What I mean is, why do you restrict your claim about the nature of evidence to the situations where those premises hold? Why do you not make the same claim more generally?
(To put it another way, where, in such reasoning as you may have in mind from those premises to the stated conclusion (“It is support”), do you see those premises being invoked?)
Another thing I might ask about, in line with the symmetry-breaking of Hempel’s paradox: since “All ravens are black” and “All non-black things are non-ravens” are logically equivalent, why have a premise “At least one raven exists” but not a premise “At least one non-black thing exists”?
Well, it’s definitely the case that if no ravens existed, then “All ravens are black” would be trivially true. In fact, any statement of the logical form:
if IS-RAVEN then FOO
would be trivially true.
For those who want the logical reasoning:
if A then B
is defined as:
¬A or B
So if no object satisfies A, then the statement trivially holds.
Edit: As a homework assignment, it should be obvious from the logical definition of implication as ¬A or B why:
That depends on how the green apple was “selected,” which I think is, or at least relates to, the important point that Chronos made in Post #17.
Imagine the world as a very large (finite or infinite) urn and all of the objects in the world as balls in the urn. So, we have an urn filled with balls of different colors and labeled according to what they are: there are black balls labeled “RAVEN,” green balls labeled “APPLE,” red balls labeled “APPLE,” red balls labeled “STRAWBERRY,” and so on and so on and so on. Then, the statement that “All ravens are black” would mean every ball labeled “RAVEN” is a black ball.
The only way to know for sure whether this is true would be either to (1) look at all the balls in the urn that were labeled “RAVEN” and make sure they were all black, or (2) look at all the non-black balls and make sure none of them were labeled “RAVEN.” If you could only look at some of the balls—say, a randomly-selected statistical sample—you wouldn’t have conclusive proof but you could have evidence. Pulling out a “RAVEN” ball and seeing that it was black would be evidence, and so would pulling out a green ball and seeing that it was labeled “APPLE” rather than “RAVEN.”
Right. Although people tend to have an easier time believing that “if A then B” is true if B is always true than they do believing that it’s true if A is always false.
It’s not enough merely to have seen all the balls labelled “RAVEN” and observed them to be black. One also needs to know that those were all the balls labelled "RAVEN’. Similarly with looking at all the non-black balls.
Also, there’s nothing particularly special about your two ways; one could also look at all the balls which were both non-black and ravens, and make sure that there actually aren’t any of them, or whatever (after all, “All Ts are Ps” and “All non-Ps are non-Ts” are also both equivalent to “All (T and non-P)s are non-existent”). In a sense, that’s the minimal set to look at, the two sets you propose looking at being sufficient because they contain it.
Indeed. Though perhaps this is because much of ordinary-language implication isn’t material implication; it’s important to remember that it isn’t an error to speak in a manner which works differently, just a situation that calls for a different analysis. [Of course, typically, this will require implication to be an intensional (i.e., non-truth-functional) connective]
Not to deny that people do screw up and hold inconsistent beliefs about the nature of implication or have difficulty bringing themselves to understand the conventional mathematical formalization or so on…
I wouldn’t say that they were wrong. Generally the claims made by various scientists in specific are in the form of particular observations, and in the general by theories which are supportable by the evidence they have. I’d say my idea with what evidence is really isn’t all that different - if your premise involves A, or which B, C and D are subsets, that B might be observed to be accurate is not (in my eyes) evidence for A, only for B. But if you do have B, C and D, then you do have evidence for A. And even if you don’t, you’re still alright with B.
It seems to me scientists make many general claims for which their main evidence is inductive reasoning from specific observations; for example, I have no doubt that physicists are willing to say “All electrical charges experience attractive/repulsive force in the manner described by Coulomb’s Law”, with their main evidence being that this is how it’s been observed many times without fail. Is your interpretation that they make a weaker claim, or that they have different evidence, or that there are further implicit premises that need to be taken into account?
I’d say that physicists are willing to say that mainly because we do tend to talk more in terms of absolutes, more in terms of facts, than of theories, when talking informally. I would say when talking in scientific terms, then it would be the first of your options; they make a weaker claim than “All things act like this”.
As evidenced by this thread, meta-wankery is a popular past-time, and so it is important.
The “paradox” itself says nothing more than that “If I think about something that exists in the world–like an apple–and then ignore that one and just think about every single other thing in the world that there is, everything that I’m thinking about has no relevance to the apple! That is, until I think about everything else sooo hard that an apple shaped vacuum appears, and then well, duuude, I’m thinking about my apple again just by not thinking about it.” This is of course true, and of course entirely worth never being said nor debated. You could say that there’s a paradox in that you are thinking about and not thinking about the thing (apple) at the same time when you work in negative, but again this isn’t really worth pointing out for any sake other than to wank over.
The question is, what counts as evidence? You seem to feel that no amount of observations is sufficient to make a universal claim, and that confirming observations aren’t really evidence at all.
That is indeed the point. It is hard to talk about without sounding like a wank, but it’s not.
I like the “indoor ornithology” way of framing this: suppose that you are inside with the curtains closed. How can anything you observe about objects in the room count at all as evidence about birds?
Negative evidence for the proposition that “All ravens and black” would be non-black ravens. If you know that a particular collection of objects contains no ravens, then there’s no point in further examination: you know you will get no negative evidence, and finding a green apple in your closed room tells you nothing more about the colour of ravens.
Perhaps. But framing this another way, it would amount to a wide rejection of inductive inference: one thing I know up front about the collection of objects i examine is that, tautologically, it contains no objects unexamined by me. Does it follow that I couldn’t hope to gain evidence about the properties of those ravens I don’t personally examine from observations of other ravens?
A more concrete example: suppose I run a medical study today, knowing up front that none of the patients in the sample I investigate could possibly be born after the year 2008/currently living more than 100 miles away from me/religiously unwilling to volunteer for my study/etc. Do the observations I make thus give me no evidence at all for claims encompassing those who will be born after the year 2008/currently live…/etc.?
I guess I need to see it illustrated. What, when talking formally, would be the weaker, more appropriate phrasing of Coulomb’s Law? [And what problem with the stronger phrasing does it remedy? For example, if the weaker phrasing is “Charges tend to act like this…” rather than “Charges do act like this”, this is still not a claim conclusively deductively supported by observations alone; the vast majority of charges in the world are ones which haven’t been observed, and so there are no deductive grounds for saying anything about their properties, even in statistical aggregate.]