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 aright 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 Donxkin,* who, establishing a kind of metaphysical statics on proofs of the 
same nature as those which are employed in deducing @ 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 bea particular manifestation of that deeper 
* Sur la Theorie de la Combinaison des Observations. Liouvitie’s Journal de Mathema- 
tiques, tom. xv., 1850. 
