Moddiy shartli: Nima uchun shartning mavjud emasligi shartni tasdiqlaydi?

So yeah, basically from what i've read, and i've checked multiple sources on this, is that A -> B = ¬A V B.

So to really see where the confusion lies, I'll first state where it doesn't. Where A -> B, then this is saying that if A true, then B is true.

Thus 1 -> 1 is true, since this is just confirming the original statement.

1 -> 0 is false, since than A does not imply B.

Keling, men nimaga erisholmayapman:

A -> B | Truth value
0    0 |     1
0    1 |     1

Haqiqat qiymati B iborasini tasdiqlash yoki soxtalashtirishda yotadigan bo'lsa, unda 1 qiymati "ha" degan ma'noni anglatadi, "B" degan ma'noni anglatadi va 0 "yo'q, A" degan ma'noni anglatmaydi. Endi bu mantiqan aniq ko'rinib tursa, demak, agar A paydo bo'lmasa, bu B ning ma'nosini tasdiqlaydi (yoki ehtimol tasdiqlaydi).

So for instance, if A = I am a qualified chef. B = I can cook well. Then if we let A -> B, then if I am not a qualified chef, then by me being an unqualified chef, this affirms the conditional that since I am a qualified chef, thus I can cook well. But I just said that I am NOT a chef.

Menimcha, A A ning abscessesida, ya'ni B paydo bo'ladimi yoki yo'qmi, lekin biz bilmaymiz. Nima uchun biz faqat shartli qisman haqiqat jadvaliga olib boramiz deb aytmaymiz, unda biz tekshiradigan yagona xulosalar oldingi holat sodir bo'lgan joy.

Demak, B-ning natijasi ham shunga o'xshash, chunki A tufayli A, shuning uchun A-ning sodir bo'lmaganligi sababli A (yoki yo'qligi) natijalari haqida bilishimiz mumkin emas.

Va halol bo'lish uchun nima uchun bu me'yorda ekanini bilmayman. A negizida ishlashning sababi, bu yangi narsani mantiqiy (masalan, o'zimga) aralashtirib yuboradi.

1
Nima uchun nima uchun soxta oldindan tanlangan shartli so'zlar juda to'g'ri ekan?
qo'shib qo'ydi muallif MattH, manba
Vakolatli tarkibida texnik jihatdan (noto'g'ri) ma'no bor
qo'shib qo'ydi muallif MattH, manba
Erm, em emassan. Men bu so'zni "zudlik bilan" ishlatmoqchi emasman, chunki u ba'zi kishilarni bezovta qilishi mumkin. Shuni aytishimga qaramay, albatta, sezgir sezgandek tuyuladi.
qo'shib qo'ydi muallif LooyeD, manba
Ajoyib, siz yuborgan aloqani tekshirib ko'raman, Jozefni xursand qilaman :)
qo'shib qo'ydi muallif LooyeD, manba
@JosephWeissman Ushbu tahrirda savol yana ochiladimi?
qo'shib qo'ydi muallif richard, manba
Buni yozing bilan bog'liq munozarasi uchun.
qo'shib qo'ydi muallif Mauro ALLEGRANZA, manba

3 javoblar

Sizning chalkashliklaringiz tushunarli. Moddiy ahamiyatga ega bo'lgan narsa matematik kontekstlarda va ba'zi bir ilmiy nuqtai nazardan foydali takliflarni taklif qilishda foydalidir, ammo odatdagi oddiy konditsionerlarni ifodalash uchun juda kam foydali bo'ladi. Hatto A va B ning mutlaqo haqiqiy yoki mutlaqo noto'g'ri ekanligi haqida gapiradigan bo'lsak, faqatgina alohida vaziyatda ishlash mumkin. Haqiqiy dunyoda bu haqiqatan ham haqiqat bo'lsa, kamdan-kam hollarda bo'ladi, shuning uchun moddiy tavsif oddiy sharoitlarni yaxshi ifodalamaydi.

As soon as things are uncertain, material implication gives completely the wrong answer to simple questions. Suppose I roll a regular 6-sided die and ask you, what credence do you attach to the conditional, "if it comes up even, it will be a six"? Nearly everyone will say one third. This of course is the value of the conditional probability P( six | even ). By contrast, the probability of the material implication P( even -> six ) is two thirds. The example generalises completely. Pick any typical conditional you like, just choose one where the A and B are not certainly true or false, and you will get the same result: the credence you attach to the conditional is the conditional probability, not the probability of the material implication. This has been tested experimentally in numerous trials conducted by cognitive psychologists: by and large we understand conditionals to mean that it is probably the case that B on the supposition of A. I have to qualify this with "by and large" because conditionals are very messy and unruly and there are many strange uses of them in English.

Ernest Adamsning "Shartli vaziyatlar mantiqiy" va "Ehtimollar mantig'i ustidagi primer" kitoblarida tushunish uchun ushbu yondashuvni kashf etgan. U, bu sizning savolingizga javob beradigan paradoks deb ataladigan paradokslarni qanday tushuntirishga xizmat qilganini, ya'ni "agar A dan keyin B" ni tushuntirishga odatiy emasligini ko'rsatdi. Mening fikrimcha, dastlabki mantiq darsliklari o'quvchilarga cheklovlarni zudlik bilan ogohlantirmasdan, moddiy jihatdan ahamiyatga ega bo'lgan narsalarni keltirib chiqarmoqda.

2
qo'shib qo'ydi

Bu rasmiy ravishda tez-tez duch keladigan odamlar odatda ko'p o'ylaydigan ko'rinadi. "Men cho'chqalar uchib ketganda buni qilaman" kabi iboralarning navbatining orqasida fikr. Biz hammamiz shunday narsalarni darrov anglaymiz, shuning uchun chuqurroq bo'la olmaydi. Bu ibora "men buni qilmayman" degan ma'noni anglatadi, chunki bu to'g'ridan-to'g'ri, agar boradigan bo'lsam, cho'chqalar uchib ketadi va ular yo'q. Lekin, bu so'z haqiqiy bo'lishi mumkin, lekin potentsial yolg'on emas, chunki cho'chqalar aslida uchib ketmaydi.

Klassik matematikada rasmiy ravishda qabul qilinishining sababi, ziddiyatni bartaraf etishga qaratilganligi va u hech qachon noo'rin ziddiyat tug'dirmasligi. Operatorning to'liq aniqlanishi va barcha hollarda tegishli qiymatlarga ega bo'lishi qulay bo'lib, bu holda bu holatda operator xavfsizligini ta'minlaydigan yagona qiymat hisoblanadi.

Boshqa tarafdan, bu ta'rif to'g'ri emas, deb matematikaning aniq versiyalari mavjud. "Intuitisizm" va boshqa "konstruktiv" matematika shakllari, bu algoritmlarni osonlik bilan o'zgartiradigan batafsil va ishonchli dalillarni taklif qilish uchun salbiy foydalanishni keskin cheklab qo'yadi.

Ular o'zlarining nazariyalarida noaniq bo'lgan negativlikning kiritilishida bolmoqdalar. Konstruktiv nuqtai nazardan, biz biror narsani bilolmaymiz, chunki bu to'g'ri emas, chunki bu ikkalasi o'rtasida bir xil turda bo'lishi mumkin. Biz, albatta, bunday deb taxmin qila olmaymiz, chunki u qarama-qarshilikka olib kelmaydi. . Ular bizni qachon qabul qilsak, shubhasiz, muammoga duchor bo'lishimizni isbotlashimizni kutishadi.

Biroq, bu juda qiyin matematik er maydoniga olib keladi. Evrett Bishop dastlabki yil kursini hisob-kitob qilish orqali amalga oshirdi va hamma narsaning konstruktiv tarzda maqbulligini isbotladi. Natijada qariyb besh barobar ko'p, va bularning ko'pi taqiqlangan. Bu matematikaning barcha usullarini bu tarzda amalga oshirishni talab qiladigan ko'pgina odamlar uchun haddan ziyod tuyuladi, lekin buning o'rniga uning ziddiyatlardan xavfsiz bo'lishiga ehtiyoj bor.

0
qo'shib qo'ydi

Buni quyidagi kabi o'ylashga yordam berishi mumkin:

Javob: Men malakali shifokorman

B: Menda katta pichoqlik qobiliyati bor

I pick this example because it's absolutely impossible to be a decent chef, much less a qualified one, if you can't properly use a knife. You'll chop ingredients too slowly, cut yourself (or others) and not know when your knife is dull. I don't like your example because cooking well & being a qualified chef are less distinct from each other than knife skills and how good a chef one is.

Lets say A -> B = ¬A V B, as you did. In the absence of A, it still may be true that B. It's not hard to imagine an assassin or samurai who is an awful chef yet still has amazing knife skills (i.e. ¬A & B). We also know that ¬A & B -> ¬A V B (there's a technical name for this that escapes me).

In my case, where I exhibit both ¬A & ¬B (i.e. I'm both awful with knives and a poor chef) it is still true that A -> B = ¬A V B - it's just that in this case the OR operator is picking out ¬A instead of either one being a possible option. Since ¬A V B is still true, the material conditional itself is also true because of this equality.

Umid qilamanki bu siz uchun narsalarni tozalaydi.

0
qo'shib qo'ydi