8/14 Open Thread: Why is a Raven Like a Writing Desk?
The above conundrum comes to us courtesy of Charles Lutwidge Dodgson (January 1832 – 14 January 1898), He was a mathematician, logician, author, lecturer, inventor, photographer, and Anglican deacon. In spite of his prodigous chops as a logician and mathematician, he was better known as Lewis Carroll, a non de plume he used to write "children's" fiction, notably Alice's Adventures in Wonderland and its sequel Through the Looking-Glass. HIs poems Jabberwocky and The Hunting of the Snark are acclaimed as part of the literary nonsense genre. That may not be strictly accurate. Dodgson was an astute student of all things epistemological without overtly categorizing them as such. Both of the Alice books, to some extent, but much more so Sylvie & Bruno take a lot of metaphorical pokes at established epistemological assumptions and paradigms. They are also subtly educational if read from the proper perspective and in the proper frame of mind. Beyond that, they are sneakily existential, even there was no such thing in his day. Way back some 55 yearss ago, I wrote a paper that made a strong cse that the Alice books to some extent, Sylvie and Bruno even more so, and The Hunting of the Snark vehemently and explicitly should be viewed at least in parts as allegorical expositions on the existential dilemma, existential fear and existentialism in general, but without specifically using those concepts or that framework, because it really didn't have a name or formalism yet. In fact, the Snark can even be viewed as a proto-absurdist work. Cast its characters with humans, throw them on stage and you have a serious foreshadowing of Ionesco et. al.
First, let's put some context around that conundrum:
The Hatter opened his eyes very wide on hearing this; but all he said was, `Why is a raven like a writing-desk?'
“Have you guessed the riddle yet?” the Hatter said, turning to Alice again.
“No, I give it up,” Alice replied: “What’s the answer?”
“I haven’t the slightest idea,” said the Hatter”
`No, I give it up,' Alice replied: `what's the answer?'
`I haven't the slightest idea,' said the Hatter.
`Nor I,' said the March Hare.
Alice sighed wearily. `I think you might do something better with the time,' she said, `than waste it in asking riddles that have no answers.'
(FWIW: the entire Mad Hatter's Tea Party is worthy of a slow, thoughtful, methodical, contemplative, and inquisitive read.)
My emphasis above. There is no answer, that is the original, canonical answer, that none exists. Note that it isn't that we don't know the answer, but that none exists. Why indeed ask a question if you know that no answer exists. But can you know that no answer exists, especially in this instance?
Dodgson was far too proficient at logic to let that stand. The question presumes that a Raven is somehow like a writing desk, something seemingly not supported by the facts. Hence, this is a non-question unless it is known, (or at least strongly suspected) that there is at lest one respect in which they are indeed like each other and one of the characters should've known it and corrected Alice's assertion that there was no answer. Need I say that they both EXIST, that they are material, tangible, temporal? The key here is that the Hatter was asking a riddle and Alice knew it was a riddle. Riddlers have a storied "history" in western culture, they are archetypes who play a specific role, and riddles must have an answer and only one acceptable answer. This answer is known to the riddler who then will reward or punish those attempting to guess the riddle depending upon the correctness of their answer. So in that sense and context, the whole sociology of riddling, Alice was right, there is no answer and it is a waste of time to pose the riddle. That is because riddles do not follow the laws of logic or science or anything other than the laws of riddles. There could be 50 or 60 technically correct answers to a riddle, but only one of them will be the right answer. A gorilla which loses a hind limb in its old age would arguably be a correct answer for the Sphynx's question, but certainly not for her riddle, which could only be as it was given to her by Oedipus.
So where am I going with this? Vienna! Huh? The conundrum above is widely egarded as Dodgson poking a stick at his contemporaties in the fields of logic, math, philosophy and the like, which did not contain any members of the Vienna Circle which he and his contemporaries predate. Nonetheless, it is oddly apropos of another famous Raven conundrum that the members of the Vienna Circle stumbled into. So, on to Vienna, home to said Vienna Circle. Here's a Wikipedia super-condensed summarization:
The Vienna Circle (German: Wiener Kreis) of Logical Empiricism was a group of philosophers and scientists drawn from the natural and social sciences, logic and mathematics who met regularly from 1924 to 1936 at the University of Vienna, chaired by Moritz Schlick.
The members of this group and their eventual followers "invented", explicated and advocated "logical positivism" aka "logical empiricism". One key element of this philosophy was the verifiability criterion or verification principle. The quick and dirty of that is that something could only be meaningful if it could be verified, either by direct observation or by logical derivation from something that was observable. This wasn't about things that weren't observable because of the limitations of our senses and/or equipment, but about things that were intrinsically unobservable, like das ding an sich. Seems reasonable enough. There was also a renegade who instead opted for a falsifiability criterion (and whom I consider to be closer to the mark). That too seems reasonable enough. At any rate, they eventually ran into a Raven conundrum of their own, which will be the subject of an embedded you tube:
There's a lot there, and I intend to address some of it, in time, but what about Alice. You remember Alice. (Heh) This isn't about a riddle, but all the same, should one ask questions when one knows that there is no answer? And doesn't that violate the verifiability principle? After all, it is pretty much an empirical aphorism that one cannot prove a universal affirmative that isn't tautological and hence uninformative. Even the narrator accepts that in stating that we can only establish ever greater and greater probabilities that all ravens are black. In this case, as in most cases, we can imagine circumstances whereby we could answer the question, because the universe of discourse, or experience, or reality, as the case may be, is finite. Ravens exist here on our world and with sufficient personnel and technology we could theoretically verify that as of a specific point in time all ravens were indeed black.
Next up is the comingling of formal logic and probabilistic empiricism. That is dangerous territory, both fields can be tricky and logic is particularly prone to generating paradoxes. Here we deal with negation, which I addressed at some point in a column iirc. We move from ravens are black to not ravens are not black, or do we? First up, we cast out the identity operator, ravens aren't identical to black, that is merely one of their properties.We should preferentially say:
All members of the set of things called ravens possess the property or characteristic of blackness or being black.We might then think that an appropriate equivalent statement cast in the negative might be: All things that aren't members of the set of objects called ravens lack the property of blackness or being black, but that is clearly false. I have here a black fountain pen, a black non raven, so we have to invert the subject and predicate while we negate to get: All things lacking the property of blackness are non-members of the set of ravens. Here, nonetheless, all hell breaks loose. We have wandered into the minefield of infinities and our probabilistic explorations go directly into the toilet. The paradox and narrator are equating the seeming logical equivalence of "all ravens are black" and "all non-black things are not-ravens" to imply the equivalence of "observations of ravens with property black support the hypothesis that all ravens are black" and "observations of non-black things that are not ravens support the hypothesis that all non-black things are not-ravens." This is simply not true, and comes from smashing the logical equivalence of two seemingly logically equivalent statements.into the empirical meat grinder of probability.
Remember Alice? Remember why the whole question or proposition doesn't fail the verifiability criterion? Buried in the proposition observations of ravens with property black support the hypothesis that all ravens are black is the hidden, empirical assumption that the set of ravens is finite. We can be sure, since they only exist on earth, that they must be finite in number given their mass, volume, and various other factors. If you have a finite number of ravens, so long as you observe none with a contrary property, each observation of a black one does increase the probability that they are all black, specifically from (b/total_ravens) to ((b+1)/total_ravens) for some finite number of ravens. OTOH, the number of non-black things, like the number of non-ravens, is not finite, arguably, given your definition of "things", not even here on Earth. The probability of one non-black non-raven is 1/infinity, and the probability of 35 of them is 35/infinity which is, because of the freakishness of the mathematics of infinities, exactly the same damn number. No matter how many NBNRs you observe, it doesn't support the hypothesis that all NBs are NRs, except subjectively. This is why, IMHO, falsification is a preferable criterion to verification when dealing with empirical matters requiring inductive logic and, needless to say, be extremely meticulous and careful when mixing inductive and deductive logic..
For the record: speaking of falsification, (heh) it is well established that it is not true that all ravens are black. You yourself can simply fire up your favorite search engine in your favorite browser and check the images for each of the following: "white necked raven", "Vancouver island white ravens", and "leucistic ravens" if you really wish to know. No need for white shoes, unless you are channeling Pat Boone.
The takeaways: 1) Riddles are neither propositions nor questions and obey neither the rules of logic nor those of empiricism. 2) Mixing formal logic an probabilistic empiricism is fraught with pitfalls. 3) Not all ravens are black and, lastly, for me, the Real takeaway from Logical positivism and its philosophical descendents (barring Frege, Kuhn and Kaplan) lies in the verifiability and falsifiability criteria. There is a ton of merit to the assertion that propositions which are intrinsically non-verifiable have no cognitive content, and certainly no empirical meaning or application. There is arguably even more to the assertion that propositions which are intrinsically incapable of being falsified are meaningless. In empirical reality, we progress by falsifying things and gain increasing confidence in the truth or at least reliability of propositions and theories as more and more attempts at falsifying them fail to do so. With respect to complex systems, especially biological systems, that is arguably the only way in which we gain demonstrable confidence in things.
Image is a common raven, Corvus corax
Its an open thread so have at it. The floor is yours
edited for typo, is to in and cannot