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|Brief=an English a 19th century British philosopher, political economist and civil servant. Mill's writings cover a wide range of topics ranging from gender equality and democracy to inductive reasoning and scientific progress.|Historical Context=John Stuart Millwas an active participant in the debates surrounding epistemology of science in the mid-19th century. In order to properly contextualize Mill’s 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” (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 (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, particularly, 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” (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 (Strong, 1955).Like his predecessor William 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 will provides us with the evaluative criteria. Specifically, Whewell’s historical survey of the history of science 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(Losse, 1983).Mill disagreed in principle In particular, Whewell showed that history the historical survey of the development of a given science can provide us with a justification for an evaluative criteria for scientific theoriesreveals that the leading ideas become ‘clarified’ through progressive criticism. For himThese leading, fundamental ideas are not construed as being ‘accidental, all history of science could provide us ’ as it is information these idea that certain regularities have held in lead to the past. Mill made development of the descriptive claim that scientific inquiry is a search for causal connections---correlations that are invariable and unconditional. He maintained that all history said branch of science can provide evidence for is that certain correlations have been invariablearound which the science organizes itself (Buchdahl, 1971). It was this historicist approach against which Mill primarily argued. However, because he lived Another issue in a post-Humean contextMill’s day pertained to the justification being necessarily true, he not as opposed to being true only inherited the problem of inductioncontingently. Philosophers such as Kant and Whewell, who was heavily influenced by Kant’s work, but also were deductive necessitarians: they held that induction deductive reasoning isnecessarily true, in principle, fallible. Consequently, he argued meaning that just because certain scientific theories have thus far not been refuted (i.ethe conclusion of a deductive argument is universal and necessary.Contrarily, they have so far been invariable)for them, it does not follow inductive reasoning lead to conclusions that they will continue to be invariable. As induction is were inevitably fallible and because scientific theories are nothing more than ‘refined induction,’ the theories themselves are fallible---there is no guarantee showing that they will remain invariable in the future as well. Relatedly, he differed with 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 Kant were critically aware of science does not equip the theories with unconditionalityHume’s problem. Unconditionality of scientific theories could roughly be interpreted as theories that are ‘true’ or not in need of any qualification whatsoeverDeviating from Whewell, Mill’s empiricism favors inductive reasoning. Although Mill argued that employs terminology such as the history “invariable” and “unconditionality” when describing logic of science cannot provide scientific justification even for the invariability of scientific theories, by extension it cannot justify unconditionality either.Having showed that history of science does he is not provide the criteria of evaluation and justification for it, Mill argued for a logicist positionnecessitarian as he lived in a post-Humean context. He thought that both the formulation of the criteria and its justification should There is ongoing debate to this day whether Mill’s notions can ultimately be restricted reduced to the domain of the philosophy of scienceones requiring a ‘necessary connection. Accordingly’ If so, the appropriate role for the history of science Mill would be to provide illustrative examples of the criteria. In other wordsrendered an inductive necessitarian (Buchdahl, history of science was nothing more than a repository of examples with no bearing on the logic of scientific justification1971).[[CiteRef::Losee (1983)]]|Major Contributions=Mill’s Empiricism: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 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 observation that provides us with our ideas (SEP, Mill, 2.1). His empiricism is quite radical; : in fact, it is phenomenalistic. For himDrawing upon the works of earlier empiricist idealists such as Berkeley, Mill thinks that the mind-dependent reality is simply observer-relative sensory phenomenon (Godfrey-Smith, 2003, p.20), which means that all that exists is in the sensationswe have access to. That is, there is nothing other than sensation the ideas provided by sensations that the mind has access to. Unlike some earlier empiricists like Locke, Mill thinks that the external objects (if any) are not perceivable. The Whereas Locke believed that the object’s primary qualities and the ideas invoked by them resemble each other, Mill is more prudent in arguing that the only thing we can perceive is “a set of appearances” (System, VIII: 783). Mill’s position that we cannot know anything about how things are in-themselves, but only know how they appear to us is called the “Relativity of Human Knowledge” (Examination, IX: 4).Believing that experience and observation provide us with all knowledge, Mill rejects all forms of a priori knowledge: the doctrine that we can have knowledge that is independent of experience (SEP, Mill, 2.1). 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 (Losse, 1983). Not only does he reject that knowledge of extension, substance and place as a priori, he Mill instead argues that this type of seemingly a priori knowledge is “put together out of ideas of sensation” (Examination, IX: 9). In essence, all of our knowledge, including knowledge that is traditionally thought of as a priori, originates from and is dependent on experience.Mill provides an additional reason for rejecting a priori knowledge. To gain a priori knowledge, according to Mill, the universe of thought and the universe of reality “must have been framed [in] correspondence with one another” (Examination, IX: 68). In other words, if we were to have any a priori knowledge, we must know prior to and independent of experience that whatever is capable of existing is also capable of being conceived. However, Mill argues that the proposition that we can or do have a priori knowledge of the perfect correspondence between thought and reality lacks evidence (SEP, Mill, 2.1). Because there is no evidence whatsoever for this proposition (which is a prerequisite for allowing us to have a priori knowledge), we should not accept the proposition.

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 (SEP, Mill, 3.1). Therefore, deductive reasoning does not lead to any new knowledgeabout the world. Furthermore, Mill is, perhaps, 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 (SEP, Mill, 3.1). This The idea that mathematics and geometry employ de facto employ inductive reasoning allows him to deny the existence of even this form of knowledge, which Kant and Whewell considered a priori knowledge.Mill holds that “there is in every step of arithmetical and algebraically calculation a real induction, a real inference of facts from facts” (System, VII: 254). He contends that mathematical propositions are not true by definition (System, VII: 253); 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, he thinks 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 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 (SEP, Mill, 3.4)As explained above, Mill is a champion of empiricism who thinks that we solely engage with inductive reasoning: the notion that we can have general propositions based on a number of singular observational propositions. Like Hume, Mill believes that we are psychologically predisposed to reasoning inductively (SEP, Mill, 3.2). In other words, our minds are hard-wired to see patterns, and we cannot help otherwise. But he Mill takes this claim further: not only than Hume did. Whereas the latter argued that we are we predisposed to reason reasoning inductively(and did not consider induction necessarily true), but the latter further added that we are also justified in doing so (SEP, Mill, 3.2). (Note: as mentioned above, although there is scholarly debate whether Mill considered induction necessarily true, I am using the interpretation forwarded by Stanford Encyclopedia of Philosophy).Mill thinks that induction is justified for two reasons: iterative validation of induction, and initiating validation of induction. Iterative induction claims that induction is validjustified, because similar initial conditions always produce similar outcomes because of the principle of the ‘uniformity of nature’ (SEP, Mill, 3.2). In other terms, the universe follows the principle of uniformity of nature: whatever is true in one case is also true in all relevantly similar cases (; System, VII: 306). As explained earlier, Mill rejects all forms of a priori knowledge, including the knowledge of the principle of universal induction'uniformity of nature. ’ How, then, do we know this principle? Through meta-induction: we know by induction that inductive generalizations have been true, and therefore, they will continue to be true (SEP, Mill, 3.2). In other words, inductions in the past have shown themselves to be true; that is, all cases involving induction have been true. Therefore, we can know through induction that all future cases of induction will also be true.ClearlyDespite Mill’s attempts, this is it seems that he failed to provide a circular satisfactory solution to Hume’s problem, as the argument as for iterative induction is circular. Induction is being justified using second order (or meta-) induction (SEP, Mill, 3.2), and no independent justification for is provided. However, it was previously explained that induction is providedinevitably fallible, thereby making meta-induction fallible as well. This leads Mill to his second justification: initiating validation of induction. We 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 perfectly reasonable to use induction; indeed, unhindered critical self-reflection reveals that induction is “deserving of reliance” (System, VII: 319). This second justification is not an independentlogical justification, but one that is “anthropological” in nature: “[t]he laws of our rational faculty, like those of every other natural agency, are only learnt by seeing the agent at work” (System, VII: 833). 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,’ 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. In other wordsPut 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 (SEP, Mill, 3.2). Therefore, argues Mill, we will sharpen our reasoning abilities by being more precise in pointing out the circumstances in which inductions properly work, allowing us to refine our inductive abilities.In summary, Mill thinks that all of our knowledge originates in sense perception, observation and experience (System, VII: 7). Second, the only type of reasoning we engage in is induction (System, VII: 283). As it will become clearer, Mill’s ideas about empiricism and reasoning greatly influence his notions about science and scientific change. 

Mill believes that we improve our reasoning improves due to through self-examination of our reasoning. As was mentioned previously, this This self-examination is meta-induction: induction of induction that allows us to refine our use of ‘refined’ induction. Reasoning in science, including both formal and empirical science, is nothing more than highly improved or refined induction. ThusTherefore, scientific reasoning is similar to ‘common sense reasoning’ in that both are inductive; the difference between everyday reasoning and the scientific one reasoning is that while both are inductive, the latter has been improved due to is refined through critical self-scrutiny and examination through meta-induction (SEP, Mill, 3.3).In addition Ironically, to meta-support his arguments for ‘refined’ induction, Mill appeals drew heavily on Whewell’s “History of Inductive Science” even though he rejected Whewell’s historicist approach. Likewise, his appeal to the history of scientific knowledge science in support of induction was made possible due to justify his position that scientific reasoning is refined inductionthe work done by Alexander Bain (Autobiography, I: 215–7, 255). According to Mill, history of the growth of our knowledge reveals that reasoning himself never conducted primary research in the past was inductive reasoning; moreover, there was also a growth of inductive reasoning. That is, history of science reveals(SEP, says Mill, that our knowledge has not only grown because of induction, but also that our knowledge of induction itself has improved, allowing us to use it effectively3.3). Bolstering his views on the effective use of induction, Mill advocates the use of experiments in science. Though he argues that while it is possible concedes that we “may discovermay “discover, by mere observation without experiment, a real uniformity in nature” (System, VII: 386), using experiments in science is the best way of uncovering the causal mechanism between events. Using experiments in science enables 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” (System, VII: 381). In other words, controlled variables in experiments allow us to unearth the causal mechanism between two eventevents. 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 thinks is considers unique to and indispensable for science.Because The unearthing of how scientific knowledge has grown throughout history, four methods (or experiments) have proved successful in uncovering the causal mechanism laws of observed natural phenomenon. NOTE: I have copied the paragraph from the Stanford Encyclopedia of Philosophy as I do not fully understand it (I have changed the font): Firstly, the Method of Agreement: where instances of phenomenon A are always accompanied with phenomenon a, even when other circumstances accompanying A are varied, we have reason to believe that A and a are causally related. Secondly, the Method of Difference: where the only distinguishing feature marking situations in which phenomenon a occurs or does not occur is the presence or absence of phenomenon A, there is reason to think that A is an indispensable part of the cause of a. (If we have noted, via the Method of Agreement, that in all instances of A, a is present, we can, where possible, systematically withdraw A, to determine whether A is a cause of a by the Method of Difference. Mill terms this the Joint Method of Agreement and Difference.) Thirdly, the Method of Residues: against the knowledge that A is the cause of a, and B the cause of b, where ABC causes abc, and AB causes merely ab, we can (by ruling out that c is the joint effect of AB) regard C as the cause of c. Fourthly, the Method of Concomitant Variations: whenever a varies when A varies in some particular manner, a may be thought to eventually be causally connected to A.”Using the four aforementioned methods, Mill thinks that we can isolate the causes of natural phenomenon. The causal mechanism of individual observations are 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, or overarching law is also uncovered using induction (System, VII: 464). 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” (System, VII: 318).Mill insists that the purpose of scientific inquiry is to uncover how things are in themselves. When we engage in scientific reasoning, we try and uncover the underlying truth, or the deep structure of the world. Mill remarks that a conception is “a conception of something which really is in the facts, some property which they actually possess, and which they would manifest an appeal to our senses” (System, VII: 295; System, VII: 651). Mill views science as trying to uncover the structure age-old principle of the world that already exists. As he views that “kinds have a real existence in nature” (System, VII: 122), the purpose ‘uniformity of scientific inquiry is to uncover a “radical distinction in the things themselves” (System, VII: 123).It must be noted, however, that even though Mill thinks that science does and ought to uncover the nature of things as they are in-themselves, he denies the use of hypothesis as a valid method for doing so. Because Mill is an empiricist who believes that experience provides us with all our knowledge, he rejects the use of hypothesis as invalid, because hypotheses posit the existence of unobserved entities---something that we do not have access to given that we are restricted to the world of phenomenon’. 

Arguing in the same vein as British empiricistssuch as Locke, Mill adheres to advances the notion idea of tabula rasa---the idea that human mind does not come 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 is a clean slateWhewell. Nevertheless, Mill thinks that human mind is malleable in two different respects. First, Mill thinks that experiences and observations make their mark on the mind, thus molding it accordingly. Second, background conditions, which vary between different cultures, also play a cardinal role in shaping one’s mind. Mill thinks that the tremendous amount of “pliability” (Civilization, XVIII: 145) 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, when we make observations, they tend to be a mixture, wherein the “observation and inferences are intimately blended” in a mixture (System, VIII: 641–2). 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 (SEP, Mill, 3.5). 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 (Losse,1983).

 ===== Scientific Progress =====:Mill believes 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, Mill contends that people from all types of diverse backgrounds should have the right to fearlessly express themselves (On Liberty citation). Therefore, the ideas proposed by people from diverse vantage points lead to a plethora of novel and unique ideas or theories (Godfrey-Smith, 2003, p.142). This constant emergence of novel theories allows for allow the exploration of hitherto unexplored notions, and after evaluation, the best ones are retained (Godfrey-Smith, 2003, p.116). This process continues: new, 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 Mill, this “marketplace of ideas” is a necessary condition that allows enables the progression of science to progress (Godfrey-Smith, 2003, p.116, 142).|Criticism=Mill believes in Many commentators during Mill’s days (and until now) have made a refined and self-critical use of induction. He uses general argument against the history inductivist camp of the growth of science as evidence to substantiate his claimswhich Mill is a part. HoweverMany like Whewell argued that if inductive inferences are valid, whether they be iterative, initiating or enumerative, Mill himself was not an historian of science. As they should lead to a matter “nonfalsifiable establishment of fact, his knowledge of the subject was based mostly on secondary sources connections between truths” (SEPBuchdahl, Mill1971, 3p.3364). In particular, Mill drew heavily on William Whewell’s History himself concedes that the ‘certainty’ of inductive inferences is ‘absolute’ inasmuch as we are concerned with practical purposes. Inductive Scienceinferences do not hold absolutely “in circumstances unknown to us, John Herschel’s Discourse on and beyond the Study possible range of Natural Philosophy and August Comte’s Cours de Positive Philosophie. Likewiseour experience, Mill’s appeal to ” such as the history of science for his claims in support “distant parts of induction was made possible due to the work done by Alexander Bain stellar regions” (AutobiographyBuchdahl, I: 215–71971, 255p.365). According to Christopher MacleodIt is not fully clear how Mill can, on the one hand, concede that inductive inferences are inevitably fallible, and on the other hand, Mill most likely would not have viewed induction use such terms as being exhaustive of reasoning in science had he conducted primary research in the history of science “unconditional” and “invariable” to describe inductive inferences (SEPBuchdahl, Mill, 3.31971). In other words, if Another objection to Mill himself had engaged by Whewell is with primary research material on respect to the confirmed novel predictions. Mill agrees that a hypothesis is seen as favorable if it explicates the history of scientific practicepreviously unexplained facts. However, it is unlike that he would have viewed scientific growth considers the corroboration of novel facts as being a result of progressively refined induction mere “coincidence” striking as profound only to the “ignorant vulgar” (SEPStrong, Mill1955, 3p.3228). Macleod contends Whewell objects to Mill that the history of successful scientific practice science reveals thatthe opposite: when hitherto unobserved facts, which were posited by certain theories, were discovered, instead this new information was seen as confirming evidence in support of mere refined inductionthe theory. In fact, creative use some of hypothesis-making has also played a critical role (SEPthe best theories, Millaccording to Whewell, 3earned their prestigious place in the scientific mosaic in virtue of the confirmation of their novel predictions.3). ThereforeWhewell cites as an example the observance of the return of Haley’s comet as evidence confirming Newtonian theory, Mill cannotthereby demonstrating that, if we view the historical record on one handscience, declare imaginative hypothesis-making as invalid and, on it becomes clear that the discovery of new facts predicted by the other handtheories do, claim use history of science is indicative of proper reasoningindeed, serve as history reveals that hypothesis-making hasconfirming evidence, which is contrary to Mill’s ideaswhat Mill thought (Strong, contributed enormously to the growth of scientific knowledge.The contradiction between us not having access to how things are in-themselves, and the apparent role of science as uncovering the underlying structure of the universe will be explored here1955).