One of the oft-overlooked peculiarities in Hume's argument against testimony for miracles is his notion of balancing. When we entertain two thoughts, each one comes with its own force or vivacity; if the thoughts conflict, we weigh the thoughts against each other, subtracting the force or vivacity of Thought A from that of Thought B, and assent to Thought A with the force or vivacity by which A exceeds B. In the case of testimony that conflicts with our normal experience, we weigh the force or strength of the testimony against the force or strength of the experience. Hume's argument consists in arguing that, however strong the testimony for a miracle may be, by the nature of the case the experience with which it conflicts has the strongest possible force or strength. In the following passage from A Dissertation on Miracles, Campbell attacks this notion of balancing. The passage is of especial interest because the assumption criticized by Campbell here is a common one.
There is in arithmetic a rule called REDUCTION, by which numbers of different denominations are brought to the same denomination. If this ingenious author shall invent a rule in logic analogous to this, for reducign different classes of evidence to the same class, he will bless the world with a most important discovery. Then indeed he will have the honour to establish an everlasting peace in the republic of letters; then we shall have the happiness to see the controversy of every kind, theological, historical, philosophical, receive its mortal wound: for though, in every question, we could nto even then determine, with certainty, on which side the truth lay, we could always determine (and that is the utmost the nature of the thing admits) with as much accuracy as geometry and algebra can afford, on which side the probability lay, and in what degree. But till this metaphysical reduction be discovered, it will be impossible, where the evidences are of different orders, to ascertain by subtraction the superior evidence. We would not but esteem him anovice in arithmetic, who being asked, whether seven pounds or eleven pence make the greater sum, and what is the difference, should, by attending solely to the numbers, and overlooking the value, conclude that eleven pence were the greater, and that it exceeded the other by four. Must we not be equal novices in reasoning, if we follow the same method? Must we not fall into as great blunders? Of as little significancy do we find the balance. Is the value of things heterogeneal to be determined merely by weight? Shall silver be weighed against lead, or copper against iron? If, in exchange for a piece of gold, I were offered some counters of baser metal, is it not obvious, that till I know the comparative value of teh metals, in vain shall I attempt to find what is equivalent, by the assistance either of scales or of arithmetic?
(A Dissertation on Miracles (1839 edition), pp. 23-24)
