ganai-gi and if-then

[ravas]

first second result
True  True   True
True  False  True
False True   True
False False  False

...

Perhaps the most important of the truth functions commonly expressed in forethought is TFTT, which can be paraphrased as “if ... then ... ”
...

8.3)   ro da zo'u ganai da klama le zarci gi cadzu le foldi
       For-every X: if X is-a-goer-to the store then X is-a-walker-on the field.

----

Why is ganai-gi (TFTT) the preferred gek-gik structure for "if...then..."?
Given my limited understanding of "truth functions" it seems like ge-gi (TFFF) is clearer.
Isn't the first row the only thing we want to result in True?

Something else I don't understand:
"Since GA cmavo precede the first bridi, a following “nai” negates the first bridi instead."

Why are we negating anything?
Aren't we trying to assert both bridi are true?

[ravas]

Note that the truth table at the top of my last email was copied from http://lojban.github.io/cll/14/1/
and I didn't change it from TTTF.

[Michael Turniansky]

  No.  You are making a common mistake of confusing the English "if" with the logician's if.  When we are not talking about one thing depending on another ("if I get my car fixed, then we can go to the movies"), but rather logical implication (two statements that relate in their truth value) ("if it is raining, then the ground is wet").  Is that statement true if the ground is wet from a sprinkler, but yet it is sunny?,   Yes, because we are only told what happens if it is rainy.  But if it is NOT rainy, we aren't making any conclusion about the wetness of the ground, so the combined statement is still true.  The only time it can be false if the hypothesis ("it is sunny") is true, but the conclusion ("the ground is wet") is false.

  (read articles about implication for more details)

          --gejyspa

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[Michael Turniansky]

  Sorry, that penultimate parenthetical should have read ("it is rainy") obviously

[Stela Selckiku]

You're not alone if you feel confused by logical conjunctions. If by any chance there's some sort of Sapir-Whorfian benefit to learning the logic logical parts of Lojban, then that strange disorienting presently unpleasant feeling is actually the feeling of you being Sapir-Whorfed by grokking deeply how to logically conjunct things. I don't know either if that's true but it's reassuring to think anyway while you're being overwhelmed by it.

The "A" and/or conjunction affirms three cases and denies only one. So I find it's marginally less confusing to consider it in terms of the single case that it denies, just because then we're thinking about one thing instead of three. So with {ga B gi C} there's three affirmed cases, that it's just B, just C, or both B and C. Which is simple enough if nothing's negated. ;) But let's just think about the remaining case, the one case denied: It is NOT the case that neither B nor C. The only case that doesn't happen is that neither side is true.

OK so keep thinking about just that one negative case, and look at {ganai B gi C}-- the only case that doesn't happen is when neither side is true, that is, when NOT not B (that is, B) and also not C. Confusing as mabla, but at least it's one thing to think about instead of three. One case is denied: That B happens, but C doesn't. It doesn't happen that B happens but C doesn't happen. In every case where B happens, C happens. It's not being asserted the other way around, we're not saying C implies B-- that's one of the three affirmed cases, is when C, but not B. The only case denied is the case where B happens but C does not.

Mostly you don't need to say that. Mostly you're not trying to logically associate events in the world. You're just trying to talk about hypothetical causation. {lo nu broda cu jalge da'i lo nu brode} Theoretically, an event of broda would result from an event of brode. You can say that with only slightly more vagueness and fairly concisely as {brode ja'e da'i lo nu broda} which is the sort of construction I usually speak in myself. If you're just interested in expressing the relationships between hypothetical events, and you don't care at the moment about expressing a particular logical relationship, that's the set of tools you want. It's slightly confusing because it's in two parts: One part shows the relationship between the events (the causal brivla and their abbreviations) and the other part, {da'i}, just throws it into the hypothetical. But I'm sure you'll agree it's still less alien than logically connecting things. ;)

As far as understanding {ganai .. gi ..} in the wild, frankly you'll get farthest just reading it as "if .. then .." because people (mis)learned to (mis)use it that way. Do your best to get it right yourself, but just read it that way unless someone asks you to correct their Lojban. :D

mu'omi'e la stela selckiku

[ravas]

On Monday, February 2, 2015 at 8:11:23 PM UTC-8, Michael Turniansky wrote:

  No.  You are making a common mistake of confusing the English "if" with the logician's if.  When we are not talking about one thing depending on another ("if I get my car fixed, then we can go to the movies"), but rather logical implication (two statements that relate in their truth value) ("if it is raining, then the ground is wet").  Is that statement true if the ground is wet from a sprinkler, but yet it is sunny?,   Yes, because we are only told what happens if it is rainy.  But if it is NOT rainy, we aren't making any conclusion about the wetness of the ground, so the combined statement is still true.  The only time it can be false if the hypothesis ("it is sunny") is true, but the conclusion ("the ground is wet") is false.

In the example I provided, why is ganai-gi (TFTT) preferred over ge-gi (TFFF)?
I don't understand how the last two rows of the truth table resulting in True is useful to the statement.
Can the example be translated the same way if we replace ganai with ge?
If not: why not, and what changes?

[ravas]

On Monday, February 2, 2015 at 9:55:37 PM UTC-8, la stela selckiku wrote:

{lo nu broda cu jalge da'i lo nu brode}

{brode ja'e da'i lo nu broda}

i'o do pu jarco

[Pierre Abbat]

On Monday, February 02, 2015 22:59:59 ravas wrote:
> In the example I provided, why is ganai-gi (TFTT) preferred over ge-gi
> (TFFF)?
> I don't understand how the last two rows of the truth table resulting in
> True is useful to the statement.
> Can the example be translated the same way if we replace ganai with ge?
> If not: why not, and what changes?
>
> 8.3) ro da zo'u ganai da klama le zarci gi cadzu le foldi
> For-every X: if X is-a-goer-to the store then X is-a-walker-on the
> field.

That should be "... gi da cadzu le foldi", right?

ro da zo'u ganai da klama le zarci gi da cadzu le foldi
Everyone doesn't go to the store or does walk on the field.
Everyone, if he goes to the store, walks on the field.

ro da zo'u ge da klama le zarci gi da cadzu le foldi
Everyone goes to the store and walks on the field.

The first sentence can be true; the store can be surrounded by the field in such
a way that the only way to go to the store is to walk on the field. The second
is clearly false, as there are people who live their entire lives without
going to any store.

Pierre
--
sei do'anai mi'a djuno puze'e noroi nalselganse srera

[Ian Johnson]

Part of the reason why ganai gi is the preferred truth function for implications is actually because it works better in *predicate* logic, not propositional logic. We want our rule for

p => q

for propositions p and q, to have the right meaning when we extend it to

for all x, p(x) => q(x)

for predicates p and q. So here's my attempt at explaining why that should be "for all x, p(x) or ~(q(x))".

The statement should mean "if x satisfies p, then x satisfies q, no matter what x is". For example, "for any day d, if it is raining on d, then it is cloudy on d." This statement should be false exactly when there is an x which satisfies p and does not satisfy q. In the preceding example, this would be a day on which it is raining but somehow not cloudy.

This means that the negation of the statement should be

there exists x such that p(x) and ~(q(x)).

The negation of that is

for all x, ~(p(x)) or q(x)

So the double negation of "for all x, p(x) => q(x)" should be "for all x, ~(p(x)) or q(x)". In classical logic a proposition is either true or false, which means that the double negation of a statement must be equivalent to the statement. So "=>" should be "ganai gi". In other logics such as intuitionistic logic, the double negation is generally *weaker* than the original statement. This may reflect why you are having difficulties: human "if ... then" is usually *stronger* than "ganai gi", since it usually implies a causal relationship. For such issues we have words like {rinka}, {nibli}, etc. in Lojban.

mi'e la latro'a mu'o

[ravas]

On Tuesday, February 3, 2015 at 12:00:09 AM UTC-8, Pierre Abbat wrote:

That should be "... gi da cadzu le foldi", right?

lo nu mi na viska zo da ku spaji mi
http://lojban.github.io/cll/16/8/

.i do pu dudna lo xance pe'a .i'o

[ravas]

ki'e latro'a.

.i u'i la'a mi ca jimpe