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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	الضرورية المطلقة
	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	Inverse
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
الشكل الرابع	…

Proceed to the next lesson: Proof by Contradiction

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