"The search for a unity of knowledge may at first be seen as a prison for creativity. The truth, however, is the opposite.
A unitary system of knowledge is the surest means of identifying as yet unexplored domains of reality" (Edgar O. Wilson).
"One of the greatest problems for society in general is the synthesis of knowledge" (J. Doyne Farmer).
Induction
The concept of induction
The initial source of the study of induction comes from Aristotle: "induction is a transit from individual things to universal concepts". This definition is valid today, although it is usually extended to also contemplate the passage from the general to something of an even more general kind. In any case, the original definition can be valid if we consider that individual things (facts) can also be of a general type.
Induction is the reverse process of deduction, and is different from abduction.
Deduction is a top-down logical process, from premises to conclusion. The conclusion is always true if the premises are true, since the conclusion is totally contained in the premises. Deduction is a safe, closed process, where there are no alternatives. For example, "All men are mortal. Peter is a man. Therefore Peter is mortal".
Induction is an ascending logical process that allows us to go ("transit") from the known (the facts) to the unknown (the inference), to make predictions, to propose theories whose knowledge is superior to the original knowledge (the facts). But there is not the certainty that is given in deduction, because it may happen that the inference is false. Since several hypotheses could be put forward to explain the facts, induction is an insecure, open process, where there are always several possible alternatives. For example, "Peter (who is a man) is mortal, Paul (who is a man) is mortal, and so on. Then all men are mortal."
Abduction is a logical process that does not lead for sure to the truth, but its usefulness lies in the fact that it allows us to formulate hypotheses that may be true. For example, "All men are mortal. Peter is mortal. Therefore Peter is a man."
In the Middle Ages, scholasticism, the theological-philosophical current that revived Greco-Latin philosophy, took respect for deductive logic to the most extreme limits, limiting itself to cultivating the theory of the Aristotelian syllogism, ignoring inductive argumentation. Then came Bacon.
Bacon's inductive experimental method
The Enlightenment was the origin of the modern intellectual tradition of the West. It demystified the world and opened itself to science in an attempt to make the universe comprehensible. It believed in the unity of all knowledge, in natural law, and in the power of science and reason as the engine of human progress.
Science was the engine of the Enlightenment and its great architect was Francis Bacon. Philosopher, politician, lawyer and writer, he is considered the founder of the philosophy of science and the "father" of empiricism. He had a great influence on the development of the scientific method, especially the inductive experimental method.
Bacon denounced the abuse of Aristotelian syllogism by scholasticism (which disdained sensible experience) as the main cause of the stagnation of science, since it was incapable of serving as a method of discovery. The progress of science should be based on induction, on obtaining conclusions and general laws through observation and experimentation.
His philosophy in this regard was as follows:
Knowledge is the fruit of experience, not of authority. Knowledge is power.
Nature must be "interpreted". Reason is "the key to the interpretation" of observations. Observation and reason, empiricism and rationalism must be harmonized.
Truth cannot be based on syllogistic reasoning, for it is a closed system, condemned to go round and round about the same knowledge. Truth must be based on experience, and not on metaphysical speculations, on invisible things.
The best method of scientific investigation is induction, the detection of general patterns. It is the method of discovering the "forms," the unchanging and hidden essences of phenomena. These essences are not of a metaphysical order, but of a physical, observable kind. There are first-class forms or simple natures (such as color, size, etc.), which constitute the qualities (or characteristics) of something, and specific forms or composite natures (such as lion, oak, etc.).
To obtain maximum objectivity in scientific research, it is necessary to eliminate dogmas, prejudices, preconceived ideas ("the idols of the mind"), and by means of detailed and controlled observations, to make generalizations.
The process of inductive reasoning must be progressive, of continuous ascent, from the particular facts to the minor axioms, from them to the medium axioms, and finally to the more general axioms or principles. Conclusions must be inferred at the highest possible level and by analogy.
Regarding the method of induction itself, Bacon improved on the traditional method, which was based simply on drawing conclusions from particular facts, without considering any kind of structure to the set of facts. The improvement consisted in:
Consider the variables or circumstances that may or may not have influence on the phenomenon, eliminating the variables that have no influence, i.e. when the phenomenon remains unchanged. These are the so-called presence tables (of positive variables) and absence tables (of negative variables).
Consider, not only the presence of the variables, but also their degree, to create the degree table.
Classify the facts. Distinguish between privileged, borderline, and causal facts.
Bacon has remained the great promoter of the inductive experimental method and of what was called "experimental philosophy," one of the foundations of modern thought. His method is set out in detail in his work "Novum Organum" (1620), so called because it was intended to replace the old Aristotelian Organum. Bacon's empiricism was continued by John Locke and George Berkeley, until its culmination with David Hume.
William Whewell's induction
William Whewell-philosopher, historian of science, specialist in scientific nomenclature, prolific and multifaceted writer-had a great influence in his time. Today Whewell is best known for his works on philosophy and history of science. As a curiosity, he coined the terms "anode," "cathode," and "ion" for Faraday, and invented the term "scientist" (previously referred to as "natural philosopher" and "man of science").
Whewell also coined the term "consilience" in 1840 in his "History of the Inductive Sciences" [1967]. It literally means "jumping together", and Whewell used it, not as an isolated term, but as part of the phrase "the consilience of inductions". According to Whewell, consilience of inductions takes place when an induction obtained from one class of facts coincides with an induction obtained from a different class. The term "consilience" could be roughly translated as "coherent or coincident confluence or concurrence".
An illustrative example of "consilience of inductions" was Kepler's laws and Newton's law of universal gravitation. Kepler established his famous 3 laws of planetary orbits based on experimental data. Newton was inspired by Kepler's laws, the fall of bodies and the motion of tides, to establish his law of universal gravitation: two bodies are attracted by a force that is inversely proportional to the square of the distance separating them. In reality, Newton performed a higher-order induction, since he generalized a generalization (Kepler's laws), although Newton can also be considered to have used Kepler's laws as "facts".
Whewell considered himself a follower of Bacon, but claimed to have renewed his inductive method. Whewell's philosophy is as follows:
Science is primarily a human construction carried out at the historical level in a progressive way, in which induction plays a fundamental role. Science must proceed by successive steps of generalization.
Induction is "a formative act exercised by the understanding," a creative process of the mind, the creation of a new concept, of a new vision. Thus, for Whewell, induction is not a passive description of what occurs, but is an active process. Inductions are not found, but forged.
The act of inductive thinking he called "colligation" (colligation, union or link), the mental operation of associating empirical facts with a concept. For example, the known points of the Martian orbit were colligated by Kepler through the concept of "elliptic curve". There is a crucial element in induction: the role of the human mind. It is necessary to unite fact and concept, thing and thought, nature and mind. "Facts imply thoughts, for we know facts only by thinking about them."
For Whewell, the known facts are disconnected (like loose pearls) and it is the mind that supplies the string that connects them. This is genuine induction. The string is the new conception that connects and unifies the facts. Thanks to this new conception, the facts are "colligated". Colligation" is the mental process of associating particular facts to a new conception, the conceptualization of the facts. Induction is the colligation of facts.
In the case of the Martian orbit, the metaphor of the pearls and the string is most clearly appreciated: the pearls are the points (positions of Mars relative to the Sun), and the string is the elliptical curve connecting the points.
Everything has an objective dimension and a subjective dimension. He called it the "fundamental antithesis of knowledge". He criticizes Kant (for focusing only on the subjective) and Locke (for focusing only on the objective). Whewell sought the "middle way" between rationalism and empiricism.
In every act of knowledge there are two opposite elements: Fundamental Ideas and Perceptions. The Fundamental Ideas are supplied by the mind itself, are part of the structure and functionality of the mind, and are independent of all experience. The mind is an active element and not a passive receiver of observations. Every observation implies "unconscious inference" through the Fundamental Ideas.
All sciences possess their particular Fundamental Ideas. For example, space (in geometry), substance (in chemistry), cause (in mechanics), and so on. The Fundamental Ideas have certain similarities with the Kantian categories. For Kant, we only have knowledge from our categorized experience. In contrast, for Whewell, Fundamental Ideas represent objective characteristics of the external and internal world; they unite mind and nature.
Each Fundamental Idea contains certain conceptions, which are "special modifications" of the Fundamental Idea when applied to particular types of circumstances. For example, the conception of force is a modification of the Fundamental Idea of cause applied to the particular case of motion.
We have knowledge of the world because the Fundamental Ideas we use are similar to the ideas of God when He created the physical world. Our ideas are "shadows" or reflections of the Divine Ideas.
Necessary truths are truths that can be known a priori. There is no distinction between truths that can be idealized and those that cannot. Whewell thus united the laws of nature and abstract ideas.
Edward Wilson's consilience
"Consilience" is the term - taken from Whewell - used by Edward O. Wilson [1999] - Darwinian biologist, entomologist, "father" of biodiversity and sociobiology - to refer to the unity or unification of different branches of knowledge. The meaning given by Wilson to the term "consilience" as "unity of knowledge" is not exactly the same as Whewell's original; it would be a universal coherent confluence of all knowledge, a grand unified theory, a kind of "theory of everything."
Wilson's general philosophy is as follows:
The fundamental goal of science must be consilience, the search for the unification of knowledge to overcome the division between natural, human and social sciences. This unification is difficult, but possible, necessary and inevitable. It is the path that science must follow.
The search for consilience is the greatest of intellectual challenges. If achieved, it will enable us to understand complexity from the hidden essence behind all phenomena.
The mythical image of the labyrinth symbolizes the real world, complex, confusing, entangled, impossible to know thoroughly and completely, with almost infinite possibilities. Consilience is the "Ariadne's thread" that allows us to go through it.
He calls "Ionian enchantment" −an expression borrowed from Gerald Holton, physicist and historian of science− the belief in the unity of science, in unified knowledge, in the profound conviction that the world can be explained by a small number of basic laws.
The qualifier "Ionian" is after Thales of Miletus (6th century B.C.), of Ionia, the pioneer of this unifying philosophy [see Addendum]. Einstein was "Ionian to the core", since he always tried to unify concepts in physics (space-time, matter-energy, gravity-acceleration), although he did not achieve the holy grail of the great unification, although he tried until the end of his life.
The present fragmentation of knowledge, and the resulting disorder, is not a reflection of the real world, but of our mind, which has failed to discover the deep roots hidden behind all phenomena.
Everything has an objective existence that man can know, and not only the exterior, but also the interior (the mind, the thoughts, the psyche).
Science and humanities need each other. Science needs intuition and metaphorical thinking, and the humanities need rational power.
The sciences and the humanities have a common goal: to provide a sense, an overall understanding of the order of the world. This can only be achieved if they are founded on the same basic principles. Even the terminology must be identical.
The humanities are coming closer and closer to the sciences and must in the end merge with them. As much philosophy as possible must be converted into science. Philosophy must play a vital role in the desired unification.
From the lower arises the higher: from physics arises genes, from genes arises the brain, from the brain arises the mind, from the mind arises culture. Therefore, all knowledge can be reduced to a few laws of physics.
The ultimate and only basis of reality is the material matrix. All phenomena, from the birth of stars to social events are based on material processes ultimately reducible to physical laws. An organism is a machine. Everything, from the smallest particle to the most complex system, functions as a machine, so by knowing its mechanisms we can explain absolutely everything, including thoughts, emotions, creativity, ethics and spirituality.
All aspects and activities of living beings are governed by the information contained in genes. Genes determine all organic processes, including our thoughts. All forms of knowledge, including the social sciences and the humanities must be the subject of natural science and can be reduced to the deep truths of the genetic game. And genes are grounded in the physical.
The mind is a mere by-product of the brain; it is the brain at work. Psychology is reduced to neurology. Mind is "cognitive neuroscience." Concepts are links of neural networks. Emotions are mere manifestations of neural activity.
The failure of unity-of-science programs (such as logical positivism) is due to ignorance about how the brain works.
Consilience is not a science but "a metaphysical worldview," whose greatest appeal lies in the "intellectual adventure" it offers. Consilience cannot be demonstrated by logic based on first principles or by a definitive set of empirical tests.
To achieve this desired unifying worldview:
Complexity must be approached by the method of scientific reductionism. Science is the most effective intellectual tool we know. The scientific method, which has worked so well in the natural sciences, is the way to achieve unity of knowledge of everything, including metaphysical questions. All paths to truth must be scientific. Science always builds up particular knowledge from the bottom-up, in an orderly and systematic way, and condenses it into verifiable general laws and principles.
It is necessary to try to clarify "the operations that compose the mind", today scarcely understood. To understand the mind is to understand its functions. It is necessary to search for the "universal foundational concepts" to achieve the unifying consciousness. Science is neither a philosophy nor a system of beliefs, but a method, "a combination of mental operations".
The consilience of Stephen Jay Gould
The posthumous work of biologist Stephen Jay Gould (who died in 2002), "Once upon a time there was a fox and a hedgehog" [2004], is a reflection on the traditional confrontation between the sciences and the humanities. For Gould, the fox symbolizes the sciences, and the hedgehog symbolizes the humanities.
Gold considers Whewell's consilience to be correct: the inductive step from scattered observations to a common explanation, a "jumping together," a strategy of convergence from different angles toward objectivity, and pointing the way forward for the integration of different domains under a unified explanatory scheme. But he rebuts Wilson harshly on the method for achieving unity of knowledge:
He agrees with Wilson's claim about the importance of uniting sciences and humanities, but considers that Wilson distorts Whewell's original meaning by claiming that the unity of knowledge can be achieved by reductionism: that everything (including mind, ethics, and religion) is ultimately reduced to physical processes; that sciences and humanities share the same principles, and that the difference between the two is only one of magnitude.
Wilson's reductionism cannot explain two things:
The emergent phenomena that appear in complex systems, which cannot be explained from the properties of the parts. The whole is greater than the sum of its parts.
The contingency of important historical "accidents" which, in principle, cannot be predicted.
The humanities are the most glorious emergent properties of the human brain. They cannot be reduced to any kind of logic. They are essentially different from the sciences and cannot be approached or formalized by the reductionist methods of science.
Biology is much more complex than physics and chemistry, and the humanities are more complex than biology.
Organisms must be understood at their own level, as a product of massive nonlinear interactions between their genes and their environments.
The factual implies neither ethics nor aesthetics. Ethics and aesthetics have neither a genetic nor a physical basis. For example, the qualities and impact of music are not explained by the analysis of notes.
Consequently, sciences and humanities cannot achieve the kind of consilience that Wilson proposes. Wilson makes "conflation"(which, in essence, means "confusion"), i.e., the inappropriate confluence of concepts.
In contrast to Wilson's conception, Gould proposes a consilience that effectively reconciles the sciences and the humanities:
that takes into account the intrinsic differences between the two fields, differences that are not at odds with each other, but complement each other. Science and humanities are two different ways of interpreting the world around us.
That it serves to outline general theories of an intuitive type, and not of a deductive type. These theories would serve to cover the deficiencies that the sciences have in this sense.
That would effectively allow the sciences and the humanities to "jump together" in mutual collaboration to achieve greater coherence in knowledge.
To overcome the exclusionary dichotomies and, in particular, the historical cliché of the two cultures. Today, the opposition between sciences and humanities is not justified.
Gould identifies Whewell's consilience with that which he himself practices in the exposition of his discoveries. The most complex scientific concepts can be explained in simple language, without trivializing them and without distorting their original meaning. Precisely, part of the humanist tradition is the popularization of science.
Gould proposes an integration between science and humanism that responds to the U.S. national motto "E pluribus unum" (one composed of many) to integrate the knowledge of the plural under a unifying perspective.
Gould also sees no conflict between science and religion. He proposes a basic concept called "Non-Overlapping Magisteria" (NOMA), magisteria that do not overlap, that do not interfere with each other.
Critique and Comments
Whewell's conception
Whewell never spoke of the possibility of the unification of knowledge, which would be the supreme induction, induction taken to the extreme, which would lead to the philosophical ground, to the universal categories of things. However, Whewell intuited the existence of some Fundamental Ideas, which would lead to the unification of knowledge, although he did not manage to draw up a complete and formal list of those ideas and how they would be combined.
Whewell also intuited that the Fundamental Ideas represent objective characteristics of the inner and outer worlds. Both worlds, indeed, coincide. Ontology and epistemology, at the fundamental level, are the same thing: the primary archetypes.
Wilson's conception
Wilson's universalist conception of consilience and the search for the principles of knowledge is of great value and entirely necessary, given the current fragmentation of knowledge. It is true that consilience is the most important intellectual challenge we have. However, his conception suffers from serious flaws:
Wilson's consilience is an epistemological thesis that holds that all knowledge is ultimately derived from and reduced to physical phenomena. It is a materialistic or physicalistic monism that claims to be, at the same time, a metaphysical worldview, which is a contradiction.
It also claims that everything is reducible to physical principles, and at the same time advocates the search for the basic operations of the mind. Another contradiction, which in turn contradicts the above.
He also contradicts himself when he affirms that it is necessary to unite the intuition of the humanities with the rationality of science, and then pretends to build everything (including the humanities) on the material.
Wilson says that consilience cannot be demonstrated by logic based on first principles. But consilience, if it exists, must consist precisely of first principles that ground everything, including logic.
Wilson says that consilience must also be achieved by holistic synthesis, which is the opposite of reduction.
For Wilson the mind is the brain at work. But the mind is another level of reality, higher than the physical level. The brain is an instrument of the mind. Mind is not an epiphenomenon of the brain. The physical world is a particularization of the mental world, and not the other way around. The physical is the bottom rung of reality. Paradoxically, it seems the most "real", but it is not. The real is what we do not see, what is on a higher level.
Consilience is not a science. It is only a philosophy inspiring the unification of knowledge, but without any concrete proposal of those supposed laws or general principles.
When Wilson states that "everything works like a machine" he is declaring himself an orthodox reductionist and going back to the era of Newtonian determinism, ignoring the discoveries of modern physics (for example, the influence of consciousness on subatomic entities). He also declares himself an objectivist and experimental positivist.
As Stephen Jay Gould says, biology is much more complex than physics and chemistry, and the humanities are more complex than biology. Reducing everything to physics implies, for example, that social conflicts such as wars can be explained by the activity of atoms.
Wilson speaks of a "common vocabulary" (which would imply a common language) when that desired unity of knowledge is achieved. But that common vocabulary must correspond to concepts of the highest level of abstraction. From that point on, the vocabulary and the corresponding concepts must be derived from those first concepts.
The reduction to physics of all phenomena implies greater complexity of descriptions. What we need is a universal language, capable of describing the simple and the complex, the lower and the higher, the internal and the external, the particular and the general.
Wilson mixes and does not distinguish between the two kinds of consilience: the ontological (the higher levels are "made" of the lower levels) and the epistemological (the higher levels are explained, we can know them, by the lower levels).
In short, Wilson's proposal is ambitious, but naive, simplistic, superficial, diffuse and incoherent.
Gould's conception
Gould claims that it is not possible to apply reductionist methods to the humanities. But we can affirm that it is possible to establish universal principles, which are both holistic and reductionist, from which it is possible to contemplate and analyze everything.
Gould declares himself a materialist, like Wilson, in asserting that the capacities of the brain arise from material properties of an evolved neurology, and not from an independent plane of a higher type. He does not consider the issue of consciousness or considers it the same as mind, when consciousness is at a higher level than mind (as a faculty of the soul).
MENTAL and the Unity of Knowledge
MENTAL, the supreme induction
MENTAL can be considered the result of a universal abstract induction. In MENTAL there is universal consilience (coherent confluence) of inductions. From different domains (mathematics, cybernetics, artificial intelligence, etc.) the same general principles, which were hidden and which constitute a universal language, are inferred inductively. When these principles (which are principles of consciousness) come to light, everything is better understood, frontiers are dissolved and everything is simpler.
If formal sciences such as mathematics, computer science, etc. are abstract inductions, MENTAL would be an abstract induction of a higher order, a generalization of generalization.
MENTAL is a consilience of inductions (according to Wheeler's conception), since the inductions of the different fields converge coherently in universal concepts.
The universal semantic primitives of MENTAL can be considered as inductive elements, inferences or general conclusions obtained a posteriori, from the experience of the different domains, applying the highest possible level of abstraction. We can qualify them as supreme inductions, which are the result of intuition. They are also axioms established a priori from which reality can be constructed, general laws can be established and deductions can be made. Thus, there is union of the two movements of consciousness: the ascending (induction) and descending (deduction).
The search for the universal principles common to the inner and the outer, to which Wilson refers, already appear in MENTAL, in the sense that the abstract archetypes are the same at the inner and the outer level, that ontology and epistemology coincide at the deep level, that MENTAL language connects and reflects them.
MENTAL is the reflection of the Ionian spirit of which Wilson speaks, that indeed everything can be explained by a reduced set of basic principles, concepts or laws. And not only on a theoretical level, but also on a practical level. Discovering the simple is, paradoxically, the most complex. But once achieved, everything becomes simpler, clearer and more understandable.
MENTAL, strategy model for the unity of knowledge
The solution to the unity of knowledge has to come from the primary archetypes, from the higher, from the abstract and universal. Causes and principles proceed from the higher. The lower is only a manifestation of the higher. MENTAL has already traced the path in this direction. The archetypes of MENTAL already cover philosophical (the philosophical categories) and psychological (the primary archetypes) aspects. That is why we say that MENTAL is a scientific and humanistic language.
The following steps would be:
At a lower level, describe the laws of physics with MENTAL, to show that the mental world is broader than the physical world, that the physical world is a particularization of the mental world. It is not possible to speak of unification between the physical and mental worlds because they are two different levels of reality, although connected at a deep level.
Trying to find and describe general concepts or principles that allow to understand the humanities.
All knowledge converges in something that is the essence common to all things. That essence must necessarily be something archetypal and abstract because reality, at a deep level, is archetypal and abstract.
Only from the higher can the unity of knowledge be achieved. MENTAL is the demonstration that it can be achieved.
Induction is an ascending movement of consciousness. The problem is to know if there is a "ceiling" for this vertical process. And the answer is yes: it is the abstract archetypes or philosophical categories common to mind and nature. The archetypes are the centers of maximum consciousness, which unite the opposites, the inner and the outer, the concrete and the abstract, mind and nature.
In the case of integration of the humanities, the archetypes must have a deep, mythical and symbolic character, where eternal themes such as the eternal return, the hero's journey, the labyrinth, etc. must appear.
Addenda
Thales of Miletus, the pioneer
Thales of Miletus −Greek philosopher, mathematician and astronomer− is considered the "father" of philosophy, the first philosopher in the history of Western civilization. He was the founder of the Ionian school of philosophy and the first and most famous of the seven wise men of Greece. He is attributed the authorship of the legend that appeared on the frontispiece of the temple of Apollo in Delphi: "Know thyself". He introduced pure geometry in Greece and predicted an eclipse of the Sun.
Thales was the first philosopher who tried to give a rational and physical explanation of the universe, without resorting to the metaphysical or supernatural, and elaborating the first unified theory: water is the primary and universal substance of all matter, the source of all that exists; all material substances are manifestations or aspects of water; the Earth is a circular disk floating on water.
Thales has the merit of having intuited the essential unity of nature. Aristotle considered Thales the founder of the physical sciences.
Thales was the initiator of an "intellectual fever" that spread throughout Greece: rational thought. The term "Ionian fever" was used by Arthur Koestler in his work "The Sleepwalkers".
The debate between Whewell and Mill
Philosopher, logician and politician John Stuart Mill, author of "System of Logic", after reading Whewell's "History of the Inductive Sciences", decided to expand his own treatise on deductive logic with a new book devoted to inductive logic. The result was Book III of his System of Logic, which contained concepts different from those of Whewell. This gave rise to an interesting debate on the nature of the inductive process between the two authors. Whewell's reply to Mill appeared in his work "Mr. Mill's Logic" (1849).
For Mill, induction is a process in science that leads from particular facts to general properties, or from observations to theories. For Mill, for there to be true induction, the conclusion must be broader than the facts (premises). Whewell agreed with this definition.
The typical form "Peter (who is a man) is mortal, Paul (who is a man) is mortal, and so on. Then all men are mortal" is an induction for Mill because a general property is inferred from particular facts.
But for Whewell, surprisingly, this is not a true induction, but a mere juxtaposition of particular facts. For there to be true induction, there must be a new conception added by the mind, not by the facts.
Whewell and Mill discuss Kepler's discovery of the elliptical orbit of Mars from particular observations (positions). For Whewell, conceptualization occurs during the process of induction. In the data-points there is no reference to the ellipse. The ellipse is a mental creation, the concept is put into the data. This is the genuine induction: the colligation between the facts and the concept. Therefore,we must distinguish between the ideas used to express the facts and the conceptions used to colligate the facts.
For Mill, conceptualization occurs prior to induction. The property of the data-points to lie on an ellipse is determined by the points themselves. The concept is already in the data, and in induction one sees the concept in the data. The introduction of a new conception is part of every process of discovery or invention. According to Mill, Whewell confuses invention and demonstration.
For Whewell, every theory is questionable, even if it predicts new instances of the same type (for example, new points on the Martian orbit). The validity of a theory passes through the consilience of inductions. Consilience of inductions is the justification of any scientific theory. Colligation is the essential characteristic of all induction, but it is not a justification. In this sense, Whewell is stricter than Mill in the justification of every theory, for he always demands consilience of inductions.
Whewell and Mill also differ on the issue of the language of science. For Mill, the language of science is a matter that is independent of inductive processes. For Whewell, science is continually rewriting its language by introducing new conceptions or extending existing ones.
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