[Xmca-l] Re: thoughts on Mathematics of Mathematics by Wolff-Michael Roth

Sat Apr 14 12:43:44 PDT 2018

Bill

       The Origin of the Logic of Symbolic Mathematics by Hopkins as an ebook is only about $10 if you have a Kindle (and about $40 for hard copy). I would say that this is quite relevant to your interests.. You should also be able to pick up Klein’s book Greek Mathematical Though and the Origin of Algebra for about $10. The book by Lachterman is more than nice, but used copies are a little pricey.. You might find Hoyrup in Measure, Number, and Weight useful (he has some interesting things to say about the transition from Greek to Arab to European) and then there is are a number of people who have looked closely at ‘geometric’ proof as practiced by the Greeks; eg Reviel Netz (his work is now running in the $70s). 
      I personally feel that I would rather have a good Samaritan give me a copy of Lachterman than a copy of the Foundations of Mathematics (I have read all of Livingston’s stuff and from a certain perspective it is interesting). Klein, by the way, does discuss the change in word view - mathematically that is - between Greeks and Moderns. Hopkins nicely expands on Klein’s thoughts versus those of Husserl. Lachterman and Netz come from other angles. Then there is the work of Kay O’Halloran "Mathematical Discourse: Language, Symbolism and Visual Images” which provides another slant. There is quite a bit more, but probably of less relevance to you. Oh, going back and looking at the actual mathematics of that time is interesting and there is quite a bit available.

Ed

"The opposite of a correct statement is a false statement. The opposite of a profound truth may well be another profound truth" - Niels Bohr

> On Apr 13, 2018, at  11:07 PM, Bill Kerr <billkerr@gmail.com> wrote:
> 
> Thanks Ed,
> 
> A good Samaritan sent me a copy of "The Ethnomethodological Foundations of
> Mathematics”. I've ordered a copy of "Ethnographies of Reason.”
> 
> I looked up the other two. Once again, they are quite expensive. I am
> interested in that change of world view that occurred b/w the Greeks and
> the Moderns. I read a short book about Francis Bacon by Benjamin Farrington
> that went into that .
> 
> Cheers, Bill
> 
> On Sat, Apr 14, 2018 at 9:38 AM, Edward Wall <ewall@umich.edu> wrote:
> 
>> Bill
>> 
>>     The book "The Ethnomethodological Foundations of Mathematics” - an
>> ‘interesting' take on Godel’s First Incompleteness Theorem - is just a nice
>> typeset copy of his dissertation (he may have a few extra things; I think I
>> looked at it once and didn’t see much different but perhaps Michael thinks
>> otherwise) which you can get from ProQuest for about $35 or whatever the
>> going price is now. There are also a few articles which are reasonably
>> available and, as MIchael, mentioned "Ethnographies of Reason.” If you like
>> this sort of things, I would recommend The Ethics of Geometry by Lachterman
>> and perhaps The Origin of the Logic of Symbolic Mathematics which takes on
>> Husserl and Klein. There is, of course, a long list of other people who
>> have interesting takes on some of this.
>> 
>> Ed Wall
>> 
>> "The opposite of a correct statement is a false statement. The opposite of
>> a profound truth may well be another profound truth" - Niels Bohr
>> 
>> 
>> 
>> 
>>> On Apr 11, 2018, at  9:40 PM, Wolff-Michael Roth <
>> wolffmichael.roth@gmail.com> wrote:
>>> 
>>> Bill, the book that I really found good (I have read all of his) is
>>> "Ethnographies of Reason". Lots of good materials for helping readers
>>> understand. Michael
>>> 
>>> On Wed, Apr 11, 2018 at 7:08 PM, Bill Kerr <billkerr@gmail.com> wrote:
>>> 
>>>> Michael wrote:
>>>> the critique that E. Livingston articulates concerning
>>>> social constructionism, which takes the social in a WEAK sense; and the
>>>> social in the strong sense is not a construction.
>>>> 
>>>> I looked up Eric Livingston, The Ethnomethodological Foundations of
>>>> Mathematics, referenced on p. 56 of your book. The price was $202, ouch!
>>>> Publishers put marxist ideas from academics out of the reach of the
>> poor.
>>>> Can this problem be solved or mitigated under capitalism?
>>>> 
>>>> On Thu, Apr 12, 2018 at 12:36 AM, Wolff-Michael Roth <
>>>> wolffmichael.roth@gmail.com> wrote:
>>>> 
>>>>> Andy, to construct is a transitive verb, we construct something. It is
>>>> not
>>>>> well suited to describe the emergence (morphogenesis) of something new.
>>>>> This is why Richard Rorty (1989) rejects it, using the craftsperson as
>> a
>>>>> counter example to the poet in the larger sense, the maker of new
>> things.
>>>>> He writes that poets know what they have done only afterward, when,
>>>>> together with the new thing they have found themselves speaking a new
>>>>> language that also provides a reason for this language.
>>>>> 
>>>>> I also direct you to the critique that E. Livingston articulates
>>>> concerning
>>>>> social constructionism, which takes the social in a WEAK sense; and the
>>>>> social in the strong sense is not a construction.
>>>>> 
>>>>> Also interesting in this is the question of origins, and there the
>> French
>>>>> philosophers (Derrida and others) have had a lot of discussion. Mead's
>>>>> fundamental point is that "before the emergent has occurred, and at the
>>>>> moment of its occurrence, it does not follow from the past" (1932,
>> xvii).
>>>>> 
>>>>> And concerning relations, Marx/Engels write (German Ideology) that the
>>>>> animal does not relate at all, for it, the relationship does not exist
>> as
>>>>> relationship
>>>>> 
>>>>> m
>>>>> 
>>>>> Rorty, R 1989, *Contingency, Irony, and Solidarity*, CUP
>>>>> 
>>>>> On Wed, Apr 11, 2018 at 7:29 AM, Andy Blunden <andyb@marxists.org>
>>>> wrote:
>>>>> 
>>>>>> Well, I can see that as an argument, Michael. My response:
>>>>>> 
>>>>>> The thing is, to interpret "construction" in an intellectual
>>>>>> way, leads to the conclusion that to give construction a
>>>>>> fundamental place in human evolution is "intellectualism,"
>>>>>> and actually, interpreted that way, would be utterly absurd.
>>>>>> But the fact is that all human actions are teleological,
>>>>>> that is, oriented to a goal. Of course!! no hominid ever
>>>>>> said to herself: "I think I will now take another step to
>>>>>> evolving homo sapiens." AN Leontyev does exactly the same
>>>>>> move in his criticism of Vygotsky.
>>>>>> 
>>>>>> Actually, I don't know just how the formation of social
>>>>>> customs, speech and tool-making interacted in the earliest
>>>>>> stages of phylogenesis, ... and nor do you. We do know that
>>>>>> all three are intimately interconnected from the earliest
>>>>>> times we have any real knowledge of, though.
>>>>>> 
>>>>>> As to "emergence," in my opinion "emergence" is the modern
>>>>>> word for God. I don't know how this happens, so it must be
>>>>>> Emergence.
>>>>>> 
>>>>>> Andy
>>>>>> 
>>>>>> ------------------------------------------------------------
>>>>>> Andy Blunden
>>>>>> ttp://www.ethicalpolitics.org/ablunden/index.htm
>>>>>> On 12/04/2018 12:18 AM, Wolff-Michael Roth wrote:
>>>>>>> Andy, there is nothing of construction. Construction may be an effect
>>>>> of
>>>>>>> mind, but mind did not emerge as a construction. It is a
>>>> manifestation
>>>>>> of a
>>>>>>> relationship.
>>>>>>> 
>>>>>>> Emergence means that what comes after cannot be predicted on the
>>>> basis
>>>>> of
>>>>>>> what comes before. The construction metaphor implies that (e.g., the
>>>>>>> craftsman in the Marx/Engels case who is superior to the bee, an
>>>>> example
>>>>>>> that Vygotsky takes up).
>>>>>>> 
>>>>>>> Construction smacks of intellectualism, precisely the intellectualism
>>>>>> that
>>>>>>> Vygotsky made some moves to overcome at the end of his life
>>>>>>> 
>>>>>>> m
>>>>>>> 
>>>>>>> On Wed, Apr 11, 2018 at 7:09 AM, Andy Blunden <andyb@marxists.org>
>>>>>> wrote:
>>>>>>> 
>>>>>>>> All of those quotes make my point, Michael, in ever so
>>>>>>>> slightly different words.
>>>>>>>> 
>>>>>>>> a
>>>>>>>> 
>>>>>>>> ------------------------------------------------------------
>>>>>>>> Andy Blunden
>>>>>>>> ttp://www.ethicalpolitics.org/ablunden/index.htm
>>>>>>>> On 12/04/2018 12:02 AM, Wolff-Michael Roth wrote:
>>>>>>>>> I do not think mind is a construction,
>>>>>>>>> 
>>>>>>>>> Vygotsky (1989) writes: "Any higher psychological function ... was
>>>>> the
>>>>>>>>> social relation between two people" (p.56)
>>>>>>>>> 
>>>>>>>>> And Mikhailov (2001) suggests: "the very existence of the
>>>>>>>>> mind is possible only at the borderline where there is a continual
>>>>>>>>> coming and going of one into the other, at their dynamic interface,
>>>>>>>>> as it were—an interface that is defined ... by the single process
>>>> of
>>>>>>>> their
>>>>>>>>> [self and other] mutual generation and mutual determination"
>>>>> (pp.20-21)
>>>>>>>>> 
>>>>>>>>> Bateson (1979): Mind is an effect of relations, an aggregate
>>>> effect,
>>>>>> like
>>>>>>>>> stereo (spatial) vision
>>>>>>>>> is the emergent effect of two eyes with planar images.
>>>>>>>>> 
>>>>>>>>> Mead (1932): "the appearance of mind is only the culmination of
>>>> that
>>>>>>>>> sociality which is found throughout the universe" (p.86).
>>>>>>>>> 
>>>>>>>>> Nobody says anything about construction. The to eyes don't
>>>> construct
>>>>>>>>> stereovision and space. It is an emergent phenomenon,
>>>>>>>>> an ensemble effect deriving from relations.
>>>>>>>>> 
>>>>>>>>> m
>>>>>>>>> 
>>>>>>>>> 
>>>>>>>>> On Wed, Apr 11, 2018 at 6:47 AM, Andy Blunden <andyb@marxists.org>
>>>>>>>> wrote:
>>>>>>>>>> I always thought that the mind was a construction of human
>>>>>>>>>> culture. But of course, that was not what Spinoza thought.
>>>>>>>>>> 
>>>>>>>>>> Andy
>>>>>>>>>> 
>>>>>>>>>> ------------------------------------------------------------
>>>>>>>>>> Andy Blunden
>>>>>>>>>> ttp://www.ethicalpolitics.org/ablunden/index.htm
>>>>>>>>>> On 11/04/2018 11:44 PM, Wolff-Michael Roth wrote:
>>>>>>>>>>> No, I am not saying that there were human beings. Anthropogenesis
>>>>> and
>>>>>>>>>>> generalized (societal) action *come* together. But we have to
>>>>> explain
>>>>>>>>>>> culture and cognition as emergent phenomena not as
>>>> *constructions*
>>>>> of
>>>>>>>> the
>>>>>>>>>>> mind. m
>>>>>>>>>>> 
>>>>>>>>>>> On Wed, Apr 11, 2018 at 6:15 AM, Andy Blunden <
>>>> andyb@marxists.org>
>>>>>>>>>> wrote:
>>>>>>>>>>>> So, Michael, you are saying that there were human beings
>>>>>>>>>>>> before there was culture. And I gather you do not count
>>>>>>>>>>>> tools as units of culture.
>>>>>>>>>>>> Do we have to await a Psychologist to invent the word
>>>>>>>>>>>> "meaning" before we can poke a stick into an ant-hill?
>>>>>>>>>>>> Creationism makes more sense, Michael, at least it offers
>>>>>>>>>>>> /some/ explanation for the existence of human life.
>>>>>>>>>>>> 
>>>>>>>>>>>> Andy
>>>>>>>>>>>> 
>>>>>>>>>>>> ------------------------------------------------------------
>>>>>>>>>>>> Andy Blunden
>>>>>>>>>>>> ttp://www.ethicalpolitics.org/ablunden/index.htm
>>>>>>>>>>>> On 11/04/2018 9:57 PM, Wolff-Michael Roth wrote:
>>>>>>>>>>>>> Hi Bill,
>>>>>>>>>>>>> it is not so much "socially constructed." My key point in the
>>>>> book
>>>>>> is
>>>>>>>>>>>> that
>>>>>>>>>>>>> it is social BEFORE there can be any construction. It is
>>>> social,
>>>>>> and
>>>>>>>>>> this
>>>>>>>>>>>>> is where I refer to a Vygotsky that has not been taken up,
>>>>> because
>>>>>>>>>> "every
>>>>>>>>>>>>> higher psychological function ... was a social relation between
>>>>> two
>>>>>>>>>>>>> people." That is, in this specific case, mathematics is social,
>>>>> was
>>>>>>>> the
>>>>>>>>>>>>> relation between two people before you see it in individuals...
>>>>>>>>>>>>> 
>>>>>>>>>>>>> I think the construction metaphor breaks down when you look at
>>>>> our
>>>>>>>>>>>> species
>>>>>>>>>>>>> becoming human. So before there was culture, before we used
>>>>> tools,
>>>>>>>>>> where
>>>>>>>>>>>>> were those tools for constructing anything of the likes that
>>>>>>>>>>>>> constructivists say that we use to construct? How can a hominid
>>>>>>>>>> construct
>>>>>>>>>>>>> "meaning" of the branch as tool to start digging for roots or
>>>>>> fishing
>>>>>>>>>> for
>>>>>>>>>>>>> termites? And how do they construct meaning of the first
>>>>>> sound-words
>>>>>>>>>> when
>>>>>>>>>>>>> they do not have a system that would serve as material and tool
>>>>> for
>>>>>>>>>>>>> building anything like "meaning?"
>>>>>>>>>>>>> 
>>>>>>>>>>>>> So yes, a learning theory has to be able to explain learning
>>>> from
>>>>>>>>>> before
>>>>>>>>>>>>> culture (phylogenesis), before language and meaning
>>>>> (ontogenesis).
>>>>>>>>>>>>> 
>>>>>>>>>>>>> And about eclecticism---I think we would be a step further if
>>>> we
>>>>>>>>>> listened
>>>>>>>>>>>>> to and pondered A.N. Leont'ev's complaint about the "eclectic
>>>>> soup
>>>>>>>>>>>>> [eklekticheskoj pokhlebke] ... each to his own recipe" that
>>>>>>>>>> psychologists
>>>>>>>>>>>>> are trying to cook (in his foreword to *Activity.
>>>> Consciousness.
>>>>>>>>>>>>> Personality*).
>>>>>>>>>>>>> 
>>>>>>>>>>>>> Cheers,
>>>>>>>>>>>>> Michael
>>>>>>>>>>>>> 
>>>>>>>>>>>>> On Tue, Apr 10, 2018 at 7:15 PM, Bill Kerr <billkerr@gmail.com
>>>>> 
>>>>>>>> wrote:
>>>>>>>>>>>>>> One interpretation of Vygotsky (Wolff-Michael Roth) argues
>>>> that
>>>>>> all
>>>>>>>>>>>>>> knowledge is socially constructed and that ethnomethodology,
>>>>>> paying
>>>>>>>>>>>>>> detailed attention in the now, is the best or only way of
>>>>>> detecting
>>>>>>>>>> and
>>>>>>>>>>>>>> evaluating what is going on . Human activity can’t be reduced
>>>> to
>>>>>>>>>>>> individual
>>>>>>>>>>>>>> actions. Anything individual originates in the social, be it
>>>>>> words,
>>>>>>>>>>>>>> mathematics or by implication computer science (mentioned not
>>>> in
>>>>>> the
>>>>>>>>>>>>>> original but because it is a current interest of mine).
>>>> Moreover
>>>>>>>>>>>> internal
>>>>>>>>>>>>>> representations or schemas seem to be denied because that
>>>> would
>>>>>> be a
>>>>>>>>>>>>>> capitulation to dualism, emphasising brain / mind activity
>>>>> whereas
>>>>>>>> the
>>>>>>>>>>>> real
>>>>>>>>>>>>>> deal is an integrated thinking body.
>>>>>>>>>>>>>> 
>>>>>>>>>>>>>> This world view is critical of other learning theories be they
>>>>>>>>>>>>>> behaviourist, cognitivist, enactivist or constructivist.
>>>>>>>>>>>>>> 
>>>>>>>>>>>>>> The question that I want to explore here is the pragmatic one
>>>> of
>>>>>>>>>> whether
>>>>>>>>>>>>>> and how learning theory (an abstraction) makes a difference in
>>>>>>>>>> practice,
>>>>>>>>>>>>>> for busy, hard working (usually overworked) teachers. An
>>>>>> alternative
>>>>>>>>>>>>>> epistemology/ies which might appeal more in practice to real
>>>>>>>> teachers
>>>>>>>>>>>> under
>>>>>>>>>>>>>> pressure is an eclectic one centred around the issue of “what
>>>>>>>> works”.
>>>>>>>>>>>>>> I believe I am better read on learning theory than most
>>>>> teachers.
>>>>>>>> See
>>>>>>>>>>>>>> http://learningevolves.wikispaces.com/learning%20theories
>>>>>>>>>>>>>> 
>>>>>>>>>>>>>> Up until now I've developed an eclectic / pragmatic approach
>>>> to
>>>>>>>>>> putting
>>>>>>>>>>>>>> learning theory into practice. Take something from Seymour
>>>>>> Papert's
>>>>>>>>>>>>>> constructionism, something from Dan Willingham's cognitivism,
>>>>>>>>>> something
>>>>>>>>>>>>>> from Dan Dennett's behaviourism, something from Andy Clarke’s
>>>>>>>>>> enactivism
>>>>>>>>>>>>>> and roll them altogether in an eclectic mix. The authors in
>>>> this
>>>>>>>> list
>>>>>>>>>>>> could
>>>>>>>>>>>>>> be multiplied. My underlying belief was that it was not
>>>> possible
>>>>>> to
>>>>>>>>>>>> develop
>>>>>>>>>>>>>> a unified learning theory, that human learning was too complex
>>>>> for
>>>>>>>>>>>> that. As
>>>>>>>>>>>>>> Marvin Minsky once said in 'Society of Mind', "the trick is
>>>>> there
>>>>>> is
>>>>>>>>>> no
>>>>>>>>>>>>>> trick", I think meaning no overarching way in which human's
>>>>> learn.
>>>>>>>>>>>>>> 
>>>>>>>>>>>>>> One big surprise in reading Wolff-Michael Roth is his serious
>>>>>>>> attempt
>>>>>>>>>> to
>>>>>>>>>>>>>> put an end to such eclectism and develop what appears to be a
>>>>>> unfied
>>>>>>>>>>>>>> learning theory.
>>>>>>>>>>>>>> 
>>>>>>>> 
>>>>>> 
>>>>>> 
>>>>> 
>>>> 
>> 
>> 