological method was modernized by Karl Hempel (1902-1972), then improved and revised by Karl Popper (1902-1994), and then later criticized by Willard V. Quine (1908-2000).
-  David Hume, Enquiry Concerning Human Understanding (Promotheus Books: 1988) pp. 135-136
-  see Karl Popper’s The Logic of Scientific Discovery (Routledge: 1992) sections 1 and 80; as well as Norman Geisler’s Introduction to Philosophy (Baker Books: 1980) p. 87
-  Geisler (1980), p. 87
-  Kazuyoshi Kamiyama, “No Need to Justify Induction Generally in Theory of Knowledge (vol. 53, 2003) abstract.
-  Harold Himsworth, Scientific Knowledge and Philosophic Thought (John Hopkins University Press: 1986) p. 35
-  see Dan Cryan, Sharon Shatil, and Bill Mayblin, Introducing Logic, 3rd edition (Icon Books: 2001) p. 116
-  Ibid., p. 118