226 
PEOFESSOE BOOLE ON THE THEOET OF PEOBABILITIES. 
Now the first principle upon which the method rests is the following : — 
Principle I. — The difierent forms which a problem may be made to assume by 
difierent elections with respect to the simple terms of its expression are mutually 
equivalent. 
For instance, if the following data were given, 
The probability of rain is^. 
The probability of rain with snow is q, 
the form which the problem would assume in a language in which there was no word 
for snow, but in which the combination of snow with rain was called sleet, would be 
The probability of rain is^, 
The probability of sleet is q, 
■with the added condition, expressed as a logical proposition, that sleet always implies 
rain. And this as a statement of the data would, it is affirmed, be equivalent to the 
former statement. If these were the data of an actual problem, the event of which the 
probability is sought would require similar translation. 
I desire to guard here against a possible misapprehension. I have said that the 
choice of simple terms, if considered with respect to our power of choice, is arbitrary. 
I do not mean by this to affirm that the actual growth of language is arbitrary. We 
know that it is far otherwise. Unity of sensuous impression in the early stages of its 
growth, unity of thought in the latter, seems to govern the invention and introduction of 
simple terms. It has indeed been said that there is a Xoyoc in the constitution of things 
of which language in its varied forms is the human reflexion, but never without the 
inseparable human element of choice and voluntary power. 
It is then affirmed that whatever the grounds of fitness or propriety (and the existence 
of such grounds is fully conceded) may be, which have governed the actual choice of the 
simple terms of language, those grounds have nothing whatever to do with the calcula- 
tion of probability. This depends upon the information contained in the data, informa- 
tion supposed to be derived from actual experience, or at least to be of such a natmre 
that experience might have furnished it. 
The different forms in which a problem is capable of being expressed, though difiering 
in consequence of the difierent arbitrary elections which are possible with respect to 
its simple terms, are not independent of each other. They are connected together by 
the Laws of Thought, and pass one into the other by the processes of the Calculus of 
Logic, which is an organized expression of those Laws. 
Among these forms there is one which presents exclusive advantages. It is that in 
which those events, however originally expressed, the probabilities of which constitute the 
data, are assumed as the simple events of the problem, and expressed by logical symbols 
corresponding to the simple terms of ordinary language ; the event of which the proba- 
bility is sought being also expressed logically by means of the same symbols. The 
Calculus of Logic enables us to do this, determining at the same time in an explicit 
form, e. in a form capable of expression in ordinary language by definite logical pro- 
