Introduction:the nature of science 11 Hume's point can be put another way.How could we improve our inductive argument so that its justification would not be in question?One way to try would be to add an additional premise that turns the argument into a deductive one.For instance,along with the premise "all observed cases of colitis have been accompanied by anaemia"we may add the premise "unobserved cases resemble observed cases"(let us call this the uniformity premise).From the two premises we may deduce that unobserved colitis sufferers are anaemic too.We are now justified in believing our conclusion,but only if we are justified in believing the uniformity premise,that unobserved cases resemble observed ones.The uniformity premise is itself clearly a generalization.There is evidence for it-cases where something has lain unobserved and has at length been found to resemble things already observed.The lump of ice I took out of the freezer an hour ago had never hitherto been observed to melt at room temperature(16C in this case).but it did melt,just as all previous ice cubes left at such a temperature have been observed to do.Experience tells in favour of the uniformity premise.But such experience can only justify the uniformity premise if we can expect cases we have not experienced to resemble the ones we have experienced.That expectation is just the same as the uniformity premise.So we cannot argue for the uniformity premise without assuming the uniformity premise.But without the uniformity premise-or something like it-we cannot justify the conclusions of our inductive arguments.Induction cannot be made to work without also being made to be circular.(Some readers may wonder whether the uniformity premise is in any case true.While our expectations are often fulfilled they are frequently thwarted too.This is a point to which we shall return in Chapter 5.) If the premises of an inductive argument do not entail their conclusions,they can give them a high degree of probability.Might not Hume's problem be solved by probabilistic reasoning?I shall examine this claim in detail in Chapter 6.But we can already see why this cannot be a solution.Consider the argument "all observed colitis suffers are anaemic, therefore it is likely that all colitis sufferers are anaemic".This argument is not deductively valid,so we cannot justify it in the way we justify deductive arguments.We could justify it by saying that arguments of this kind have been successful in many cases and are likely to be successful in this case too.But to use this argument is to use an argument of the form we are trying to justify.We could also run the argument with a modified uniformity premise:a high proportion of unobserved cases resemble observed cases.But again,we could only justify the modified uniformity premise with an inductive argument.Either way the justification is circular. Goodman's problem There is another problem associated with induction,and this one is much more recent in origin.It was discovered by the American philosopher Nelson Goodman.Hume's problem concerns the question:Can an inductive argument give us knowledge (or justification)?If the argument employed is right,it would seem that those arguments we would normally rely upon and expect to give us knowledge of the future or of things we have not experienced,cannot really give us such knowledge. This is a disturbing conclusion,to find that our most plausible inductive arguments do not give us knowledge.Even if there is a solution,there is the further problem ofHume’s point can be put another way. How could we improve our inductive argument so that its justification would not be in question? One way to try would be to add an additional premise that turns the argument into a deductive one. For instance, along with the premise “all observed cases of colitis have been accompanied by anaemia” we may add the premise “unobserved cases resemble observed cases” (let us call this the uniformity premise). From the two premises we may deduce that unobserved colitis sufferers are anaemic too. We are now justified in believing our conclusion, but only if we are justified in believing the uniformity premise, that unobserved cases resemble observed ones. The uniformity premise is itself clearly a generalization. There is evidence for it—cases where something has lain unobserved and has at length been found to resemble things already observed. The lump of ice I took out of the freezer an hour ago had never hitherto been observed to melt at room temperature (16°C in this case), but it did melt, just as all previous ice cubes left at such a temperature have been observed to do. Experience tells in favour of the uniformity premise. But such experience can only justify the uniformity premise if we can expect cases we have not experienced to resemble the ones we have experienced. That expectation is just the same as the uniformity premise. So we cannot argue for the uniformity premise without assuming the uniformity premise. But without the uniformity premise—or something like it—we cannot justify the conclusions of our inductive arguments. Induction cannot be made to work without also being made to be circular. (Some readers may wonder whether the uniformity premise is in any case true. While our expectations are often fulfilled they are frequently thwarted too. This is a point to which we shall return in Chapter 5.) If the premises of an inductive argument do not entail their conclusions, they can give them a high degree of probability. Might not Hume’s problem be solved by probabilistic reasoning? I shall examine this claim in detail in Chapter 6. But we can already see why this cannot be a solution. Consider the argument “all observed colitis suffers are anaemic, therefore it is likely that all colitis sufferers are anaemic”. This argument is not deductively valid, so we cannot justify it in the way we justify deductive arguments. We could justify it by saying that arguments of this kind have been successful in many cases and are likely to be successful in this case too. But to use this argument is to use an argument of the form we are trying to justify. We could also run the argument with a modified uniformity premise: a high proportion of unobserved cases resemble observed cases. But again, we could only justify the modified uniformity premise with an inductive argument. Either way the justification is circular. Goodman’s problem There is another problem associated with induction, and this one is much more recent in origin. It was discovered by the American philosopher Nelson Goodman. Hume’s problem concerns the question: Can an inductive argument give us knowledge (or justification)? If the argument employed is right, it would seem that those arguments we would normally rely upon and expect to give us knowledge of the future or of things we have not experienced, cannot really give us such knowledge. This is a disturbing conclusion, to find that our most plausible inductive arguments do not give us knowledge. Even if there is a solution, there is the further problem of Introduction: the nature of science 11