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|First Name=John S.Stuart

|Brief=a 19th century British philosopher, political economist , and civil servant. Mill's His writings on scientific change cover a wide range of topics ranging from gender equality the nature of scientific reasoning to theory-ladenness and democracy scientific progress|Summary=Although Mill's writings primarily covered topics unrelated to inductive science and scientific change, he was a passionate interlocutor in the mid-19th century debates on science. Developing his notions mostly as a response to other philosophers, Mill wrote on the primacy of induction in scientific reasoning , advocated for the use of logic in scientific justification instead of the study of history, and construed science as being embedded in the greater social context. His principal work on these ideas is presented in his 1843 book, [[Mill (1974a)|''A System of Logic, Ratiocinative and scientific progressInductive'']].|Historical Context=Mill was an active participant in the debates surrounding epistemology of science in the mid-19th century. In order to properly contextualize Mill’s 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 nature’, which often served as 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 and immutable laws that were considered immutable. This idea is also sometimes characterized described as the ‘law of causation’--- “it is a law that there is a law for everything”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 as well as their followers maintained adhered to this principle. Kant himself , too, 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 also implicitly agreed assented to it, and later 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 we make universal generalizations based on our finite and limited set of particular experiences we generalize the results, thereby thinking that the future will resemble the past. However, since our experience is limited, but while the future universalization is infinite, there is no justification that the future will resemble the past. Take a classic example: one 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 All swans that will be observed in the future will also be whitejust as those (white) swans observed in the past. However, no matter how many singular observational instances of white swans there may be, it cannot be guaranteed that a future instance may not refute the past. That is, we : We cannot necessarily claim that there will never be a non-white swan (e.g., a black swan). This is Hume’s ‘problem of induction,’ which plagues all empirical sciencessince the limited data is used to support the supposedly universal laws of nature. Inheriting the British empiricist tradition, Mill had to, broadly speaking, justify provide a justification for induction andthat would, particularlyin turn, provide a sound justificatory grounding for empirical sciences as well. The As such, the ‘problem of induction’ provided the context within which Mill workeddeveloped his ideas.

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 William Whewell's 1837 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 proved popular among the British empiricists. One of the reasons that the intellectual community disregarded Whewell’s ideas on science was his departure from the British empiricist 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 alike 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 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‘accidental’,’ as it is precisely these idea that lead to the development of the said branch of science around which the science then organizes itself .[[CiteRef::Buchdahl (1971)]]. It was this historicist approach against which Mill primarily argued.

Another issue in Mill’s day pertained to the justification being necessarily true, as opposed to being true only contingently. Philosophers such as Kant and Whewell, who was heavily influenced by Kant’s work, were deductive necessitarians: they They held that deductive reasoning is necessarily true, meaning that the conclusion of a deductive argument is universal and necessary. ContrarilyThey maintained that inductive reasoning, for themon the contrary, inductive reasoning lead to conclusions that were inevitably fallible, showing thus implying that Whewell and Kant were critically aware of Hume’s problem. Deviating from Whewellapproach, Mill’s empiricism favors favored inductive reasoning. Although Mill employs employed terminology such as “invariable” and “unconditionality” when describing logic of scientific justification, he is not a necessitarian as he lived in a post-Humean context. There is ongoing debate to this day whether Mill’s notions can ultimately be reduced to ones requiring a ‘necessary connection.’ If that is so, Mill would be rendered an inductive necessitarian .[[CiteRef::Buchdahl (1971)]].

Mill is an empiricist who believes that all our ideas are gained through sense perception. Departing from the rationalist doctrines, which hold reason as the primary source of knowledge, Mill follows a long line the British empiricist tradition of British empiricists such as Locke, Berkeley , and Hume. The ‘source’ of ideas primarily refers to where the ideas come from, as opposed to denying the role that reason plays. As such, Mill holds that the mind is furnished with ideas through experience, and ''then '' reason can use these ideas. His empiricism is thoroughgoing: there There is no source other than experience and or observation that provides us with our ideas .[[CiteRef::Macleod (2016)]]. His Indeed, his empiricism is quite radical: in fact, to the degree that it is may be characterized as phenomenalistic. Drawing upon the works of earlier empiricist idealists such as Berkeley, Mill thinks that the mind-dependent reality is all we have access to. That isFor him, there is nothing other than the ideas provided by sensations that the mind has access to. Unlike some earlier empiricists like Locke, Mill thinks holds that the external objects (if any) are not perceivable. Whereas Locke believed that the object’s objects' primary qualities and the ideas invoked by them resemble each other, Mill is more prudent in arguing that the only thing we can perceive perceivable entity is “a set of appearances” appearances.”[[CiteRef::Mill (1974b)]]. Mill’s position that we cannot know anything about how things are in-themselves, but only know how they appear to us , is called termed the “Relativity of Human Knowledge” Knowledge.”[[CiteRef::Mill (1979)]].

Believing that experience and observation provide us with all knowledge, Mill rejects all forms of ''a priori '' knowledge: the The doctrine that we can have knowledge that is independent of (or prior to) experience .[[CiteRef::Macleod (2016)]]. Indeed, this departure is a response to Whewell, and more broadly to Kant, who believed that ''a priori '' knowledge are necessary pre-conditions of the mind that enable experience .[[CiteRef::Losee (1983)]]. Not only does he reject that knowledge of extension, substance , and place as ''a priori'', Mill instead argues that this type of seemingly ''a priori '' knowledge is “put together out of ideas of sensation” sensation [that are ''de facto'' ''a posteriori''].” [[CiteRef::Macleod (2016)]][[CiteRef::Mill (1979)]]. In essence, all of our knowledge, including knowledge that is traditionally thought of as ''a priori'', originates from and is dependent on experience.

Mill and Scientific Change:===Against the History of Science:===Most of Mill’s work against the history of science as 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 inductioninduction’,’ 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 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 those that are 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 isIn other terms, history of science cannot be used as evidence in support of the idea that scientific theories as are (or can be) necessarily true.

After showing that the history of science provides neither the criteria of evaluation itself nor any justification for an existing criteria, Mill argued for a logicist position. He thought that both the formulation of the criteria and its justification should be restricted to the domain of the philosophy of science. Accordingly, the appropriate role for the history of science would be to provide illustrative examples of the criteria. In other words, history of science was, for Mill, nothing more than a repository of examples with no bearing on the logic of scientific justification .[[CiteRef::Losee (1983)]].

In particular, Mill favored an inductivist logical approach, which holds that theories must be justified based on inductive inferences. He went further in arguing that, until there is inductive justification provided for the theory, any additional supplementary consolidation, increased simplicity or , and analogous situations do not prove useful. Indeed, these additions are meaningless until an inductive justification is provided. The most fundamental tent tenet or starting assumption of Mill’s inductivist logic is the belief in the principle of the ‘uniformity of naturenature’,’ the notion that nature behaves in a law-like and constant manner .[[CiteRef::Buchdahl (1971)]].

===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” 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, we know that 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 allows 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)]].

As explained above, Mill is a champion of empiricism who thinks that we solely engage with inductive reasoning. Like Hume, Mill he believes that we are psychologically predisposed to reasoning inductively .[[CiteRef::Macleod (2016)]]. In other words, our minds are hard-wired to see patterns, and we cannot help otherwise. But Mill takes this claim further than Hume did. Whereas the latter argued that we are predisposed to reasoning inductively (and did not consider induction as necessarily true), the latter further added adds that we are justified in doing so employing inductive reasoning.[[CiteRef::Macleod (2016)]]. (Note: as mentioned above, although there is scholarly debate about whether or not Mill considered induction as necessarily true, I am using the interpretation forwarded by the Stanford Encyclopedia of Philosophythat he deemed induction as apodictically true).

Mill thinks that induction is justified for two reasons: iterative Iterative validation, and initiating Initiating validation. Iterative induction claims that induction is justified, because similar initial conditions always produce similar outcomes because of the principle of the ‘uniformity of nature’ nature.’ [[CiteRef::Macleod (2016)]]; System, VII: 306). As explained earlier, Mill rejects all forms of ''a priori knowledge'', including the knowledge of the principle of the 'uniformity of nature.’ How, then, do we know this principle? Through meta-induction: we We know by induction that inductive generalizations have been true, and therefore, they will continue to be true .[[CiteRef::Macleod (2016)]]. In other words, inductions in the past have shown themselves to be true. Therefore, we can know through induction that all future cases of induction will also be true.

Despite Mill’s attempts, it seems that he failed to provide a satisfactory solution to Hume’s problem, as the argument for iterative induction is circular. Induction is being justified using second order (or meta-) induction [[CiteRef::Macleod (2016)]], and no independent justification is provided. However, it was previously explained that induction is inevitably fallible, thereby making meta-induction fallible as well. This leads Mill to his second , initiating justification: initiating validation of induction. Drawing on the work of Hume, Mill postulates that we are, from a psychological perspective, naturally inclined to reason inductively (i.e., we spontaneously initiate induction). He thinks that it’s it is perfectly reasonable to use induction; indeedin fact, unhindered critical self-reflection reveals that induction is “deserving of reliance” reliance.”[[CiteRef::Mill (1974a)]]. This is not an independent logical justification, but one that is “anthropological” in nature: “[tT]he laws of our rational faculty, like those of every other natural agency, are only learnt by seeing the agent at work” work.” [[CiteRef::Mill (1974a)]]. Implicit in this statement is an assertion from the Aristotelian-Medieval method, wherein all things were considered to be properly scrutinized only in their ‘natural‘natural’,’ as opposed to artificial, context. It seems that Mill, perhaps unwittingly, construes humans as ‘natural’ beings, and therefore, draws from it his justification for initiating induction.

After we accept the descriptive, initiating validation for induction, we can refer back to iterative validation, which will help us improve induction. Put differently, accepting initiating validation as a baseline justification for induction would allow us to engage in iterative inductions such that we would be critically aware of how we use induction .[[CiteRef::Macleod (2016)]]. Therefore, argues Mill, we will sharpen our reasoning abilities by being more precise in pointing out the circumstances in which inductions properly work, allowing which will allow us to refine our inductive abilities.

Mill believes that we improve our reasoning in science through self-examination. This self-examination is that can be interpreted as ‘refined’ induction. Reasoning in science, including both (formal and empirical ) science, is nothing more than highly improved or refined induction. Therefore, whereas both the difference between everyday and scientific reasoning is that while both are inductive, the latter is refined through critical scrutiny and examination .[[CiteRef::Macleod (2016)]]. Ironically, to support his arguments for ‘refined’ induction, Mill drew heavily on Whewell’s “History of Inductive Science” even though he rejected Whewell’s the historicist approachadvanced by Whewell. Likewise, his appeal to the history of science in support of induction was made possible due to the work done by Alexander Bain .[[CiteRef::Mill (1981)]]. Mill himself never conducted primary research in the history of science .[[CiteRef::Macleod (2016)]].

Bolstering his views on the effective use of induction, Mill advocates for the use of experiments in science. Though he concedes that we may “discover, by mere observation without experiment, a real uniformity in nature” [[CiteRef::Mill (1974a)]], he regards using experiments in science is as the best way of uncovering the causal mechanism between events. Experiments enable us to “meet with some of the antecedents apart from the rest, and observe what follows from them; or some of the consequents, and observe by what they are preceded” preceded.” [[CiteRef::Mill (1974a)]]. In other words, controlled variables in experiments allow us to unearth the causal mechanism between two events. For example, we can either see how, given A, we can reach its effect B, or if we were given the effect B, we could infer the cause A. Hence, this form of refined induction is possible in a controlled experimental setting, a feature that Mill considers unique to and indispensable for science.

The unearthing of causal laws of natural phenomenon can eventually be described using general laws, which are arrived at by means of induction. Similarly, inductions continue and we may find that the law that explained the individual observations’ causal mechanism is, itself, part of a larger law. Of course, this larger, overarching law is also uncovered using induction .[[CiteRef::Mill (1974a)]]. This process of scientific reasoning continues, and we discover more and more laws through induction. The laws of nature that induction reveals are, according to Mill, “nothing but the uniformities which exist among natural phenomena” [[CiteRef::Mill (1974a)]], an appeal to the age-old principle of the ‘uniformity of nature.’

Theory-Ladenness:===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, like 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 the inferences that one hasmakes. 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 it is repeated induction in the similar same 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 individualindependent, underlying ontological basis against which theories can be tested, thus precluding the making of inference from the data .[[CiteRef::Losee (1983)]].

Mill makes universal and normative claims about how science progresses in any given society. He thinks that a society makes scientific (and other types of) progress when it allows the free flow of ideas by everyone. The ability to express oneself freely is not restricted to social and economic elite. Rather, people from all types of diverse backgrounds should have the right to fearlessly express themselves. Therefore, the ideas proposed by people from diverse vantage points lead to a plethora of novel and unique ideas or theories .[[CiteRef::Godfrey-Smith (2003)|p.142]]. This constant emergence of novel theories allow the exploration of hitherto unexplored notions, and after evaluation, the best ones are may be retained .[[CiteRef::Godfrey-Smith (2003)|p.116]]. This process continues: new, New and radical ideas are continuously (and without hindrance) proposed, they are explored, they may challenge orthodox scientific beliefs, and if they become accepted, the best ideas then become the scientific belief. Thus, for MillAs a result, this “marketplace of ideas” is a necessary condition that enables the progression of for and allows science to progress.[[CiteRef::Godfrey-Smith (2003)|p.116,142]].|Criticism=Many commentators during from Mill’s days (and until now) have made time to this day make a general argument against the inductivist camp of which Mill is a part. Many like Whewell argued that if inductive inferences are valid, whether they be iterative, initiating or enumerative, they should lead to a “nonfalsifiable establishment of connections between truths” truths.”[[CiteRef::Buchdahl (1971)|p.364]]. Mill himself concedes that the ‘certainty’ of inductive inferences is ‘absolute’ inasmuch as we are concerned with practical purposes. Inductive inferences do not hold absolutely “in circumstances unknown to us, and beyond the possible range of our experience,” such as the “distant parts of the stellar regions” regions.” [[CiteRef::Buchdahl (1971)|p.365]]. It is not fully clear how Mill can, on the one hand, concede that inductive inferences are inevitably fallible, and on the other hand, use such terms as “unconditional” and “invariable” to describe inductive inferences .[[CiteRef::Buchdahl (1971)]].

Another objection to Mill by Whewell is with respect to the idea of confirmed novel predictions. Mill agrees that a hypothesis is seen as favorable if it explicates the previously hitherto unexplained facts. However, he considers the corroboration of novel facts as a mere “coincidence” striking as profound only to the “ignorant vulgar” vulgar.”[[CiteRef::Strong (Strong, 1955, )|p.228). ]] Whewell objects to Mill that the history of science reveals the opposite: when hitherto unobserved facts, which were posited by certain theories, were discovered, this new information was seen as confirming evidence in support of the theory. In fact, some of the best theories, according to Whewell, earned their prestigious place in the scientific mosaic in virtue of the confirmation of their novel predictions. Whewell cites as an example the observance of the return of Haley’s comet as evidence confirming Newtonian theory, thereby demonstrating that, if we view the historical record on of science, it becomes clear that the discovery of new facts predicted by the theories do, indeed, serve as confirming evidence, which is contrary to what Mill thought .[[CiteRef::Strong (1955)]].|Page Status=StubNeeds Editing