Re: [lojban-beginners] ganai-gi and if-then

[Ian Johnson <blindbravado@gmail.com>]

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

On Tue, Feb 3, 2015 at 3:00 AM, Pierre Abbat <phma@bezitopo.org> wrote:

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

--
You received this message because you are subscribed to the Google Groups "Lojban Beginners" group.
To unsubscribe from this group and stop receiving emails from it, send an email to lojban-beginners+unsubscribe@googlegroups.com.
To post to this group, send email to lojban-beginners@googlegroups.com.
Visit this group at http://groups.google.com/group/lojban-beginners.
For more options, visit https://groups.google.com/d/optout.

-- 
You received this message because you are subscribed to the Google Groups "Lojban Beginners" group.
To unsubscribe from this group and stop receiving emails from it, send an email to lojban-beginners+unsubscribe@googlegroups.com.
To post to this group, send email to lojban-beginners@googlegroups.com.
Visit this group at http://groups.google.com/group/lojban-beginners.
For more options, visit https://groups.google.com/d/optout.