John D. Norton (of the Center for Philosophy of Science at the University of Pittsburgh) wrote an essay back in 2012 called “What is Time? Or, Just What do Philosophers of Science Do?” I figure that as an attempt to define a word it’s LH material, but it also confirms me in my belief that philosophers think they have a better grasp on language than they do. He begins:
There is a competition, the “Flame Challenge,” underway at the time I write these words for the best answer to the question “What is time?” The target audience is eleven year old children and children of this age will be the ultimate judges. […]
The challenge is introduced with a perfunctory and familiar disclaimer. First comes a celebrated quote from Augustine
“What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.”
– Saint AugustineThe sentence that follows arrives with reliability that night follows day follows night and was offered, I expect, without reflection. Doesn’t everyone know that…
It’s a deep question, and it has no simple answer.
Is that really so?
He goes on to say that “the question ‘What is time?’ as asked is not really a scientific question at all”:
Scientists trying to answer this question will almost invariably start by trying to deflect the question. If you ask them the question, you may first get the rather superficial quips:
“Time is what clocks measure.”
“Time is what stops everything happening all at once.”
They are not real answers, but merely amusing retorts that often serve to quieten an annoying questioner.
A more serious attempt to answer will tell you not what time is but about some interesting temporal phenomenon.
In his special theory of relativity, Einstein showed that different observers can disagree on which of two events happened first and that can happen with neither being wrong. Or in his general theory of relativity, we learn that space and time together have a geometry and that its curvature is gravity. Or we learn from thermal physics that time increases with a thermodynamic quantity, entropy, under the guidance of the Second Law.
This may satisfy you. Or you might press harder and complain that these responses only report some facts about time. But they do not say what time IS. What IS time? you insist.
This display of stubbornness will likely be met with awkwardness. The conversation may end with a cough or another deflection. The answering scientists will be able to proceed only if they adopt a different style of analysis. That is, they will need to approach the question “What is time?” like a philosopher.
How do philosophers approach this question? Or at least how do philosophers of science of my stripe do it? They are much less confused by the question. They see that the core difficulty is that “What is time?” is itself a bogus question or, to use the more technical term beloved by philosophers, it is a pseudo-question.
The grammatical form of the question makes it look like other simple questions such as:
“What is the Atlantic Ocean?”
“What are submarines?”
“What are stars?”
“What is the Leidenfrost effect?”All these questions admit straighforward answers: a certain body of water; a boat that goes underwater; very hot balls of gas; what happens when a water drop is suspended above a very hot plate by a layer of vapor.
The question “What is time?” has no corresponding answer. The “IS” question demands that we identify time with something else typically but not necessarily better known to us, much as we identify submarines with boats that go underwater. The very asking of the question in this illicit form is what makes time mysterious.
He complains that any attempt to define time “degenerates into a circular word game.” What he does not seem to realize is that that is true of all attempts to define words. Keep asking “but what is that?” and you will just wind up with more words. There is no escape from language; to quote Godard/Wittgenstein:
… We could say that the limits of language are the limits of the world… that the limits of my language are the limits of my world. And in that respect, whatever I say must limit the world, must make it finite.
Time is, of course, mysterious, but Norton has not (as far as I can see) rendered it either more or less so; he has just scored some philosophical points in a game that does not interest me.
He goes on to say that “the question ‘What is time?’ as asked is not really a scientific question at all”:
I wonder how he might define “a scientific question “.
Presumably it would be easier to answer than an unscientific question.
A dog chases its tail; a bird flies into a mirror.
Somewhere or other quite recently, I was reading an essay that soberly asserted that “time” was itself a modern concept, due to Newton or something. (It may have been one of those Eon things which seem all very authoritative and wise until you actually start thinking about them.)
Given that there are numerous language families of impressive time-depth with unequivocal tense systems, this is a perfectly inane thesis. And of course, there are no natural languages which altogether lack words referring to time.
It is true that plenty of languages don’t have a “word for ‘time'”; many African languages have clearly borrowed their words for “time” from (ultimately) Arabic, for example, including, naturally, Kusaal. But then Kusaal has no “word for ‘colour'” either, and that doesn’t prevent it from having perfectly good colour terms.
You’d think that philosophers, at least, would have realised by now that a concept can be perfectly useful even when it defies any neat definition. Just as well, really …
And in fact, plenty of philosophers have made this grand intuitive leap, St Ludwig (obviously) among them. I suspect that this Norton is just not very good at his job. One should not judge all philosophers by his performance.
Planck time is roughly 5.4 * 10 to the -44 seconds; we cannot define or observe any kind of sequence of events or change below this level. So time is a sequence of Planck units, or, in the language of the normals, one damn thing after another.
Following St. Augustine’s befuddlement, we might observe that self-conscious reflection on the nature of capital-T Time tends to evoke utterances that sound vaguely poetic and perhaps profound but also tend towards incoherence upon closer parsing. E.g.,
We are made of it, and if we give submission
Among our chances there’s a chance we can choose
And if we take it by uncertainty’s permission,
Then it’s impossible to lose
https://genius.com/Richard-hell-and-the-voidoids-time-lyrics
Time is what stops everything happening at once.
It seems deeply unfair to pick on “time” for this kind of treatment. You could perform the same kind of rigmarole with “space”, “matter”, “energy” … or, come to that, with “colour.” Or “knowledge.”
In fact, virtually any abstract noun …
Come to that, how about “What is ‘three’?” is itself a bogus question?
Units with names like Space, Time, and Causation are a staple of undergraduate philosophy. All three offer immediately accessible challenges for the beginner, kindling a sense of vertiginous unknowing that perdures through the entire philosophical career. (The aptest collective noun, according to one colleague: a baffle of philosophers.)
Yes, DE: we could of course readily resort to matter, life, person, world, mind, and so on if the dizziness ever threatened to recede. (Which it doesn’t.) But like tinnitus, this vertigo is only a problem if thinking makes it so. (Which it sometimes does.)
»Das issen Knochenberg,« sagte sie und half mit dem Daumen nach. Viele und Harry widersprachen, ohne genau zu sagen, was südlich der Batterie zuhauf lag.
Störtebekers Antwort lag, obgleich frisch ausgesprochen, schon seit Wochen bereit: »Wir müssen das Zuhaufliegen in der Offenheit des Seins, das Austragen der Sorge und das Ausdauern zum Tode als das volle Wesen der Existenz denken.«
Tulla wollte es genauer wissen: »Und ich sag Dir, die kommen direkt aus Stutthof, wetten?«
Störtebeker konnte sich geografisch nicht festlegen lassen. Er winkte ab und wurde ungeduldig: »Quatscht doch nicht immer mit Euren abgeklapperten naturwissenschaftlichen Begriffen. Allenfalls kann man sagen: Hier ist Sein in Unverborgenheit angekommen.«
—
That’s a heap of bones, she said, giving additional support by pointing at it. Viele and Harry disagreed, without saying exactly what it was that lay in a pile south of the artillery post.
Störtebekers answer, although apparently spontaneous, had already been prepared weeks previously: “We must consider in-a-pile-laying in the openness of Being, bringing away of worry and holding on until death as the complete nature of Existence.”
Tulla thought more precision was needed. “And I’m telling you, the bones have come right from Stutthof, want to bet on it?”
Störtebeker could not allow himself to be pinned down geographically. He shook his head and said impatiently “Why do you keep on blabbing about your obsolete scientific concepts? In any case one can say: Being has arrived at Unconcealment here.”
Günter Grass, Hundejahre
well, man, could it be that the girls and boys
are trying to be heard above your noise?
and the lonely voice of youth cries:
“what is three?”
5.4 * 10 to the -44 seconds; we cannot define or observe any kind of sequence of events or change below this level.
I find these days about ten minutes is my limit for ‘sequence of events’. Did I turn the iron off? I’d better go back and check. Whereas the episode of the Christchurch earthquake — 4:35 am September 4th 2010 — is seared in lucid memory.
@AntC, 10 minutes is about 1.11 * 10 to the 46th Planck units. So you’re doing very well indeed if you can follow that!
Planck time is roughly 5.4 * 10 to the -44 seconds; we cannot define or observe any kind of sequence of events or change below this level. So time is a sequence of Planck units, or, in the language of the normals, one damn thing after another.
I disagree with that last sentence. There’s good reason to think that somewhere around that time scale (and the associated scales of length, mass, energy, etc.), current theories won’t be valid, and maybe even that spacetime will be “foamy” and a sequence of events will be even harder to define than it is in present quantum mechanics. But it doesn’t mean that time is a sequence of Planck units.
I agree, though, that time is one damn thing after another.
(The aptest collective noun, according to one colleague: a baffle of philosophers.)
A Loveliness of Ladybugs
A picture of this wonderful concept is here:
https://www.ctdaylily.com/productsa/p/a-loveliness-of-ladybugs-fall
Some collectives are timeless.
David Eddyshaw: “You’d think that philosophers, at least, would have realised by now that a concept can be perfectly useful even when it defies any neat definition.”
John D. Norton: “What does this failure mean? Does it mean that this innocent question has pressed us to confront a dark and shameful chasm in our knowledge? Hardly.” Followed by a paragraph of explanation from a fake 11 year old’s point of view.
Some random thoughts:
The problem is not how to define the word “time”, but what is the concept behind it.
“Time is what clocks measure.” This was a definition from my undergraduate physics textbook. It was a source of considerable amusement over the years. But in fact, it is a reasonably deep answer. Maybe ultimately incorrect or limited, but not trivial.
Many physicists, including those not prone to philosophical aspirations, do feel that there is a necessity to clarify what we mean by time at a fundamental level. Philosophical denials as well as suggestions that 11 year olds know all there is to know about it somehow are not convincing.
Norton: “Perhaps we might be assured that time is really just one of the dimensions of a four dimensional spacetime manifold… What makes some candidate four-dimensional manifold a spacetime manifold as opposed merely to some four-dimensional space with no association with time?” — Metric signature. Satisfied? Neither am I.
As far as I’ve been able to observe, a linguistic philosopher’s “pseudo-question” coincides almost perfectly with what everyone else calls a “philosophical question”. The claim is that all such questions are so misleading in their presuppositions that they need to be unasked and reduced to studies of word usage. In which case, why not just leave the job to lexicographers? (And perhaps consider extending the exercise to languages other than the philosopher’s L1?)
I think it’s a trick question, in that it presumes an answer formed as a reasonably readable sentence starting something like “Time is…”, with no presuppositions. You’d need a story, followed by “… in these circumstances, we say that time…”
It reminds me of the less difficult case of mathematical definitions, which depend on a long chain of other definitions. How do you give a concise, naive answer to “what is a fibration”? (The mathematicians here could come up with worse examples, I am sure.) At least there there is no uncertainty over the meaning of the terms, once a definition has been stated.
“The answering scientists will be able to proceed only if they adopt a different style of analysis. That is, they will need to approach the question ‘What is time?’ like a philosopher.”
I found that kind of amusing, given that I had just come across a podcast by the cosmologist Sean Carroll titled “Does Time Still Exist?”, which included the following introductory comment:
(I haven’t really listened to it yet, so I’m afraid I can’t comment on how useful or question-answering the podcast actually is.)
The claim is that all such questions are so misleading in their presuppositions that they need to be unasked and reduced to studies of word usage. In which case, why not just leave the job to lexicographers?
This is what I’ve been wondering ever since I learned about the linguistic turn in philosophy. What makes them think they’re competent to analyze language? Because they speak one? (Cue “I’m qualified to do surgery because I have a gall bladder.”)
See also: “what is life”, a question biologists aren’t much concerned with.
freshly pronounced
said out loud for the first time
the in-a-pile-lying
the lying there in a pile
Maybe “carrying to term”, maybe “delivering”.
He made a dismissive gesture with his hand.
Maybe; but maybe what has arrived is Being in a state of Unconcealment.
Philosophy of nature has been replaced by the natural sciences, but it took the philosophers a while to notice. Philosophy of language has been replaced by linguistics, but it seems the philosophers haven’t quite grasped it yet.
“I’m qualified to do surgery because I have a gall bladder.”
I’ve practised surgery for years without a gall bladder.
Philosophy of language has been replaced by linguistics, but it seems the philosophers haven’t quite grasped it yet
Maybe some philosophers …
Again, many linguists (like other scientists) make elementary errors that any real philosopher would never fall into, because they arrogantly assume that all of philosophy has been rendered obsolete by the March of Science.
Exhibit A: Noam Chomsky, supposed by himself and his acolytes to be a “major analytic philosopher.” Esa Itkonen is good at exposing Chomsky’s fundamental (in the fullest sense) misunderstandings in this domain.
And the Chomskyan edifice itself is a near-perfect example of what Lakatos called a “degenerating research programme.” We need the philosophy of science, which is not itself subsumable under “science.”
David Eddyshaw: three is the canonical representation for the result of applying the successor function to the result of applying the successor function to the result of applying the successor function to the primitive zero, defined as analogous to the empty set.
https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers
@dm
Thanks, I thought you would like that text. It is true that I translated rather freely, and a head shake is not a dismissive hand gesture.
If anyone wants to see the R. Mannheim translation of this passage, here is a link:
https://archive.org/details/dogyears0000gras_f4p8/page/313/mode/1up
@Yuval:
That does not tell me what “three” is. It’s not a set, unlike many of the things mathematicians like to play with, for example.
What is this “analogous” that you speak of? Analogous how? In what respect?
What do you mean by “applying” a function? Is this a primitive concept, impervious to further scrutiny?
More to the point, numbers are not the sole property of mathematicians, and mathematical definitions of them, though useful in mathematics (sometimes*), have no particular claim to ontological priority.
In some languages, the cardinal numbers are verbs. (In Koasati, such verbs conjugate differently, depending on whether the number has come about by accident or by design.)
* In fact, the definitions are largely irrelevant. What matters is whether the numbers, however “defined”, behave, for example in Peano’s axioms. There is more than one way of “defining” the real numbers, for example: the industry-standard Way of the Dedekind Cut is not the only way of creating “entities” with all the desired behaviour. But there are those amongst us who know vastly more about this than I do …
Questions about the structure of time and the universe have immense literatures in physics, where they are usually considered in terms of models, for example
https://ncatlab.org/nlab/show/Wick+rotation …
They are of course controversial – \cf current dissatisfaction with string theory … but there does seem to be progress. Such work is written in a highly mathematical register but it is by now well-documented – the book of nature is an open book but to read it requires commitment…
FWIW a beautiful alternative approach to the real numbers
https://en.wikipedia.org/wiki/Surreal_number
(from John Conway of the Game of Life fame) begins with Dedekind cuts interpreted as positions in two-person game theory: the `value’ of the resulting position defines a real number with all its appropriate calculational bells and whistles. I guess it’s related nicely to the indifference curves of classical economics…
In Koasati, such verbs conjugate differently, depending on whether the number has come about by accident or by design.
That’s the best thing I’ve learned this week.
It’s from Geoffrey Kimball’s highly recommendable Koasati Grammar (also, incidentally, the main reason why I recognised Muskogean vocabulary in Cahokia Jazz, though the language family is actually pretty well-described in general, as these things go.)
Of course. I was careful to say “philosophy of nature” and “philosophy of language”, not “philosophy of science”. Also, science replacing philosophy of nature or language does not make any scientist a philosopher – analytic or otherwise.
+ 1
And I learn from the Wikipedia article on Koasati that /s/ has the palatal allophone [š] intervocalically, hence the alternate name Coushatta.
Also, it’s got some serious suppletion; ‘to dwell’: singular aat, dual asw, plural is.
See also: “what is life”, a question biologists aren’t much concerned with.
See also “what is an organic compound”, a question chemists aren’t much concerned with.
Do you know if these conjugations also apply to other verbs? Some type of evidentiality?
Hat: Also, it’s got some serious suppletion; ‘to dwell’: singular aat, dual asw, plural is.
That is, was and will always be unique.
The claim is that all such questions are so misleading in their presuppositions that they need to be unasked and reduced to studies of word usage. In which case, why not just leave the job to lexicographers?
Which made me wonder how lexicographers have done it in this case. The OED’s relevant definition of ‘time’ (IV.34.a) is
…which is no more self-referential than any more philosophical answers I’ve come across, and has the added benefit of being generally comprehensible.
erm, `consumed’? we wonders, yes we wonders…
I’m reminded of Myles na gC fighting that strange irregular object, one’s corner,,,
In the early 20th century there was a brief vogue among (some) physicists for something called operationalism, one of the chief cheerleaders being Percy Bridgman. The general idea was that the way to understand any fundamental quantity was to understand how it was measured or observed; this view had some utility in the early days of quantum mechanics.
Saying that time is the thing measured by time-measuring devices was therefore fundamental and definitional. It sounds circular, of course, but that was the point: in physics, what you need is a definition of time that is self-consistent, and also consistent with other metrical definitions.
Asking “what is time?” and hoping for a deeper answer is therefore Metaphysics, an issue to be sternly avoided by pragmatically-minded scientists.
Do you know if these conjugations also apply to other verbs? Some type of evidentiality?
All from Kimball:
Koasati has the most complicated conjugation system among extant Muskogean languages, along with Alabama, its closest relative. No less a scholar than Mary Haas herself did the fundamental work on it all.
The distinction does indeed apply more widely in the verbal system, but it’s not a matter of evidentials but an active/stative opposition in intransitive verbs.The difference is semantic in Koasati, with active verb subjects regarded having control over the action, stative verbs not: individual verbs often can be inflected either way, as appropriate, so that e.g. afá:kalit is “I laughed” and acafá:kat is “I burst out laughing.”
Koasati stative verbs seem historically to have developed from impersonal verbs with what is now the subject marked as object. There are two conjugations of them, which seem originally to have been temporary versus enduring, but now is just lexically determined.
Kimball gives a couple of pages of verbs which are outright suppletive for singular/dual/plural. A great many other verbs make such distinctions too, though they are more often achieved by swapping verb stem subcomponents. The “plurality” involved is verbal: a plural intransitive verb may signal a plural subject, a plural transitive verb, a plural object, or the verb action itself may be plural (same with dual.) Nouns themselves mostly do not mark number, causing well-merited theoretical difficulties for any passing Chomskyans.
Ablaut (segmental and tonal) is very common in the tense system too, though that at least is generally predictable.
erm, `consumed’? we wonders, yes we wonders…
Don’t waste too much time wondering.
I’m reminded of Myles na Cg fighting that strange irregular object, one’s corner,,,
It’s gC ye’ll be thinkin of.
Some of us are, and have been for more than 20 years, but in general you’re right, we’re a tiny minority, perhaps 0.1% of biologists.
Kimball doesn’t give specific natural examples to explain the context of stative vs. active numeral verbs. I am guessing you’d use them to say “there are three of us here” (people in an elevator who happened to be there) vs. “there are three of us here” (people at a restaurant requesting a table).
@David E.: So not completely unlike Eng. (suffixed, active) __ed vs. (circumfixed, stative) was__ing. We’re three vs. We’re being three?
Athel: Some of us are, and have been for more than 20 years
Yes, I immediately thought of you.
No, that one seems historically to have been the distinction between the two stative conjugations, rather than between active and stative.
It’s more like, “we’re three-ing” versus “we’ve got three’d.” I think. But as Y says, Kimball doesn’t give any actual examples.
Kusaal cardinals are just boring old quantifiers, though throughout Oti-Volta the numbers 2 through 9 are unique in having noun-class agreement via prefixes – the only flexional prefixes in any of the languages.
Kusaal does have distinct forms for “two exactly” and “three exactly”, and quantifier phrases like those for 23 and 42 in which those numbers come last. They are peculiar in never accepting constituent focus. No idea why …
Now I think of it, the Kusaal prefixes used with numbers have caused the same tone changes in the following stem as those caused by subject pronouns on following verbs in subordinate clauses, whereas the segmentally identical possessive pronouns do not affect the tone of the following possessum at all. So at a pinch, you might suggest that e,g. biisa atan’ “three children”, where the a- of atan’ “three” is an old plural agreement prefix, derived historically from a sort of relative clause structure: “children which are-three.”
It’s all a bit of a stretch, though, to put it mildly. There is no sign of number-word stems turning up in verbs, and some other Oti-Volta languages do in fact show tone changes after possessive pronouns. It would explain the unique class-affix-before-stem ordering, though: all the “Gur” languages are SVO or SOV.
Another unsolved-by-me problem with Oti-Volta number words is that cognates turn up in some languages as bare roots, and in others with a variety of CV suffixes that resemble noun-class suffixes but are fixed in each case and don’t signify agreement, e.g. Kusaal ayi “two”, but Mooré ayiibu. All these languages frequently make deverbal nouns by just adding noun class suffixes to verb stems, so I suppose it’s conceivable that the suffixed forms are actually derived nouns from number verbs, with the preceding subject pronouns reanalysed as possessive pronouns. Pretty thin stuff, though …
Jack Martin’s Creek grammar shows that number words are verbs in that language too; they usually appear in the “falling-tone” verbal grade (grades are effectively aspects), which is resultative with other verbs. However, you can still tell the grade by comparison with derived forms: the causative forms of the numbers are used in expressing people’s ages, for example.
In Choctaw and Chickasaw, apparently, the number words have got “frozen” in one grade, so their verbal origin is moot synchronically.
i feel remiss in not having realized – even as i quoted st. johnny – that i could answer, if not a philosopher’s “what is three?”, at least the version of the question embodied in the traditional phrasing “who knows three?”. rejecting the more didactic versions i know (which agree, in yiddish or ladino/judezmo, that three is abraham, isaac, and jacob), i place my trust in the first cousin of the song-family i learned, which declares that three is “the rivals”. and if the Authorities seem entirely uncertain what that means, well, i try not to argue with age-old traditions when they’re so satisfyingly surreal. but i do have confidence that if anyone can offer insight, it’s the hattery – especially given a proposed welsh connection.
In the Timimoun version of that song-family, the answer to “what is three?” is “the people of the mausoleum”, apparently an allusion to Abd al-Qadir al-Jilani and two other prominent medieval Sufis. I’m guessing they’re probably not the rivals in question there, though.
In the early 20th century there was a brief vogue among (some) physicists for something called operationalism, one of the chief cheerleaders being Percy Bridgman. The general idea was that the way to understand any fundamental quantity was to understand how it was measured or observed; this view had some utility in the early days of quantum mechanics.
See Paul Lorenzen and the Erlanger Schule des methodischen Konstruktivismus from around 1960 on. For some reason the English version calls this the “Erlangen school of epistemological constructivism”. Oh well, some people just can’t get along without “epistemology”.
I read Lorenzen’s Logische Propädeutik – Vorschule des vernünftigen Redens and Janich’s Die Protophysik der Zeit in the 80s. It was fascinating. At this period of time I also read the TLS regularly and thought it was fascinating. But I could do nothing with this stuff in real life (konnte damit nichts anfangen). Later I came to my senses.
The past is not a foreign country*. That’s why it often seems so strange. If it were just a bunch of furriners all living in the same place, that wouldn’t faze me.
*Also, I recommend reading the “Eustace and Hilda Trilogy”
Another language in which the cardinal numbers are verbs:
https://www.academia.edu/1330286/Araki_A_disappearing_language_of_Vanuatu
Favourite example: Co dua “Join me!”, literally “Let’s two.”
Are the ordinals adverbs ?
To read even the abstract I would have to reveal myself to academiaedu, which I refuse to do again. It took a year to shake them off.
https://marama.huma-num.fr/data/AlexFrancois_Araki-grammar_2002_PL522.pdf
The pdf will be delivered wrapped in brown paper, without a return address.
Ground control to Major Tom
Your circuit’s dead, there′s something wrong
Can you hear me, Major Tom?
Pursuing a description of numbers in the related Tongua language, I found a paper on Polynesian numbering from the Journal on Mathematics and Culture with this interesting idea:
>Notations and language are not the only forms numbers can take. Material forms other than notations are used to represent and manipulate numbers: the fingers; devices that accumulate, like tallies; and devices that accumulate and group, like the abacus. While the ubiquity of such devices has long been acknowledged (e.g., Ifrah, 1981; Menninger, 1992), their influence on the conceptualization of numbers has been poorly understood, until recently. New analyses suggest that such devices precede and inform the development of notations; occasion the naming of numbers in language; give numbers their properties of linearity, manipulability, dimensionality, and concision; and act as the mechanism of numerical elaboration (Overmann, 2016a, 2016b, 2018, 2019). [note that Overmann is the author of the paper I’m quoting]
>These contributions position material devices and their manuovisual engagement as a means of accessing numerical intuitions that is distinct from language, a means that acknowledges quantity as a perceptual primitive (Dehaene, 2011; Piazza, 2011) and material rearrangement and display as implicit to mathematical visualization (Dreyfus, 1991; Kaput, 1987) and epistemology (Giaquinto, 2007; Nelsen, 1993).
>Traditional Polynesian number systems provide an ideal case study for testing the hypothesis that numbers have a material basis, as they have hitherto been studied through language, appear to have lacked notations prior to European contact,’ and have been perceived as using few material devices to represent and manipulate numbers.
She later describe the one of the “devices” as an “ephemeral abacus with human rods and verbal behavioral beads.” Though I think another description might be a material, terrestrial abacus.
The article never did offer anything on Araki or Tonguan, which are related but not part of the Polynesian grouping.
Tongua? Is that a typo? Tongan is a Polynesian language.
Stu—worked then, works now.
Sorry. Not quite. It’s a typo for Tangoa, a sister language to Araki on another small island off the main island of Vanuatu. But apparently a lingua franca.
The Wiki for Tangoa also says
> Tangoa is generally described as a language,[2][3] but also as a dialect of the proposed, lexicostastically defined Southwest Santo language along with Araki, Akei, and Wailapa.
So I wondered whether this somewhat better used lect might be better documented than Araki and offer more numeric info.
The Polynesian paper mentions that higher level numbers and other complexities can be lost through progressive colonization and shrinkage in the speaking population. I wonder whether Araki, native to an island whose population just barely breaks into the 3 digits, might have attrited this way.
Though I guess if Tongoa is that closely related and in use on Araki, they’d likely just have assimilated the Tongoa higher numbers.
According to the Araki grammar, Tangoa speakers say that they can’t understand Araki. The situation is confused by the fact that all Araki speakers know Tangoa, and indeed Araki is severely endangered because it’s almost been replaced by Tangoa.
Lexicostatistics is a crap way of trying to decide language-versus-dialect questions. My own Swadesh lists make Kusaal and Mampruli look near-identical from a lexicostatistical standpoint, but I have seen with my own eyes that the languages are definitely not mutually comprehensible.
(There’s a lot of bad information out there on mutual comprehensibility within Western Oti-Volta. WP claims that Dagbani is mutually comprehensible with Farefare, which is emphatically not the case: the reference is to Rattray’s 1932 The Tribes of the Ashanti Hinterland, which is in many ways quite wonderful but is hardly a reliable source for that kind of thing. Rattray also claims that Kusaal is extremely similar to Mooré, which is true to about the degree that French is extremely similar to Italian. I mean, they’re very similar to each other compared with Swahili/Russian, sure …)
Revisiting the construction of numbers with nouns in various Oti-Volta languages, I notice that Mbelime actually inserts the particle ǹ between the agreement prefix and the number stem:
bɛ̄ nı̄tìpūōbɛ̀ bɛ̄-ǹ-dúò “the six women.”
This (as Neukom actually points out in his grammar) is exactly parallel to the relative construction with verbs:
ā bı̄enɛ̀ yɛ̄ ǹ pàǹtɔ̀ “the years which have passed.”
Moba also inserts n:
nììb̀ bá-ńlé “two people.”
I’d assumed that this n was carried over from the forms used in counting, which throughout Oti-Volta begin with a nasal representing the agreement for the mass/abstract gender. But I may have been too hasty in making that assumption.
No other Oti-Volta languages do this AFAIK; on the other hand, the number agreement prefixes consistently differ in tone from the segmentally identical possessive pronouns.
With the Grusi languages, Kassem has agreement prefixes on numbers, like Oti-Volta, but no inserted n. Kabiye 2-5 agree: they all begin with na-, and infix the class marker after that: nalɛ “two”, nasilɛ etc. Dunno what’s up with that.
Miyobe numbers agree, with no n.
Farther afield in Gur, Koromfe numbers don’t agree, but do prefix i- to numbers used in counting. Baatonum numerals don’t agree with the counted noun, though their forms show fossilised agreement prefixes; Baatonum number words have their own genders. Supyire numbers don’t agree, and they too have their own individual genders.
So the peculiar (for Gur) agreement of numbers by class prefix is an Oti-Volta/Grusi/Miyobe thing, with a few relics in Koromfe and Baatonum. “Central Gur”, basically.
I still think the evidence that this arose via construing the number words as verbs is weak, but maybe less weak than I initially supposed. And as verbal number words are unusual cross-linguistically, it wouldn’t be too much of a stretch to imagine that proto-Central Gur had verbal numbers, but the construction has been repeatedly independently altered in the daughter languages to make it less weird (much as in Chickasaw and Choctaw.)
Stu’s question about ordinals that I initially took as mostly joking seems interesting. It seems tougher to talk about the 4th of something with verbal number words, but maybe that’s just my ignorance.
We had looked at a paper on the prevalence of numbers above five in hunter gatherer languages in the thread where we talked about the possibility of wanderworts for 6 and 7 in a set of Eurasian languages.
I wonder whether numbers construed as verbs might have been more common for the smaller set of numbers in use in ancient hunter-gatherer communities. Where the meaning was less “there were two of us” than “we paired up”; the “the plantains hand-bundled” rather than “there were five plantains”. A few roots that looked at the information being provided as how things grouped rather than conceiving how many.