Hume introduces his skeptical approach to Inductive-inferences and that they could rationally justified if we had good reasons for expecting that future cases will resemble past cases of causal regularity. For Hume, there seems to be no grounds for supposing the principle of the uniformity of nature that the future will resemble the past.
Foster allows that that if our reasoning about future cases (prediction) or generalizations is based on inductive inference, then its problematic. For Foster, induction is not fundamental. There’s a more basic kind of inference that underlies our reasoning about future cases. Foster’s solution is inference to the best explanation.
inference to the best explanation = inferences are made from the available evidence to the hypothesis that would, if correct, best explain that evidence
Also known as abductive arguments, explanatory inferences …
This method can be used to justify the expectation that past regularities will persist in the future. This is because
- the best explanations of observed regularities typically take the form of explanatory laws / laws of nature
- because laws of nature are expressions of natural necessity
natural necessity = the necessity dictated by the laws of nature
Foster’s view supports how the history of science has actually progressed towards more general and fundamental laws.
Examples given by Foster
Water is H2O
Foster notes that Humean induction would give the following account: “scientists observed certain samples of water had this composition, and extrapolated to the generalization that all water is H2O by an inductive inference. i.e. reasoning from what they saw in the observed samples to a general conclusion about all water.”
Foster notes that the Humean answer is probably incorrect since the starting point isn’t to observe the composition; instead, the starting part is to take the samples and subject them to certain testing procedures and see how the sample responded to these tests.
Foster argues that inference to the best explanation is used to determine that the best explanation of how water responded to the tests was the hypothesis that water’s chemical compositions is H2O. Foster concludes that the generalization that all water is H2O is rationally grounded in an inference to the best explanation, rather than induction.
Gravitational behavior = Foster’s account is that gravitational behavior is an observed regularity in our experience of material objects. Two possible explanations of why the regularity occurs:
- first explanation is that the consistently is just purely accidental. It’s just a happenstance that regularity occurs and comes to our attention in experience
- second possible explanation is that the consistency is no accident at all, and that the consistency arises from an underlying Natural necessity
Foster believes in the second explanation that observed regularity gives us a rational ground for inferring that the law of gravity is operative. Once we’ve accepted the law of gravity and accepted it as a form of underlying natural necessity, we have a natural basis for inferring that bodies will behave gravitationally in the future as well. If it is necessary that bodies behave gravitationally, we can infer they will continue to do so in the future.
Nomological-Explanatory Solution (NES) = Inference to the best explanation
Features of the nomological-explanatory solution to the problem-of-induction:
“The only primitive rational form of empirical inference is inference to the best explanation.”
For Foster, induction reasoning is made up of two deeper, more basic kind of reasonings:
- inference to the best explanation = from an observed regularity, we can drive an inference to the best explanation of this regularity
- deduction from that law = once we’ve inferred that a law of nature explains the observed pattern, we can deductively conclude that the same regularity will hold in unobserved cases, because laws of nature are, by definition, universal and time-invariant. This is a deductive inference
Foster’s account suggests that we should replace induction with inference to the best explanation because the laws of nature used are expressions of natural necessity and therefore gives us grounds for explaining regularities that will persist in time.
NES is a reductive account of Inductive-inferences, since induction is reduced to two more fundamental forms of inference.
Natural necessity
Foster believes that natural necessity is preferable to the view that regularities are mere accident.
“The past consistence of gravitational behaviour calls for some explanation. For given the infinite variety of ways in which bodies might have behaved non-gravitationally and, more importantly, the innumerable occasions on which some form of non-gravitational behaviour might have occurred and been detected, the behaviour would be an astonishing coincidence if it were merely accidental — so astonishing as to make the accidental hypothesis quite literally incredible.”
A.J Ayer’s objection to using the notion of natural necessity to solve the problem of induction is outlined by Foster:
consider “All observed A’s are B’s”. Two conclusions can be drawn based on this evidence:
- All A’s are B’s. the observed regularity gives evidence of unobserved cases
- All A’s must be B’s. This provides a generalization that involves natural necessity i.e. A necessitates being B
According to Ayer, it will be easier to use the evidence that “All observed A’s are B’s” to support the first claim (All A’s are B’s), than to support the second claim (All A’s must be B’s). The generalization involving natural necessity adds something extra to the mere inductive generalization.
If generalizations involving necessity are harder to support than mere inductive generalizations, then it must be illegitimate to appeal to them in trying to solve the problem of induction.
Foster’s answer to this problem is that Ayer’s argument would pose a real problem if the only kind of inferences we appeal to are inductive inferences. Appealing to inference to the best explanation allows a different kind of dynamic and entitles us to infer laws, even if they are stronger claims than mere inductive generalization.
The scope of scientific laws
The scope objection questions how far laws of nature actually extend beyond our observed evidence. Why should we assume that a law derived from certain past cases applies to all future or unobserved cases?
In order for Foster to make his point, he compares two hypothesis concerning gravity:
- It is a law that at all times bodies behave gravitationally
- It is a law that at all times before t, bodies behaved gravitationally Foster maintains that hypothesis 1 is preferable to hypothesis 2 as an explanation, because hypothesis 2 introduces a new mystery of why the kind of natural necessity that gravity seems to impose upon objects should work only up to a certain time, and then stop working altogether. It’s unsatisfactory from an explanatory point of view.
“Why should time t have this unique significance in the structure of the universe that all bodies are gravitationally constrained in a period up to t, but not thereafter?”
Foster argues that the very nature of scientific explanation drives us towards laws with broader and more general scope. The more limited a law is, the weaker and less fundamental it’s explanatory power becomes, since restricting a law without justification from the evidence makes it seem arbitrary. Thus, explanations gain strength from generality, which helps justify extending laws beyond the cases we have directly observed.
Is the tendency towards explanation of greater generality rationally justified =
- This tendency presupposes that the workings of nature don’t change over time.
- Foster’s view is based on the fact that our usual conception of scientific laws and explanations presupposes conformity between past and present