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[2607:f8b0:400d:c00::230]) by gmr-mx.google.com with ESMTPS id s10si477446qcl.3.2015.02.03.10.21.08 for (version=TLSv1 cipher=ECDHE-RSA-RC4-SHA bits=128/128); Tue, 03 Feb 2015 10:21:08 -0800 (PST) Received-SPF: pass (google.com: domain of blindbravado@gmail.com designates 2607:f8b0:400d:c00::230 as permitted sender) client-ip=2607:f8b0:400d:c00::230; Received: by mail-qa0-x230.google.com with SMTP id v8so34920793qal.7 for ; Tue, 03 Feb 2015 10:21:08 -0800 (PST) MIME-Version: 1.0 X-Received: by 10.140.95.179 with SMTP id i48mr51825250qge.4.1422987668758; Tue, 03 Feb 2015 10:21:08 -0800 (PST) Received: by 10.140.92.213 with HTTP; Tue, 3 Feb 2015 10:21:08 -0800 (PST) In-Reply-To: <2856335.3Zhz41LSmU@caracal> References: <555b3462-f947-42b0-8dc8-00782f128988@googlegroups.com> <2856335.3Zhz41LSmU@caracal> Date: Tue, 3 Feb 2015 13:21:08 -0500 Message-ID: Subject: Re: [lojban-beginners] ganai-gi and if-then From: Ian Johnson To: lojban-beginners@googlegroups.com Content-Type: multipart/alternative; boundary=001a11c16dfc842637050e332287 X-Original-Sender: blindbravado@gmail.com X-Original-Authentication-Results: gmr-mx.google.com; spf=pass (google.com: domain of blindbravado@gmail.com designates 2607:f8b0:400d:c00::230 as permitted sender) smtp.mail=blindbravado@gmail.com; dkim=pass header.i=@gmail.com; dmarc=pass (p=NONE dis=NONE) header.from=gmail.com Reply-To: lojban-beginners@googlegroups.com Precedence: list Mailing-list: list lojban-beginners@googlegroups.com; contact lojban-beginners+owners@googlegroups.com List-ID: X-Google-Group-Id: 300742228892 List-Post: , List-Help: , List-Archive: , List-Unsubscribe: , X-Spam-Score: 0.8 (/) X-Spam_score: 0.8 X-Spam_score_int: 8 X-Spam_bar: / X-Spam-Report: Spam detection software, running on the system "stodi.digitalkingdom.org", has NOT identified this incoming email as spam. The original message has been attached to this so you can view it or label similar future email. If you have any questions, see @@CONTACT_ADDRESS@@ for details. Content preview: 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 [...] Content analysis details: (0.8 points, 5.0 required) pts rule name description ---- ---------------------- -------------------------------------------------- 0.0 URIBL_BLOCKED ADMINISTRATOR NOTICE: The query to URIBL was blocked. See http://wiki.apache.org/spamassassin/DnsBlocklists#dnsbl-block for more information. [URIs: googlegroups.com] 2.7 DNS_FROM_AHBL_RHSBL RBL: Envelope sender listed in dnsbl.ahbl.org [listed in googlegroups.com.rhsbl.ahbl.org. IN] [A] 0.0 T_HEADER_FROM_DIFFERENT_DOMAINS From and EnvelopeFrom 2nd level mail domains are different -0.0 SPF_PASS SPF: sender matches SPF record 0.0 FREEMAIL_FROM Sender email is commonly abused enduser mail provider (blindbravado[at]gmail.com) 0.0 DKIM_ADSP_CUSTOM_MED No valid author signature, adsp_override is CUSTOM_MED -0.0 RCVD_IN_MSPIKE_H3 RBL: Good reputation (+3) [209.85.213.186 listed in wl.mailspike.net] 0.0 HTML_MESSAGE BODY: HTML included in message -1.9 BAYES_00 BODY: Bayes spam probability is 0 to 1% [score: 0.0000] -0.1 DKIM_VALID Message has at least one valid DKIM or DK signature 0.1 DKIM_SIGNED Message has a DKIM or DK signature, not necessarily valid 0.0 T_FREEMAIL_FORGED_FROMDOMAIN 2nd level domains in From and EnvelopeFrom freemail headers are different -0.0 RCVD_IN_MSPIKE_WL Mailspike good senders Content-Length: 9251 --001a11c16dfc842637050e332287 Content-Type: text/plain; charset=UTF-8 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 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. --001a11c16dfc842637050e332287 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
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 l= ogic. We want our rule for

p =3D> q

for= propositions p and q, to have the right meaning when we extend it to
<= br>
for all x, p(x) =3D> q(x)

for predicates p and q. So her= e's my attempt at explaining why that should be "for all x, p(x) o= r ~(q(x))".

The statement should mean "if x satisfies p, t= hen x satisfies q, no matter what x is". For example, "for any da= y d, if it is raining on d, then it is cloudy on d." This statement sh= ould be false exactly when there is an x which satisfies p and does not sat= isfy q. In the preceding example, this would be a day on which it is rainin= g 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) =3D> q= (x)" should be "for all x, ~(p(x)) or q(x)". In classical lo= gic a proposition is either true or false, which means that the double nega= tion of a statement must be equivalent to the statement. So "=3D>&q= uot; should be "ganai gi". In other logics such as intuitionistic= logic, the double negation is generally *weaker* than the original stateme= nt. This may reflect why you are having difficulties: human "if ... th= en" 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
<= /div>

On Tue, Feb = 3, 2015 at 3:00 AM, Pierre Abbat <phma@bezitopo.org> wrote:<= br>
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 result= ing 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
>=C2=A0 =C2=A0 =C2=A0 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 sec= ond
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 &= quot;Lojban Beginners" group.
To unsubscribe from this group and stop receiving emails from it, send an e= mail to = lojban-beginners+unsubscribe@googlegroups.com.
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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 &= quot;Lojban Beginners" group.
To unsubscribe from this group and stop receiving emails from it, send an e= mail to lo= jban-beginners+unsubscribe@googlegroups.com.
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Visit this group at http://groups.google.com/group/lojban-beginners.
For more options, visit http= s://groups.google.com/d/optout.
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