This folio in hand of Colls.

29 July 1815

Campbel and Price

15

Price

7

(1)

Let us apply to the mathematical Doctor's mathematical argument a counter argument which is in use with mathematicians—the argumentum

ab

absurdo: let us pursue the Doctor's through its consequences, and observe to what it leads.

1. Improbable as it is, and in the degree in question, that the reported number should have been first drawn, so is it and in the same degree that any other number should have been the first drawn: and this is equally true of every other.

2. This is as much as to say in every lottery of 50,000 tickets it is 50,000 to one that no one ticket will be drawn first.

3. Whence again it follows that in that same degree it is improbable that in a lottery of that number of tickets any ticket should be drawn at all.

4. As it is improbable, and in this degree, that a lottery of 50,000 tickets should be drawn at all, at the same time that in London alone lotteries of this same or a greater number of tickets are actually drawn every year, it is in the same way in the power of government to give existence to facts that are in any given degree improbable. In this way it shall be in the power of government to give existence to facts more improbable than the most improbable of any that ever were pretended to have had existence: and those transcendently, not to say infinitely, improbable facts shall still be capable of being rendered credible by ordinary evidence.

5. In the same way it may be proved that scarce any fact ever does take place that is not improbable: improbable in an indefinite not to say infinite degree. Look at any one of the boards on which you are treading: observe the veins in it. If in that same floor that are 20 boards—look at them all, there is not one, to a given extent of surface, in which the picture made to the eyes shall be exactly the same as in the first. Repeat—this survey upon all the floors in your house: upon all the houses in your street; upon all the streets in your town: upon all the towns in your province, till you have surveyed a million of boards or any number of millions that you think fit. Say for shortness one million. In this degree—the degree of a million to one—is it improbable that upon any one board such a set of configurations should exist as those which