John Venn - Collected Quotes

"Probability has been very much abandoned to mathematicians, who as mathematicians have generally been unwilling to treat it thoroughly." (John Venn, "The Logic of Chance", 1866)

"[...] for merely theoretical purposes the rule of formation would be very simple. It would merely be to begin by drawing any closed figure, and then proceed [sic] to draw others, subject to the one condition that each is to intersect once and once only all the existing subdivisions produced by those which had gone before." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

"[…] it must be noticed that these diagrams do not naturally harmonize with the propositions of ordinary life or ordinary logic. […] The great bulk of the propositions which we commonly meet with are founded, and rightly founded, on an imperfect knowledge of the actual mutual relations of the implied classes to one another. […] one very marked characteristic about these circular diagrams is that they forbid the natural expression of such uncertainty, and are therefore only directly applicable to a very small number of such propositions as we commonly meet with." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

"[...] we can not readily break up a complicated problem into successive steps which can be taken independently. We have, in fact, to solve the problem first, by determining what are the actual mutual relations of the classes involved, and then to draw the circles to represent this final result; we cannot work step-by-step towards the conclusion by aid of our figures." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

"Whereas the Eulerian plan endeavoured at once and directly to represent propositions, or relations of class terms to one another, we shall find it best to begin by representing only classes, and then proceed to modify these in some way so as to make them indicate what our propositions have to say. How, then, shall we represent all the subclasses which two or more class terms can produce? Bear in mind that what we have to indicate is the successive duplication of the number of subdivisions produced by the introduction of each successive term. and we shall see our way to a very important departure from the Eulerian conception. All that we have to do is to draw our figures, say circles, so that each successive one which we introduce shall intersect once, and once only, all the subdivisions already existing, and we then have what may be called a general framework indicating every possible combination producible by the given class terms." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

"It will be found that there is a tendency for the resultant outlines thus successively drawn to assume a comb-like shape after the first four or five [...]The fifth-term figure will have two teeth, the sixth four, and so on. [...] There is no trouble in drawing such a diagram for any number of terms which our paper will find room for. But, as has already been repeatedly remarked, the visual aid for which mainly such diagrams exist is soon lost on such a path."  (John Venn, "Symbolic Logic", [footnote], 1881)

"There is no need here to exhibit such figures, as they would probably be distasteful to any but the mathematician, and he would see his way to drawing them readily enough for himself [...]" (John Venn, "Symbolic Logic", 1881)

"We endeavour to employ only symmetrical figures, such as should not only be an aid to reasoning, through the sense of sight, but should also be to some extent elegant in themselves." (John Venn, "Symbolic Logic", 1881)

"We must say that the complete results of the elimination of any term from a given equation are obtained by breaking it up into a series of independent denials, and then selecting from amongst these all which either do not involve the term in question, or which by grouping together can be made not to involve it. […] So understood, the rule for elimination in Logic seems complete." (John Venn, "Symbolic Logic", 1881)

"Without consummate mathematical skill, on the part of some investigators at any rate, all the higher physical problems would be sealed to us; and without competent skill on the part of the ordinary student no idea can be formed of the nature and cogency of the evidence on which the solution rest. Mathematics are not merely a gate through which we may approach if we please, but they are the only mode of approach to large and important districts of thought." (John Venn, "Symbolic Logic", 1881)

"Boole's work is not so much an attempt (as used to be commonly said) to 'reduce logic to mathematics', as the employment of symbolic language and notation in a wide generalisation of purely logical processes. His fundamental process is really that of continued dichotomy, or subdivision, in respect of all the class terms which enter into the system of propositions in question. [...] This process in its priori form furnishes us with a complete set of possibilities, which, however, the conditions involved in the statement of the assigned propositions necessary necessarily?) reduce to a limited number of actualities: Boole's system being essentially one for displaying the solution of the problem in the form of a complete enumeration of these actualities." (John Venn, [in "Dictionary of National Biography"], 1886)

"If we start with the assumption, grounded on experience, that there is uniformity in this average, and so long as this is secured to us, we can afford to be perfectly indifferent to the fate, as regards causation, of the individuals which compose the average. (John Venn, "The Logic of Chance: An Essay on the Foundation and Province of the - Theory of Probability, Chance, Causation, and Design", 1887)

"In studying Nature, in any form, we are continually coming into possession of information which we sum up in general propositions. Now in very many cases these general propositions are neither more nor less certain and accurate than the details which they embrace and of which they are composed." (John Venn, "The Logic of Chance: An Essay on the Foundation and Province of the - Theory of Probability, Chance, Causation, and Design", 1887)

"How can a single introduction of our own [average], and that a fictitious one, possibly take the place of the many values which were actually given to us? And the answer surely is, that it can not possibly do so; the one thing cannot take the place of the other for purposes in general, but only for this or that specific purpose." (John Venn, “On the Nature and uses of Averages”, Journal of the Royal Statistical Society Vol. 54, 1891) 

"At the basis of our Symbolic Logic, however represented, whether by words by letters or by diagrams, we shall always find the same state of things. What we ultimately have to do is to break up the entire field before us into a definite number of classes or compartments which are mutually exclusive and collectively exhaustive." (John Venn, "Symbolic Logic" 2nd Ed., 1894)

"The best way of introducing this question will be to enquire a little more strictly whether it is really classes that we thus represent, or merely compartments into which classes may be put? […] The most accurate answer is that our diagrammatic subdivisions, or for that matter our symbols generally, stand for compartments and not for classes. We may doubtless regard them as representing the latter, but if we do so we should never fail to keep in mind the proviso, 'if there be such things in existence'. And when this condition is insisted upon, it seems as if we expressed our meaning best by saying that what our symbols stand for are compartments which may or may not happen to be occupied." (John Venn, "Symbolic Logic" 2nd Ed., 1894)

"The weak point about these (Eulerian circles) consists in the fact that they only illustrate in strictness the actual relations of classes to one another, rather than the imperfect knowledge of these relations which we may possess, or wish to convey, by means of the proposition. Accordingly they will not fit in with the propositions of common logic." (John Venn)