PRO 
and is enough to induce tiie mind to judge 
the proposition to be true or false, rather 
than the contrary. 
Of probability there are degrees from the 
neighbourhood of certainty and demonstra- 
tion, quite down to improbability and un- 
likeness, even to the confines of impossibi- 
lity ; and also degrees of assent, from cer- 
tain knowledge, and, what is next to it, full 
assurance and confidence, quite down to 
conjecture, doubt, distrust, and disbelief. 
That proposition then is probable for which 
there are arguments, or proofs, to make it 
pass or be received for true. -Probability 
being then to supply the defect of our 
knowledge, is always conversant about a 
thing whereof we have no certainty, but 
only some inducements to receive it for 
true. The grounds of it are, in short, these 
two following : First, the conformity of any 
thing with our own knowledge, experience, 
or observation. Secondly, the testimony of 
others vouching their observation and ex- 
perience. In the testimony of others, is to 
be considered, 1. the number; 2. the inte- 
grity ; 3. the skill of the witnesses ; 4. the 
design of the author, if it be a testimony 
cited out of a book; 5. the consistency of 
the parts and circumstances of the relation; 
6. contrary testimonies. The mind, before 
it rationally assents or dissents to any pro- 
bable proposition, ought to examine all the 
grounds of probability, and see how they 
make more or less, for or against it ; and, 
upon a due balancing the whole, reject or 
receive it, with a more or less firm assent, 
according to the preponderance of the 
greater grounds of probability, on one side, 
or the other. 
Probability of an event, in the Doc- 
trine of Chances, is the ratio of the number 
of chances by which the event may happen, 
to the number by which it may both hap- 
pen and fail. So that, if there be constituted 
a fraction, of which the numerator is the 
number of chances for the events happen- 
ing, and the denominator the number for 
both happening and failing, that fraction 
will properly express the value of the pro- 
bability of the event’s happening. Thus, if 
an event have 3 chances for happening, and 
s' for failing, the sum of which being 6, the 
fraction | will fitly represent the probability 
of its happening, and may be taken to be 
the measure of it. The same thing may be 
said of the probability of failing, which will 
likewise be measured by a fraction, whose 
numerator is the number of chances by 
which it may fail, and its denominator the 
PRO 
whole number of chances' both for its hap- 
pening and failing : so the probability of 
the failing of the above event, which has 2 
chances to fail, and 3 to happen, will be 
expressed or measured by the fiaction 
Hence, if there be added together the 
fractions which express the probability for 
both happening and failing, their sum will 
always be equal to tinity, or 1 ; since the 
sum of their numerators will be equal to 
their common denominator. And since it 
is a certainty that an event will either hap- 
pen or fail, it follows that a certainty, which 
may be considered as an infinitely great 
degree of probability, is fitly represented 
by imity. See Ch.ances ; Life, duration of, 
PROBATE of wills, is the exhibitipgand 
proving wills and testaments before the 
ecclesiastical judges, delegated by the 
bishop, who is ordinary of the place where 
the party dies. 
By the- stamp acts, a very heavy duty is 
now payable upon these instruments, and a 
man can entitle himself to personal property 
only by means of a probate; that is, by 
having proved the will. 
PROBLEM, in logic, a proposition that 
neither appears absolutely true or false; 
and, consequently, may be asserted either 
in the affirmative or negative. A logical or 
dialectical problem, according to the school- 
men, consists of two parts; a subject, about 
which the doubt is raised; and a predicate, 
or attribute, which is the thing doubted 
whether it be true of the subject or not. 
Problems may be divided into physical, 
ethical, and metaphysical ; physical, when 
it is doubted whether such and such pro- 
perties belong to certain natural bodies ; 
ethical, when the doubt is, whether or not 
it be proper to do or omit certain actions ; 
and metaphysical, when the doubt relates 
to spirits, &c. 
Problem, in geometry, is a proposition 
wherein some operation or construction is 
required ; as, to divide a line or angle, erect 
or let fall perpendiculars, &c. A problem 
is said to consist of three parts ; the propo- 
sition, which expresses what is to be done ; 
the -solution, wherein the several steps 
whereby the thing required is to be effect- 
ed, are rehearsed in order ; and, lastly, the 
demonstration, wherein is shown, that by 
doing the several things prescribed in the 
solution, the thing required is obtained. 
Problem, in algebra, is a question or 
proposition which requires some unknown 
trutli to be investigated, and the truth of 
