Demonstrative inferences “purchase truth preservation by sacrificing any extension of content.”  All information in the conclusion is contained in the premises.
However, nondemonstrative inferences are ampliative, they contain information in the conclusion that is not contained in the premises.

Is there any type of inference whose conclusion must, of necessity, be true if the premises are true, but which is ampliative?

Hume’s position:
We cannot justify any kind of ampliative inference.

This might be called “Hume’s paradox,”... We know (“in our hearts”) that we have knowledge of unobserved fact.  The challenge is to show how that is possible.  (in P & B, p. 232)

If there is no logical justification for believing in scientific predictions, why isn’t it just as reasonable to believe in astrological predictions?

Modern Replies to Hume

1.Inductive Justification
-characterized as the suggestion that the scientific method is justified just by the fact that it works.

Reply:
This is not the issue.  The question is whether we should predict that science will continue to work in the future.

See the discussion of Black in the section “Inductive justification” (pp. 232-5) of the text.  The inductive justification offered there isn’t defeated as easily.

Black admits that the appeal to induction’s past success in attempts to justify its application to future events seems circular.
However, it does not involve the implicit assumption of the conclusion as one of the premises (premise-circular).
Instead, induction is a rule of inference, i.e. a rule governing how we might proceed in arguments, rather than an explicit premise in the argument.

Salmon’s reply: The argument for induction is still rule circular.

 2. Uniformity of Nature

Hume’s concerns rest on the possibility that nature may not be uniform.
Kant argued that Hume’s approach was wrong, the uniformity of nature is a synthetic a priori truth.  The uniformity of nature is a prerequisite for any rational discourse or understanding and/or a prerequisite for perception of the physical world.

Reply:  Hume would probably deny that the notion of a synthetic a priori truth makes sense.
second concern:  How do we “ferret out the genuine uniformities”?

3. Postulational Approach
Accept the principle of induction as a postulate, i.e. take it as a given.

Reply:  But why should we accept it as a postulate, don’t we need some explanation?

 4. Probabilistic Approach
Can’t we simply say that scientific predictions are more probable than those of astrology or crystal gazing?

What is meant by probability?
i) frequency (283, column 1)
Reply: If probabilities are based on past frequencies how does this help the argument for induction?  The difficulty lies in the prediction, not in the nature of the prediction.

ii) rational credibility
We should never expect our scientific outcomes to be anything more than probable, i.e. based on the best possible evidence.  But good scientific predictions, by definition, are predictions based on the best possible evidence.  To be rational is just to believe on the basis of evidence.

Reply:  This assumes that the concept of evidence is clear but isn’t this the question at issue?  If we could be confident that experiments provide evidence we would indeed have evidence for the law, but the very question is why these kinds of results are evidence.
 

5. Deductivist Approach
Science is not about predicting the future.  Rather, science’s role is to provide general hypotheses that explain all facts up until now.  When these generalizations succeed we hang on to them, when they don’t we throw them away.  Good scientists will try to refute these general hypotheses, find instances which falsify them.

Response:  This approach deprives science of its predictive function.  However, as a matter of fact, we do use the theories (general hypotheses) for prediction, don’t we need to explain this?

6. Pragmatic Approach
If nature is uniform, the scientific method or inductive method will work, if it isn’t I’m out of luck whatever I do

Reply: we need to appeal to laws of nature to discuss uniformity but it is very difficult to give an account of laws of nature.
 
 

 7. Laws of Nature

1) (in article) To talk about uniformities in nature we need to talk about laws of nature.  What are these?
How do we distinguish true laws from accidental generalizations (or dismissals of possible but unlikely events)?  Do such distinctions need to appeal to laws of nature?

2) Laws of nature are relationships between universals.  Good generalizations predict well because they refer to a connectedness between universals.
 
But how do we gain knowledge of the connection between universals, doesn’t the problem of induction still arise?

We never see these universals, we only see instantiations of them.  Isn’t it a bit odd to make claims about connections between things that we can never observe?
 
 
 
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