William M. Briggs

Statistician to the Stars!

Induction & Essence

Not that kind of induction!

Suppose we observe a raven. It’s black. We see a second, also black. And so on for a few dozen more. We reason, or rather we argue with ourselves, “Since all the many ravens I’ve seen have been black, the next raven I see will be black.”

There are seeming problems with this self-argument, this induction-argument. It appears to be invalid since, as is probably obvious, it might be that a non-black raven, perhaps even an albino raven, exists somewhere. And if that’s true, then the next ravens I see might not be black. Also, the argument is incomplete—as written, though not as thought. As thought, it contains the implicit premise “All ravens are the same color.” That makes the entire argument: R = “All ravens are the same color and every raven I have seen was black; therefore the next raven I see will be black.” That argument is valid.

Therefore, it is a local truth that “The next raven I see will be black” given those premises. We are back to the same kind of situation as when we discussed Gettier problems. What is our goal here? Is it to assess the truth or falsity of the premises? Or to make predictions? Given the premises are true, then it necessarily follows we will make flawless predictions.

Now “every raven I have seen is black” is true (I promise), so the only question is “All ravens are the same color.” Where did that arise? That was an Induction-intuition, arising from the judgment that having black feathers is the essence of being a raven, or at least part of the essence. If this judgement is true, if having black feathers is essential to being a raven, then the this premise is also true and the conclusion to R follows.

The crux is thus the step, i.e. the induction, from the observations to an understanding of what it is to be a raven. But there have been observed white ravens, and it is said (by biologists) that these suffer from a genetic defect. A defect is thus a departure from the “norm”, from what is expected, and what is expected is the form given by the essence.

With this in mind we can fix the argument. R’ = “All the ravens I’ve seen have been black and it is the essence of ravens to be black; therefore the next raven I see which is properly manifesting its essence will be black.” This is a valid argument, and sound if indeed, as induction tells us, ravens having black feathers is part of the essence of being a raven.

Some people have mistakenly identified features of things thought to be essential but which were instead accidents. It is not for instance essential that swans have white feathers; some have black. But because mistakes are made in the induction of essences does not prove that inductions are of no use, nor does it prove things do not have essences. Many people make mistakes in math—surely more than who make mistakes in inductions of essences—yet we do not say math is a “problem”, where that word is used in its modern philosophical sense as an unresolved, unresovlable or paradoxical question; and we do not say math is invalid and not to be trusted. We do not seek for alternatives to math that explain how it could possibly be, given that some have erred in the calculation, that 1 + 1 = 2. We are not mathematical skeptics. Yet the mere possibility of mistake in induction is enough, for some, to cast doubt on the whole of induction.

Induction, as outlined in this must-have book, comes in various flavors. The kind of induction that extracts essences is not the same as the kind of induction that is statistical and that lets us make empirical predictions.

We did this before: we know via one kind of induction that dogs essentially (and I do not mean this word in its more-or-less connotation, but in the rigorous must-have) have four legs, but we know via statistical induction that some dogs do not fully evince this essence. The kind of prediction we wish to make varies with the type of induction we have in mind. If we want to know via the essential-induction whether all dogs have four legs, the answer is always yes, since it is essential for dogs to have four legs. But if we want to know via statistical-induction how many dogs have four legs in some certain situation, then the answer will be different, and will instead be a counting of the departures from essence. Read the linked article for more.

16 Comments

  1. The second sentence triggered me; retreating to my safe space.

  2. Black Ravens Matter. Where do I sign up to get funding from Mr. Soros?

  3. Ravens are like writing desks because they both have feathers.
    and that’s not what I meant by essence.
    The word form is also problematic, strictly speaking.

  4. Joy,

    When is a door not a door?

    When it’s ajar.

    Being problematic is what makes word forms fun. 😉

  5. Some people have mistakenly identified features of things thought to be essential but which were instead accidents.

    Obviously or one could never find a white raven.

    Essence allows identification. Defining the essence of something is nothing more than the problem of classification. There is likely no single feature which does this. Essence must have more than one set of features. For example, if you chop off a raven’s wings is it still raven? Can any one feature be removed that will make it a non-raven? Can a feature remain but others removed to lead one to think t is no longer a raven?

    This s true not just with ravens but a host of other things. When does a pile of dirt become a hill?

    Most of our world models are built using induction. These models embody the ‘Essence’. They are potentially different for each of us. Which perhaps is why you might ‘see’ a horse in the clouds but I can’t even if you can list why it seems a horse to you. A better word might be ‘resemblance’ along with the acknowledgement that ‘resemblance’ comes in degrees.

    Encountering a white raven should lead to the conclusion that not all ravens are black vs. the conclusion that white ravens are defectively colored. The latter is a judgement of how the raven became that way (note that it is still a raven) — a why. What is the basis for this? If you had drawn dozens of balls from an urn — all black — and then encountered a white one would you conclude the white one was defective? Why?

  6. I sure would, DAV, if I bought a bag of black colored ping-pong balls to put in the urn, then pulled out one or more white ones or any other color than black.

  7. I bought a bag of black colored ping-pong balls

    Apples and oranges. You bought a bag of balls that by definition should be black versus developing a definition of ping-pong ball through observation. You still haven’t explained why observing a white one would lead to the conclusion (and not just hypothesis) it is a defective ping-pong ball . Why you think it was a ping-pong ball if all ping-pong balls are black?

  8. He he, you fell for it ;p. Yes, I answered your literal question. I can’t, directly, answer your figurative question for it posits facts not in evidence. So, if I get your ultimate premise correctly, and I accept that premise, I can still come up with an answer that the white one is defective; but it will have to be a statistical one, pending further review.

  9. Fr. John Rickert, FSSP

    February 13, 2017 at 2:49 pm

    An engineer, a physicist, and a mathematician are driving through Scotland. They see a sheep. The engineer observes, “The sheep in Scotland are black!” The physicist corrects him, saying, “Well, -some- of the sheep in Scotland are black.” The mathematician then says, “No, there exists at least one sheep in Scotland, at least one side of which is black.”

    Lonergan, in his book “Insight,” makes a good point: The problem is not that people generalize; the problem is in getting them to frame their generalizations accurately.

    The Medieval Metaphysicians were fond of saying, “Quid est equinitas? Equinitas tantum.” “What is ‘horsiness’? Nothing more than horsiness.” You can’t get a horse from its definition, any more than you can get a winged horse from its definition, or one with a single horn, or one with both wings and a single horn. So, we have to rely on actually existing, extramental things to bootstrap our understanding, and there can be a danger of sampling error in this.

    Still, I do not think the analogy of ping-pong balls is correct, because ping-pong balls are not the offspring of other ping-pong balls.

  10. All this reminds me of the specious sophistry that Alinskyite “reformers” used back in the ’70’s to induct vulnerable adolescents into esoteric relativism… that things don’t have any objective “isness” or essence… everything is whatever the ego wants it to be according to situation and/or convenience.

    Particularly in the case of utensils and utilities the “essence” of a thing is determined by its intention and functionality; for example, a table can be made of just about anything of enormously variable size or shape and ornamentation… but its a table because that’s what its intended to be and what its used for. A bouncing ball or a bird or a bolting bull can’t be a table because they can’t function as such. See? the “isness” of a thing is not determined by the fancies of an out-of-control ego.

    The essence of a raven is that which distinguishes it from everything that is not a raven… the essence of my pet raven (and we had one when we were kids… a most endearing, annoying, and cunning beast he was too) is that which distinguishes it from all other ravens.

    Simple example. Say you ran over your 6yo daughter’s white, fluffy, cart-it-around-in-the-pram pet Fido. Oh! hell! Rush to the pet shop and buy replacement Fido which just happens to be a Doberman Pincer. The girl would say with utmost confidence “it’s a dog but it’s not MY dog”. You only need higher education esoterica to NOT be able to see essences.

  11. “When does a pile of dirt become a hill?”
    A pile of dirt is not a substance.

  12. Yes, a pile of dirt is not “a substance” but it is essentially different to a flat space in the garden.

    Neither is a hole in the ground “a substance” but, still, it’s not a good thing to walk into in the dark.

    look, you can’t have a pile of dirt without the dirt that makes up the pile. You can’t have a hole without the lack of dirt that makes the hole.

    Ultimately, reality is not a figment of an insane ego. (Or any cleverly contrived mathematical trickery). Reality is what it is and it doesn’t need any “mathematicians”, or “philosophers”, or “scientists”, to make it what it is. Nor can any of the aforementioned make the slightest alteration to reality. What they can, and do, do, though, is to distract and brainwash ordinary folk into servile incomprehension even contradicting what everyone knows intuitively.

  13. I think I’m in agreement with DAV here…

    There are many subspecies of the common raven: https://en.wikipedia.org/wiki/Common_raven

    Animalia : Chordata : Aves : Passeriformes : Corvidae : Corvus : Corvus Corvax : C. c. corvax

    There is even a Corvus albicollis a subspecies called the ‘white-necked’ raven, a raven that is not all black. The extinct Pied raven (https://en.wikipedia.org/wiki/Pied_raven) was mostly *white*.

    So is the essence of a Raven to be black or not? Seems to me not… But if essence is *not* taxonomy, then what is it?

  14. Another example: About 6% of the jaguar population in South America are black. https://en.wikipedia.org/wiki/Jaguar

    Is the essence of the jaguar to be orange with black spots? The black panther is a jaguar and breeds with orange/black jaguars just fine. Is the black panther an ‘accident’ or mistake, if it regularly occurs? Is essence simply a percentage? (‘most have X’ means that the that X is part of the essence)?

  15. Didn’t Nassim Nicholas Taleb already cover this in his book, The Black Swan.

    Here’s an article of his that summarizes much of that: http://www.edge.org/conversation/the-fourth-quadrant-a-map-of-the-limits-of-statistics

  16. It has apparently escaped the notice of some who have a subliminal assumption of empiricism and materialism that I never made any claims based on the numerical or statistical preponderance of any particular characteristics.

    The essentials (universals or essences, if you like) of a raven are those characteristics or qualities that distinguish a raven from everything that is not a raven… usually a great combination of appearance, behaviourisms and lots of other things that may, or may not, be defined or even definable. Taxonomists amuse themselves trying to identify and define some of the physical characteristics common to various species etc. But even a cat can, without the assistance of taxonomy, distinguish between a dove and a raven.

    How can there be a white raven, or a large raven, or one deformed or injured or dead without the essence of “ravenness”?

    How can a man be tall, powerful and black, or slight, quick and yellow, or short, grumpy and white without the common essential “humanness”.

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