1846. Theory of the Syllogism

‘In the year 1846,’ Mr. De Morgan wrote, ‘I had begun to collect various matters which had suggested themselves at different times, connected with the theory of the Syllogism in Logic.’ In the year 1847 the Formal Logic was published.

The memoirs On the Syllogism, Nos. I., II., III., IV., and V., are Mathematical workings of the principles developed in the Formal Logic; and the tracts On the Structure of the Syllogism, and On the Application of the Theory of Probabilities to Questions of Argument and Authority, immediately preceded it.

The first chapter of Formal Logic consists, with a few alterations, of the tract entitled First Notions of Logic preparatory to the Study of Geometry; London, 1839. The work as a whole, and in its higher parts, is original, but the author has been careful to distinguish between what he claimed as exclusively his own and the work of others by printing in italics, in the Table of Contents, the headings of those articles which refer to his peculiar system. A reference to this table will show how large and essential a portion was claimed as entirely new. After working these points out in his own mind, the author found that he was able to explain by their means passages of Aristotle till then obscure to himself as well as to others.

1856. Death of Mr. De Morgan's mother

My mother-in-law died after a long illness this year, to the great sorrow of her three sons. Though there was great difference of opinion, chiefly on doctrinal matters, between my husband and herself, there was strong mutual affection, and some resemblances of character. He shared with her the quality which he used to find troublesome when he lived in her house; namely, anxiety to a morbid degree about those she loved when they were out of her sight. If he came home an hour later in the evening than she expected, she conjured up all kinds of terrible accidents which he might have met with. One reason of this, on Augustus's account, was his want of sight on the right-hand side. He was very like her in this morbid anxiety, so that those who left the house in the evening had to be punctual in the time of their return if they wished him to be easy. From his mother he inherited his musical talent, and most probably his mathematical power, for she was the granddaughter of James Dodson, the author of the Mathematical Canon, a distinguished Mathematician, the friend of Demoivre, and of most other men of science of his time, and an early F.R.S. But he was Mathematical master at Christ's Hospital, and some of his descendants seem to have thought this a blot on the scutcheon, for his great-grandson has left on record the impression he had of his ancestor.

To Sir John Herschel.

Camden Street, June 8, 1856.

1856

My dear Sir John,—I have long had the idea of a pianoforte in which each set of strings belonging to one note is to communicate with a pipe for resonance; and sometimes I have thought that a spring at the mouth of a pipe struck by a hammer would make a good instrument. In this case we might have various pedals opening and closing the upper end of the pipe. But I never imagined anything so grand as the introduction of a vast force by means of electro-magnetism. I should propose to call your instrument the electro-magnetic whack-row-de-dow.

What is the reason why thirds and sixths, major or minor, are more pleasant to the ear than fourths and fifths, which are consonances of simpler ratio of vibration? Fifths, by themselves, have a certain something which the ear does not like much of, and consecutive fifths we all know are forbidden. But thirds and sixths are very pleasant. If Dr. Smith's theory of beats be true, I almost suspect I spy a way to explain this. But I must get hold of an organ tuner, and learn whether they are actually effective.

I need hardly say that in the following pages I have not attempted a scientific memoir. My object has been to supply that part of my husband's life the material for which would not be within the reach of another biographer.

The selection from his letters might have been much larger, if I could in all cases have inserted those of his correspondents. Without these many would have been incomprehensible. As it is, I may have over-estimated the attention which readers will be disposed to give to them. My rule in choosing the letters has been to take those which are most characteristic of the writer, and in this way to give to readers already acquainted with him through his writings a more familiar knowledge of him as a man.

His connection with University College, and the events which led to his leaving it, are necessarily made prominent. So long a time has elapsed since their occurrence, and I have known so little during that time of the Institution, that I cannot even surmise how the present Council would in like circumstances share the convictions or conform the action of its predecessors. After the lapse of sixteen years I trust that the narrative will provoke no revival of the somewhat acrimonious controversy which ensued. It might perhaps have been in some ways better that Mr. De Morgan should have published a fuller statement of his views at the time, and have thus left less to be done by his biographer.

1831

At the time when he left the College, Mr. De Morgan was living with his family in Guilford Street, but removed in the autumn of 1831 to 5 Upper Gower Street, where he lived till our marriage in 1837. His only sister had been married the year before to Mr. Lewis Hensley, a surgeon of ability and good practice. My own family left Stoke Newington and settled at 31 Upper Bedford Place, Russell Square, in 1830.

State of Science

In May 1828, shortly after his first coming to London, Mr. De Morgan had been elected a Fellow of the Astronomical Society, and in February 1830 took his place on the Council. Of the state of Science just before that period, Sir John Herschel said: ‘The end of the eighteenth and the beginning of the nineteenth century were remarkable for the small amount of scientific movement going on in this country, especially in its more exact departments. … Mathematics were at the last gasp, and Astronomy nearly so—I mean in those members of its frame which depend upon precise measurement and systematic calculation. The chilling torpor of routine had begun to spread itself over all those branches of Science which wanted the excitement of experimental research.’

1836

Soon after Mr. De Morgan's return to the college a great affliction befell the family in the sudden death of his sister Mrs. Hensley in her confinement. Her brother had left his home in Gower Street, satisfied that she was doing well, and on his return in the afternoon inquired as he entered the house how she was going on. The servant replied that Mrs. Hensley was dead. It had been quite unexpected, and was a terrible blow to her mother, her husband, and brothers. Mrs. Hensley left three daughters and the infant son whose birth immediately preceded her own death. It was many months before her brother Augustus recovered from the shock he received in hearing so suddenly of the event. In writing to my mother of the affliction of his own, he added, ‘As for me, I am stunned, and hardly know what I write.’ And it was far longer before the grief caused by this, his first experience of the death of one whom he loved most affectionately, abated.

The religious doubts and difficulties created in his mind by the doctrinal teaching of his early years were not the only troubles arising from the same cause. It was natural that a mother, so anxious and true-hearted as his, should not see without pain anything like what she thought carelessness in religious matters, and that her anxiety to produce a belief like her own should be intensified by her recent sorrow.