‘The analysis of counterfactual conditionals is no fussy little grammatical exercise. indeed, if we lack the means for interpreting counterfactual conditionals, we can hardly claim to have any adequate philosophy of science…What then is the problem…?’
Goodman starts with a conditional whose antecedent and consequent are both ‘inalterably false’ like this one ‘If that piece of butter that I ate yesterday had been heated to 150 degrees F, it would have melted.’ We can’t get far considering them as ‘truth functional compounds’ with the standard logical rules as they would all qualify as ‘true’ because they have a false antecedent. So ‘the problem is to define the circumstances under which a given counterfactual holds while the opposing conditional with the contradictory consequent fails to hold…in the face of the fact that a counterfactual by its nature can never be subjected to any direct empirical test by realizing its antecedent.’ Additionally, to make matters worse, ‘The problem of counterfactuals is equally a problem of factual conditionals, for any counterfactual can be transposed into a conditional with a true antecedent and conseqent; e.g. Since that butter did not melt, it wasn’t heated to 150.’ This rephrase that includes a notion of ‘since’ is key for Goodman, it ‘shows that what is in questino is a certain kind of connection between the two component sentences; and the truth of statements of this kind…depends on whether the intended connection obtains.’
‘As I see it, there are two major problems…A counterfactual is true if a certain connection obtains between the antecedent and the consequent. But as is obvious from the examples already given, the consequent seldom follows from the antecedent by logic alone. (1) In the first place, the assertion that a connection holds is made on the presumption that certain circumstances not stated in the antecedent obtain…Thus the connection we affirm may be regarded as joining the consequent with the conjunction of the antecedent and other statements that truly describe relevant conditions…in asserting the counterfactual we commit ourselves to the actual truth of the statements describing the relevant conditions. The first major problem is to define relevant conditions…(2) But even after the particular relevant conditions are specified the connection obtaining will not ordinarily be a logical one…but what we call a natural or physical or causal law. The second major problem concerns the definition of such laws.’
G- then walks us down a garden path, considering various potential methods of constructing this set of relevant conditions which he refers to as ‘S’. The upshot of this discussion seems to be that we ought to avoid admitting anything into S which would, in conjunction with the antecedent ‘A’ of a counterfactual in question, lead logically to anything whatsoever. We have to avoid contradiction. But, G- says, examine the method you try to use to determine which sentences are allowed to be members of S. One of these will be what he calls ‘cotenability’, A and S must be ‘cotenable’ which means ‘it is not the case that S would not be true if A were.’ His example here; ‘If match m had been scratched, it would have lighted.’ as the counterfactual, and as a possible member of S, ‘Match m did not light’. So to walk through cotenability, if A were true [Match m is scratched] then it is not the case that S would not be true [it is not the case that match m lit]. But notice that the move we just made is itself a counterfactual! So I think what is going on here is that G- argues: If you don’t have cotenability between A and S, then you have a contradiction and anything follows. But in order to determine cases of cotenability, you must construct a(nother) counterfactual [‘If A were true, then S would not be true’] statement and consider that, which is an infinite regress.
In Goodman’s words, ‘the really serious difficulty that now confronts us. In order to determine the truth of a given counterfactual it seems that we have to determine, among other things, whether there is a suitable S that is cotenable with A…But in order to determine whether or not a given S is cotenable with A we have to determine whether or not the counterfactual”If A were true, then S would not be true” is itself true. But this means determining whether or not there is a suitable S1 cotenable with A that leads to -S and so on. Thus we find ourselves involves in an infinite regressus or a circle; for cotenability is defined in terms of counterfactuals yet the meaning of counterfactuals is defined in terms of cotenability. In other words to establish any counterfactual it seems that we first have to determine the truth of another.’
But, look out now because, ‘Even more serious is the second of the problems mentioned earlier: the nature of general statements that enable us to infer the consequent upon the basis of the antecedent and the statement of relevant conditions.’ We do this by generalization; if we’re considering match m, to get the ‘law’ we generalize to something like ‘Every match that is scratched, well made, dry, in enough oxygen, etc., lights’. Something like that is supposed to be the statement of the law that legitimizes our counterfactual inference. But, says G-, it’s not that simple. How are we going to determine which generalizations are laws of this type that permit inference from ‘accidental’ generalizations. Another example runs this way: Supposed that all the coins in Goodman’s pocket on VE day were silver. Examine this counterfactual: If the penny P had been in my pocket on VE day, P would have been silver. If we assume the antecedent to be true [Ok let’s say that P was in your pocket on that day…] and we accept the generalization [Every coin in that pocket on that day was silver] we still refuse to buy it. We won’t infer that the penny ‘would have been’ silver. Instead we ‘would assert that if P had been in my pocket then this general statement would not be true. The general statement will not permit us to infer the given consequent from the counterfactual assumption…Though the supposed connecting principle is indeed general, true, and perhaps even fully confirmed by observation of all cases, it is incapable of sustaining a counterfactual because it remains a description of accidental fact, not a law…our problem is to distinguish accurately between causal laws and causal facts.’ Or in other words, to distinguish laws which legitimize counterfactual inference from statements of accident.
Goodman’s discussion suggests that this problem ‘reduces to…the question how to define the circumstances under which a statement is acceptable independently of the determination of any given instance.’ And neither he or I have a clue how this could be done.