ganai, gi

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ganai ... gi ...

This is the logical version of if, i.e. "material implication"; "Either not p or q, or both".

  • It indicates correlation, not causality.
  • It is exactly equivalent to "nage ... ginai ...", i.e. "not both p and not q". If that paraphrase works as well as "if ... then ..." in a given phrase, then "ganai ... gi ..." is acceptable.
  • Lojban is the logical language, as so should say things in the logical way whenever possible.
  • .i krinu tadji di'e The reason is as follows:

X Y not X if X then Y (not X or Y or both)

bu'a bu'e nabu'a ganai bu'a gi bu'e

1 1 0 1

1 0 0 0 <-- jitfa .iseni'ibo ko toljundi False, so ignore it. BTW, my ignoring it isn't logically implied by it being false. .ienai .i po'o le sedu'u ko toljundi le 2moi tcini kei cu smuni le sedu'u ganai

0 1 1 1

0 0 1 1

.i po'o 3mei tcini .iseni'ibo le di'e pagbu cu vajni Only 3 situations, so these parts (below) are important.

X Y

bu'a bu'e

1 1

0 1

0 0


In reorganizing the terribly cluttered if page, I'm not sure what to do with the huge chain of responses below. Much of it has been made irrelevant by the existence of mu'ei, or the possibility of using a selbri like krinu, nibli, mukti, or rinka. --rab.spir


Con:

  • If as we understand it cannot be reduced to NOT p OR q, for the simple reason that it doesn't behave like it under negation (McCawley p. 224). If if was the same as NOT p OR q (naja), then its negation, it is not the case that if... should be NOT (NOT p OR q) = p AND NOT q (genai). But to use McCawley's example, "It is not the case that: If God is dead, everything is permissible" is not the same thing as "God is dead, and not everything is permissible."
    • mi'e xod .i ganai da'i do ba'o cusku bau la lojban. gi do na pu srera .i le jei lo'u ganai gi le'u cu prije cu traji .i ma'i le pu lojycartu goi L le pu'u natfe tu'a lu ganai bu'a gi bu'e li'u seljalge le L 2moi tcini po'o poi ke'a selsmuni le du'u bu'a jetnu gi'e bu'e jitfa .i ru'a bu'a du mi ricfu .i ru'a bu'e du mi gleki .i ja'o lu ganai bu'a gi bu'e li'u selsmuni le du'u ganai mi ricfu gi mi gleki .i ja'o lu naku ganai bu'a gi bu'e li'u selsmuni le du'u naku ganai mi ricfu gi mi gleki kei poi ma'i L ca'i le 2moi tcini ku ke'a selsmuni le du'u ge mi ricfu gi mi na gleki .i melbi .i le li'i ce'u ricfu jena gleki kei po'o tadji le mu'e jarco le du'u lu ganai mi ricfu gi mi gleki li'u na fatci
      • .i doi xod. mi'e nitcion. na'i go'i .i bau le glico zoigy. It's not true that, if I'm rich, I'm happy gy. ba'e na nibli zoigy. I'm rich gy. noi li'a se nibli zoigy. I'm rich and I'm not happy gy. .i seni'ibo zoigy. if na dunli "lo'u ganai le'u" .i bau la lojban le mupli pe do cu jai snada; ki'u le li'a du'u "lo'u ganai le'u" dunli "lo'u ganai le'u" .i ku'i mi na casnu le smuni be "lo'u ganai le'u" .i mi casnu le smuni be zoigy. if gy. .e ledu'u jimpygau leri smuni bau la lojban sepi'o makauIn other words: I know that's what ganai does; it's just not what if does, so ganai is not equivalent to if. (I don't think the counterargument is that it's na'i, not na; no, it really is "it is not the case that" which throws if off like that.) This is one more reason why this cannot be discussed in Lojban, btw: if if is not the same as ganai, then what you say about ganai has no bearing on how to say if. In !McCawley's example above, if is clearly not ganai at all, but ni'i. OK you have a point. ganai collapses all the possible worlds into here & now. The only way you can say "It's not true that, if I'm rich, I'm happy" is if you really are rich, and are unhappy. The answer probably lies with da'i and da'inai, but I am afraid I lack the philosophical bone to carry this much further. At least I know how to use it. It sure would be handy to have a nice, slim volume on Lojban and Logic that I could understand. Perhaps a college Freshman Intro to Logic, but in Lojban. --xod
      • An important difference between if and ganai is that if presupposes a preceding universal quantification, and ganai does not. For example: if someone is rich, then they are happy means roda zo'u ganai da ricfu gi da gleki. It does not mean just ganai da ricfu gi da gleki. The negation, it is not the case that if someone is rich then they are happy is of course naku roda ganai da ricfu gi da gleki, which in turn is equivalent to su'oda ge da ricfu ginai da gleki, i.e. there is at least someone who is rich and not happy. What about the case with mi? Again we need a universal quantification: In every possible world, I am either not rich or I am happy, that's what if I'm rich then I'm happy means. So if we insist on translating it with ganai, we must introduce a universal quantification over possible worlds, over possible circumstances, or something similar. Then the negation works fine: There is at least one world in which I am rich and not happy. In English, if already has this universal quantification included in its meaning, in Lojban ganai does not, and it has to be made explicit for it to have the meaning of if. --mi'e xorxes
        • Good point. This is why we need tense cmavo for possible worlds. Loglan figured out that they were necessary, yet they are sorely lacking in Lojban. --rab.spir Watch out, we only get ten indentations, then the Wiki breaks. Is da'i, da'inai good enough for you, Rob? --xod
          • (Well, this is only the 5th indentation, so we're doing okay.) da'i and da'inai are okay, but just barely. Other attitudinals have a way to express a similar concept explicitly; there is no such method for da'i and da'inai. Plus da'i might have other meanings besides possible worlds. I think that if possible worlds could be tenses but the option of just using the fuzzy da'i was still available, things would work fine.And, it appears, the tense cmavo which does this is mu'ei. Now that I understand what the PA is for in its definition, I love it. This is what I'll use for counterfactuals. --rab.spir
        • Maybe bai.
  • It doesn't work for "counterfactuals", as in "If I had a million dollars...". Since we know that the first part is false, the entire statement is necessarily true in Lojban ("ganai mi megdo rupnu ponse gi co'e")
    • And neither does va'o. co'e va'o lenu mi ca megdo rupnu ponse cannot say anything about co'e, because lenu mi ca megdo rupnu ponse does not exist. The sentence reduces to co'e va'o noda.
      • Sure it does. Events in Lojban can exist even if they don't happen. After all, would you say that mi djica le nu ca megdo rupnu ponse reduces to mi djica noda? Some people seem to think it's a problem; xorxes wants to use lo'e nu when the event doesn't occur, I think. If you pressed me, I would make the distinction with ka'e nu vs. ca'a nu, but it doesn't overly concern me. If usage has ever decided anything, it's decided that events can exist without occurring. Not that "va'o" necessarily works, just that this isn't the reason.-- Adam
        • I would say that, yes. "I want to have a million dollars" would not be translated with a ca in it. It would be tenseless; "I want to have a million dollars, sometime." It might in fact use ba. Future events exist at least in possibility; saying that I want this event means that I'm not sure whether this event will ever exist, but if it does, I want it. However, I believe that talking about present events which are known not to exist cannot convey anything. --rab.spir
          • That's begging the question. I may want a million dollars sometime, but I may also want a million dollars now, and there's no reason I can't express this with a tense on the subordinate bridi. I can even say that I (now) want to have had a million dollars: mi ca djica le nu mi punau megdo rupnu ponse. (Though this can't happen, I can still want it.) Not only that, but predications about events that might not actually happen in this world are common and very useful: bredi, kakne, pacna, etc.
            • Of course there must be constructions available in Lojban (and any human idiom) where an event "takes place" in a world other than this one, i.e. doesn't really happen and infact cannot take place, e.g. because of the fact that the opportunity to make it true has already been missed. This aspect most obviously is part of our existing world, often dealt with by "subjunctive constructions" and uttered in many, many exclamations of remorse on passed-up opportunities. - mi'e .aulun.
    • If you resolve the phrase too soon, replacing the phrase with its value, you end up with nonsense. This is something to watch out for! Lojban has no cmavo for indicating when to resolve a phrase quickly and when do so later, so you must use common sense and cooperation. This would prevent the above catastrophe. And use da'i! --xod

la'e di'u ba'e jitfa .i ganai le 1moi bridi cu jitfa gi na djuno fi le jei 2moi bridi .ini'ibo stura le de'u cmalu lojycartu {That is false. If the first bridi is false, we don't know the truth value of the second bridi Actually it says "the truth value of being a second bridi", since it's the structure of the aforementioned small truth table.}

No, we don't know the truth value of the second bridi, but we do know that the entire sentence is true. Both "ganai mi megdo rupnu ponse gi mi ricfu" (If I have a million dollars, I'm rich) and "ganai mi megdo rupnu ponse gi mi pindi" (If I have a million dollars, I'm poor) are true, since I don't have a million dollars.

    • Perhaps we need to look at this from a different angle. In regular arithmetic, division by zero is not allowed, although the notation itself is possible, because that would enable us to prove, among other undesirable things, that any number equals any other number. So, I think the jbojbe may end up using ganai with the understanding (call it logical etiquette) that they are not to use this with a counterfactual clause. (There are, after all, other ways to express those kinds of statements. Which also goes for the other kind of statement that in English uses an "if" and in Lojban cannot as well be handled by ganai --the sort of command or warning: "if you do this, I will do that".)
      • Yes. Absolutely. In fact, the word if has the same thing - it refers to the logical if of ganai, but it is used for counterfactuals because otherwise it would be useless outside of discussions of logic. I propose that we agree to do that before any native speakers bojbe have to even exist. - mi'e. .kreig.daniyl.

ganai do lanli le 2moi lojycartu gi do zgana le du'u da jitfa kei na bapli dida'o

ni'o ma'a sruma le du'u le jufra cu jetnu kei ki'u le du'u cusku le jufra .i sepi'o le jetnu selsruma ma'a lanli le ckini be fa da bei de

ni'o le kamlogji ka'enai jimpe le du'u lu ganai mi ponse le megru'u gi mi pindi li'u cu jitfa .i le kamfatci po'o cu kakne .i ba'o le mu'e sruma tu'a le mulno jufra kei ku joi le du'u krici tu'a pa selxu'a to poi pagbu le mulno jufra toi kei ku lanli fi le ka dida'o poi drata cu jetnu

ni'o le mu'e do galfi zo da zo bu'a kei zo'u mi pu zmanei zo bu'a .i ku'i la xorxes. cu xlura cusku le sedu'u .ei na pilno zo bu'a ki'u le du'u cizra seltarti ti'a zo zo'u

  • It doesn't specify the the relationship between the two bridi. "ganai le tsani cu blanu gi li pa su'i pa du li re" is true in Lojban, though "If the sky is blue, then 1+1=2" sounds silly in English.

la'e di'u na vajni .i ji'a bebna cusku lu li pa su'i pa du li re va'o le du'u le tsani cu blanu li'u .i ja'o le kambebna na sarji zo va'o .i ji'a .i'anai do lacri le kamglico {That isn't important. You can also sillily say "1+1=2 if va'o the sky is blue". Therefore, silliness doesn't support "va'o". Also, you're relying on English.}

Keep in mind also that the sentence is either describing a specific circumstance or a general rule, and it's a fallacy to suddenly switch it. If you mean ganai le tsani ca blanu gi li pa su'i pa ca du li re, then you are making a statement about the state of the world right now -- the sky is blue, and 1+1=2 -- and even rephrasing that with "if" doesn't make it into a general statement. You can make it look like it does when you convert it to English, and convince a lot of people that way, but that doesn't mean it's true.The general statement ganai le tsani ca blanu gi li pa su'i pa ca du li re (you can make that more explicit with a ci'iroiku) is also true only because of the fact that there is no conceivable time when 1+1 will not equal 2. Try reversing the statement, though:

ci'iroiku ganai li pa su'i pa du li re gi le tsani cu blanu (Always, the sky is blue if 1+1=2.) This is not true, because there are in fact times when the sky is black, or gray, or red.

ganai li pa su'i pa ca du li re gi le tsani ca blanu (The sky is currently blue if 1+1 currently equals 2.) This is true if the sky happens to be blue, but it has minimal meaning, because you cannot imply a general statement from this.

Is there any reason to use va'o besides assumptions based on incorrect translations into English?

rab.spir


Sure, you can say that, but the idea is that "va'o", in addition to claiming the relationship about the truth values of the sentences involved like "ganai ... gi ...", also claims that there is a certain relationship between the events described in the sentences themselves (exactly what hasn't been worked out yet, but it involves more that just having truth values that line up in a table.) Thus, I would consider that the entire sentence "li pa su'i pa du li re va'o le nu le tsani cu blanu" (1+1=2 if va'o the sky is blue) is false, since the two sentences have nothing to do with one another, even though both parts are true by themselves. (The translation into English was just an example to show approximately what the problem is. I think that our result in Lojban needs to be much better defined that English.)

1+1=2 if anything. That makes it an extremely bad example for this purpose. That's why above I switched the example around.

.ie ju'o lo'u ganai le'u selsmuni na'ebo le kamkrinu goi ko'a .e le kamselzgana goi ko'e .i ko'e zmadu ko'a le ka ka'e fatci cusku ce'u

.i le fatci ckini be sera'a le 2mei jufra cu selsku le 2moi lojycartu