Inductive Generalizations

We all have favorite examples of bad arguments, but after a good martini with my son last night, his latest example struck me as extremely funny and I love it so much I’m going to post it. He’s getting married soon, and was remarking on the possibility of future children. He said that he was certain they’d have some, because if you look at history, as far back as you care to go, every single one of his ancestors has had them…

He then pointed out the resemblance between the above argument and some he’s seen by epistemologists…!


Inductive Generalizations — 36 Comments

  1. Your son is clever enough that I hope, for the sake of the gene pool, he has many, many children.

    But I can’t resist using this opportunity to talk about Hume’s Riddle! (My position being basically that Hume got it all wrong eight ways from Sunday, and that this is important.) Anybody who likes this topic might click on my name, above, to get started.

  2. This is more like Goodman’s riddle than Hume’s. It’s rather like saying — all the green emeralds observed in the past have been grue (note that this is tautological evidence, given our background knowledge) — so all the green emeralds observed in the future will be grue (and this is a substantive empirical hypothesis). Grue is a bit more striking, since observed-after-t-and-grue entails BLUE, which CONTRADICTS observed-prior-to-t-and-grue. But, in the example at hand, being my ancestor entails having children, whereas being ME does NOT entail having children, but it also does not entail NOT having children. Nonetheless, the former (weaker “grue”) is sufficient to motivate the deeper asymmetry Goodman had in mind.

  3. Actually, my intention wasn’t to advertise, but to avoid posting a too-long post, by linking to the only place I have online now where my argument can be accessed. Unfortunately, the whole book can’t be read there, though I wish it could. I plan to make the whole thing available for free online, just as soon as I can figure out how.

    To make it too short, my argument against Hume’s kind of approach is that it neglects the possibility that what is actually possible or impossible can be due to reasons that are not logical but physical.

  4. Branden,

    Grue is a bit more striking, since observed-after-t-and-grue entails BLUE, which CONTRADICTS observed-prior-to-t-and-grue.

    Observed-before-t-and-grue entails blue-at-t-and-later which seems consistent with Observed-at-t-and-grue-(and blue), no?. Otherwise we’d have two properties, one the object has before t and one it has at t and later.

  5. Mike. Let me be more precise here. Let Ox = x is examined prior to t, Gx = x is green. A simplified definition of Grue(x), which I will abbreviate as Rx, is Rx = Ox iff Gx. In fact, this is how Goodman originally defined it (originally, he didn’t use green/blue, he used green/non-green). On this understanding, Oa&Ga entails Ra, and ~Oa&Ga entails ~Ra. This is what I had in mind. Thus, if we say all green emeralds that have been examined prior to t have been grue — this comes out as an analytic truth. However, when we say all green emeralds examined after t will be grue, we are not saying something analytically false, since there may be no emeralds examined after t. And, whether there will be any is an empirical issue. That’s (I hope) a clearer way of making my point. The disanalogy with the ancestor case is that if there ARE some green emeralds that will be examined after t, then these cannot be grue (on pain of contradiction). This is disanalogous to the ancestor case, since there is no contradiction in assuming that I will (or will not) have kids. Despite this disanalogy, I think the underlying structure is relevantly similar.

  6. Why drag the temporal quirks of ‘grue’ into this? Being an ancestor entails the having of a child&mdashit is analytic—but being a child doesn’t entail being an ancestor.

    If you assume that a child must have a pair of ancestors (debatable, given advances in reproductive medicine, but let’s not spoil the fun), then the joke turns on introducing an analytic truth that follows from information you already have—i.e.,that your ancestors had children—as if that information could provide a decisive answer to the empirical question at hand when it actually provides nothing at all.

  7. Greg,

    I think that is the joke. But he might have had in mind–probably did, actually–the nonanalytic proposition that all of his ancestors (de re) had children. He might have said those guys had children, so I probably will. It is certainly true that my father (de re) might have had no children at all. But that’s killing more joy.

  8. Greg. Time has nothing essentially to do with grue. We can define grue as observed iff green. Then, the same analyticity point applies concerning grue (it is analytic that all green observed emeralds are grue, and it is not analytic that — indeed, it is an empirical matter whether — all green unobserved emeralds are grue). That was my point.

  9. The idea is supposed to be that this is a “bad argument.” But it isn’t. It’s a good one. It really is the case that his likelihood of having children is increased by the fact that his ancestors successfully did so. Not everybody succeeds in reproducing. That’s how natural selection ends up producing animals with this very amazing and almost miraculous-seeming ability (and drive and tendency) to reproduce, which is no simple task, physically. As we all know, people tend to take after their ancestors, thanks to genes.

    If it’s not a bad argument, then why does it make us laugh?

    I think it’s simply because of birth control. It suddenly no longer makes sense to say that, because now he has a choice. He can pretty easily decide NOT to have children. If this was 1850, and he very much wanted children, then what he said would not be silly at all.

    Not all reasons are logical. Some reasons are physical.

  10. Quee. I think you’re changing the subject here. The question is whether the fact that all my ancestors had children gives good reason for me to believe that I will have children. I know A PRIORI that all of my ancestors had children — it follows from the DEFINITION of “ancestor” that all ancestors are parents. Are you claiming that something that is true BY DEFINITION can constitute good evidence for something that is contingent and empirical? How does that work, exactly?

  11. Why should it be a problem? If we know or agree A PRIORI that ancestor means genetic parent, and we know A POSTERIORI by EXPERIENCE that fertility is to a large extent genetically heritable, then what is to stop us combining these, to arrive at an empirical conclusion?

    For that matter, why should we segregate the two so severely? In the olden days at least, an A PRIORI truth was said to be something a person could know to be true without depending upon experience. But that can’t be quite right, since you can’t know that all ancestors are parents, or that all bachelors are single, unless you have discovered, through EXPERIENCE, the fact that this is the way pretty much all English speakers use the word ancestor, and the word single, etc., etc. So you might be tempted to conclude that there is no such thing as A PRIORI knowledge.

    On the other hand, if we say that something being true A PRIORI is just a way of saying what we ordinarily mean when we say true by definition, then we have to admit that there’s an A PRIORI element in every contingent or empirical sentence, since, when you utter an empirical claim, some people might dispute the idea that it corresponds to things as they really are or contradicts our experience, while others might take a different approach and quibble over your terms, quibble over your definitions, or take issue with your conceptual scheme.

  12. If you were observing a family where every single member of the family liked toast, and the family had a new child, I think most of us would say the CHANCES of that child liking toast are pretty high. It is a simple matter of conditioning. For the most part, I think this is Quee’s point.

    However, it does not follow from the fact that every previous family member liked toast that we can be CERTAIN the new child will like toast. This I believe is fitelson’s point.

    What interests me is that if we want to asses the possibility of the new child liking toast (or having children if you prefer the original formulation) it does not seem we will have any analytic/a priori information to go on. Certainly toast-liker or children-haver is not an essential feature of being human. What then are we left to reason with in cases where we want to make predictions about the future? It seems to me making probability judgements based on historical precedent might be the best we can do in some cases. This may be weaker than certainty, but is it really that bad?

  13. I agree that chasing the mirage of CERTAINTY is a fool’s errand. (What does it even mean?) But Hume boasted that he could shoot down PROBABILITY too. (See his skeptical arguments about induction in the first Enquiry.) Hume knows that an anti-skeptic like me might not claim to have obtained certainty, but only probability. So that’s the ground I’m fighting for. But neither am I willing to accept Hume’s caricature of science as a mindless process like pulling balls from an urn. (Doesn’t even a brief discussion of Mill’s methods show that Hume’s picture is a false cartoon?)

  14. Quee. I am no inductive skeptic. Nor do I have any problem with empirical knowledge or inductive inference. I am making a very simple point. Claims that are true by definition do not BY THEMSELVES provide reason to believe empirical claims. I don’t see how anything you’ve said counts against THAT. This is consistent, of course, with such claims being an integral part of a SYSTEM in which empirical knowledge is arrived at (or couched). But, that is simply a different claim. That’s what I meant by “changing the subject”.

  15. Addendum. There may be PRAGMATIC information that is conveyed (in a context) when I ASSERT an analytic claim (for instance: “A bargain is a bargain”). Grice discusses this phenomenon. But, this sort of pragmatic implicature is not what I’m talking about. I’m talking about WHAT IS SAID and whether IT can support empirical claims. Why do you think THAT happens — and can you give an example?

  16. I’ll give it a try. I once had a debate with my Dad, who was complaining about the fact that, in an unbridled market economy, housing costs too much, and even when we provide below-market (price) housing by means of special legal interventions, there obviously isn’t enough of it, since there’s always a shortage of it with waiting lists, etc. I laughed and said, Dad, I can assure you that there is no politician who will solve that problem, because the market price is by definition the market-clearing equilibrium price, which simply means that’s the price at which neither glut nor shortage persists, and therefore we may be sure that there will always be a shortage of below-market housing, no matter who we vote for, or how much below-market housing is created.

  17. This is a non-example. In this case, the “hypothesis” is of the form:

    For all x, if x is a politician, then x won’t solve problem P.

    And, in this case, the “evidence” is something like:

    P is — analytically (or by definition) — an unsolvable problem.

    If the evidence really is analytic (true by definition), then so is the hypothesis. Thus, this is NOT a case of an analytic claim supporting an empirical claim — the hypothesis is itself non-empirical because IT is analytic, provided the evidence is.

    Of course, if your father didn’t KNOW P was analytically unsolvable (perhaps he thought it was solvable), then he just didn’t understand what the hypothesis SAID in the first place (that is, he lacked the conceptual understanding needed to see THAT the claims in question were analytic). That’s not a case of “support” — that’s a case of concept acquisition.

    We’re not talking about concept acquisition cases here — we’re talking about cases in which people understand the concepts involved in the hypothesis and evidence, and yet an analytic claim (a claim they KNOW TO BE analytic) somehow provides support for an EMPIRICAL claim. You have not provided an example of this.

  18. Yes, I think I understand. I guess my trouble is that I had a certain prejudice which made me want to classify these concept acquisitions as a posteriori events which confer new knowledge that is empirical and contingent. (Like the knowledge that this is how economists use the word market.)

  19. A different question, one raised by Branden’s invocation of definitions – Why think that ‘ancestor’ by definition entails having had children? I mean, I get the force of the joke, but surely Kvanvig’s son has uncles or aunts who never had children… and I wouldn’t think that the very term ‘ancestor’ excludes them by being limited strictly to those of parental ancestry (or does it? Consider a practical case: would my doctor be concerned if I have cancer in my family history, but the instance of it is confined to an uncle?)

    And wouldn’t it be a much more impressive inductive generalization by Kvanvig’s son if it indeed were the case that EVERY member of his traceable ancestry (who lived to adulthood, and married, etc.) had had children? I think that the answer is ‘yes’ shows the relevance of this point: it would show that his heritage is maximally stable reproductively (perhaps amongst those who try to have children)… whether that would warrant ‘certainty’ on his part is another question.

  20. Matt. I’m just going by the dictionary definition of “ancestor”. For instance, the OED says:

    “One from whom a person is descended, either by the father or mother; a progenitor, a forefather.”

    You cannot descend from someone that had no children (no children implies no descendants). That’s why it’s a joke, and that’s also why I made the remarks I did. I’m not sure what you have in mind here.

  21. Ah, but, being an ancestor is not sufficient for the joke: it works because descending from ancestors is the only way for one to have become a child. This is not analytic, which is why the qualification in [7].

    If we manage to figure out how to descend from a non-person, or parts of people, we might mark that distinction by restricting ‘ancestor’ to people…for sentimental reasons, if for no other…and artificial ancestor for the remainder. If you grant this much, then consider the following example.

    Suppose that children of artificial ancestors are known to have lower reproductive rates than children of ancestors. Then, although not decisive evidence, the report that one’s ancestor’s had children would contain useful information after all: it would signal that you are a member of a sub-population that has a higher rate of reproductive success than the complement of that sub-population.

    It seemed like Quee was after something like this, but on his formulation the partition would divide the population into the living and the never-existed.

    So, it’s Fisher we should be talking about, not Hume, not Goodman, not Carnap… 😉

  22. What about my point up in box in 12 that if somebody who wanted children said this in 1850, it would:

    a) not be funny or silly, and

    b) not be a bad argument.

    Doesn’t this prove something?

  23. I’m with Branden on that one.

    [24] is garbled. (Ah, blogging.) It’s being a descendent of ancestors that’s not sufficient because of the reasons mentioned rather than being an ancestor. And ‘managing to descend’ is a weird way of putting ‘manage to create children without ancestors’.

  24. Do you mean you think it would be bad reasoning if offered in 1850 by somebody who wanted kids?

    If you agree that it would NOT be wrong in that case, then what changed in history to make it suddenly a silly/bad argument now? Not the laws of logic.

  25. I’m confused by Greg’s post. The argument in question is this (in the mouth of Branden, here):

    All of Branden’s ancestors had children.
    Therefore, Branden will have children.

    Greg — are you saying that the premise of this argument is not analytic? Why not? All of Branden’s ancestors are (by definition) people with some descendants. How can they have descendants if they have no children?

  26. Branden: In short, yes, I deny that the first premise is analytic.

    I understood the punch of the joke to turn on saying that You (to borrow Peter Walley’s royal second person) can learn something about Your chances of having children by learning that Your ancestors had them. The point is pushed to the limit by saying that You would learn decisively from learning this.

    A. It is tempting to represent this as an unsound demonstrative inference, but the joke is funny because the discovery of useless information is dressed up as useful information, indeed, decisive information. Do we agree on A? If so:

    B. The general situation then is You, a child who has ancestors, are uncertain about whether You will produce off-spring or not. Yes? Then:

    C. You point out that Your ancestors had children; However, two things are expressed by this assertion:

    C1: The analytic truth that ancestors have children, which we agree is analytic, and
    C2: The claim that You are a child of some ancestors, which is not analytic if you buy the story I told about artificial ancestors. But:

    D: For the joke to be maximally funny, I think you need C1 and C2 to turn out analytic, and so for C to express absolutely no information whatsoever and yet for You to claim that You can arrive at a definitive answer from discovering C. (This is a matter of interpretation, but this is how I would play it for laughs.) Otherwise:

    E. C2 could convey information if (a) there were children without ancestors and (b) there was an identifiable subclass of ancestor-less children, all of whom were sterile. The information conveyed being that you are in the class of not-necessarily-sterile offspring.

    [Con]. Knowing that You were a child of ancestors rather than a child of sterile artificial ancestors could then be non-trivial, useful information (so long as you adjust the proportions of the subpopulations accordingly).

  27. Greg. I don’t think I get it. As far as I can see, you have not shown how:

    All of Branden’s ancestors had children.

    can be false. So, please explain that for me again. I just don’t see how the artificial ancestors story works, or is relevant to the necessity of the premise above. The premise seems to me to be entailed by the definition of ancestor (as I understand it — maybe we’re just working with different definitions here?).

  28. ‘For all x, Ancestor(x) –> Has-a-child(x)’ is true because it is analytic.
    ‘For all x, Is-a-child(x) –> Has-Ancestors(x)’ is true, but it is not analytic.

    HeYou are right that Branden’s ancestors are no different than anybody else’s ancestors in their having children. However, we aren’t directly interested in Branden’s ancestors per se. We are interested in whether Branden will beget a child.

    The idea behind the artificial ancestor story is to break the analytic link between off-spring and child, where ‘off-spring’ here is behaving as the converse relation of ‘ancestor’.

    It turns out that in our world, now, we are coming upon the knowledge of making young animals from the parts of other animals in artificial ways. This creates a new class of young animals, and introduces a partition in the class of children (say) that was not there before (i.e., between offspring and artificial offspring).

    If the population of artificial offsrping has reproductive rates different from natural offspring, we know about this difference, and ancestors beget natural offspring and god-knows-what is behind the creation of artificial off-spring, then the *assertion* that instantiates Branden into ‘For all x, Ancestor(x) –> Has-a-child(x)’ is true but informative.

  29. Bah. Another post spoiled. The instantiation in the last paragraph is wrong, of course. Sorry for that. Just drop that part. Is it clear without that, or should I add the suppressed premises for linking your having ancestors to use this generalization? (Sorry again; I’m late for a lecture…)

  30. OK, I see that we’re just using the word “child” differently. You’re assuming that “child” means “young person”. But, how young? After all, Jon was having a martini with him, so he can’t be THAT young! The “young” definitions of “child” in my dictionary are the following four:

    A person between birth and puberty.
    A person who has not attained maturity or the age of legal majority.
    An unborn infant; a fetus.
    An infant; a baby.

    I assume Jon’s son is neither of these. So, we must revert to the next definition, which, in my dictionary, is:

    A son or daughter; an offspring.

    And, if THAT is the applicable definition here — which is what I’ve been assuming all along, and I see no reason to reject — then your claim is simply false. It DOES follow from being a child (in the salient sense) that one has ancestors. So, I just don’t think your reading or analysis of the joke hold water.

  31. ‘Child’ here is used in the general sense of off-spring. I do not deny that there is a sense of off-spring that fits your reading, but I deny that the entailment you need is analytic.

    The case for anticipating the division of the class of off-spring into natural and artificial is making its way into the newspapers, after all. It is not implausible to anticipate changes to the dictionary to reflect this.

    I’m happy that I’ve got you to agree that you need this extra condition for linking child to ancestor. The point is that whatever the meaning of the constituents of the joke/argument, you need to account for this link between the classes. And if you go back to 7, you’ll see that I include the clause to close that loop hole.

  32. OK, Greg. I see your point now. Of course, I doubt that’s the sense of “ancestor” that is intended here — since this joke is a rather old one. But, I suppose, in the future, someone could utter this joke in a context that would make the entailment in question non-analytic. I just don’t think that’s what’s happening here. I think the premise that was uttered by Jon’s son in that context has as its content an analytic truth.

  33. We agree that the joke is funniest when the entailments in both directions are analytic. And we agree that in the direction from ancestor to child that this is a rock solid analytic truth. I was just highlighting that you need to account for the other direction, and that the analyticity of this converse entailment is less solid.

    Well, it is bedtime now in (smoggy) Kanpur. Enjoy your weekend, -g

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