Women, Fire and Dangerous Things...

Come to think of it, I do know how to do it...

Suppose one makes two lists of all the propositions in a given language, say Japanese. One list would contain all the true propositions; the other, all the false ones. The lists would be infinitely long, of course, allowing for arbitrarily complex expressions. It would clearly be possible to do it, since one could sort the propositions alphabetically.

Do the same thing with another language, say Hopi.

Now translate all the true Japanese propositions into true Hopi propositions by matching up the two lists. And translate all the false Japanese propositions into false Hopi propositions by matching up the two lists. Such a translation would preserve the truth value of each statement -- even though meanings would become totally lost.

It would clearly work for any two languages that allowed for infinitely many propositions. It would also work for any two languages which allowed the same (finite) number of propositions.

I'm not sure this is what Lakoff had in mind, but it seems to match what he wrote...

Two conceptual systems are commensurable if each language can be translated into the other, sentence by sentence, preserving truth conditions.

~ Page 322.

It certainly seems that something needs to be added to translatability to make any sense of it. I suspect that Lakoff would add the restriction that a translation represents the same external reality as did the original statement. That would seem to be the bare minimum that one could add to make sense of it.

How do jokes and Haiku fit in as external representations? Humor and the appreciation of beauty seem to be internal judgments. They are externalized in the sense that men talk about them. So I would expect that any literal translation would satisfy such an amended version of Lakoff's translatability criteron. But who am I to say?

Lakoff quickly cedes the high ground in regard to the first point, translation. Personally, I think he could have fought to convince people that even here, languages are incommensurable. Perhaps it was professional pride that stopped him. What linguist would imagine that he could not translate from one arbitrary language into another?

Certainly there are points at which translation is difficult, if not impossible. Humor can -- so I understand -- present extreme difficulties to a translator: A joke from one language, accurately translated into another language, may completely fail to amuse any prospective audience...

The second criterion is understanding.

Two conceptual systems are commensurable if they can both be understood by a person--presumably via the preconceptual (sic) structure of his experiences and his general conceptualizing capacity.

~ Page 322.

Some things to consider...

• The first criterion equates conceptual system and language. The second does not seem to do that.[/*:m:3qpj2uj7]
• Does it count if a machine understands two conceptual systems? (As if such a question really meant something!!) Personally, I believe that is what Lakoff was trying to setup with the first criterion -- some sort of computer analog.[/*:m:3qpj2uj7]
• If a conceptual system is not a language, what is it? Presumably it is something that a person might understand. A person might understand jokes and Haiku. Are they commensurable conceptual systems according to this second criterion? They don't seem particularly commensurable to me.[/*:m:3qpj2uj7]
• Perhaps we should apply the term conceptual system to something a bit more globally applicable than either jokes or Haiku. But the second criterion supposes that a person might be able to understand two of whatever a conceptual system is.[/*:m:3qpj2uj7]
• Would a computer operating system count as a conceptual system? There was a time when a single person might claim to understand the internals of such a system. So one might ask whether two such systems might be considered commensurable if one person understands them both. Is that what Lakoff is getting at?[/*:m:3qpj2uj7]
• What is to be said of things one does not understand -- or understands incompletely? That one might not understand jokes and Haiku tells us that they are not part of his conceptual system. But it does not tell us that they are not commensurable. Is it ever possible to know that two conceptual systems are incommensurable? If not, then the second criterion is fairly meaningless in practice.[/*:m:3qpj2uj7]
• Are there grades of commensurability corresponding to things incompletely understood?[/*:m:3qpj2uj7]

The second criterion is understanding.

Two conceptual systems are commensurable if they can both be understood by a person--presumably via the preconceptual (sic) structure of his experiences and his general conceptualizing capacity.

~ Page 322.

Some things to consider...

• The first criterion equates conceptual system and language. The second does not seem to do that.[/*:m:23u5b4z2]
• Does it count if a machine understands two conceptual systems? (As if such a question really meant something!!) Personally, I believe that is what Lakoff was trying to setup with the first criterion -- some sort of computer analog.[/*:m:23u5b4z2]
• If a conceptual system is not a language, what is it? Presumably it is something that a person might understand. A person might understand jokes and Haiku. Are they commensurable conceptual systems according to this second criterion? They don't seem particularly commensurable to me.[/*:m:23u5b4z2]
• Perhaps we should apply the term conceptual system to something a bit more globally applicable than either jokes or Haiku. But the second criterion supposes that a person might be able to understand two of whatever a conceptual system is.[/*:m:23u5b4z2]
• Would a computer operating system count as a conceptual system? There was a time when a single person might claim to understand the internals of such a system. So one might ask whether two such systems might be considered commensurable if one person understands them both. Is that what Lakoff is getting at?[/*:m:23u5b4z2]
• What is to be said of things one does not understand -- or understands incompletely? That one might not understand jokes and Haiku tells us that they are not part of his conceptual system. But it does not tell us that they are not commensurable. Is it ever possible to know that two conceptual systems are incommensurable? If not, then the second criterion is fairly meaningless in practice.[/*:m:23u5b4z2]
• Are there grades of commensurability corresponding to things incompletely understood?[/*:m:23u5b4z2]

The third criterion is use.

Two conceptual systems are commensurable if they use the same concepts in the same ways.

~ Page 322.

Some things to consider...

• This third criterion is actually what led me to the amended first criterion that I posted. I kept coming back in my mind to this criterion. I realized that for Lakoff the essential distinction between the two must consist in the distinction between what is objective, external and what is subjective, internal. Hence the amendment I offered.[/*:m:23u5b4z2]
• Like the second criterion, no mention is made of language. So, once again, it is not clear what Lakoff means by conceptual system.[/*:m:23u5b4z2]
• One might consider modifying this third criterion to say...
  

  Two conceptual systems are commensurable if each language can be translated into the other, sentence by sentence, preserving their conceptual context.

  [/*:m:23u5b4z2]
• In practice, two things which are subjective can not be objectively compared. So it would seem that this third criterion -- even as amended -- requires speculative knowledge.[/*:m:23u5b4z2]

The third criterion is use.

Two conceptual systems are commensurable if they use the same concepts in the same ways.

~ Page 322.

Some things to consider...

• This third criterion is actually what led me to the amended first criterion that I posted. I kept coming back in my mind to this criterion. I realized that for Lakoff the essential distinction between the two must consist in the distinction between what is objective, external and what is subjective, internal. Hence the amendment I offered.[/*:m:28l3w37e]
• Like the second criterion, no mention is made of language. So, once again, it is not clear what Lakoff means by conceptual system.[/*:m:28l3w37e]
• One might consider modifying this third criterion to say...
  [quote:28l3w37e]Two conceptual systems are commensurable if each language can be translated into the other, sentence by sentence, preserving their conceptual context.
  

• [/*:m:28l3w37e]
• In practice, two things which are subjective can not be objectively compared. So it would seem that this third criterion -- even as amended -- requires speculative knowledge.[/*:m:28l3w37e]

[/quote:28l3w37e]
The fourth criterion is framing.

Two conceptual systems are commensurable if they frame situations in the same way and if there is a one-one (sic) correspondence between concepts in the two systems, frame by frame.

~ Page 322.

Some things to consider...

• Like the second and third criteria, no mention is made of language. So, once again, it is not clear what Lakoff means by conceptual system.[/*:m:28l3w37e]
• It would seem that any two conceptual systems which are commensurable by this fourth criterion would also be commensurable by the third criterion since there would be a one-to-one correspondence between concepts in the two systems, frame by frame.[/*:m:28l3w37e]
• One might consider modifying this fourth criterion to say...
  

  Two conceptual systems are commensurable if each language can be translated into the other, sentence by sentence, preserving conceptual framing.

  [/*:m:28l3w37e]
• Once again... two things which are subjective can not be objectively compared. So it would seem that this fourth criterion -- even as amended -- requires speculative knowledge.[/*:m:28l3w37e]

The fourth criterion is framing.

Two conceptual systems are commensurable if they frame situations in the same way and if there is a one-one (sic) correspondence between concepts in the two systems, frame by frame.

~ Page 322.

Some things to consider...

• Like the second and third criteria, no mention is made of language. So, once again, it is not clear what Lakoff means by conceptual system.[/*:m:1ksrcdih]
• It would seem that any two conceptual systems which are commensurable by this fourth criterion would also be commensurable by the third criterion since there would be a one-to-one correspondence between concepts in the two systems, frame by frame.[/*:m:1ksrcdih]
• One might consider modifying this fourth criterion to say...
  [quote:1ksrcdih]Two conceptual systems are commensurable if each language can be translated into the other, sentence by sentence, preserving conceptual framing.
  

• [/*:m:1ksrcdih]
• Once again... two things which are subjective can not be objectively compared. So it would seem that this fourth criterion -- even as amended -- requires speculative knowledge.[/*:m:1ksrcdih]

[/quote:1ksrcdih]
The fifth criterion is organization.

Two conceptual systems are commensurable if they have the same concepts organized relative to one another in the same way.

~ Page 322.

• Once again, there is no reference to language. So it is not clear what Lakoff means by conceptual system[/*:m:1ksrcdih]
• It would seem that any two conceptual systems which are commensurable by this fifth criterion would also be commensurable by the third criterion, since the fifth criterion merely adds organization requirements to the third criterion.
  One might consider modifying this fourth criterion to say...
  Quote:
  Two conceptual systems are commensurable if each language can be translated into the other, sentence by sentence, preserving conceptual organization.[/*:m:1ksrcdih]
• It is difficult to say how one can define the organization of concepts independently of the conceptual system in which they exist. So it would seem that this fifth criterion -- even as amended -- requires speculative knowledge. [/*:m:1ksrcdih]

I don't personally see much in these criteria. They do not seem to prove the case for relativism, as Lakoff hoped.

It might bother me if it could be shown that the mere process of translation introduced inescapable paradoxes.

I believe that if there is a need for fuzzy logic in terms of translation it would be in translating grammatical terms. I once read that Chinese does not divide words into categories like noun, verb, adjective, etc. but into yang words and yin words. That might make perfect sense to someone who speaks Chinese, I suppose. But it doesn't help me much to understand grammatical structure of the language.

Consider a simpler case. Take the expression "This expression is English." Suppose I translate it into French. I might arrive at "Cette expression est l'anglais," as a perfectly literal translation. I say it is a literal translation because I generated using a translation engine available on the internet...

http://translation2.paralink.com/

The English version is true; the French translation, false. A paradox? Not to me, since the phrase is reflexive, referring to itself precisely in terms of its language. Certainly any paradox involved is not inescapable. The reflexive nature of the expression can be avoided by considering, instead, the expression, "The expression, 'This expression is English,' is English," translated to, "L'expression, 'This expression is English,' est l'anglais," both of which are true.

I suppose I should confess, however, that I cheated here. The translation engine I referred to above really translated "The expression, 'This expression is English,' is English," to "L'expression, 'Cette expression est l'anglais,' est l'anglais," but I replaced the inner expression with the English original. So which is right, machine or the me?

Regardless of how one answers the question, I think it clear that there is nothing inescapable in any paradox one sees here.

But Lakoff, himself, admitted that translations do not provide any interesting challenges...

Having considered each of the points which Lokoff says we "must leave behind," I must move on. Specifically, I would o consider some of the positive points of the book...