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I'm reading Samir Okasha's article "Does Hume’s argument against induction rest on a quantifier-shift fallacy?" and in page 240 there is this:

Consider a typical inductive inference of the sort Hume was interested in, e.g. from ‘The sun has risen every day in the past’ to ‘The sun will rise tomorrow.’ If we add in the premise ‘Nature is uniform’ or ‘The future will resemble the past’, we may perhaps be able to make the inference deductively valid. But it is not true that this premise is needed to convert the argument into a valid one: any number of additional premises could be invented that would do the trick. No logically invalid inference has the property that there is only one additional premise which can be added to make it valid; there is always an innumerable number of such premises. If Hume meant that ‘Nature is uniform’ must be added to the premises of an argument from experience in order to make it deductively valid, as Stove and Mackie allege, it is hard to avoid the conclusion that he was guilty of an elementary logical error.

Why does he think the premise is not needed? Does he mean it is logically straightforward or obvious to convert any invalid argument into a valid one? If so, how?

  • Can you specify a little further what you're looking for an explanation about here? (In particular it seems a little unclear what problem you might be encountering w.r.t. your second question about triviality.) – Joseph Weissman Feb 9 '14 at 3:17
  • @JosephWeissman When he says "there is always an innumerable number of such premises", he seems to be stating something supposed to be obvious or trivial. So what I don't understand is how he concludes the premise is not needed and what is it that I'm missing from his supposedly obvious/trivial logical line of thought? – Koeng Feb 9 '14 at 3:41
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It sounds like the quote is referring to charity of interpretation which is a general expectation in philosophy. This concept means that when I read someone's argument or position, I should try to understand it in the most charitable light and then find flaws with that. In other words, ideally I am not attacking them for misspelling words or for failing to include very obvious premises.

Of course, charity of interpretation is a virtue -- which means there's no manual on how to do it perfectly. So the question in the case of what Hume does is whether he's really presenting a position anyone holds. As in, do people hold a stupid view that expects the sun to rise tomorrow merely because it rose yesterday and today OR is there an implied premise taken to be so trivial that its inclusion is pedantic. In other words, is the argument Hume must really deal with one that includes a premise that "the world is uniform in its operation"? But the problem with seeing that as the charitable interpretation per the quote is that there are many different premises that could give validity to the argument.

Formalized, it's something like this:

(1) S-1 [sun rose yesterday]

(2) S0 [sun rose today]

Therefore

(C) S+1 [sun will rise to tomorrow]

On a direct reading, this argument is invalid... to make it valid we can add several different entities:

strategy I: assert that anything that happens both yesterday and today is bound to happen tomorrow.

strategy II: expand the set we are looking at further into the past and add a premise that things with a regularity above 1000 instances will happen again.

strategy III: expand the set we are looking at further into the past 1000x and assert that things which happen every time out of a 1000 times will happen again in the 1001st instance.

strategy IV: strategy III + the restriction of this to natural phenomenon

...

And the problem is that with so many different strategies it is not clear what the most charitable route to go is. So he's asserting that the route Stove et al. use would make Hume guilty of a simple logic error. Presumably, he will defend Hume against this.

  • Okasha does discuss two interpretations of Hume and argues for the most charitable. And I do understand the strategies you suggested. You may be right, but I honestly have the impression that he means somethig more formal when he makes that point. The statement "No logically invalid inference has the property that there is only one additional premise which can be added to make it valid" seems very strict. Do you have any particular reason to think that is what he meant by the "innumerable premises"? Are those strategies something common or well known on logic? Maybe a reference I can read? – Koeng Feb 9 '14 at 14:46
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    I haven't read this particular volume, so I can only guess but I take his point merely to be that there's an infinite number of different ways to bring an incomplete argument to validity -- they just vary in complexity and content. At face value, that claim seems both trivial and true to me. – virmaior Feb 9 '14 at 14:53
  • @virmair His wording seems to imply that any invalid argument can be brought to validity. I'm not sure it makes a difference, but he also says invalid, not incomplete, argument. Intuitively it seems true to me that you may turn an invalid argument into a valid one (maybe by including a contradiction?). It's just not really clear to me, specially since he is talking about such an important problem. – Koeng Feb 9 '14 at 18:11
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    Not quite that any invalid argument can be brought to validity. Any logically invalid inference can be brought to be validity. The distinction is important. Because the way an inference works is that there must be a principle to justify the inference. Some invalid arguments cannot be fixed by the addition of a premise. – virmaior Feb 9 '14 at 22:02

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