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Logic Reference

What is this Tutorial About?

This is a reference for all concepts studied in Classical Logic at LearnArabicOnline.com. Here we present brief summaries of the various discussions as well as the charts from the various logic tutorials . Charts that were left incomplete in their respective tutorials out of simplicity are now completed.

The Science of Logic

Definition

a science whose principles protect one from making mental mistakes

Subject Matter

this is achieved by studying definitions and proofs

Holy Grail

complete command of a type of proof known as the برهان

Need

a primary but small subset of knowledge comes from senses and experience, then the principles of logic are required to induce further knowledge

Status

one of the central sciences in Islamic and Greek academia whose principles are seen extensively even in the Koran

Other Designations

The Tool (because it is a ubiquitous tool used to judge between valid and invalid thought processes), The Scale

Pioneers

Aristotle, Farabi, Avicenna

 

Things that exist

and some that don’t

 

Their representations

in our mind

 

Our expression of these representations

 

 

 

 

علم (مدلول)

-دلالة-

دال

 

 

Semiosis (دلالة)

Types of Semiosis

 

دلالة التزامية
(entailed indication)

دلالة تضمنية
(component indication)

دلالة مطابقية
(congruent indication)

 

the word “Washington” indicating on the president
(who is associated to the city)

the word “Washington” indicating on the Whitehouse
(which is part of the city)

the word “Washington” indicates on the city thanks to a naming process

دلالة لفظية وضعية
(verbal, coinage)

A person’s cough naturally indicates on distress

دلالة لفظية طبعية
(verbal, natural)

Someone’s senseless noise in an adjacent room

rationally indicates their presence therein

دلالة لفظية عقلية
(verbal, reason)

A red hexagon indicates on stopping by coinage

دلالة غير لفظية وضعية
(non-verbal, coinage)

A dog’s showing his teeth naturally indicates on danger

دلالة غير لفظية طبعية
(non-verbal, natural)

Seeing smoke rationally indicates on fire

دلالة غير لفظية عقلية
(non-verbal, reason)

 

Types of Thought

علم (مدلول)
(thought)

 

تصديق
(assent)

تصور
(concept)

 

immediately accepted claims

(logic does not deal with these)

obviously understood concepts

(logic does not deal with these)

بديهي
(inconspicuous)

claims that need to be proven

(logic deals with these)

concepts that need to be defined

(logic deals with these)

نظري
(conspicuous)

 


 

The Indicating Coined Speech (دال) for Concepts

مفرد
(simple speech)

 

متكثر المعنى
(many meanings)

متوحد المعنى
(single meaning)

 

كلي غير مشترك
(single coinage, separate usages)

كلي مشترك
(separate coinages)

كلي
(indefinite)

جزئي حقيقي
(definite)

 

منقول
(transferred)

حقيقة/مجاز

(literal / figurative)

 

كلي مشكك
(anisometric)

كلي متواطي
(isometric)

 

 


 

The Indicated Idea (مدلول) for Concepts

Division by Universality

مدلول
(the indicated concept)

كلي
(universal – the concept whose conceptualization allows reference to multiple entities)

جزئي
(particular – the concept whose conceptualization allows reference to only one specific entity)

عرضي
(non-constitutive – universals that are accidental)

ذاتي مقوم
(constitutive – universals that help make a thing what it is)

خاصة
(unique)

عرض عام
(non-unique)

فصل
(differentia)

نوع
(species)

جنس
(genus)

 

 

عرض عام
(not unique)

خاصة
(unique)

 

Being Born is not unique to Human but necessary and inseparable for it

Being More/Less Rational Than Another  Human is unique to Human and cannot be taken away from Humans

لازم
(concomitant)

Walking is not unique to Human and it can be taken away (e.g. by injury)

Bipedal is unique to Human but it can be taken away (e.g. by injury)

مفارق
(separable)

 

Relationship Between Universals

 

Definitions

قول شارح
(explanation of a universal)

تعريف حقيقي
(using actual explanation)

تعريف لفظي
(using synonymy)

رسم ناقص
(distant or not genus + accident)

رسم تام
(closest genus but unique qualities)

حد ناقص
(distant or no genus)

حد تام
(closest genus, all differentiae)

 

 


 

The Indicating Coined Speech (دال) for Assents

اللفظ الدال
(the indicating speech)

مركب
(compound – that whose parts indicate on parts of the meaning)

مفرد
(simple – that whose parts don’t indicate on parts of the meaning)

مركب ناقص
(phrase)

مركب تام
(sentence)

...
(...)

 

إنشاء
(non-informative)

قضية
(informative)

 

 

Categorized Based on Equation

قضية حملية
(atomic clause)

حمل بالاشتقاق
(non-equation)

حمل بالمواطاة
(equation)

 

Categorized Based on the Subject

قضية حملية
(atomic clause)

قضية كلية
(general)

.

قضية شخصية
(singular)

Zaid is eating

.
(quantified)

.

كلية طبعية
(non-quantified)

men eat

 

قضية محصورة
(explicitly quantified)

.

قضية مهملة
(esoterically quantified)

the men are eating

 

 

موجبة جزئية
(affirmative existential)

some of the men are eating

موجبة كلية
(affirmative universal)

all of the men are eating

سالبة جزئية
(negative existential)

some of the men are not eating

سالبة كلية
(negative universal)

all of the men are not eating

 

 

 

 

Categorized Based on Affirmation & Negation

قضية حملية
(atomic clause)

غير معدولة
(not internally negated)

معدولة
(internally negated)

بسيطة
(negative statement)

محصلة
(affirmative statement)

·         affirmative, affirmative subject, negative predicate

·         affirmative, negative subject, affirmative predicate

·         affirmative, negative subject, negative predicate

·         negative, affirmative subject, negative predicate

·         negative, negative subject, affirmative predicate

·         negative, negative subject, negative predicate

 

Categorized Based on Modality

قضية حملية
(atomic clause)

غير موجهة
(un-moderated)

موجهة
(moderated)

 

Simple Modalities


Explanation

Arabic Term

possible (because the opposite is not necessary)

الممكنة العامة

 

during the time that the inherent attribute holds

الحينية الممكنة

Necessary

الضرورية

 

unconditionally

الضرورية المطلقة

 

so long as the subject exists

 

so long as the subject is attributed with the intrinsic quality it bears

المشروطة العامة

 

during the inherently understood timeframe

الوقتية المطلقة

 

during some unspecified timeframe

المنتشرة المطلقة

 

in actual fact and not just potentially

المطلقة العامة

 

in actual fact and not just potentially, while the inherent attribute holds

الحينية المطلقة

Not necessary, but coincidentally perpetual

الدائمة

 

unconditionally

الدائمة المطلقة

 

so long as the subject is attributed with the non-intrinsic quality it bears

العرفية العامة

 

Compound Modalities


Explanation

Arabic Term

necessarily so long as the subject is attributed with the intrinsic quality it bears, but not perpetually

المشروطة الخاصة

perpetually so long as the subject is attributed with the non-intrinsic quality it bears, but not perpetually otherwise

العرفية الخاصة

in actual fact and not just potentially, but not out of necessity

الوجودية اللاضرورية

necessarily in actual fact and not just potentially, but not perpetually

الوجودية اللادائمة

necessarily during the inherently understood timeframe, but not perpetually

الوقتية

necessarily during some unspecified timeframe, but not perpetually

المنتشرة

possible (because both it and its opposite are not necessary)

الممكنة الخاصة

 


 

The Indicated Idea (مدلول) for Assents

Contradiction

Original

Contradictory

universal

existential

 

Original

Contradictory

الضرورية المطلقة

الممكنة العامة

الدائمة المطلقة

المطلقة العامة

المشروطة العامة

الحينية الممكنة

العرفية العامة

الحينية المطلقة

 

Inverse

Original

Inverse

Quantifier

Affirmativeness

Modality

Universal

Affirmative

الممكنة

 

الضرورية المطلقة

Existential Affirmative حينية مطلقة

المشروطة العامة

Existential Affirmative حينية مطلقة

الوقتية المطلقة

 

المنتشرة المطلقة

 

الدائمة المطلقة

Existential Affirmative حينية مطلقة

العرفية العامة

Existential Affirmative حينية مطلقة

Negative

 

الممكنة

 

الضرورية المطلقة

Universal Negative الدائمة المطلقة

المشروطة العامة

Universal Negative العرفية العامة

الوقتية المطلقة

 

المنتشرة المطلقة

 

الدائمة المطلقة

Universal Negative الدائمة المطلقة

العرفية العامة

Universal Negative العرفية العامة

Existential

Affirmative

الممكنة

 

الضرورية المطلقة

 

المشروطة العامة

 

الوقتية المطلقة

Existential Affirmative مطلقة عامة

المنتشرة المطلقة

 

الدائمة المطلقة

 

العرفية العامة

 

 


 

Proofs

حجة
(Proof or pseudo-proof)

قياس ج. أقيِسة
(Deduction)

استقراء
(Induction)

تمثيل
(Generalization)

 

 

دوران
(through a shared meaning)

سبر
(through a shared attribute)

 

قياس
(Deduction)

 

برهاني

premises are axioms or already proven theorems

 

 

جدلي

premises are widely accepted to be true, or accepted for the sake of the argument

 

 

خَطابي

premises are accepted to be true because they come from a trusted authority

 

 

شعري

premises are based on axioms that have been well-convinced

 

 

سفسفطي

premises are plausible but deceptive axioms

 

Syllogisms

 

If

And

Then

الشكل الاول

All of A is B

All of B is C

All of A is C

All of A is B

None of B is C

None of A is C

Some of A is B

All of B is C

Some of A is C

Some of A is B

None of B is C

Some of A is not C

الشكل الثاني

All of A is B

None of C is B

None of A is C

None of A is B

All of C is B

None of A is C

Some of A is B

None of C is B

Some of A is not C

Some of A is not B

All of C is B

Some of A is not C

الشكل الثالث

All of B is A

Some of B is C

Some of A is C

All of B is A

None of B is C

Some of A is not C

Some of B is A

All of B is C

Some of A is C

Some of B is A

None of B is C

Some of A is not C

All of B is A

Some of B is not C

Some of A is not C

الشكل الرابع

All of B is A

Some of C is B

Some of A is C

...

 

 

 



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