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116-430: Isidore Auguste Marie François Xavier Comte ( / k ɒ n t / ; French: [oɡyst kɔ̃t] ; 19 January 1798 – 5 September 1857) was a French philosopher, mathematician and writer who formulated the doctrine of positivism . He is often regarded as the first philosopher of science in the modern sense of the term. Comte's ideas were also fundamental to the development of sociology , with him inventing

232-409: A Plan de travaux scientifiques nécessaires pour réorganiser la société (1822) ( Plan of scientific studies necessary for the reorganization of society ). But he failed to get an academic post. His day-to-day life depended on sponsors and financial help from friends. Debates rage as to how much Comte appropriated the work of Saint-Simon. Comte married Caroline Massin in 1825. In 1826, he was taken to

348-492: A certain time period is that the system "has lost its power" and is preventing the progression of civilization, causing complicated situations in society. (Lenzer 1975, pg 10) The only way to escape the situation is for people within the civilized nations to turn towards an "organic" new social system. Comte refers to kings to show the complications of re-establishment in society. Kings feel the need to reorganize their kingdom, but many fail to succeed because they do not consider that

464-472: A continuous cycle of theory and practice through the four-part cycle of Plan-Do-Check-Act ( PDCA , the Shewhart cycle ). Despite his advocacy of quantitative analysis, Comte saw a limit in its ability to help explain social phenomena. The early sociology of Herbert Spencer came about broadly as a reaction to Comte; writing after various developments in evolutionary biology, Spencer attempted to reformulate

580-477: A financial economist might study the structural reasons why a company may have a certain share price , a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the corresponding value of derivatives of the stock ( see: Valuation of options ; Financial modeling ). According to the Dictionary of Occupational Titles occupations in mathematics include

696-406: A loving disposition, the only special quality in which women are irreplaceable, and the power of which modern anarchy prevents them from appreciating as they should. Thus, my philosophical endeavors have been carried on and completed not only in the face of material difficulties, as you know, but also in the midst of more painful and absorbing disturbances, the result of an almost constant civil war of

812-400: A manner which will help ensure that the plans are maintained on a sound financial basis. As another example, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while

928-460: A mental breakdown. Comte took refuge in a hotel in Saint Denis , from where he wrote to Caroline, then disappeared. She guessed that he had gone to Montmorency , one of his favorite places, and found him there trying to set fire to his room. With the help of a local doctor she calmed him down. She returned to Paris to get help from Cerclet, and he was able to find a place at the asylum run by

1044-494: A mental health hospital, but left without being cured – only stabilized by French alienist Jean-Étienne Dominique Esquirol – so that he could work again on his plan (he would later attempt suicide in 1827 by jumping off the Pont des Arts ). In the time between this and their divorce in 1842, he published the six volumes of his Cours. Comte developed a close friendship with John Stuart Mill . From 1844, he fell deeply in love with

1160-788: A political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles). Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based primarily on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages

1276-422: A provisional theory,… which immediately groups the first facts, with its help, by cultivating our capacity for observation, we were able to prepare the age of a wholly positive philosophy." (Comte 149) Comte believed the theological stage was necessary because of the foundational belief that man's earliest philosophy of explanation is the act of connecting phenomena around him to his own actions; that man may "apply

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1392-414: A result of an unfortunate love to a woman of rare moral and intellectual qualities, but brought up under blameworthy principles and with a false notion of the essential function that her sex must play in the human economy. Her total lack of affection for me has never made it possible for me to overlook either her resistance to my authority or her despotic character. There have been none of the compensations of

1508-470: A single being for the varied play of numerous independent gods which have been imagined by the primitive mind." These Gods often took on both human and animal resemblance. In Egypt, there were multiple gods with animal body parts such as Ra, who had the head of a hawk and had sun associations with the Egyptians. The polytheistic Greeks had several gods such as Poseidon who controlled the sea and Demeter who

1624-486: A system". Though, according to Comte, it could not last, this stage was able to establish an intellectual unity that made an impressive political system. The theological state was also necessary for human progress on account that it creates a class in a society dedicated to "speculative activity". It is in this way that Comte sees the theological stage continue to exist into the Enlightenment. Comte momentarily admires

1740-526: A time off the proceeds. In February 1824 she and Comte moved into an apartment just off the rue Saint-Honoré for which she supplied the furniture. They settled into a regular and happy routine, eating at home and retiring early. In letters written in 1824 Comte described Caroline as "very spiritual, very kind, and pretty." He loved "her good heart, her graces, her rare spirit, her kindness, her happy character and her good habits." His best friend Pierre Valat wrote that she had great charm and high intelligence, and

1856-420: Is mathematics that studies entirely abstract concepts . From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics , and at variance with the trend towards meeting the needs of navigation , astronomy , physics , economics , engineering , and other applications. Another insightful view put forth is that pure mathematics

1972-451: Is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on problems, often concrete but sometimes abstract. As professionals focused on problem solving, applied mathematicians look into the formulation, study, and use of mathematical models in science , engineering , business , and other areas of mathematical practice. Pure mathematics

2088-408: Is broken into three sections: The second stage, the metaphysical stage, is merely a modification of the first because a supernatural cause is replaced by an "abstract entity"; it is meant to be a transitional stage, where there is the belief that abstract forces control the behavior of human beings. Because it is a transitional stage between the theological stage and the positive stage, Comte deemed it

2204-427: Is complete. The last stage – the positive stage – is when the mind stops searching for the cause of phenomena and realizes that laws exist to govern human behavior and that this stage can be explained rationally with the use of reason and observation, both of which are used to study the social world. This stage relies on science, rational thought, and empirical laws. Comte believed that this study of sociology he created

2320-502: Is equally true that facts can not be observed without the guidance of some theories. Without such guidance, our facts would be desultory and fruitless; we could not retain them: for the most part, we could not even perceive them." Comte's emphasis on the interconnectedness of social elements was a forerunner of modern functionalism . Nevertheless, as with many others of Comte's time, certain elements of his work are now viewed as eccentric and unscientific, and his grand vision of sociology as

2436-433: Is in the past are still relevant to recent knowledge. It is what is before our time that guides why things are the way they are today. We would always be relying on our own facts and would never hypothesize to reveal the supernatural if we do not observe. Observing strives to further our thinking processes. According to Comte, "‘The dead govern the living,’ which is likely a reference to the cumulative nature of positivism and

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2552-411: Is no other use for this stage. Although it is the least important stage, it is necessary because humans could not handle the significant change in thought from theological to positivity. The metaphysical stage is just a slight modification of the previous stage when people believed in the abstract forces rather than the supernatural. The mind begins to notice the facts themselves, caused by the emptiness of

2668-488: Is not a result of the way we think, rather our perspective that guides the way we think. Comte expresses the idea that we have to open our eyes to different ideas and ways to evaluate our surroundings such as focusing outside of the simple facts and abstract ideas but instead dive into the supernatural. This does not make mean that what is around us is not critical to look out for as our observations are critical assets to our thinking. The things that are "lost" or knowledge that

2784-400: Is not necessarily applied mathematics : it is possible to study abstract entities with respect to their intrinsic nature, and not be concerned with how they manifest in the real world. Even though the pure and applied viewpoints are distinct philosophical positions, in practice there is much overlap in the activity of pure and applied mathematicians. To develop accurate models for describing

2900-498: Is the necessary starting point of human intelligence. The human mind primarily focuses its attention on the "inner nature of beings and to the first and final causes of all phenomena it observes." (Ferre 2) This means that the mind is looking for the cause and effect of an action that will govern the social world. Therefore, it "represents these phenomena as being produced by a direct and continuous action of more or less numerous supernatural agents, whose arbitrary interventions explain all

3016-448: Is through observation that humanity is able to gather knowledge. The only way within society to gather evidence and build upon what we do not already know to strengthen society is to observe and experience our situational surroundings. “In the positive state, the mind stops looking for causes of phenomena, and limits itself strictly to laws governing them; likewise, absolute notions are replaced by relative ones,” The imperfection of humanity

3132-550: The metaphysical stage, and (3) the positive stage. Comte's law of three stages was one of the first theories of social evolutionism . He once wrote: 'It is evident, the Solar System is badly designed' The other universal law he called the "encyclopedic law". By combining these laws, Comte developed a systematic and hierarchical classification of all sciences, including inorganic physics (astronomy, earth science and chemistry) and organic physics (biology and, for

3248-653: The Pythagorean school , whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria ( c.  AD 350 – 415). She succeeded her father as librarian at the Great Library and wrote many works on applied mathematics. Because of

3364-596: The Religion of Humanity for positivist societies to fulfil the cohesive function once held by traditional worship. In 1849, he proposed a calendar reform called the ' positivist calendar '. For close associate John Stuart Mill , it was possible to distinguish between a "good Comte" (the author of the Course in Positive Philosophy ) and a "bad Comte" (the author of the secular-religious system ). The system

3480-676: The Schock Prize , and the Nevanlinna Prize . The American Mathematical Society , Association for Women in Mathematics , and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics. Several well known mathematicians have written autobiographies in part to explain to a general audience what it is about mathematics that has made them want to devote their lives to its study. These provide some of

3596-522: The epistemological perspective of positivism in The Course in Positive Philosophy , a series of texts published between 1830 and 1842. These texts were followed by the 1848 work, A General View of Positivism (published in English in 1865). The first 3 volumes of the Course dealt chiefly with the physical sciences already in existence (mathematics, astronomy, physics, chemistry, biology), whereas

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3712-478: The graduate level . In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a doctoral dissertation . Mathematicians involved with solving problems with applications in real life are called applied mathematicians . Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of

3828-447: The École Polytechnique . In December 1839 Caroline told Blainville she thought Comte was on the verge of another attack like that of 1826. For the last year he had treated her with coarse reproaches, harsh words and violence out of all proportion to her offenses. She did not know what to do, and feared that if he went mad again he would be lost forever. At yet another crisis in the relationship, Caroline found an apartment for herself in

3944-413: The "general laws of the inorganic world", and are harder to distinguish. Physiology completes the system of natural sciences and is the most important of all sciences because it is the "only solid basis of the social reorganization that must terminate the crisis in which the most civilized nations have found themselves". This stage will fix the problems in current nations, allowing progression and peace. It

4060-399: The "science that relates to the measurement of magnitudes", is the most perfect science of all, and is applied to the most important laws of the universe. Astronomy is the most simple science and is the first "to be subjected to positive theories". Physics is less satisfactory than astronomy, because it is more complex, having less pure and systemized theories. Physics, as well as chemistry, are

4176-524: The 9th arrondissement and moved there on 5 August 1842. This time the separation proved final. She left Comte just after the completion of his Cours de philosophie positive . Caroline recognized that the problems with the marriage were due to her insistence on equality. She wrote, I have always been devoted to you, but I was not at all submissive. If there had been less real devotion and more submission, things would have been better between us. Many times you were basically right, but you asked me to yield in

4292-589: The Catholic Clotilde de Vaux , although because she was not divorced from her first husband, their love was never consummated. After her death in 1846 this love became quasi-religious, and Comte, working closely with Mill (who was refining his own such system) developed a new " Religion of Humanity ". John Kells Ingram , an adherent of Comte, visited him in Paris in 1855. He published four volumes of Système de politique positive (1851–1854). His final work,

4408-529: The Grand Hierarchy of Abstract Science." Comte's explanation of the Positive philosophy introduced the important relationship between theory, practice, and human understanding of the world. On page 27 of the 1855 printing of Harriet Martineau 's translation of The Positive Philosophy of Auguste Comte , we see his observation that, "If it is true that every theory must be based upon observed facts, it

4524-586: The Italian and German universities, but as they already enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment , the same influences that inspired Humboldt. The Universities of Oxford and Cambridge emphasized the importance of research , arguably more authentically implementing Humboldt's idea of a university than even German universities, which were subject to state authority. Overall, science (including mathematics) became

4640-750: The Minister of Public Works, and wrote follow-up letters that eventually resulted in renewal of the authorization. Due to the breakdown of their marriage, and because he had fallen in love with another woman, Clotilde de Vaux , Comte later tried to destroy her reputation. He wrote a "secret addition" to his will in which he insinuated that she was a prostitute. Comte blamed Caroline for causing his mental breakdown in 1826-27, which he claimed had cost him four years of lost productive time. He described her as meretricious, unworthy, heartless and ungrateful. Caroline heard of Comte's death in September 1857 and attended

4756-486: The apparent anomalies of the universe." (Ferre 2) This primary subset of the theological state is known as fetishism, where the phenomena must be caused and created by a theological supernatural being such as God, making humans view every event in the universe as a direct will from these supernatural agents. Some people believed in souls or spirits that possessed inanimate objects and practiced Animism. These natural spiritual beings who possessed souls and may exist apart from

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4872-578: The best glimpses into what it means to be a mathematician. The following list contains some works that are not autobiographies, but rather essays on mathematics and mathematicians with strong autobiographical elements. Caroline Massin Caroline Massin was born in Châtillon-sur-Seine on 2 July 1802. Her parents were Louis Hilare Massin and Marie Anne Baudelot, provincial actors. They were not married and separated soon after she

4988-401: The break Comte began in visit his benefactors in person rather than have the funds delivered by Littré. He continued to give half his money to Caroline. Caroline continued to correspond with Comte, and continued to help him. When the government refused to authorize him to continue teaching his course on the history of humanity in 1850, Caroline obtained an interview with Jean-Martial Bineau ,

5104-545: The care of his father. They appeared before a judge on 2 June 1826 and declared to the judge that they were the only people in Paris close to Comte, making no mention of his wife but saying he had a mistress whose depravity was the cause of his madness. The interdiction was granted. When Caroline heard of this she asked Blainville for help and he arranged to have the interdiction cancelled. Rosalie Comte stayed in Paris for six months, spending much time with Caroline, and began to feel her daughter-in-law had been maligned. She checked

5220-427: The cause of all phenomena. In this stage, humans focus on discovering absolute knowledge. Comte disapproved of this stage because it turned to simple explanation humans created in their minds that all phenomena were caused by supernatural agents, rather than human reason and experience. Comte refers to Bacon's philosophy that "there can be no real knowledge except that which rests upon observed facts", but he observes that

5336-503: The centerpiece of all the sciences has not come to fruition. His emphasis on a quantitative, mathematical basis for decision-making remains with us today. It is a foundation of the modern notion of Positivism, modern quantitative statistical analysis , and business decision-making. His description of the continuing cyclical relationship between theory and practice is seen in modern business systems of Total Quality Management (TQM) and Continuous Quality Improvement where advocates describe

5452-443: The civilizations in the distant past. Having been used before the 1300s, this is a very basic view of the world with little to no involvement in the world of science, and a world of illusions and delusions, as Freud would put it. To seek the nature of all beings, mankind puts its focus on sentiments, feelings, and emotions. This turned mankind towards theology and the creation of gods to answer all their questions. The Theological Stage

5568-409: The commemorative ceremony in his apartment, to the horror of his disciples. When she heard of the contents of the "secret addition" she was furious. She exercised her rights as widow of an author and owner of their common property. The marriage contract between her and Comte said she had contributed 20,000 francs to the household, and she exerted the rights to this amount in cash or property. She also had

5684-577: The development of non-theistic religious humanist and secular humanist organisations in the 19th century. He may also have coined the word altruisme ( altruism ). Auguste Comte was born in Montpellier , Hérault on 19 January 1798, at the time under the rule of the newly founded French First Republic . After attending the Lycée Joffre and then the University of Montpellier , Comte

5800-428: The discipline in what we might now describe as socially Darwinistic terms. Comte's fame today owes in part to Émile Littré , who founded The Positivist Review in 1867. Auguste Comte did not create the idea of Sociology, the study of society, patterns of social relationships, social interaction, and culture, but instead, he expanded it greatly. Positivism, the principle of conducting sociology through empiricism and

5916-500: The earliest known mathematicians was Thales of Miletus ( c.  624  – c.  546 BC ); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry , by deriving four corollaries to Thales's theorem . The number of known mathematicians grew when Pythagoras of Samos ( c.  582  – c.  507 BC ) established

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6032-504: The exactness of a science is in inverse proportion to its complexity. The degree of exactness or positivity is, moreover, that to which it can be subjected to mathematical demonstration, and therefore mathematics, which is not itself a concrete science, is the general gauge by which the position of every science is to be determined. Generalizing thus, Comte found that there were five great groups of phenomena of equal classificatory value but of successively decreasing positivity. To these, he gave

6148-524: The fact that our current world is shaped by the actions and discoveries of those who came before us," As this is true, the observations only relevant to humanity and not abstractly related to humanity are distinct and seen situationally. The situation leads to human observation as a reflection of the tension in society can be reviewed, overall helping to enhance knowledge development. Upon our observation skills, our thinking shifts. As thinkers and observers, we switch from trying to identify truth and turn toward

6264-399: The first time, physique sociale , later renamed Sociologie ). Independently from Emmanuel Joseph Sieyès 's introduction of the term in 1780, Comte re-invented "sociologie", and introduced the term as a neologism , in 1838. Comte had earlier used the term "social physics", but that term had been appropriated by others, notably by Adolphe Quetelet . The most important thing to determine was

6380-535: The first volume of La Synthèse Subjective ("The Subjective Synthesis"), was published in 1856. Comte died in Paris on 5 September 1857 from stomach cancer and was buried in the famous Père Lachaise Cemetery , surrounded by cenotaphs in memory of his mother, Rosalie Boyer, and of Clotilde de Vaux. His apartment from 1841 to 1857 is now conserved as the Maison d'Auguste Comte and is located at 10 rue Monsieur-le-Prince, in Paris' 6th arrondissement . Comte first described

6496-442: The focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. The German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of

6612-1060: The following. There is no Nobel Prize in mathematics, though sometimes mathematicians have won the Nobel Prize in a different field, such as economics or physics. Prominent prizes in mathematics include the Abel Prize , the Chern Medal , the Fields Medal , the Gauss Prize , the Nemmers Prize , the Balzan Prize , the Crafoord Prize , the Shaw Prize , the Steele Prize , the Wolf Prize ,

6728-521: The good of others as the end of moral action.” (Britannica, T, 2013). Furthermore, Comte explains sociocracy as the governance by people who know each other, friends, or allies. After the French revolution, Comte was looking for a rational basis for government, after developing the Positivism philosophy he developed sociocracy to the “scientific method” of the government. In later years, Comte developed

6844-514: The growth of the human mind progresses in stages, and so must societies. He claimed the history of society could be divided into three different stages: theological, metaphysical, and positive. The Law of three Stages, an evolutionary theory, describes how the history of societies is split into three sections due to new thoughts on philosophy. Comte believed that evolution was the growth of the human mind, splitting into stages and evolving through these stages. Comte concluded that society acts similarly to

6960-432: The human will, to which all classes of society contributed, and of which kings themselves have often been the first agents and most eager promoters". The people themselves have the ability to produce a new system. This pattern is shown through the theological stage, metaphysical stage, and positive stage. The Law of Three Stages is split into stages, much like how the human mind changes from stage to stage. The three stages are

7076-406: The idea of a religion of humanity and his injunction to "vivre pour autrui" ("live for others"), from which comes the word " altruism ". Comte was agitated by the fact that no one had synthesized physics, chemistry, and biology into a coherent system of ideas, so he began an attempt to reasonably deduce facts about the social world from the use of the sciences. Through his studies, he concluded that

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7192-633: The imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, and localized constructs, applied mathematicians work regularly in the study and formulation of mathematical models . Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers. The discipline of applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics"

7308-432: The influence of his first teacher and protestant pastor Daniel Encontre. In August 1817 he found an apartment at 36 Rue Bonaparte in Paris's 6th arrondissement (where he lived until 1822) and later that year he became a student and secretary to Henri de Saint-Simon , who brought Comte into contact with intellectual society and greatly influenced his thought therefrom. During that time, Comte published his first essays in

7424-580: The kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of "freedom of scientific research, teaching and study." Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education , and then proceed to specialize in topics of their own choice at

7540-474: The king of Prussia , Fredrick William III , to build a university in Berlin based on Friedrich Schleiermacher 's liberal ideas; the goal was to demonstrate the process of the discovery of knowledge and to teach students to "take account of fundamental laws of science in all their thinking." Thus, seminars and laboratories started to evolve. British universities of this period adopted some approaches familiar to

7656-481: The latter two emphasised the inevitable coming of social science . Observing the circular dependence of theory and observation in science, and classifying the sciences in this way, Comte may be regarded as the first philosopher of science in the modern sense of the term. Comte was also the first to distinguish natural philosophy from science explicitly. For him, the physical sciences had necessarily to arrive first, before humanity could adequately channel its efforts into

7772-429: The least important of the three stages and was only necessary because the human mind cannot make the jump from the theological to the positive stage on its own. The metaphysical stage is the transitional stage. Because "Theology and physics are so profoundly incompatible", and their "conceptions are so radically opposed in character", human intelligence must have a gradual transition. Other than this, Comte says that there

7888-419: The material bodies were capable of interacting with humans, therefore requiring sacrifices and worship to please the agents. With all these new reasons behind phenomena, numerous fetishisms occur, needing several gods to continue to explain events. People begin to believe that every object or event has a unique god attached to it. This belief is called polytheism. The mind "substituted the providential action of

8004-443: The metaphysical agents through "over subtle qualification that all right-minded persons considered them to be only the abstract names of the phenomena in question". The mind becomes familiar with concepts, wanting to seek more, and therefore is prepared to move into the positive stage. In understanding Comte’s argument, it is important to note that Comte explains the theological and positive stages first and only then returns to explain

8120-405: The metaphysical stage. His rationale in this decision is that “any intermediate state can be judged only after a precise analysis of two extremes”. Only upon arrival to the rational positive state can the metaphysical state be analyzed, serving only a purpose of aiding in the transition from the theological to a positive state. Furthermore, this state “reconciles, for a time, the radical opposition of

8236-633: The mind. The law is this: that each of our leading conceptions – each branch of our knowledge – passes successively through three different theoretical conditions: the Theological, or fictitious; the Metaphysical, or abstract; and the Scientific, or positive. The Law of Three Stages is the evolution of society in which the stages have already occurred or are currently developing. The reason why there are newly developed stages after

8352-427: The modern-day debate. Some intellectuals allude to the fact that the utopian system of modern life "served as a catalyst for various world-making activities during the nineteenth and early twentieth centuries" (Willson, M. 2019) . In this utopian project, Comte introduces three major concepts: altruism, sociocracy, and the religion of Humanity. In the 19th century, Comte coined altruism as "a theory of conduct that regards

8468-426: The most challenging and complex "Queen science" of human society itself. His work View of Positivism would therefore set out to define, in more detail, the empirical goals of the sociological method. Comte offered an account of social evolution , proposing that society undergoes three phases in its quest for the truth according to a general law of three stages. Comte's stages were (1) the theological stage, (2)

8584-472: The most intimate kind, the confrontation in the home. The event which has just taken place makes me hope that from now on, even if I lack the happiness at home for which I was made but which I had to give up a long time ago, I shall at least have the sad peace of my loneliness that now completely envelops me. Caroline Massin was intelligent and had some education. She was offered a job as a governess immediately after she finally separated from Comte. After Comte

8700-813: The name of your authority, and I stood up to you when I should have submitted. Really, I did not know how to be submissive, but even so, I did love you. You know that very well.... My great crime was to see in you a husband, not a master. I know very well that you are superior to me in many respects, and besides, this comparison has always seemed to me . . . most absurd. We did not do the same things. Comte wrote to John Stuart Mill on 24 August 1842 to pour out his troubles, Our personal friendship (...) causes me not to wait any longer to give you an important piece of personal news. A fundamental change, more favorable than unfavorable, has occurred in my household since my last letter. Madame Comte has left me voluntarily and probably irrevocably. For seventeen years I have been married, as

8816-538: The names: astronomy, physics, chemistry, biology, and sociology. This idea of a special science (not the humanities, not metaphysics ) for the social was prominent in the 19th century and not unique to Comte. It has recently been discovered that the term "sociology" (as a term considered coined by Comte) had already been introduced in 1780, albeit with a different meaning, by the French essayist Emmanuel Joseph Sieyès (1748–1836). The ambitious (or many would say 'grandiose') ways that Comte conceived of this special science of

8932-425: The natural order in which the sciences stand – not how they can be made to stand, but how they must stand, irrespective of the wishes of anyone...This Comte accomplished by taking as the criterion of the position of each the degree of what he called "positivity", which is simply the degree to which the phenomena can be exactly determined. This, as may be readily seen, is also a measure of their relative complexity, since

9048-400: The origin of human knowledge, Comte claims that humans would have been "incapable of remembering facts", and would not have escaped the circle if it were not for theological conceptions, which were less complicated explanations to human life. Although Comte disliked this stage, he explains that theology was necessary at the beginning of the developing primitive mind. The first theological state

9164-453: The other two, adapting itself to the gradual decline of the one and the preparatory rise of the other”. Therefore, the transition between the two states is almost unperceivable. Unlike its predecessor and successor, the metaphysical state does not have a strong intellectual foundation nor social power for a political organization. Rather it simply serves to guide man until the transition from imaginative theological state to rational positive state

9280-403: The primitive mind could not have thought that way because it would have only created a vicious circle between observations and theories. "For if, on the one hand, every positive theory must necessarily be founded upon observations, it is, on the other hand, no less true that, in order to observe, our mind has need of some theory or other". Because the human mind could not have thought in that way in

9396-531: The probability and likely cost of the occurrence of an event such as death, sickness, injury, disability, or loss of property. Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk. Using their broad knowledge, actuaries help design and price insurance policies, pension plans, and other financial strategies in

9512-416: The progress of civilization needs reform, not perceiving that there is nothing more perfect than inserting a new, more harmonious system. Kings fail to see the effectiveness of abandoning old systems because they do not understand the nature of the present crisis. But in order to progress, there need to be the necessary consequences that come with it, which is caused by a "series of modifications, independent of

9628-576: The psychiatrist Jean-Étienne Dominique Esquirol . Cerclet, Caroline and Comte's friend the celebrated biologist Henri Blainville managed to move Comte there through a ruse. Louis Massin, Caroline's father, had appeared just before Comte's breakdown to ask her for money. She refused, and in revenge he slandered her to Comte's very respectable parents, telling them her infidelities had driven their son mad. Comte's mother Rosalie came to Paris to help her son. The family tried to obtain an "interdiction", which would remove Comte's legal rights and place him under

9744-442: The rationality and reason nature brings, giving us the ability to observe. This distinct switch takes on the transition from the abstract to the supernatural. Mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems . Mathematicians are concerned with numbers , data , quantity , structure , space , models , and change . One of

9860-484: The real world, many applied mathematicians draw on tools and techniques that are often considered to be "pure" mathematics. On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research. Many professional mathematicians also engage in the teaching of mathematics. Duties may include: Many careers in mathematics outside of universities involve consulting. For instance, actuaries assemble and analyze data to estimate

9976-426: The reason behind phenomena, the polytheistic gods are fillers that can be replaced by monotheistic gods. The theological stage shows how the primitive mind views supernatural phenomena and how it defines and sorts the causes. "The earliest progress of the human mind could only have been produced by the theological method, the only method which can develop spontaneously. It alone has the important property of offering us

10092-431: The register of prostitutes and found no trace of her name. She showed Caroline the letter her father Louis Massin had written, and Caroline was profoundly shocked. On 2 December Esquirol declared that he could not cure Comte, and returned him to Caroline. He was forced to submit to a Catholic wedding that Rosalie had arranged. At first Comte was violent and unpredictable, but Caroline began to nurse him back to sanity. He

10208-511: The relations among philosophy of science, history of science, and sociology of science be seen." He says that sociology and history are not mutually exclusive, but that history is the method of sociology, thus he calls sociology the “final science.” This positive stage was to solve social problems and forcing these social problems to be fixed without care for “the will of God” or “human rights.” Comte finds that these stages can be seen across different societies across all of history. The first stage,

10324-481: The rights to his writings, and could decide what could be published. She specifically wanted the will and the correspondence between her husband and Clotilde de Vaux suppressed. She encouraged Littré to write a biography of Comte in which he would promote his scientific positivism, but discredit the last years of his life when his mind was degenerating. She also helped establish the Revue de la Philosophie Positive , which

10440-431: The scientific method, was the primary way that Comte studied sociology. He split sociology into two different areas of study. One, social statics, how society holds itself together, and two, social dynamics, the study of the causes of societal changes. He saw these areas as parts of the same system. Comte compared society and sociology to the human body and anatomy. "Comte ascribed the functions of connection and boundaries to

10556-403: The seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle , and at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics . Moving into the 19th century, the objective of universities all across Europe evolved from teaching the "regurgitation of knowledge" to "encourag[ing] productive thinking." In 1810, Alexander von Humboldt convinced

10672-473: The social structures of language, religion, and division of labor." Through language, everybody in society, both past, and present, can communicate with each other. Religion unites society under a common belief system and functions in harmony under a system. Finally, the division of labor allows everyone in society to depend upon each other. Comte is often disregarded when talking about utopia. However, he made many contributions to utopian literature and influenced

10788-415: The social, however, was unique. Comte saw this new science, sociology, as the last and greatest of all sciences, one which would include all other sciences and integrate and relate their findings into a cohesive whole. It has to be pointed out, however, that he noted a seventh science, one even greater than sociology. Namely, Comte considered " Anthropology , or true science of Man [to be] the last gradation in

10904-441: The study of external nature to his own". This first stage is necessary to remove mankind from the "vicious circle in which it was confined by the two necessities of observing first, in order to form conceptions, and of forming theories first, in order to observe". Additionally, the theological stage is able to organize society by directing "the first social organization, as it first forms a system of common opinions, and by forming such

11020-409: The theological stage for its remarkable ability to enact this activity amidst a time when it was argued to be impractical. It is to this stage that the human mind owes "the first effectual separation between theory and practice, which could take place in no other manner" other than through the institution provided by the theological stage. The Theological Stage is the stage that was seen primarily among

11136-403: The theological stage, relies on supernatural or religious explanations of the phenomena of human behavior because "the human mind, in its search for the primary and final causes of phenomena, explains the apparent anomalies in the universe as interventions of supernatural agents". The Theological Stage is the "necessary starting point of human intelligence" when humans turn to supernatural agents as

11252-457: The theological stage, the metaphysical stage, and the positive stage, also known as the Law of Three Stages. The theological stage happened before the 1300s, in which all societies lived a life that was completely theocentric. The metaphysical stage was when the society seeks universal rights and freedom. With the third and final stage, the positive stage, Comte takes a stand on the question, “how should

11368-436: The times they were apart show mutual affection, but also show tension. Caroline and Comte separated for a third time on 3 May 1838. She was given a financial settlement and moved to a new apartment. The break did not last, and she returned later that month. Comte was unable to get a full-time teaching appointment, and survived through low-paid jobs like teaching mathematics at a private school and being an external examiner at

11484-401: The universe because everything is under one ruler. This leaves no confusion of how to act or who is the superior ruler out of the several gods seen in polytheism. The theological state functions well as the first state of the mind when making a belief about an event because it creates a temporary placeholder for the cause of the action which can later be replaced. By allowing the brain to think of

11600-434: The various publications headed by Saint-Simon, L'Industrie , Le Politique , and L'Organisateur ( Charles Dunoyer and Charles Comte 's Le Censeur Européen ), although he would not publish under his own name until 1819's "La séparation générale entre les opinions et les désirs" ("The general separation of opinions and desires"). In 1824, Comte left Saint-Simon, again because of unbridgeable differences. Comte published

11716-511: The very term and treating the discipline as the crowning achievement of the sciences. Influenced by Henri de Saint-Simon , Comte's work attempted to remedy the social disorder caused by the French Revolution , which he believed indicated imminent transition to a new form of society. He sought to establish a new social doctrine based on science, which he labelled positivism . He had a major impact on 19th-century thought, influencing

11832-444: The work of social thinkers such as John Stuart Mill and George Eliot . His concept of Sociologie and social evolutionism set the tone for early social theorists and anthropologists such as Harriet Martineau and Herbert Spencer , evolving into modern academic sociology presented by Émile Durkheim as practical and objective social research . Comte's social theories culminated in his " Religion of Humanity ", which presaged

11948-411: The world can be rationally explained through science, rational thought, laws, and observation. Comte was a positivist, believing in the natural rather than the supernatural, and so he claimed that his time period, the 1800s, was in the positivist stage. He believed that within this stage, there is a hierarchy of sciences: mathematics, astronomy, terrestrial physics, chemistry, and physiology. Mathematics,

12064-943: Was Al-Khawarizmi . A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics , maths and astronomy of Ibn al-Haytham . The Renaissance brought an increased emphasis on mathematics and science to Europe. During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting ); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer). As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in

12180-452: Was "the science that [came] after all the others; and as the final science, it must assume the task of coordinating the development of the whole of knowledge" because it organized all of human behavior. The final, most evolved stage is the positivist stage, the stage when humans give up on discovering absolute truth, and turn towards discovering, through reasoning and observation, actual laws of phenomena. Humans realize that laws exist and that

12296-570: Was admitted to École Polytechnique in Paris. The École Polytechnique was notable for its adherence to the French ideals of republicanism and progress . The École closed in 1816 for reorganization, and Comte continued his studies at the medical school at Montpellier. When the École Polytechnique reopened, he did not request readmission. Following his return to Montpellier, Comte soon came to see unbridgeable differences with his Catholic and monarchist family and set off again for Paris, earning money by small jobs. Comte had abandoned Catholicism under

12412-422: Was born. She was raised in a warm and upright environment in Paris by her maternal grandmother, wife of a tailor. In 1813 her grandfather died. Her grandmother could no longer support her and returned her to her mother. Her life in the next few years is obscure. She seems to have been given some education since her surviving letters show she wrote well. She may have worked as a laundress, seamstress or actress. She

12528-518: Was dismissed from the École Polytechnique in 1844, his English collaborator John Stuart Mill gave him some immediate funds and arranged for three of his wealthy friends to provide him with a pension. Later his supporter Émile Littré arranged for a group of 73 of his French supporters to provide a stipend on which he could live comfortably. Some sources say that Caroline began an affair with Émile Littré. Certainly Comte broke with Littré due in part to jealousy of Littre's friendship with Caroline. After

12644-538: Was during the marriage that Comte wrote his masterwork, the six volume Cours de Philosophie Positive ( Course in Positive Philosophy ). The couple had little money and Comte could not find work he liked, but at the end of July they managed to make a visit to Comte's parents in Montpellier . Caroline and Comte's parents did not get on. Comte suspected that Caroline was being unfaithful, possibly with Cerclet and others. They separated in March 1826, and soon after Comte had

12760-431: Was ongoing throughout the reign of certain caliphs, and it turned out that certain scholars became experts in the works they translated, and in turn received further support for continuing to develop certain sciences. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support

12876-428: Was passionately loved by Comte. They decided to marry, and Comte wrote to ask his parents for their approval. The marriage took place on 19 February 1825. Caroline's mother attended and gave her consent. Both she and Caroline gave their occupations as washerwomen. There were four witnesses, including Antoine Cerclet. The marriage was unhappy, often violent, stressed by lack of money and with several separations, but it

12992-399: Was running a bookshop or reading room in 1822 when Auguste Comte met her through a mutual friend, a young and liberal lawyer named Antoine Cerclet. Comte and Caroline Massin began meeting occasionally in public. In the autumn of 1823 Comte began giving Caroline mathematics lessons at her apartment, and they became intimate. Early in 1824 Caroline sold the reading room, planning to live for

13108-458: Was still unstable and depressive. In March 1827 Comte tried to kill himself by jumping into the Seine from a bridge, but was prevented by a passing royal guard. After his second attempt at suicide he decided he had been saved so he could undertake his life's work, the description of a positivist philosophy. Caroline supported him throughout this time. She acted as Comte's full-time secretary while he

13224-419: Was the goddess of fertility. However, with all these new gods governing the phenomena of society, the brain can get confused with the numerous gods it needs to remember. The human mind eliminates this problem by believing in a sub-stage called monotheism. Rather than having multiple gods, there is simply one all-knowing and omnipotent God who is the center of power controlling the world. This creates harmony with

13340-498: Was unsuccessful but met with the publication of Darwin 's On the Origin of Species (1859) to influence the proliferation of various Secular Humanist organizations in the 19th century, especially through the work of secularists such as George Holyoake and Richard Congreve . Although Comte's English followers, including George Eliot and Harriet Martineau, for the most part rejected the full gloomy panoply of his system, they liked

13456-472: Was writing his book. Caroline fell ill with smallpox in late 1832. Comte was not helpful during her convalescence, and they lived apart from the middle of March to the end of August 1833. Caroline's mother died on 29 August 1833 and she suffered a strong emotional crisis. Comte did what he could to help her through this period. The marriage continued to be strained by lack of money, particularly in 1834. The letters exchanged between Caroline and Comte during

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