Robert Spillane thought this was particularly important and requested a direct answer. Here it is:
1. Two simple answers to #1 and #2 will suffice - yes or no.
2. 1+1=2 is a necessary truth; '1 pint of water + 1 pint of alcohol = 2 pints of the mixture' is not. Can you not see the difference between the two?
They have many differences and many similarities.
By "the" difference, I guess you mean: that "1+1=2" is a "necessary truth", while the other statement isn't. I don't agree with that because I don't think anything is a necessary truth.
Regarding induction, I've asked several times about a set of instructions someone could follow to do induction. I've been unable to get answers which address basic issues like telling you which ideas to induce and how much inductive support they have. Here's another failure to address the issue, and my comments. This is extremely typical of inductivists. They don't have answers to these questions and wouldn't be inductivists if they understood the questions.
You asked me for details about Stove's Rationality of Induction. Here is a very brief summary (pp. 3-5, 22) which addresses your concerns:
(1) 'That all the many observed ravens have been black is not a completely conclusive reason to believe that all ravens are black' is true and not contingent, even though it mentions two propositions which are contingent:
(2) 'All the many observed ravens have been black.'
and
(3) 'All ravens are black.'
But (1) is not contingent since it is enough to entail the truth of (1) that it is logically possible that (2) be true and (3) false, whereas something's being logically possible is not enough to entail the truth of any contingent proposition. Therefore, (1), being true and not contingent, is a necessary truth.
Another way of saying (1) is:
(4) 'The inference from (2) to (3) is fallible' and this is also a necessary truth.
The inference from (2) to (3) is an inductive one. So there is at least one inductive inference of which it is necessarily true that it is fallible.
This doesn't answer my question about how (2) and (3) were selected from the infinity of propositions which do not contradict the observation data under consideration. Why those statements instead of some other statements?
I asked about which statements to induce and for instructions someone could follow to do induction, but this description doesn't provide instructions for how to select or create statements (2) and (3) in the first place.
What are the rules of induction? Could one write any statements at all in place of (2) and (3), or what? (I'm familiar with many proposed rules of induction, but none of them work. You apparently think you know of some rules of induction that do work, so I'm asking what they are.)
(5) 'That all the many observed ravens have been black is a reason to believe that all ravens are black' is like (1) in that it is true but not contingent. Like (1) it mentions two contingent propositions, but it does not assert either of them. Its truth, therefore, does not depend on what their truth values happen to be.
Another way of saying (5) is:
(6) 'The inference from (2) to (3) is rational' and this, also, is a necessary truth (pp. 3-5).
Since induction is necessarily fallible, the validity of induction is a subject easily exhausted. 'And as to the truth of the conclusion of an induction, or whether the conclusion of an induction with true premises is true, or whether more of such conclusions are true than are false: well, these of course are all contingent matters, with which philosophers have nothing to do. The success rate among inductions is as little the concern of philosophers as the blackness rate among ravens. Hume, in particular, was as little concerned as the next philosopher with what the long-run success rate of induction might be, and of course he said nothing about this subject; and a fortiori, he said nothing discouraging about it. Yet there are philosophers who do not shrink from the absurdity of implying that in order to 'answer' what Hume said about induction, we would need to establish something encouraging about the long-run success rate of induction. Some people just like to make rope neckties for themselves. But, in general, it is scarcely possible to exaggerate the harm that has been done to the philosophy of induction by philosophers who drift from the success of induction to the rationality of induction, and back again, and all over the place. Squalor rules, OK?' (p. 22).
Now, you will probably reply that this is irrelevant to your concerns since it assumes induction and engages in arguments for and against its rationality. You, on the other hand, insist that induction is a myth. If by 'myth' you mean 'the presentation of facts belonging to one category in the idioms appropriate to another' (Ryle), this means that you accept that there are inductive arguments - from the observed to the unobserved - but believe they are inevitably invalid because the conclusions are not contained within the premises.
But this is not your position. You claim that by 'induction is a myth' you mean that there are NO inductive arguments - that there cannot be (and never have been) arguments from the observed to the unobserved. This is a much stronger claim than 'inductive arguments are invalid'. It is also a claim that is so obviously false that further argument should be unnecessary.
My position that induction is a "myth", in the sense I've described (no one has ever induced anything), is from Popper. Do you know that's Popper's published view and know his reasoning? You are calling Popper's position "so obviously false that further argument should be unnecessary".
I (following Popper again – see e.g. his discussion of manifest truth) don't think that's a reasonable thing to say about anyone's position. The truth isn't obvious, and argument is necessary for dealing with disagreements.
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