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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)]]

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, 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 soemploying 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.’ [[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.”[[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.” [[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)]]