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7 Camden St. and Town - Thanks him for his paper on mental philosophy. 'At first glance, I see an approximation between my ideas & yours in finding that you can admit the phrase "laws of mental activity" in place of "fundamental ideas". If your meaning of the latter phrase is interchangeable with any sense in which I can use the former, I have read much of your writing at cross-purpose'. He has no doubt on the 'absolute substantive reality of all the primary truths of maths. I have never had any doubt: but I have an idea that different people hold them by different hooks'.

7 Camden Street and Town - Asks him to write a notice of [Henry] Coddington to include in the Annual Report of the Astronomical Society. He is aiming for fuller biographies and worries 'that unless we can get all our Fellows to interest themselves, we stand a good chance of losing our existence. Every person who can be quoted as having done any work for us is strength just now, when Baily's [Francis Baily] loss has thrown us upon ourselves'.

7 Camden St. & Town - The Astronomical Society is 'under a conviction of weakness, which may prove its strength', their efficient Assistant Secretary [Richard] Harris has been ill. All the observatories are working so hard that the Society hardly gets any papers from them: 'It is a fact, that as astronomy becomes more active the supply of communications sensibly declines'.

7 Camdn. St. & Town - He is going to publish the theory of the syllogism in a work on formal logic next year. The 'subject of a proposition is the more likely to be objective and the predicate more likely to contain the part which is subjective'. Can Whewell suggest any words? Could he use 'internal & external, or notional and actual'? Like others, ADM finds he 'always has to find out the meaning of these words afresh, every time they come to the subject'.

7 C. St. & T. - Acknowledges receipt of Whewell's paper. Whewell's 'conception of objective must be subjective, these words make a crabbed question'. De Morgan would like nothing more than 'to give impulse to the making of words - if I were etymologist enough'. He has always liked the phrases 'vitreous and resinous electricity - they express one fact and no theory'. He thinks 'retinal and radial' would do to describe 'the action of rays on the retina, as an easily perceptible instance of an external agent and a produced condition'. If we admit objective 'is it likely that the ordinary antithesis of language should express an antithesis which people in general never think of'. He thinks 'objective and reflective might be made to do - but the idea we want is not that of turned back, but roused by means of, state produced by the suggestion of'.

7 Camden Street, Camden Town - Thanks WW for the invitation but his lectures are 'imperative'. If his papers are to appear together he wants copies all at one time and does not care whether they are printed in the form of two papers or one. He is to publish a work on logic soon after the papers appear, and will think of Whewell's suggestion about taking a subject, but 'what subjects run very thickly in syllogisms...[and the] syllogistic examples in books of logic are literally nothing more than terms of one word or so substituted in the formal syllogism'. Instead of subjective and objective he will use ideal and objective, and explains how he will use it in terms of the mind. He writes this to show Whewell 'how far our language agrees'. Writers on Formal Logic are often confused - they 'speak ideally, and not objectively', and 'admit contradictory propositions as ideally enunciable'. He then presents some phraseology, 'seven definite relations of term and term: identical and contrary, sub-identical and super-identical, sub-contrary and super-contrary, and mixed. He concludes with a dialogue he had with his daughter as to the ideas of necessary and contingent.

7 Camden Street, Camden Town - He has been meaning to respond to the last point of Whewell's letter on enunciation, but he has been looking through the proofs of an account of Newton by David Brewster. He describes how his check of the references has shown a story to be false: the story about Newton being offended by being represented as an Arian by Whiston that he blocked the latter's entry to the Royal Society. De Morgan discusses his definition of enunciation at length.

7 Camden Street & Town - He has found some very queer things about the Aristotelian syllogism - deficiencies and redundancies which he will publish in a treatise of technical logic. He would like 'the mathematical world to see how necessary mathematical considerations are to common logic'. He has a logical paper ready on the 'mode of balancing the joint effect of testimonies and arguments for and against'; diagrees with [Richard] Whately's formulas and shows his own.

7 Camden St. & Town - Charles Babbage has written to the Vice-President, Capt. Smyth, 'charging our minutes' with negligence. He claims Whewell made a motion at the general meeting which was seconded, and when put from the chair it was negatived, he has no memory of this and asks for his recollection of the event.

Entries in index: 'on the connection of M W N & m n page 428'; 'on changing the sums of Square by altering the Root p 284'; '2nd Communication [to the Royal Society]', 298; 'Fermat's theorems. Paper for Royal Society p. 250'; 'on the gradation series, 338'; 'letter to Mr De Morgan proving that the two forms (a² + a + b² + c²)= (m² + m + n² + p² + p), 142'; 'Numbers - Forms of which make 4 sqr roots =1 etc tc, p 190'; 'Triangular nos p. 475'.

Other page headings not mentioned in the index include: 'on the division of odd nos into 4 square & other forms', p. 2; 'on Fermat's mysteries of numbers', p. 162. The title in full of the paper for the Royal Society which begins on p. 250 is 'On the first and second Theorems of Fermat relating to the polygonal numbers and on the forms not exceeding 4 into which odd numbers may be divided'.

Two large sheets dated 1867 and labelled 'Diagram no. 1' and 'Diagram no. 2'

Entries in index: 'De Morgan - correspondence with - p. 1'; 'Differences of Squares - that compose the odd nos. 120'; Differences of Roots. 230'; 'Gradation - Series. 50'; 'Paper for Royal Society - p. 562'; 'Roots - changing roots by diminishing them till a+b-c-d+1. 300'; 'on the differences a Sum of Roots of 1, 3, 7, 13, 21 &c. 130'; 'Roots may always = 1. 320'; 'Properties of 3 Squares. 348. 'These Properties applied to the series 1 3 7 13 21 &c. 360'; 'Series - oon the Series 1, 3, 13 & c... 84'.

The first version of the title of the 'Paper for Royal Society', as given on p. 562, is 'On a method of proving by means of indices a limit within which any No. may be formed of the terms of certain series, including a proof of Fermat's Theorems of the Polygonal numbers'.

7 Camden Street, Camden Town - Sir William Hamilton has accused De Morgan of having taken his 'paper on logic from private communication with him'. As he had no communication with Hamilton till after his paper had been dispatched to Whewell, the date of the letter could become the turning point of a priority controversy.

7 Camden St. & Town - WW's practice of keeping letters will rank next to George Airy 'for extreme method', which he caricatures. Discusses his dispute with Sir William Hamilton, who is recovering from illness and will be treated with consideration; describes what he did when he realised their conclusions were similar. Is glad Whewell's recollection of the meeting is the same as De Morgan's, and will have a meeting with Charles Babbage privately about it.

7 Camden St. & Town - Thanks Whewell for the second memoir, he has only just read it as he was engaged 'upon the antithesis of symbol and explanation'. Whewell has 'done the German philosophers much good': De Morgan stops at Kant who is far too unclear - 'so turbid that I want a filtering machine'. De Morgan presents an argument claiming 'all inference consists in four parentheses and two dots', followed by a knife and fork theory of the use of figure; and lastly claims that there is a form of thought which has never entered into formal logic which is neither affirmation or denial e.g. 'Though + yet = cannot'.

7 Camden St. & T. - The spoon is a good representation of inductive logic. Whewell's notion of induction contains more than logic. Spoon feeding is synthetical (induction) and knife and fork feeding is analytical. Whewell will probably see a scene at the Astronomical Society as Jerwood, who accused Airy and Le Verrier of conspiring to defraud Adams [regarding the discovery of Neptune], has been proposed as a fellow. He describes his friend [Joshua Ryland] Marshman's suitability for the Professorship of Law at Cambridge.

7 Camden St. & T. - Thanks WW for his paper on curves: 'It is a clear addition to our means of expression'. ADM is surprised at 'the arcs which become negative in turning a cusp'. How does WW know that his solution is the correct one? - there 'may possibly be an infinite no. of solutions'. Sketches his pen, and describes how the ink is added at one end, and the other end is merely capillary, sees that with improvements it will mean a pen with no dipping needed, and no blots.

7 C St. & T. - Further to his remarks [letter written earlier that day] on Whewell's paper on curves. ADM could not rest with WW's unexplained 'change of sign at the cusp' and attempts to begin one, which he shows, but is 'not familiar enough with your processes yet to attempt anything in the way of explanation'.

7 Camden St. & Town - De Morgan admits all Whewell urges against his 'loose expression - which probably conveyed the idea that I meant a cusp must be a defunct loop - what I ought to have said is, show me a cusp - and I show you its curve as an individual of one family in which a loop dies at the cusp. But then I can show it you as an individual of an infinite number of other families - some of which have that cusp permanently'. You may be able to explain the deviation of a cusp in one family but the difficulty may remain in another. The same thing is applicable with a conjugate point. De Morgan has been 'trying to ascertain that 'from and after' and also 'after' in old English includes the day from which reckoning is made - in opposition to lawyers and others'.

7 Camden St. & T. - He sends Whewell 'a piece of audacity of which your eye will detect the visible signs at a glance'. He gives an example of the knife and fork theory of figure he previously sent WW [see ADM to WW, 1 Apr. 1849]. He finds it easier to get the more difficult cases of syllogism by 'figuring the symbol in my head - and detecting the symbol of inference - than by thought'.

7 Camden St & T - Notes that Whewell is 'propagating an undulation through the College - a very elastic medium'. He hopes the matter will not lead to a gown (nominalist) and town (realist) dispute. He suspects Aristotle shares the fate of Euclid, namely, that 'everybody believed him to be so near perfection, as to be willing to give him the finishing touch'. Ptolemy - 'the real original -' has escaped this fate because he 'was comparatively little read'. He is sorry Whewell is against the Royal Commission since it 'would much tend to open the public eye to what the Univ. really do - So very little is known about them that something of the kind is much wanted'. In a postscript, he adds a humorous definition of metaphysics.

7 Camden Street, Camden - Whewell is to receive a copy of De Morgan's paper on logic. He has Sir William Hamilton's system of logic in the work of Hamilton's pupil, Thomas S. Baynes, An Essay on the New Analytic of Logical Forms. The requisites of this essay made the foundation of Hamilton's charge on him of intellectual theft. He and Boole come in for a lecture against meddling with logic with help of mathematics. He asks Whewell to read it and inform him 'if these things will strike others as being as monstrous as they do me' De Morgan will next look at 'the relation between the laws of enunciation and the laws of thought', and reminds WW of their former discussion on enunciation.

7 Camdn. St. & T. - Thanks WW for the number 2 of the intrinsic equation and for the paper on Political Economy [Mathematical Exposition of some Doctrines of Political Economy: Second Memoir, 1850], is 'always stopped in political economy by that diabolical currency'. ADM picked up today his own 'note of an old Hindoo rule in Viga Granita which has never to my knowledge been made European', on how to extract the square root of a + √b + √c + √d. 'Really these elephant riding widow burning [?] were noways contemptible.'

7 Camdn. St. & T. - He has received 'the Newton' [Edleston ed. Correspondence of Sir Isaac Newton and Professor Cotes]: 'It is that kind of book of which one's opinion is not made up in a month or two'. He 'expected a strong Anti-Leibnitio-Flamsteedian bias'. He is to send Whewell a copy of the Logic and his new mathematical paper. Has Whewell seen the recent article in the Athenaeum [Dec. 21 1850] claiming William Hamilton's quantification of the predicate was first published by George Bentham in A New System of Logic (1827). De Morgan confirms that three of Hamilton's 'great points' are to be found in this work. Hamilton had in fact reviewed the book which 'stands at the head of his celebrated article on logic' in the Edinburgh Review.

7 Camdn. St. & T. - ADM sends an example 'of logical extravagance' to WW: 'If three points be taken on a straight line, in any order, these, lines being supposed to have their proper signs, we have in all cases AB=-BA, AB+BC=AC'. ADM gives all the ways A,B, B,C, compounded gives A,C.