Confirmability and Meaningfulness

R. G. Swinburne attempts to show by means of counter-examples that the confirmability criterion of meaningfulness (which he calls the ‘confirmationist principle’) is false (‘Confirmability and Factual Meaningfulness’, Analysis 33.3, pp. 71-6) [I am grateful to John Heintz and Richard Robinson for their comments and suggestions]. He holds that although the following statement which he labels p1 cannot be confirmed or disconfirmed by any conceivable kind of evidence, it is nonetheless meaningful. I would like to argue, on the contrary, that it can be confirmed or disconfirmed.
p1: Among possible claims about the pre-human past which the best evidence ever to be obtained by man makes highly improbable some are nevertheless true (p. 74).
Swinburne supposes that in order to make p1 more or less probable, you would have to consider an example of the sort of claim identified in p1 and show that it could be made more or less probable. That is, you would have to show that a statement having the following form could be made more or less probable:
Claim q (a claim about the pre-human past) is highly improbable in terms of the best evidence ever to be obtained by man, and claim q is true.
But anything that counts as evidence for the first part of the conjunction will count as evidence against the second part of it and vice versa, so no evidence can count for or against the conjunction as a whole. Nevertheless a statement having the form in question (henceforth I shall call such statements Q statements) is meaningful.

This argument seems plausible, but it doesn’t work. Besides holding that everything that counts for one conjunct of a Q statement counts against the other conjunct, Swinburne must hold that the evidence would count for and against the respective conjuncts to just that extent that would be required to keep the probability of the Q statement constant. It is, to say the least, not at all obvious that the evidence would meet this requirement. Surely the claim that it would needs a defense, but none is provided. This is enough to show that Swinburne hasn’t succeeded as yet in proving that a statement can be meaningful but not subject to confirmation. However, I would like to go further and show that the sort of statement he is considering actually is confirmable.

There is a maximum probability that a statement can have and still remain highly improbable. Let us suppose that the probability in question is .001. If the best evidence available to man were in, the probability of Q would be maximum when the probability of q was .001. Any increase in the probability of q beyond .001 would make the probability of Q zero because the first conjunct (which I shall henceforth call the improbability conjunct) would then be false; the best evidence attainable to man would be in and q would not be sufficiently improbable. On the other hand, any decrease in the probability of q below .001 would decrease the probability of Q because it would decrease the probability of the conjunct asserting the truth of q (henceforth the q conjunct) without increasing the probability of the improbability conjunct, which would remain at 1.

Unfortunately, this argument is not as effective against Swinburne as it might seem, because in almost all cases the evidence that determines the probability of q would not be the best evidence available to man. Also one would never know for sure that one had the best evidence available to man.

Therefore I will have to consider cases that rest on evidence that is other than the best. In such cases, when the probability of q is either 1 or zero the probability of the Q statement will be zero because in either of these cases it would be certain that one of the conjuncts of the Q statement was false. However when the probability of q was anywhere between 1 and zero the probability of the Q statement would not be zero because in such cases there would be some chance that q would be highly improbable when the best evidence was in and that q would nevertheless be true. It follows from this that when the probability of q was either zero or 1 the probability of the Q statement would be lower than it would be when q had any probability between zero and 1. However, this is not as telling against Swinburne as it might seem, because he could claim that it is logically impossible to show that the probability of q is either zero or 1 and therefore that it is not logically possible to disconfirm Q in this manner.

Fortunately, there is another way of showing that the probability of a Q statement may vary even when the best evidence to man is not yet in. The probability of a Q statement will never be higher than the probability that its q conjunct is true, because the probability of a conjunction will never be higher than the probability of either of its conjuncts. It follows that for any probability between zero and 1 that we assign to the Q statement the probability of that statement would be reduced if on further evidence q  were to be assigned a lower probability than that assigned to the Q statement originally. This is clearly incompatible with Swinburne’s claim, because he must hold that the probability of a Q statement will remain constant for all probabilities attributed to q with the possible exception of zero and 1. He must hold this because q is confirmable, and, if the probability of a Q statement is dependent on the probability of q, the Q statement is also confirmable.

The argument I have just given shows that Q statements are confirmable, but it is obvious that they are only confirmable to a very limited extent. However, a person who was concerned to confirm p1 the statement that some Q statements are true, could go on to consider other Q statements; and the more Q statements he found with a probability of greater than zero, the greater the probability would be that some Q statement was true and, therefore, the more probable it would be that p1 was correct.

This puts Swinburne in a considerably worse position. If p1 had to be confirmed by confirming a single Q statement, it could receive only a very small amount of confirmation, and some confirmationists might regard this as being almost as objectionable as no confirmation. But if more than one Q statement is considered, there is no such limitation and a defender of the confirmability criterion should be perfectly happy.

However, Swinburne could overcome this part of his problem by offering a Q statement instead of p1 as his candidate for a statement which is meaningful although unconfirmable. This would eliminate the possibility of his test statement being subjected to a high degree of confirmation, but (as we have seen) his Q statement would still be subject to limited confirmation. Swinburne could reduce the extent of possible confirmation still further by offering as his example of a meaningful but (almost) unconfirmable statement one which specified the exact degree of improbability required in a statement about the pre-human past. Here the statement would not merely have to be true and highly improbable, but it would have to have a precise degree of improbability.

Swinburne considers two additional statements which are similar to p1:
  • p2: Some claim about the state of an uninhabited planet which is highly probable on the best evidence which men will ever obtain is in fact false.
  • p3: Some claim about the future of the earth after men have ceased to live on it which is very probable on the best evidence which men will ever obtain is in fact false (p. 76).

These statements can be treated in essentially the same way as p1 Since p3 is not significantly different from p2, I shall just consider p2. Let us call a conjunctive claim that meets the requirements of p2 a P claim, and let us call the second conjunct of the claim not-p. The probability of p will never be higher than the probability that not-p is true, that is, that p is false. Accordingly, however low the probability of P may be, it is possible to determine that it is even lower by finding evidence that makes the probability of not-p lower than the probability initially assigned to P. From this point on p2 and p3 can be treated in exactly the same way as p1.

Confirmability and Meaningfulness
Author(s): Richard I. Sikora
Source: Analysis, Vol. 34, No. 4 (Mar., 1974), pp. 142-144
Published by: Oxford University Press on behalf of The Analysis Committee
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