Biography

... one of the ignorant Sir Johns of Queen Elizabeth's time; could only read the prayers of the church and the homilies; and valued not learning, as not knowing the sweetness of it.

... he would get himself into a corner, and learn his lesson by heart.

1603

He did not much care for logic, yet he learned it, and thought himself a good disputant. He took great delight there to go to the bookbinders' shops and lie gaping on maps.

1608

1610

1626

1628

1631

1629

He was forty years old before he looked on geometry; which happened accidentally. Being in a gentleman's library Euclid's Elements lay open, and 'twas the forty-seventh proposition in the first book. He read the proposition. 'By God,' said he, 'this is impossible!' So he reads the demonstration of it, which referred him back to such a proof; which referred him back to another, which he also read. ... at last he was demonstratively convinced of that truth. This made him in love with geometry.

1629

1631

1631

1631

1642

1634

1637

1637

Whatsoever accidents or qualities our senses make us think there be in the world, they be not there, but are seemings and apparitions only; the things that really are in the world without us, are those motions by which these seemings are caused.

1640

1640

(

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1642

Hobbes's theory of optical images [ was ] developed in his optical magnum opus "A minute of first draught of the optiques" (1646) and published in abridged version in "De homine" (1658) . ... Hobbes's theory of vision and images serves him to ground his philosophy of man on his philosophy of body. Furthermore, since this part of Hobbes's work on optics is the most thoroughly geometrical, it reveals a good deal about the role of mathematics in Hobbes's philosophy.

1647

1650

Ⓣ ( Human nature )

Ⓣ ( Of the body politic )

1646

1648

1651

... he hath much injured the mathematics, and the very name of demonstration, by bestowing upon it some of his discourses, which are exceedingly short of that evidence and truth which is required to make a discourse able to bear that reputation.

1655

Ⓣ ( On the Body )

Ⓣ ( On the city )

(1642)

Ⓣ ( On man )

1658

Ⓣ ( On the Body )

12

20

3

Ⓣ ( On the Body )

(

)

If the magnitude of a body which is moved ( although it must always have some ) is considered to be none, the path by which it travels is called a line, and the space it travels along a length, and the body itself is called a point. This is the sense in which the earth is usually called a point and the path of its annual revolution the ecliptic line.

Ⓣ ( Infinitesmal arithmetic )

... it is clear that he hoped to assert preeminence in the learned world largely on the basis of the solution of the problem of squaring the circle.

Ⓣ ( On the Body )

Ⓣ ( On the Body )

... the reader should take those things that are said to be found exactly of the dimension of the circle ... as instead said problematically.

Ⓣ ( On the Body )

25

Ⓣ ( On the Body )

25

... a scab of symbols [ which disfigured the page ] as if a hen had been scraping there.

Ⓣ ( On the Body )

1656

1660

Ⓣ ( Dialogue on physics or the nature of air )

(1661)

(

)

(1662)

... Hobbes's attempts to resolve three important mathematical controversies of the seventeenth century: the debates over the status of analytic geometry, disputes over the nature of ratios, and the problem of the 'angle of contact' between a curve and tangent.

... was not the ignoramus in geometry that he is sometimes supposed. His writings, erroneous as they are in many things, contain acute remarks on points of principle.

... an amateur of mathematics in the original and best sense of the word, and through his role as a minor stimulant of others' success he merits a modest place in its annals.

1670

(

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In mathematics, he corrected some principles of geometry. he solved some most difficult problems, which had been sought in vain by the diligent scrutiny of the greatest geometers since the very beginnings of geometry; namely these:



1 . To exhibit a line equal to the arc of a circle, and a square equal to the area of a circle, and this by various methods.

2 . To divide an angle in a given ratio.

3 . To find the ratio of a cube to a sphere.

4 . To find any number of mean proportionals between two given lines.

5 . To describe a regular polygon with any number of sides.

6 . To find the centre of gravity of the quadrant of a circle.

7 . To find the centres of gravity of all types of parabolas.



He was the first to construct and demonstrate these, and many other things besides, which ( because they will appear in his writings are less important ) I pass over.

91

87

91

And so, after I had given sufficient attention to the problem by different methods, which were not understood by the professors of geometry, I added this newest one.

I am about to take my last voyage, a great leap in the dark.

(

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's father, also named Thomas Hobbes, was the vicar of Charlton and Westport, close to Malmesbury in Wiltshire. Thomas Hobbes senior was described by Aubrey inas:-Thomas Hobbes senior had an older brother, Francis Hobbes, who was a wealthy merchant with no family of his own. Thomas Hobbes, the subject of this biography, had one brother Edmund who was about two years older than he him. Thomas began his schooling in Westport Church when he was four years old. However, when he was seven years old, his father had an argument with another vicar at the door of his church. Blows were exchanged and Hobbes' father ran off. It is unclear what role his mother played in his upbringing after that, but he was certainly brought up by his uncle Francis after this.From age eight Hobbes, who was by this time proficient at reading and arithmetic, attended Mr Evan's school in Malmesbury, then later Robert Latimer's private school in Westport. Hobbes showed his brilliance at this school and was an outstanding Greek and Latin scholar by the time he left this school at age fourteen, having already translated Euripides'from Greek into Latin iambics. Aubrey intells us that as a young boy Hobbes was sometimes playful, but also sometimes withdrawn and melancholy. Often at school:-After leaving Robert Latimer's school, he entered Magdalen Hall, Oxford inwhere he continued to be supported financially by his uncle Francis. At that time the teaching at Oxford was dominated by a study of Aristotle and Hobbes soon found that his opinions differed sharply from what was being taught:-He graduated with a B.A. inand on the recommendation of Sir James Hussey, Principal of Magdalen Hall, he became the tutor of William Cavendish, later the Second Earl of Devonshire. For around two years Hobbes did little in the way of academic studies, being more of a companion to Cavendish who was only a little younger that he was. InHobbes went with Cavendish on a European tour and they visited France, Germany, and Italy. He learnt French and Italian on this trip, but more importantly, it reinvigorated his desire for learning and he decided that he would pursue a study of classics. On his return Hobbes took up studying Greek and Latin again. He had progressed from being a tutor to Cavendish to being his secretary and having few duties he had plenty of time to devote to his studies.In, on the death of his father, William Cavendish inherited the title the Earl of Devonshire, but two years later William died and Hobbes lost a friend as well as his secretarial post. William Cavendish's son was only eleven years old and Hobbes' services were no longer required by the Cavendish family at this time.Hobbes was tutor to the son of Sir Gervase Clinton of Nottinghamshire, fromto. During this period, in, he published his translation of Thucydides which he had been working on for several years. So far we have not mentioned any interest by Hobbes in mathematics, and perhaps even more surprisingly no particular interest in philosophy. In fact Hobbes was about forty years old before he became fascinated by mathematics. Although Aubrey's description of Hobbes encountering mathematics for the first time is, like so much of Aubrey, rather overdone, nevertheless his description inis well worth recording:-He undertook a second trip to the continent fromtowith his new pupil. Inthe Cavendish family requested his services again and he returned from Paris to become tutor to the third Earl of Devonshire, a position he held fromto. During this time he again visited the continent, being there fromto. On the continent he met Galileo Gassendi and Roberval and became enthusiastic about the mechanical universe and began building his philosophical position relating everything to motion. In fact his views at this time appeared to be very much in line with the latest scientific ideas of the period. Back in England inHobbes worked onwhich was not published at the time. He described his mechanistic approach to perception in this work as follows:-When the Civil War began inHobbes feared for his life, especially as he was a well known Royalist, and he fled to save his life. He lived in Paris fromwhere again he made contact with Mersenne 's circle of scholars. There he wrote his objections to Descartes'and he publishedConcerning Citizenshipinwhich contained his ideas on the relation between the church and the state. After this he worked on optics, which was one of his favourite topics. Maletwrites:-Hobbes published a new expanded edition ofin, then three years later, in, his earlier workwas published without his permission. It appeared in two parts asandHobbes was the mathematics tutor of the Prince of Wales betweenand. He remained on the continent until, the year his most famous workwas published then, late in that year, he returned to England. In fact he was now in some difficulties with all sides of the political spectrum. In England the Royalists, with Charles I dead, seemed to have lost their struggle for power. Passages near the end of theappeared to indicate that Hobbes was trying to make his peace with the English government, which angered the Royalists. In fact in these passages Hobbes was remaining consistent with his view that one showed allegiance to a ruler only so long as that ruler could provide protection. Hobbes had also attacked the Roman Catholic Church which made his position in Paris pretty untenable.Hobbes' masterpieceset out his ideas with great clarity. He argued that people want to live in peace and security and to attain this they must organise themselves into communities for protection. Since there will always be some in the community who cannot be trusted, people must set up a government with their authority to make and enforce laws necessary to protect the community. It is, Hobbes argues, the rational way for people to behave so moral behaviour is rational. Although Hobbes was himself a Christian, these arguments were seen as many as removing the need for God as the giver of moral code, for Hobbes argues that it follows by reason alone. Another aspect of the work which caused many to attack it was Hobbes' vitriolic arguments against the university system.Before this Hobbes had been seen by many as promoting a mechanistic scientific approach which was much in tune with those who would form the Royal Society . Indeed he had argued that since what we know and understand only comes through our senses and all objects that our senses can detect are material, we can only view the world in a material way. He promoted an approach through language and mathematics to analyse experience which he claimed would lead to a complete mechanistic understanding of the world. The certainty of mathematics would lead to correct and indisputable conclusions about society and about man. His argument that all was material was seen as denying the existence of the immaterialistic soul and intellect. Seth Ward, the Savilian Professor of Astronomy at Oxford, wrote:-At this stage, however, although Hobbes had published little in the way of mathematics, he certainly was considered by some as a leading mathematician on a par with Roberval and Fermat InHobbes publishedwhich, was one part of his trilogy of philosophy. He had already publishedand the third part,, would appear incontained a large amount of mathematical material; in fact Chapterstoare devoted entirely to the topic. Hobbes saw mathematics as an essential part of knowledge, but he also saw his own materialistic approach as revolutionising the subject and he set out to reform mathematics in this work. His approach is certainly consistently materialistic, denying abstract ideas; for Hobbes mathematics is the study of quantity, and quantities are the measures of-dimensional bodies. His definition of a point inwhich totally differs from that of Euclid is as follows:-Lines, therefore, are the paths of moving points, surfaces are the paths of moving lines, volumes are the result of moving surfaces. He then proceeded to study ratios and angles, then acceleration, projectiles and the ideas of Galileo followed by a study of indivisibles and the ideas of Cavalieri , the rectification of the spiral, and finally squaring the circle. It is fair to say that much of Hobbes' mathematical ideas are generalised from Galileo 's study of mechanics and of motion. The new method of indivisibles, as put forward by Cavalieri , was accepted by Hobbes but he rejected Wallis 's version as given inJesseph writes of Hobbes' attempt to square the circle:-Hobbes had originally plannedwithout this result and, having added it late on, it did not really fit with the material surrounding it. Beforereached completion, however, Hobbes' friends pointed out an error in his squaring the circle argument. Hobbes did not remove the "proof" but renamed it "From a false hypothesis, a false quadrature". He then added a second proof which he quickly changed to only claim it was "an approximate quadrature". Finally he attempted a third exact proof but when the book was being printed he realised that it too, of course, was wrong. He had to leave the incorrect claim but added at the end of the chapter:-This was a phrase that Wallis would pour scorn on when he attacked Hobbes' ideas. Although Hobbes did not believe that the "proofs" inproved the result, he would go on to publish several "proofs" of squaring the circle over the nextyears which he did believe to be correct. Wallis attacked the whole of Hobbes' mathematical work ofand a vigorous argument between the two arose which lasted foryears. To Hobbes mathematics was geometry and only geometry, and Wallis 'she described as:-Hobbes claimed that the algebraic symbols could denote different things such as lines, surfaces or volumes, and therefore were unreliable in mathematical proofs. Hobbes responded to the attack by Wallis and others ofby publishinginInHobbes attacked the 'new' methods of mathematical analysis. Inhe attacked Boyle and those setting up the Royal Society which, as a matter of interest, never elected Hobbes as a Fellowit is probably that since he was perceived as an atheist entry would have been impossible Wallis replied with telling mathematical arguments, but also with unfair charges of disloyalty. Hobbes ended the argument about disloyalty with. Hobbes could win arguments when his morality was attacked, but when it came to mathematics Wallis had a clear upper hand understanding mathematics far more deeply than Hobbes.Over the years Hobbes attempted to solve a number of outstanding mathematical problems. Jesseph, in, studies:-Although Hobbes is highly regarded as a philosopher, his mathematics has been essentially laughed at. However some have seen more in it than just errors. De Morgan wrote that Hobbes:-Grant, in, evaluates Hobbes' mathematical contributions and concludes that he was:-Hobbes defended his mathematical works to the end of his life. His errors were demonstrated so clearly that byessentially everyone considered him a mathematical illiterate, yet still he wrote articles in his defence even though it is doubtful whether anyone continued to read them. Let us end with the summary of what Hobbes believed that he had achieved in mathematics, written near the end of his life. Hobbes writes about himself in the third personsee for example:-He wasyears of age when he died, a remarkable age for someone in that period. At agehe completed translating the Iliad and the Odyssey into English verse and left London, where he had lived for many years, and spent his final years with the Cavendish family with whom he had been so closely connected throughout his life. At age, shortly before his death, he was working on yet another book on squaring the circle. The dedication contains the sentence:-His final words are reported to have been:-Let us end this biography with a final thought. If Hobbes' mathematics was worthless why has so much effort been expounded on it even in the last few yearsas the references show. There is no doubt that Hobbes' mathematics is wrong, but strangely, that does not seem to make it worthless! As a philosopher he was a leading figure, having a major influence on political thought.