I drew up a detailed proof last night.
On my writing-desk.
Ah, but that’s the rub, isn’t it? All choices are not logically coherent when put to the test. My position is that this is akin to the ‘can God create a rock so big even He can’t lift it’ logic, which is to say, poor logic indeed. By choosing a simple statement as representative of ‘All A are B’, to wit: all ravens are black, there can be nothing but paradox because you and I and we all know that there exist many things which are black and not ravens, hence this is a contrived - I would argue, even nonsensical - statement intended to artificially create paradox. If I speak gibberish, it remains gibberish even when put into formal logic. Why, then, isn’t the obvious answer to remove the issue of paradox through a corrected hypothesis?
But we shall see it…
nevermore.
NaSultainne, in what way is it gibberish to say that “all ravens are black”? IANAOrnithologist, but so far as I know, that’s true.
“All Ravens are black” is NOT the same statement as “All black things are ravens”.
Different statments entirely. If all ravens are black you could still have plenty of black things that aren’t ravens, and if all black things are ravens you could have plenty of ravens that aren’t black.
And it is not true that all ravens are black: http://images.google.com/images?hl=en&q=albino+raven&gbv=2
I’m so glad that particular search doesn’t return porn.
Retroactively, I guess now I am too!
A is not B. So not B is A. 
:dubious:
I’d argue that the paradox is solved by neither the existence of the apple nor the existence of any individual or many black ravens being evidence. The existence of 9 black ravens out of 10 total doesn’t say anything about the colour of the tenth raven. A premise which requires an absolute can’t be backed up by anything less than that absolute.
Child asks:
What is a rose?
Parent says:
See that rock there, that is not a rose.
See that dog there, that is not a rose.
See that house there, that is not a rose.
See that cloud there, that is not a rose.
See that potato there, that is not a rose.
See that ice cream cone there, that is not a rose.
See that truck there, that is not a rose.
See that shoe there, that is not a rose.
See that girl there, that is not a rose.
See that shadow there, that is not a rose.
See that *n-1 *there, that is not a rose.
See that flower there, that is a rose.
Well, the whole point of inductive inference is to be looser than deductive inference, allowing confirmation of universal hypotheses from such less than conclusive evidence. Science, and indeed daily reasoning, is thoroughly infused with this kind of inference. Every ice cube ever observed has melted when heated to sufficient temperature; is this no evidence at all that the same holds true of all ice cubes, including those not tested yet? [Sorry, couldn’t think of a better example, but you get the idea]
That’s not actually the problem. As I understand it:
Premise: (1) All ravens are black.
No problem so far.
Corollary premise: (2) If something is not black, it is therefore not a raven.
Also clear enough.
Observation: I have a green apple.
Alleged Paradox: The apple is not black and is not a raven, which tends to support (2). But if (2) is equivalent to (1), my green apple must also tend to support (1). Therefore having a green apple proves all ravens are black.
The problem as I see it is that “non-contradiction” is being treated as equivalent to “support”. Sure, the green apple does not contradict (2), but I don’t see that non-contradiction as providing evidence of the correctness of (2). It would be like claiming “whatever does not disprove God, proves God”.
Lemur properly understands the problem; he was pointing out someone else’s confusion.
Also, nothing so glib as “Non-contradiction is evidence” is being appealed to (in any direct way). Rather, the intuitive plausibility of Nicod’s condition is being used (that is, the idea that observations of Ps which are Qs should be evidence for “All Ps are Qs”), plus the idea that evidence for a claim is also evidence for all logically equivalent claims. From the Nicod condition, we get that non-black non-ravens are evidence for “All non-black things are non-ravens”; then, by logical equivalence, it becomes evidence for “All ravens are black” as well.
Yes, I would argue that it is no evidence at all. The smallest possible point of data which would not only be negative evidence but disprove the premise is one ice cube that doesn’t melt. No matter how many ice cubes you melt, unless you can do so for them all there remains the possibility that that smallest point of data exists. I’d agree that you could use all those observations as evidence for “ice cubes tend to melt”, but they’re no evidence for the premise that none do.
Er, I’m not talking about negative evidence, I’m talking about positive evidence. Is there anything which, to you, would count as positive evidence for the claim that all ice cubes will melt when heated to sufficient temperature? If you say no, I’m going to say you’re fixated on deductive, indefeasible inference. That is a very nice kind of reasoning, but it is not the only kind. Surely you are familiar with a different standard of reasoning, and even employ it regularly for many purposes, under which certain observations could serve as positive evidence for such a claim (or that electrical attraction follows an inverse square law or that monkeys do not speak English or what have you), even though the possibility of fallibility remains.
It is support, as long as you accept the premises that at least one raven exists and that there are a finite number of objects in the universe.
Look at the big picture. Suppose you were able to look at every single non-black object in the universe. And when you were done, you hadn’t seen a raven. Logically, if you know ravens exist, you must conclude that ravens are black even though you haven’t seen a single raven. So every non-black non-raven that you saw supported the theory that all ravens are black.
Or bring it down to a smaller scale. Let’s say you go to shopping at a used car dealership. You know from their advertisments that they have at least one Toyota on the lot and when you get there you see that they’re having a special sale on red cars and all of the cars inside their showroom are red. But you find that the showroom is closed and you can only look at the cars parked outside. You drive around and look at every car that’s parked outside and don’t see any Toyotas.
What color are the Toyotas they have for sale? You can correctly assume that they are red because you’ve seen all the non-red cars on the lot and they’re all non-Toyotas.
Why do you impose the conditions that at least one raven exists and that there are a finite number of objects in the universe?
Yup, all ice cubes melting when heated to sufficient temperature.
Sure, but not when absolutes are used. I don’t have any problem with such observations being used as evidence for claims that there are *many * cases where electrical attraction works in that way or where monkeys don’t speak English. But were you to say that electrical attraction always works that way, or there are zero monkeys who speak English, I wouldn’t consider specific examples of instances following those premises to be evidence.
Alright. It would appear to me that you use the word “evidence” in an unusual way, then; would you say that most of the claims of physicists, chemists, etc., as they would naturally make them, are made without any evidence, and should be reformulated? And if so, what would you say is wrong with the notion of evidence they appear to be working with?
I don’t impose them. They’re premises.