626 PROFESSOR BOOLE ON THE COMBINATION 



claim to be regarded as axiomatic. In the preceding sections it presents itself 

 as a special result of a very complex analysis founded upon the logical theory of 

 probabilities. Now I wish to observe, that there is nothing in these circumstances 

 which we have a right to regard as denoting inconsistency. Of the theory of 

 probabilities it is eminently true that modes of investigation, which to our pre- 

 sent conceptions must appear fundamentally different, habitually lead us to the 

 same result. A profounder acquaintance with the laws of the human mind, and 

 a deeper insight into the relations of things, might perhaps show us that prin- 

 ciples which appear to us to have nothing in common may yet have a necessary 

 connection with each other, — may possibly spring up from a common origin. I 

 will endeavour to make my meaning clear by two illustrations, which will pre- 

 sent this question in somewhat different lights. 



30. An idea which seems naturally to suggest itself in connection with the 

 theory of probabilities is that of mechanical analogy. Evidence of this we see 

 in the language, already referred to, which attributes weight to observation. The 

 complete and scientific development of the idea will be found in a memoir by Pro- 

 fessor Donkin,* who, establishing a kind of metaphysical statics on proofs of the 

 same nature as those which are employed in deducing a priori the laws of ordi- 

 nary statics, has arrived, by legitimate deduction, at the remotest consequences 

 of Gauss's theory of the combination of observations. The mind, in the developed 

 analogy, is compared to a lever acted upon by different weights, or to a mecha- 

 nical system subject to given forces, and seeking, under this action, a position of 

 equilibrium. Now it is at least a very remarkable circumstance, that an analogy 

 of this kind should not only admit of exact scientific expression, but should, 

 through a long train of analytical consequences, present the same laws and re- 

 sults, and suggest the same methods, as the principle of the arithmetical mean 

 already referred to. All the abstract terms by which mental states and emotions 

 are expressed, derive, if philology be of any value, their origin from outward and 

 material things. And hence, though it might be impossible to ascend historically 

 to the first employment of those expressions which describe the mind under the 

 action of forces, and speak of the balancing of opinions, we cannot doubt that a 

 perceived analogy was their source. But it could hardly have been anticipated 

 that this analogy should remain complete and unimpaired through so lengthened 

 a range of scientific deductions. 



To what I have said above I will only add, that it is as instruments of ex- 

 pression and communication, rather than of thought, that material symbols, 

 and the analogies which they furnish, seem to me to possess importance. 

 Even the analogy which we have been considering cannot of itself occupy the 

 place of a first principle, but seems to be a particular manifestation of that deeper 



* Sur la Theorie de la Combinaison des Observations. Liouville's Journal de Mathema- 

 tiques, torn, xv., 1850. 



