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|Historical Context=Mill was an active participant in the debates surrounding epistemology of science in the mid-19th century. In order to properly contextualize his contributions, it is important to understand some of the major ideas that preceded him, and the most topical issues of his day.
One of the most prominent ideas that many philosophers prior to and during Mill’s time believed in was the ‘uniformity of nature.’ This concept was usually the uncritical starting assumption of many philosophers, including Mill himself. The principle of the ‘uniformity of nature’ states that the natural phenomenon behaves in a uniform, law-like fashion. The universe was thought to be governed by general laws that were considered immutable. This idea is also sometimes characterized as the ‘law of causation’--- “it is a law that there is a law for everything”.[[CiteRef::Buchdahl (1971)|p.348]]
Most influential philosophers of the past few centuries strongly adhered to this concept. Rationalist philosophers such as Leibniz and Descartes, and their followers maintained this principle. Kant himself ardently believed in the principle of the ‘uniformity of nature.’ Though Mill, and some British empiricists generally, tried to disassociate themselves from rationalist and Kantian doctrines, they nonetheless believed in this principle. Given this widespread acceptance, Mill too implicitly agreed to it, and used it to justify his claims in support inductive inferences [[CiteRef::Buchdahl (1971)]]
Another important concept that Mill inherited is Hume’s ‘problem of induction.’ The primary idea is that due to our limited particular experiences we generalize the results, thinking that the future will resemble the past. However, since our experience is limited, but the future universalization is infinite, there is no justification that the future will resemble the past. Take a classic example: one may observe million swans all of whom are white. Accordingly, one can make the universal conclusion that, given our large set of data, “all swans are white.” Importantly, this conclusion makes an assertion about the future: all swans that will be observed in the future will also be white. However, no matter how many singular observational instances there may be, it cannot be guaranteed that a future instance may not refute the past. That is, we cannot necessarily claim that there will never be a non-white swan (e.g., black swan). This is Hume’s ‘problem of induction,’ which plagues all empirical sciences. Inheriting the British empiricist tradition, Mill had to, broadly speaking, justify induction and, in particular, empirical sciences as well. The ‘problem of induction’ provided the context within which Mill worked.
Mill entered the debate on the epistemology of science through the publication of his book “A System of Logic” in 1843. Most of his work was in response to the book “History of Inductive Sciences ” by William Whewell that was published in 1837. Mill’s book, which expressed his “difference of opinion” [[CiteRef::Strong (1955)|p.209]] with Whewell, was popular among the British empiricists. One of the reasons that the intellectual community disregarded Whewell’s ideas on science was his departure from the tradition of British empiricist such as Locke and Berkeley. Instead, Whewell had aligned himself with continental philosophers such as Kant. This contention, however, was more than a mere divide between rationalist and empiricist traditions. Whewell approached science through its history, whereas Mill thought that using logic was more appropriate .[[CiteRef::Strong (1955)]].
Like his predecessor Whewell, Mill thought that one of the essential tasks of the philosophy of science was to formulate a method of evaluation for scientific theories. Unlike most philosophers before them, both Whewell and Mill were cognizant that the history of science and philosophy of science are intimately connected. Yet, they differed in their approaches for what provides, or is the source of justification for the evaluative criteria for scientific theories and laws. On one hand, Whewell took what could appropriately be termed as the ‘historicist’ approach: he thought that the study of history of science provides us with the evaluative criteria. Specifically, Whewell’s historical survey led him to conclude that the evaluative criteria are ‘distilled from’ and derive their justification out of the historical record. Hence, Whewell’s somewhat unqualified historicist approach not only ‘finds’ the scientific criteria by studying history of science, but also provides its justification based on scientific history [[CiteRef::Losee (1983)]]. In particular, Whewell showed that the historical survey of the development of a given science reveals that the leading ideas become ‘clarified’ through progressive criticism. These leading, fundamental ideas are not construed as being ‘accidental,’ as it is these idea that lead to the development of the said branch of science around which the science organizes itself [[CiteRef::Buchdahl (1971)]]. It was this historicist approach against which Mill primarily argued.
===Against the History of Science===
Most of Mill’s work against the history of science providing source of and justification for science was in response to Whewell’s “History of Inductive Sciences.” Mill disagreed in principle that the history of science can provide us with a justification for an evaluative criteria for scientific theories. For him, all history of science could provide us is the information that certain regularities have held in the past. Mill made the descriptive claim that scientific inquiry is a search for causal connections---causal relations that are invariable and unconditional. He maintained that all history of science can provide evidence for is that certain correlations have been invariable. However, because he lived in a post-Humean context, he not only inherited the problem of induction, but he also held that induction is fallible. Consequently, he argued that just because certain scientific theories have thus far not been refuted (i.e., they have so far been invariable), it does not follow that they will continue to be invariable. As induction is fallible and because scientific theories are nothing more than ‘refined induction,’ the theories themselves are fallible---there is no guarantee that scientific theories will remain invariable in the future as well [[CiteRef::Losee (1983)]]. As a result, he thought it nonsensical to study the history of science to find the evaluative criteria.
Relatedly, he differed from Whewell on a further point: because scientific theories cannot be said to be invariable due to induction (and as historical record is an inadequate justification), it follows that historical record of science does not equip the theories with unconditionality. Unconditionality of scientific theories could roughly be interpreted as theories that are ‘true’ or not in need of any qualification whatsoever. Mill argued that as the history of science cannot provide justification even for the invariability of scientific theories, by extension it cannot justify unconditionality either [[CiteRef::Losee (1983)]]. That is, history of science cannot be used as evidence in support of the idea that scientific theories as necessarily true.
===Reasoning and Science===
Mill claims that deductive reasoning is “empty”: it says nothing new about the world. Everything established in the conclusion of a deductive argument must already be present in the premises [[CiteRef::Macleod (2016)]]. Therefore, deductive reasoning does not lead to any new knowledge about the world. Furthermore, Mill is radical in his view that mathematics and geometry---areas that lead to acquisition of genuine knowledge---do not employ deductive reasoning. According to Mill, it only appears that mathematics and geometry use deductive reasoning, but on a deeper level, they are using nothing more than inductive reasoning [[CiteRef::Macleod (2016)]]. The idea that mathematics and geometry ''de facto'' employ inductive reasoning allows him to deny the existence of even this form of knowledge, which Kant and Whewell considered a priori.
Mill holds that “there is in every step of arithmetical and algebraically calculation a real induction, a real inference of facts from facts” [[CiteRef::Mill (1974a)]]. He contends that mathematical propositions are not true by definition [[CiteRef::Mill (1974a)]]; these propositions are not analytic. For example, he thinks that the number two is one plus one not because two is defined as one plus one. On the contrary, two is one plus one, because of induction. We observe, for instance, that one rock and another rock lead to two rocks; similarly, we observe that one swan and another swan lead to two swans, and so on in a multitude of cases. According to Mill, the pattern that one and one lead to two in specific singular instances allow us to generalize that one and one equal two in all cases. Hence, all mathematical and geometric propositions are arrived at and justified through induction [[CiteRef::Macleod (2016)]].
===Science and Society===
Arguing in the same vein as British empiricists such as Locke, Mill advances the idea of tabula rasa---human mind is a clean slate with no preconceived, or innate ideas. This position is consistent with his belief in the non-existence of a priori knowledge, which differentiates him from rationalists, Kant and Whewell. Nevertheless, Mill thinks that human mind is malleable in two respects. First, experiences and observations make their mark on the mind, thus molding it accordingly. Second, background conditions, which vary between different cultures, play a cardinal role in shaping one’s mind. Mill thinks that the tremendous amount of “pliability” [[CiteRef::Mill (1977a)]] exhibited by the human mind has implications for our observations.
Living in a particular culture or society, and the specific experiences tend to merge the observations and inferences that one has. Therefore, the “observation and inferences are intimately blended” in a mixture [[CiteRef::Mill (1974b)]]. In this regard, Mill agrees with Whewell who thought that, during the process of hypothesis-formation, it is not possible to distinguish between ‘sensational’ and ‘intellectual’ aspects of knowledge, hence making the distinction between ‘data’ and ‘inference’ artificial. As hinted above, for Mill this blending of observation and inference occurs due to human predisposition for induction; more importantly, it’s repeated induction in the similar cultural or societal context that compounds our observations and inferences. Thus, whenever a person makes an observation, she will have, through association, a certain inference depending on the cultural context in which she was raised [[CiteRef::Macleod (2016)]]. Even though both authors recognize the impact of theory-ladenness, they hold somewhat different views. While on one side, Mill interprets theory-ladenness as socially and culturally constructed, Whewell provides a more logical reason. For him, there are no independent ‘facts’ with individual, underlying ontological basis against which theories can be tested, thus precluding the making of inference from the data [[CiteRef::Losee (1983)]].
Clearly, then, observations are laden with theories that depend on the cultural and social context of the observer. By extension, because societies are composed of individuals who have theory-laden observations, the phenomenon of theory-ladenness in observations also manifests itself at the social level.
