Thursday, May 15, 2008

Natural and Projectible Predicates

Rachael remarks on the 'structure and similarity' discussion:
Should we distinguish between predicates that are projectable and predicates that are natural? "Green", "ultraviolety-looking to bees", "owned by Rachael", and "tasty to alpacas" are fairly projectable, but I doubt they're natural. I don't expect a bee to care which objects are green, a mouse to care which objects are owned by Rachael, or a human (who doesn't have a special interest in bees or alpacas) to care which objects are ultraviolety-looking to bees or tasty to alpacas. There's a sense in which all the above concepts are parochial, and are only worth adopting because they're convenient. Furthermore, there's a sense in which there's no conflict between these different ways of carving up the world: I don't think the alpacas are wrong, and I might find it very important to adopt their concepts when interacting with them.

Also, maybe "Having mass m before time t or mass m* after" is an example of a natural predicate that isn't projectable.

That last example sounds gerrymandered (i.e. not a natural way to carve things up) to me. I'd need to hear more about why we'd consider it 'natural'. (Note that complex predicates may invoke natural terms like 'mass' in a gerrymandered or non-natural manner.) On the other hand, I'm also unsure why green and ultraviolet are thought not to be very natural. There is a natural respect -- namely, surface reflectance properties -- in which all green things (or all ultraviolet things) exhibit a genuine similarity.

The other examples are plausibly less natural, but also (and, I imagine, to the same degree) unprojectible. Here I should clarify something that may not have been clear in my first post. 'Projectibility' does not just mean stability across time, i.e. that if something satisfies the predicate now, it will also do so in future. Any tenseless predicate, however gerrymandered -- e.g. 'exists in 1907 or 2008' -- will be temporally stable in this sense. Genuine projectibility is more general, since we can inductively project along dimensions other than time. If a bunch of Fs are green, that may be evidence that other Fs (and not just these same ones in future) are also green. On the other hand, if a bunch of Fs are owned by Rachael, that's probably not enough to justifably project ownership-by-Rachael onto any other arbitrary F.*

Overall, then, I remain of the opinion that 'natural' predicates, i.e. those that carve nature at the joints, or highlight objective similarities, are also those that will tend to support inductive projection.

[* = I'm not sure if that's the best way to explain projectibility. Any suggestions?]

4 comments:

  1. I'm flattered that you've moved my comment to a post.

    To clarify about the colors: things with the same reflectance properties have the same color, but things with different reflectance properties can also have the same color. (I'm pretty sure that two things can have the same color even if they reflect none of the same wavelengths, provided that they cause the three different kinds of cone cells to fire at the same relative rates.) So if you arrange a bunch of objects in a color space, their relative positions won't tell you much about whether their reflectance properties are similar. That's why I was worried about color properties being disjunctive. But I agree that they're a lot less disjunctive than "owned by Rachael".

    On "Having mass m before time t or mass m* after": It's only a little bit disjunctive. You can write it out in terms of two perfectly natural properties using one perfectly natural logical symbol. That's far better than you can do with color properties or the property of (say) being a garter snake. Maybe this is the wrong approach to measuring naturalness?

    On your definition of "projectible" (a word whose spelling I now realize I've been mangling): I worry that whether a predicate satisfies it is going to depend a lot on what you fill in for the variable "F". "Grapes"? "Grapes produced by the vine in Rachael's yard"? "Things with a mass between 5 and 6 grams"? "Sweaters with 'Rachael' written on the tag"? Have we got a good method for counting values of "F"?

    I tend to think of projectible predicates as those that figure in causal and inductive explanations. That something is owned by Rachael might be part of an inductive explanation as to why we should expect it to be scuffed, or part of a causal explanation as to why Richard would get in trouble if he took it.

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  2. Although "green" isn't an good description of an objects reflectance properties, it is a good description of the effect of this reflected light on the human eye. "Having mass m before time t or mass m* after" seems much more arbitrary. I think it's pretty clear that "green" is the most natural concept of the two, but it's not clear at all whether this stems simply from usefulness or something more fundamental. To clarify, "green" would not be a natural concept if humans didn't exist. In a similar way "owned by Rachael" is a natural concept because our concept of ownership exists.

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  3. Perhaps we can state the criticism as follows: given that there exist creatures (e.g. humans) that are sensitive to relatively gerrymandered properties, those properties will gain a certain explanatory significance regardless of their inherent (non-)naturalness.

    But what is the relation between 'explanatory significance' and 'projectibility'? If the former can come apart from naturalness, does that necessarily mean the latter does too? I'm not sure I have a firm enough grip on these notions to answer that. (So: more insightful comments welcome!)

    Rachael - "Have we got a good method for counting values of F?"

    Great question. I was assuming that F-ness would itself be some relatively natural grouping (e.g. emeralds). But maybe your worries could still apply against this proposal?

    "You can write it out in terms of two perfectly natural properties using one perfectly natural logical symbol... Maybe this is the wrong approach to measuring naturalness?

    Yeah, I think so. I'm trying to get at a measure of objective similarity here, and counting the disjunction symbols doesn't seem to adequately capture this (since it neglects how similar or different the two disjuncts are).

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  4. given that there exist creatures (e.g. humans) that are sensitive to relatively gerrymandered properties, those properties will gain a certain explanatory significance regardless of their inherent (non-)naturalness.

    Yes! I think that this is a good statement of what I was getting at.

    Great question. I was assuming that F-ness would itself be some relatively natural grouping (e.g. emeralds). But maybe your worries could still apply against this proposal?

    Two thoughts here.

    1. Disjunctions like "positively charged or cube-shaped" look like they'll come out as projectible: evidence that all observed samples of an element are PC or CS is evidence that all unobserved samples will be PC or CS. In fact, these disjunction will satisfy your definition of "projectible" for more values of F then their individual disjuncts.

    2. More broadly, what do we want the concept of "projectible" to do for us? I'm a little worried that "projectible" in the sense Goodman intends is part of a failed research program: namely, inventing a formal inductive logic that mirrored formal deductive logics. I get the sense that Bayesian and modeling approaches have been far more successful. (By "modeling approaches", I mean something like deductive-nomological theories with ceteris paribus clauses built in.) Do you think my assessment is accurate? If it is accurate, then what role should the idea of "projectible" play in Bayesian and modeling approaches? Or should it die a graceful death?

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