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Philosophy of Science: Theory and Observation

The Philosophy of Science, roughly speaking, is concerned with the fundamental questions about science. It will explore the analytical approach offered by philosophy to the sciences, most particularly physics, and look at the ways in which philosophy can contribute to the critique of scientific assumptions. The article thus seeks to show how and why science needs philosophy, and vice versa. Further, it aims to illustrate how philosophy can even be proactive in formulating novel, testable, and predictive theories that help set new paths for empirical research (Laplane et al., 2019).

Empirical research, the type of research undertaken in the sciences involving physical observation (i.e., measurement or detection of phenomena, experienced by the researcher), plays a large role throughout the history and philosophy of science (Aune, 1970). This article indeed introduces theory and observation, starting with David Hume’s (1739) famous argument which set this very area of philosophical study in motion. The problem of induction is first considered. Hume’s (1739) reaction to this is then assessed, before the article finally goes on to look at the new riddle of induction by Nelson Goodman (1955).

Figure 1: The problem of induction originates from David Hume (Cranston & Jessop, 2023).

The Problem of Induction

The philosophy of science generally tends to pose one very important and underlying question, namely, how does one learn about the world? The most basic answer is by making experiences. There is, however, much more required of this answer. Historically, law-like generalisations have been added so that such an answer is sufficient to explain how one learns about the world via their experiences (Armstrong, 1983). So, for instance, a generalisation like "all robins are red" or "all metal conducts electricity" can be made and is based on one’s experiences. The process of learning from experiences to create law-like generalisations is then known as induction: the inferential process by which we get from a finite set of observations to a general rule (Achinstein, 2010). There are two "versions" of this concept (Howson, 2000):

  1. Universal inductive generalisation: "all observed A are B" to "all A are B" (for example, all swans I have observed are white, so this means that all swans are white).

  2. Next case induction: "all observed A are B" to "the next observed A is B" (for example, all swans I have observed thus far are white, so the next swan I observe will be white).

Broadly, knowledge rests on past experiences and appropriate inductive generalisations (Armstrong, 1983). The problem, however, is that one’s knowledge exceeds the observational basis on which it is grounded. Induction is ampliative for inference, meaning that the conclusion asserts more than there is in the premises. The problem of induction thus questions the reason for believing—or inferring—that the future will resemble the past (Hume, 1739). It more broadly questions predictions about unobserved things based on previous observations too.

Figure 2: Hume's famous "sunrise example" says that the sun will probably rise tomorrow, but we cannot know for certain (Matthews, 2023).

To reiterate, one can only evade the problem of induction by successfully holding that (i) excess information via observations results in true generalisations about the world, and (ii) there is justification for regarding what has been observed to happen in the past as a guide to the future (Hume, 1739). Famously, however, Hume (1739) shows this to be unjustifiable. The problem of induction is thus serious, the consequence—of being unable to justify the excess—being that all hard-won factual knowledge is not secured by any process of demonstrably sound reasoning (Achinstein, 2010). Hume (1739) indeed calls into question whether there is any logical or rational basis for inductive inferences at all. His argument is thus radical, not only applying to scientific knowledge but to all—and any type of—predictions.

Hume (1739), in identifying the problem of induction, divides all reasoning into two classes. The first, named relation of ideas, refers to arguments of mathematics and pure logic (Owen, 1999). By contrast, the second class known as matter of fact includes arguments concerning knowledge gained on the basis of observation and experience (Owen, 1999). Whereas the former class is considered to be unproblematic, the latter causes some problems. It is against this that Hume’s (1739) argument is targeted, discussed next.

Figure 3: Hume's Fork, Copper Drypoint by Amy Hiley (2022).

The first problem, as mentioned, is that it is not deductively ("demonstrably") valid that the future resembles the past (Hume, 1739). This proves rather serious since it is a consequence of the definition of a deductively valid argument. Consider the following, whereby P is the conjunction of all sentences describing past experiences and F is a sentence describing a future experience:

  1. Given P, either F or not F can be true.

  2. It then follows that "P, therefore F" cannot be deductively valid because there is a possible world in which P is true, but F is false (Henderson, 2022).

The second problem concerning matter-of-fact reasoning is that other than deduction, it is not clear what else can be used to justify induction (Hume, 1739). Each possibility or potential way of justifying induction is simply question-begging. One could propose that experience itself justifies induction, for instance, but this is viciously circular. The issue is that all experience refers to the past, meaning that F will either turn out true or false (Henderson, 2022). Yet any principle claiming to justify "P, therefore F" must be question-begging. One can even counter this with an induction principle such as "more of the same" (i.e., proposing that there is no special reason to believe things will change). Again, however, this begs the question since the very question at this stage is why the principle works (Henderson, 2022). Hume (1739) is not saying that relying on scientific knowledge is in any way misguided and it is wrong to use inductive inferences, but just that the attempt to justify it by reasoning fails. As per usual in the philosophy of science, there are numerous proposed responses to Hume’s problem of induction.

Figure 4: Inductive versus deductive reasoning (Diffen, 2023).

Responses to Hume

Though their success is rather questionable, it is worth (briskly) noting the various responses to Hume’s problem, including Hume’s own reaction. The first is known as "the practitioner's reply", that there is no problem in the first place (Henderson, 2022). Predicted effects, this response claims, will be observed in practice. As such, one would be willing to bet money on it. Somewhat similar to the inductive principle that there is no special reason to believe things will change, this view says that there is particularly good reason to believe in the predicted effects occurring (Henderson, 2022). Such a reply, however, is only rhetoric and misses the point. Indeed, Hume’s (1739) primary concern is whether this practice is based on sound inference. One might therefore consider the meaning of ‘reliable’ instead, as another kind of response to Hume. Here, a hypothesis that has been correct in the past tells us that the hypothesis is thus reliable (Papineau, 1992). Therefore, such knowledge is reliable which may counter the problem of induction to make the inductive inference process justified. Or so the story goes. This type of response encounters an issue, namely that such an analysis of "reliable" is wrong. Rather "reliable" refers to a hypothesis that will continue to be true (Papineau, 1992). Hume’s (1739) very point is that there is no reason to believe this, meaning that few (if any) replies to the problem are successful.

A final reply to Hume comes from Peter Strawson (1952), who argues for ordinary language dissolution. Instead of any analysis of "reliable", Strawson (1952) calls for an analysis of the meaning of "reasonable". He claims that this is analytic since it is true by definition that induction is reasonable (Henderson, 2022). To be reasonable means to form one’s beliefs in terms of the available evidence, meaning that inductive reasoning may be justified after all. Yet again, however, this is beside the point. Claiming that "being reasonable" by definition includes the acceptance of inductive evidence does not tell us anything about the world (Henderson, 2022). Hume’s problem remains, and his own reaction to the situation is far less ambitious. According to the philosopher, one must simply shift from justification to explanation (Henderson, 2022). Hume thus takes a bite-the-bullet approach, and many modern-day philosophers fall into one of two camps either (i) still working to solve the problem of induction or (ii) embracing it.

Figure 5: Philosopher Peter Frederick Strawson (Jayasekera, 2023).

Goodman’s New Riddle of Induction

The "old" problem of induction, as discussed, is the problem of justifying inductive inferences identified by Hume (1739). What is traditionally required from such a justification is indeed an argument that establishes that using inductive inferences does not lead one astray (Goodman, 1955). According to Nelson Goodman (1955), however, no answer to this problem is really possible, nor is any answer entirely necessary. On his new riddle of induction, induction instead rests on one’s ability to distinguish lawlike from non-lawlike generalisations. Whereas lawlike generalisations are capable of confirmation, non-lawlike generalisations are not. Hence, lawlike generalisations are required for making predictions. Goodman (1955) famously illustrates his new riddle of induction—and the reason for his new riddle—with the "Grue argument", essentially holding that generalisations formed by inductive conclusions are not confirmed by their instances (like Hume says). Indeed, as Gilbert Harman (1968) notes, enumerate induction of this kind usually takes on the following form:

1. Emerald1 is green.

2. Emerald2 is green.




1000. Emerald1000 is green.


C. All emeralds are green.

Clearly, at least according to Hume (1739), inductive arguments of this form are often good arguments because they form generalisations but attempts to justify this by reasoning fail. Goodman (1955), however, seeks to go against this in his new riddle of induction, whereby it is a false step that all generalisations are confirmed by their instances. His invention of the predicate "grue" seeks to show why.

Figure 6: Philosopher Nelson Goodman (2012).

All emeralds observed so far, the philosopher argues, have been observed as green. Given this, Goodman (1955) asks, which of the two following statements is true?

F1 – All emeralds are green.

F2 – All emeralds are grue.

The argument holds that X is grue if and only if either it is examined before some future instant of time T and found green or it is not examined before time T and it is blue (Goodman, 1955). Based on past observations P, one does not seem to be able to decide which is correct; (i) "if P, then F1", or (ii) "if P, then F2" (Henderson, 2022). The problem is that one must decide between F1 and F2, but they’re incompatible.

Responses to the problem only reflect its severity, that is before Goodman (1955) himself offers a solution. The first response, briefly, is to say that "grue" makes reference to a particular instant of time, while "green" does not. Hence, this reply argues, "green" has a privileged status (Goodman, 1955). This, however, simply will not do since it entirely depends on what one takes to be primitive. Another potential response to consider is therefore that the predicate "grue" is artificial, while "green" is natural (i.e., a natural kind of term). Even so, this again does not work since it is unclear as to what artificial really means. The standards of artificiality too are unclear. Goodman (1955) thus proposes his own solution to the new riddle of induction.

Figure 7: This emerald does not appear to be green, nor grue (Briggs, 2014).

Goodman (1955) argues that one must distinguish between projectable and non-projectable predicates. Whereas the former can successfully be used to predict what happens in the future, the latter fails to do this. Hence the need for entrenchment, stating that "green" over "grue" has been successfully projected far more often making the notion of ‘grue’ irrelevant (Henderson, 2022). The decision in entrenchment indeed favours predicates that have been successfully used. Goodman’s (1955) problem of induction is therefore different to that of Hume’s, involving a choice of the description of what language one picks. Hume’s (1739) problem, on the other hand, is concerning the justification of normative versus descriptive.

Concluding discussion

Oftentimes, it is all too easy to assume that the observations we make can justify various expectations or predictions about future observations or general claims that even go beyond the observed (Henderson, 2022). Such inferences about future observations, this article has considered, are inductive inferences since they go from the observed to the unobserved (or to general laws). In what has become known as the problem of induction originally introduced by Hume (1739), one must question on what grounds they come to their beliefs about the unobserved on the basis of inductive inferences. The problem has arguably become one of the most famous in philosophy, with numerous philosophers attempting solutions since (Henderson, 2022). Whereas many are unsuccessful in their attempts, this article has also discussed the embracement of Hume’s conclusion that it is insoluble, namely Goodman’s (1955) new riddle of induction. Regardless of how inductive inference by reasoning may be justified, however, the series moves onto problems concerning confirmation next time. Interestingly, observations often qualify as evidence in the sciences thus supporting various scientific hypotheses too.

Bibliographical References

Achinstein, P. (2010). The War on Induction: Whewell Takes on Newton and Mill (Norton Takes on Everyone), Philosophy of Science, 77(5), 728–739.

Armstrong, D. M. (1983). What is a Law of Nature?. Cambridge University Press.

Aune, B. (1970). Rationalism, Empiricism and Pragmatism: An Introduction. Random House.

Goodman, N. (1955). Fact, Fiction and Forecast. MA: Harvard University Press.

Harman, G. (1968). Enumerative Induction as Inference to the Best Explanation. Journal of Philosophy, 65(18), 529–533.

Henderson, L. (2022). The problem of induction. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. Spring 2020 edition. Metaphysics Research Lab, Stanford University.

Howson, C. (2000). Hume’s Problem: Induction and the Justification of Belief. Oxford University Press.

Hume, D. (1739). A Treatise of Human Nature. Oxford University Press.

Laplane, L., Mantovani, P., Adolphs, R., Chang, H., Mantovani, A., McFall-Ngai, M., & Pradeu, T. (2019). Why science needs philosophy. Proceedings of the National Academy of Sciences, 116(10), 3948-3952.

Owen, D. (1999). Hume’s Reason. Oxford University Press.

Papineau, D. (1992). Reliabilism, Induction and Scepticism. The Philosophical Quarterly, 42(166), 1–20.

Strawson, P. F. (1952). Introduction to Logical Theory. Methuen.

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Rebecca Ivory

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