Talk:George Lakoff/Archive 1
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This is the original content of Talk:George Lakoff. The article has changed so much since these discussions that all but a few of the questions about Lakoff here are no longer relevant to the article's development, or so thinks Ryguasu. (The original debate may not have even been about the George Lakoff article at all, but about some other article about the cognitive science of mathematics.)
the quotes were already in fair use on the page of reviews of Lakoff and Nunez referenced at the bottom - I presumed (perhaps wrongly?) that this means that they were cleared for quotation. Only the Santa Fe one seemed to be long, but it's quite specific, and justifies the claims int he rest of the article, so I'm not sure the scope of this is very clear without it... but I'll go with consensus, obviously.
It's significant to the article that "counting up to four" and moving along a line are empirically observed cognitive phenomena. Does it really make sense without that?
The Sigma Xi review is of the first edition which had technical errors.
My careful read of the other reviews, which include some pretty prominent journals and institutes, didn't make note of those errors, and the reviews have been up for some time, so presumably they'd object if they thought the overall theory was wrong.
Nonetheless, it speaks to the care of the authors that the technical errors be mentioned by some neutral party, so the Sigma Xi review belongs there - maybe with a note to the effect that these errors don't seem to have caused the other later reviewers to give up on the theory.
OK- scratch that - I see there's now a link to their "warning" about this.
Removed this from the article:
- It may well be that turning mathematics into an empirical science will involve a great deal of animal testing, to determine what's shared - and what is merely a widely shared human bias, arising out of our over-complex brains.
Many things may be, but this is unlikely to be one of them. Who says this? Other than you?
The objection is legit, thanks, but when you changed it you said this was deleted for being "surreal" - I admit it's speculative, but what's "surreal" about empirical testing of a cognitive science thesis, to see what we say share with apes and what is uniquely or bizarrely human?
- Not so much surreal as a reductio of Lakoff's goofy views.
Most of anthropology and primatology recently seems to be testing what things apes can do, what they can't, where we share a foundation ontology with them, where we don't. For instance how do they see 'family', or 'friend', or etc..
I also can't be the first person to call the human brain "over-complex"... I thought it was kind of a crack on the whole community arguing this stuff, as well... many wouuld just say "mathematics works" and leave it at that...
But the article is controversial enough without this suggestion of a path to validating... I'll actually see if I can get a quote out of Lakoff or find the material on chimps being tested to determine who real "number" is to them - saw this being done in a lab in Japan - on the Discovery channel - as usual the credits scroll by too fast adn the researchers name is too Japanese. ;-) But I'll dig it up.
"Clearly, when a man shoots a bear it is not only the man whose experience of the bullet is defined by "F=MA"."
This was actually the exact sentence (in private converation) that convinced me that mathematics could not be wholly a human invention...
The bit about nuclear weapons seems to be totally unrelated to the topic in the first and second sentences of that paragraph. The article as a whole is a little confused and poorly organised - perhaps a re-write is in order? As to animal testing... You mean experiments conducted using animals which is an different kettle of fish. -- The Ostrich
No, both topics are related, and if that's not clear, I'll fix it. Tell me if it makes more sense to you this way. Lengthy but clear:
1. if mathematics is a system that arises from constraints in the cognitive makeup of humans, then we cannot know what is "human delusion" and what is "objectively real" without some non-human animals to test mathematics on. Scientists in Japan are presently testing chimps to see how much of math they can master. If it turns out that they can master all the basic traits like "counting up to four", then this cognitive science of mathematics must apply to them as much as to humans - and we ought to be able to discuss it with them, or jointly agree with them on concepts like "whether this is four coconuts or not". This amounts to a primate testing of mathematics itself.
It is certainly an experiment, and it is certainly conducted using animals, and it is being done now. It's a glaring and obvious issue with the L&N claim that somehow mathematics is "uniquely human" or that we "can't know how much of it is objectively real" - we can at least know how much is shared with near cousins.
2. more difficult, the physics question. Addressed somewhat in particle physics foundation ontology. Tom Siegfried's objection is different, that what scientists see in a particle accelerator can be modelled using math - although Dirac had to invent a different notation I think that's a side issue.
If mathematical models such as those in physics are shared only by humans, and it's not clear that the "reasons why we believe there is a new particle" can be shared beyond humans, i.e. the chimps don't know what we're talking about, and when they look at the charts they just scratch their heads like any untrained human, then the reality of these theories are on shaky ground.
If it's only highly trained humans saying that they saw this particle and that this math is therefore "real", well, we start to be on shaky ground... Siegfried's assertion may well be more controversial than any by L&N here.
3. most difficult, the ethics question. The use of nuclear weapons and particle accelerators are restricted by a lack of opportunity to test the theories. WE CANNOT SIMPLY TEST ALL THEORIES OF WHAT WILL HAPPEN EQUALLY - therefore we have a lack of objectivity in experiments the same as we (might, if you accept this cogsci of math stuff) may lack such objectivity in notation.
This is very closely related to the argument about censoring science distorting it, and the Precautionary Principle which says you should not test a theory if one of the conceived outcomes of the test is destroying something you can't replace. Probably this is too complex to bring up in this entry, but:
We have ethical obligations not to destroy the planet to see if nuclear winter will happen, and there is a limited amount of particle acclerator time for which scientists compete fiercely. So inter-human politics absolutely deterines what theories get tested, which tends to determine what theories get discussed, which is in turn going to guide what theories get proposed.
This is also called "the paradigm problem" - when do we give up on some infrastructure, and tell the scientists who were "improving" it or using it "to test a theory" to go home, and that they aren't needed any more....
Extreme form of this argument: nuclear weapons aren't needed since they lead to more trouble than they're worth. Therefore, particle acclerators aren't needed since they are likely to shed light only on more ways to get big bursts of energy and blow up more stuff at once, or make black holes to suck up the Earth. Therefore, particle physicists aren't needed, etc...
If you accept the cogsci of mathematics as real, then all this stuff that was built assuming that the mathematical models were "real" and could be validated by simulations (purely mathematical) or complex webs of assumptions about the observer infrastructure, becomes very very doubtful.
So, it's one of the objections to this, that the cogsci of math is just one of those politically motivated theories that gets in the way of "real science"
I wanted to deal with that objection, which isn't possible without laying it out a bit.
Whew.
OK, now I need a beer.
I think the "bear line" and the "primate testing" line really get across the point. However, it would be nice not to have to lay out ALL the details of the objection and debate as above.
I also still think that without the Santa Fe quote, no one is going to really understand the scope of this, or how limited it really is - making it feasible to test - even on chimps.
OK, I see what you mean about the nuclear weapons thing, it wasn't clear that this is a view of Zerzan and Waring rather than Wigner. Now it is, and there's some bridge there.
I also mentioned the relationship with the Precautionary Principle - and the common theme of limiting trust in human constructed mathematical models, and deliberately choosing "not to go there" as a consequence of nuclear standoffs.
I could have mentioned climate change too, but that's not generally seen to be something that can destroy all cognitive beings - just make us war more...
Lakoff is a highly political commentator so it's not really right to avoid the politics of his conclusions. Although he carefully quotes in his reviews people from technical communities who agree with him, his overstatement of the degree to which "mathematics is human" is a clear sign of a certain bias.
Mathematics, to the degree he's talking about it, which is not very far, is just as well understood by chimps, and probably by dolphins, horses, and dogs.
OK, I added headings that at least ask what I think are important questions.
I didn't answer the questions, really, just laid out some controversies.
Ultimately this article has more to do with the difference between ethics and morals, and the Neutral Point of View, than most other topics in the sciences.
Maybe it should link to some stuff in the meta?
OK, a bit of research has determined that this topic isn't entirely crackpot (assuming that Berkeley doesn't make crackpots professors) so for those people like myself who would be tempted to delete this article straight away as content-free ravings, don't.
However, the article seems to me to be infested with postmodernists syndrome - the inability to simply and clearly explain WTF they are on about.
Could the article please *clearly* state:
- What this theory states.
- Why the proponents believe it.
- What connections it makes with other ideas (origins etc.) Frankly, it sounds like the kind of tripe Sokal parodied.
- Who agrees with them.
- Who disagrees with them.
- Is it an active area of further work? By whom?
- Whether any actual mathematicians give a rat's.
"What this theory states" was deleted because someone was worried the quote, which was already used on L&N's own review page, was too long and copyrighted. I have stated several times it should come back. So I'll bring it back.
"Why" is anybody's guess, but I suppose it's because they came up with a rationalization that did not seem to get any major mathematicians angry... and a lot of them appear to have had a crack at the material, looking at that review page
"Connections"? Well, it's basically asking if math is really a NPOV, or if it reflects domination desires by humans over nature, extensions of things that work to blow stuff up and build infrastructure into control of humans... a lot of the issues that indigenous peoples tend to take up with colonials...
"dis/agree" - hard to say - it seems some reviewers question the implications or to what degree this is true of humans vs. apes or vs. robots or vs. dogs, but no one doubts that *some* of mathematics is basically just like numerology - sophistry that adds up internally but applies to nothing else.
I've been looking for a strong attack and it just isn't there - Lakoff is *very* respected and most people consider him the heir to Chomsky and the prime theorist of language.
L&N, and Santa fe inst., claimed it was "an extended start on a cogntiive science of mathematics" and I know the work is continuing in private and on mailing lists. There is some work on cognitive political science for instance.
Mathematicians caring wouldn't really be the point - a mathematician only cares if his work is internally consistent, not what it externally predicts or describes. Other scientists, especially physicists working on expensive infrastructure available to few people, would care more, maybe oppose more...
Mathematical epistemologists, and "foundationists" would be the people to ask.
OK, hopefully this is more structured, and puts some context in there. This is a paradigm shift, a huge program, like Principia Mathematica (1913, Russell and Whitehead)... like that program it could fail. But it's as big as that was, actually bigger.
I hope I captured the implications... without seeming to advocate any of 'em.
This is not perfect. I should ask Lakoff himself to look it over - and grant permission maybe for more extensive quotes. I don't think seven or eight lines that is basically a summary of the work as it would appear in a scientific abstract is a copyright problem - but who knows what lawyers believe?
he might also outline where the work is going next, who's doing it, and etc.
OK, I just sent the article to Lakoff, with the URL. He may edit it here, or he may respond to a list... either way I ask that people leave this alone for a week or so. Thanks.
--- This was just removed:
"[science is an ambiguous project]...One which we may well abandon.
It seems to be an ethical choice: accept a moral instinct, or engage in some ethical negotiation with some other body to gain resources to test new models.
Simply proving a model does not contradict other models may no longer be good enough to convince funders that every step of the derivation was "embodied" - that it relies on axioms and proofs that are themselves completely grounded. "
I wonder if the editor is basically practicing an ideology of "scientism", whether he knows it or not: assuming scientific knowledge not to be subject to ethical choices, e.g. to fund or not to fund, to experiment or not to...
The article makes sense without these questions being raised, but the ethical point about the practice and funding of science is now completely excised... and it's a pretty major point.
- Is this a major point that Lakos makes, or a major point that is dear to your heart and that you somehow want to weave in? AxelBoldt
If it's a philosophical issue, maybe it's another article. There are lots of writers now talking about "the death of science" and such... including the head of the AAAS who used that phrase to describe censorship of anthrax stuff.
If it's a matter of bad writing, ok, guilty, I can go back and put these concerns more cleanly elsewhere. The idea of viewing the body as an axiom base was also removed... not surprising, as this seems to also have been the issue between Lakoff and his reviewer from the MAA - one of the links at the end. Is " bodies as theses? " a fair summary title for a paragraph on this?
I believe that among technically literate people, there is a general consensus that mathematics is a neutral point of view, indeed that if logic itself is a valid mode of investigation, mathematics must equally be one. I therefore think that this article should at least refect these facts. Perhaps we should get Alan Sokal to give this one a re-write? -- The Ostrich.
That's exactly the point... that "technically literate people" assume exactly that. This analysis challenges that. If it doesn't clear define and reflect what it is challenging, that's a flaw in the introduction.
How about simply adding exactly that statement of yours near the beginning?
The issue of "logic itself as a valid mode of investigation" and assumptions about all of mathematics necessarily sharing that, is what's called a "foundation issue" in mathematics.
Perhaps a summary of Whitehead, Frege, Russell, and Godel near the beginning of this, and the present lack of agreement on what mathematics means, is required as well.
I'd suggest also that "technically literate people" are not the audience we are writing for, necessarily, and that this article addresses conflicts between a 'neutral' and 'natural' point of view (being discussed in the meta).
BTW, I consider myself "technically literate" in exactly the sense you mean, with degrees in Mathematics itself, and I do not consider something stated in mathematical or logical or set theory form to say anything about the geometry it measures.
There is a very well founded literature in cogsci of 'what measurement is' - Tversky, Kahneman, and others laid the foundation for this work in the 60s, so its not coming from left field.
Admittedly, it's a hard topic to introduce to someone unfamiliar with this material, or with a strict Western/dualist view of subject/object relations.
OK, done, to the best of my off-the-cuff ability. Does that read reasonably? It sure outlines a lot of other stuff that needs to get included...
The choice of reactions to the first nuclear explosion helps highlight the fact that humans define their own tests for what "works", and therefore that their shared belief in mathematics isn't necessarily a belief in more than their own cognition and culture.
That seems to be Lakoff's claim, based on his "there's no way we scientifically could possible tell".
Thanks for your contributions. This article is now taking shape nicely, and moving towards NPOV.
I don't agree with many of the statements in the article, but as they become increasingly attributed to their sources, as facts that 'X says Y about Z', this does not matter. Other authors can add their notes of the contrary views of others in the same format, and the Wikipedia process will polish the article.
From the article:
- Alfred North Whitehead, Bertrand Russell, and Kurt Godel established that logic and set theory were in some sense grounded on something else, something geometric and quite "real",
Please explain: Russell showed that naive set theory led to Russell's paradox, Godel demonstrated that formal axiomatic systems with enough power to do arithmetic cannot be both consistent and complete. I'm not sure that either result implies the second half of the sentence. The Anome
It's quite hard to get this to NPOV as it challenges various widely-held beliefs about what NPOV is (many people just equate it to mathematics, as Tom Siegfried does). Objections raised so far have generally improved it much... and I appreciate them...
Your point especially. My sentence was actually cut off - it should have dealt with the issue of "sacred geometry" but I just didn't know how. What I'm trying to get at in this paragraph is that naive set theory and naive logic both failed (set theory thanks to Russell, logic thanks to Godel) to prove themselves to be the underlying foundation ontology of a "consistent and complete" algebra.
There are two separate issues: one is that algebra building on itself up to first order predicate calculus becomes at that point either inconsistent or incomplete. The other is that algebra itself in the form of simple arithmetic can be justified strictly from any combination of set theory and naive logic, but those two have no agreed foundation.
Your question is how much of this did those two theorists konw and say about the foundation. You're right, they did not establish, and did not claim, that "reality was still geometric" - in fact they made the usual mathematicians' conservative claim that they just didn't know. Wittgenstein was more aggressive and some of his converations with Turing on these points are recorded. I'd actually trace the origin of the cognitive science of math to these two, but that's not really a connection made in the modern discourse.
Modern mathematicians generally point to Paul Erdos and "the well known graph" of mathematicians who proved number theorems with him, as a social basis for the validity of mathematics. But I know of no epistemologist who has investigated this rather grandiose implicit claim by mathematicians that the Erdos number is the grand hierarchy on which reality rests...!
The final missing point is the issue of sacred geometry, Platonic realism, etc., in fact some people call this "c.s. of m." just "Platonic neo-realism". The Erdos number and well-known graph *is* a "sacred geometry", clearly, but how much of all of this belongs in this article?
Philosophers of mathematics refer to all of the above as "the foundations debate" - there are many essays about it - I read a whole book of them once and all it proved to me was that AI was an obvious crock: without a body it cares about, it can't participate in any empirical process we would empathize with sufficiently to matter. Politics is prior to epistemology for most people, and if there's anything to this post-20th century discourse at all, then it will be prior to epistemology for *all* people... and lots of what was considered "objective" in the 20th century will be swept aside as conflict-causing "dominator culture". Rather like the Medieval Scholastics debating angels on heads of pins were swept aside by a more grounded group of protestants and scientists during The Renaissance.
I mean, a lot of jobs were lost in that transition. :-) This is emotional...
Proving it is emotional, Ed Poor just reacted emotionally and shoved this all under George Lakoff.
Ed, read the above. There is a foundations debate in mathematics. There is a body philosophy movement. There is a cognitive science of mathematics that goes back to Tversky & Kahneman's challenge to the objectivity of statistics, and before that to Simpson's Paradox.
The L&N thesis has met no significant challenge beyond the "sacred geometry" and "particle physics" believers, like Tom Siegfried. That is not considered a serious objection by mathematicians - as evidenced by the reviews of the work.
We may need a separate article on the foundations debate, a separate article on the cognitive science of mathematics as it evolved through T&K to L&N and is proposed to be extended by the Santa Fe Institute, and some other reviewers - hell another one entirely on "behavioral finance" or "prospect theory" and their impact on economics.
But what we don't need, is people who don't understand the material, shoving it around as if it's something personal.
I agree, in general, with the principle that flaky work done out of context of any existing field that makes outrageous claims ought to simply be filed under the primary theorist's name.
But, this simply isn't one of those cases. Lakoff's extreme claims are not wholly characteristic of the cognitive science of mathematics, they just mark out the territory nicely, and the article framed them I think perfectly well.
Before a flurry of new short articles dealign with all these issues appears, like tonight, I would appreciate knowing why you consider all this, including Nunez, to be just a figment of George Lakoff's imagination?
Now, now, don't get all emotional :-)
I think an idea should be listed under its main proponent -- especially when it's new, controversial, or not well-known by its own name.
You are free to revert my move. I won't re-revert it, as I try to avoid edit wars.
Please note that the cognitive science of mathematics link still brings up the orginal article. I am not trying to censor, just to organize. (I helped you when Z. was going to delete all your greens 'cause they weren't meaty enough; so I'm not "against" you; let's work together.)
OK, sorry, I guess the puke over peace movement, MAD, etc., has put me in a general frame of mind to expect political bias in general. You can see now from this article how it relates: some people honestly believe that the MAD mutual threat is the reason there are still human observers on the Earth - others just as honestly believe that the peace movement spread of mutually assured peace is the reason. This is a conflict on what constitutes the neutral point of view. In some ways it is irreconcilable and can only be outlined, as Gandhi thought, by a choice to follow "force" or "love". Yeesh.
My apologies for mistaking you as someone trying to marginalize a peace view.
I agree with the convention that an idea shoul be listed under its main proponent, when there is one. Applying that to this article would rename it "Embodied Mind", since that is the name of the Lakoff/Nunez thesis.
A general treatment of Lakoff and his influence would include his recent critiques of terrorism and almost ignore "cognitive science of mathematics" as a debate that he is actually a minor player in... Turing, Wittgenstein, Tversky, Kahneman, Nunez, etc., will probably be recorded as the major players by history. Lakoff's claims actually sit on the fringe of the field, especially the idea that math is *only* human... clearly contradicted by chimp experiments if nothing else...
So the schema would be: George Lakoff, Rafael E. Núñez, Embodied Mind for their shared thesis of 2000 and the general treatment now sitting here, cognitive science of mathematics for the debate back to Turing and Wittgenstein, distinct from the much more general body philosophers which would include also the postmodernists, and foundations of mathematics for the most general raising of issues with falsifiabilty, set theory and logic - for instance dealing with the well known graph around Paul Erdos and characterizing it as potentially just another sacred geometry (if Lakoff is right) or as evidence of a broad consensus of human cognition (if Tversky & Kahneman and prospect theory are right), or as evidence of some deeper shared consensus with other Hominidae, great apes, and "lesser" creatures, if Jane Goodall and the other "ape empathists" are right, or, potentially, an objective reality with another basis entirely (e.g. http://www.timecube.com). I'd love to cover Gene Ray as another extreme case, but...
...*THERE* is a guy who needs his own entry, quite separate from any other...
- -)
Is that schema reasonable?
Yes, that seems like a reasonable compromise way to proceed... welcome to Wikipedia! The Anome
Any schema you propose will be reasonable, I'm sure. As a reader of the wikipedia (not just a contributer), I'd like to be able to find articles easily.
If there is a "science of mathematics", I would like to read about it. Before this week, I had thought a mathematics being "a tool of science" rather than a science itself; similarly, I consider logic a tool used in philosophy. On the other hand my church's philosophy presents a "theory of logic", so perhaps my ideas need better organizing!
To sum up:
- I have no desire to censor any ideas.
- I don't want to use the wikipedia to endorse my pet views.
- I hope the wikipedia can distinguish between (A) what people (or specific groups) "generally believe" and (B) what various advocates maintain. This latter aim is troublesome, somehow.
I agree on all counts. I hope it's obvious now that this is an issue regarding neutral point of view itself, and thus the controversy can't be personal to us.
The entry as it presently stands, after my most recent edit, is painstakingly clear about the difference between Lakoff's pet opinion (which is an extreme claim for the exclusivity of a cognitive science of mathematics) and that which he shares with Nunez, me, and others, that there is an "embodied mind" and that this is the entity which is actually described in human mathematics.
The broader question of a cognitive science of mathematics goes back to the statistical biases in human thinking, etc., life/loyalty/locality issues in cognitive psychology, and the philosophy of mathematics. It seems most sensible to introduce the topic starting with Lakoff & Nunez's views, but to establish *here* (in "George Lakoff") that he goes further even than Nunez, and is identified with a political perspective that Nunez himself is not...
If this is controversial, I suggest we add an 'embodied mind' entry so that the thesis of lakoff & nunez is kept again separate from the earlier work in cognitive psychology and behavioral finance.
Then the "cognitive science of mathematics" would be a more neutral entry that would say "building on the embodied mind, statistical bias studies in cognitive psychology, and theories of irrational human economic behavior..." some dudes claim that the philosophy of mathematics and falsifiability to date have been a crock, merely numerology applied to theological assumptions.
But I think until there is a second book that calls the "c.s. of m." exactly that, it's fair to say that "c.s. of m." is a L&N coined term... and that the differences between it, the "embodied mind", and Lakoff's pet claim of "strict humanism" can be handled without broader treatment. "Embodied" studies are increasingly found in all sciences, so there may well be a few "embodied mind" claims out there. Although none so carefully bound to Euler's Identity!
1. The "neutral point of view" article is a statement of Wikipedia policy, not an article about any subject in the real world. It is totally irrelevant to any encyclopedia article not specifically about Wikipedia, so I'm removing the reference to it.
2. Do you have something against the ordinary conventions of English prose, like capitalizing your subheads?
3. Terms used in this article that are dependent on its context, like "reasonable method", should be either included in the article itself as a footnote, or disambiguated so they won't be confused with general subject matter. Perhaps that article should be titled "Lakoff's views on reasonable methods of investigation" or something. Please remember that this is a general purpose encyclopedia, and articles should stand on their own.
Today's version is approaching something I might be able to read. I actually skimmed it, and it looks interesting (although probably over my head). It's been a long, hard road to knock this article into shape, but I believe that it was worth it.
Wikipedia needs many contributors, and even though the old-timers may be persnickety (or even snide!) about style and neutrality issues, I hope the primary contributor of this article will stick around.
I probably never will become a green or a Lakoffite, but at least I will be able to know exactly why not -- after reading these excellent articles! Ed Poor, Thursday, March 28, 2002