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Introduction to Logic

Introduction

The science of classical logic – known in Arabic as منطق – is a discipline whose principles protect a person from erroneous noesis. The subject matter dealt with in this science is, therefore, known pieces of information in their capacity of leading to unknown pieces of information. And in practice, this amounts to the subject matter of منطق being the construction of definitions and the formulation of proofs.

 

So logic teaches us how to construct a definition and how to formulate a proof in order to protect us against perceptual mistakes. Our purposes here at Learn Arabic Online, however, are not to formally study definitions and proofs; we study logic in order to acquire the terminology used in this discipline as a prerequisite to Arabic rhetoric. This is because rhetoric draws heavily on terminology and concepts fundamental to logic.

Roadmap

The crux of منطق is something called the برهان (proof) which is a specific type of syllogism. Syllogisms, then, are constructed from a series of propositions that entail a consequence. Now, both the propositions and the consequence of a syllogism are expressed as sentences. And sentences are made of words. Hence the roadmap of logic involves the study of words, the amalgamation of words into sentences, the use of sentences as propositions, and arranging propositions to form syllogisms.

 

Definition of Logic

a science whose principles protect us from making perceptual mistakes

How this is achieved

(the subject matter of Logic)

this is achieved by studying definitions and proofs

Ultimate goals

One of the primary purposes of this is to learn the terminology used by logicians since it is used heavily in the science of rhetoric

Our approach

Let’s make The Proof our oasis. Now we need to study syllogisms, which means we need to study propositions, which means we need to study sentences, which means we need to study words. During this process, we will have learned definitions and proofs.


 

An Idea is one of Two Types:
The Concept and the Assent

Having a thought of something in one’s mind is called علم (thought or idea). This thought may be of an isolated concept or of an assent. An isolated concept is simply an idea in which nothing is being claimed, whereas assent is an idea in which there is a copula and something is being claimed.

 

Examples of the former include “president”, “his”, “is”, “Machiavellian”, “in the Whitehouse”, “before Congress”, “his cavalier attitude”, “I wish I was president”, “will the president address Congress today?” And examples of the latter include “the president exposed his Machiavellian leadership,” “his attitude is cavalier.”

 

The former of these is called تصوّر (concept) and the latter is termed تصديق (assent). Notice that this starkly mirrors the concepts of utterance, words, phrases, and sentences as learned in the science of grammar. There is a fundamental difference, though; the concepts of علم, تصور and تصديق are at a mental level. These are things that are conceived in the mind before they are realized tangibly. Once علم (thought) occurs in a person’s mind, it may then go on to be realized as utterance by the mouth, at which point grammar would discuss it. Once تصور (concept) occurs in the mind, it may then go on to be realized as words, phrases, and non-informative sentences, at which point grammar would discuss it. And once تصديق (assent) occurs in the mind, it may then go on to be realized as informative sentences, at which point, again, grammar would discuss it. Moreover, it is not the case that علم, تصور and تصديق will always be realized as speech from the mouth. They may very well be realized through other means such as sign language, or they may never be realized at all.

 

علم
(thought or idea)

تصديق
(assent – an idea which contains a copula meaning that something is being claimed)

تصور
(concept – an idea which does not contain a copula and so nothing is being claimed)

 


 

Both Types of Idea can be either
Conspicuous or Inconspicuous

An inconspicuous idea is one that does not need to be explained and it is understood without thought. One can say that it is obvious. Examples of inconspicuous concepts include our perception of hot and cold, for these are concepts that do not need to be defined. And examples of inconspicuous assent include the notion that the sky is above us, for this is axiomatic and does not need to be proven.

 

A conspicuous idea, on the other hand, is one that does need explanation. Examples of conspicuous concepts include the concept of angels, for this may not be understood by everyone and would need to be defined. Similarly, examples of conspicuous assent include the notion that the universe is finite, for again, not everyone would vie for this and so this assent would need to be proven.

 

Inconspicuous, in Arabic, is called بديهي and conspicuous is known as نظري. Notice how the notion of conspicuous ideas leads to the primary themes of logic. In the case of concept-based ideas, we study definitions, and in the case of assentive ideas, we study proofs.

 

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)

 

Tangibly Realizing Ideas:
Six Methods

Recall that ideas, concepts, and assent are at a mental level. But in order to study these things further, we need a medium through which we can realize them. Whether we use sign language, spoken word, or any other means, we will need some medium throughout the rest of our studies. Therefore, we now define the six mediums through which ideas can be realized and choose the most effective one.

 

The realization of an idea, in Arabic, is termed دلالة (indication) and is formally defined as: for something to be in a manner such that conception of it results in conception of something else. For example, the idea of president is علم of the type تصور while it is at a mental level. One of the ways we can realize this idea is to use spoken word and utter the word “president”. There are now two presidents: one at the mental level and one which is the spoken word. The spoken word is in a manner such that it indicates on the president which is at the mental level. This indication is an example of دلالة.

 

Now, realization can be done in one of two main ways, each of which is then split into three.

 

·         either the indication is spoken (دلالة لفظية)

1.       The indication is achieved thanks to coinage. For example, the name “Zaid” when spoken indicates on the individual so named. This is thanks to a naming (or coining) process where the boy Zaid was named “Zaid”. (دلالة لفظية وضعية)

2.       The indication is achieved thanks to natural understanding. For example, when a person coughs and creates noise in his throat from doing such, this indicates on the fact that he is in physical distress. This indication is thanks to natural understanding. (دلالة لفظية طبعية)

3.       The indication is achieved thanks to reason. For example, when someone in an adjacent room makes an incoherent noise, because of hearing that noise we are able to reason that a human being is situated in that room. (دلالة لفظية عقلية)

·         or it is non-spoken (دلالة غير لفظية)

4.       The indication is achieved thanks to coinage. For example, a red hexagon indicates on stopping because this has been coined to mean such. (دلالة غير لفظية وضعية)

5.       The indication is achieved thanks to natural understanding. For example, when a dog shows its teeth and stands upright, this indicates on danger thanks to an innate understanding we have. (دلالة غير لفظية طبعية)

6.       The indication is achieved thanks to reason. For example, when we see smoke rising, we can assume that there is fire, and this is due to reason and rationale. (دلالة غير لفظية عقلية)

 

The method of choice, as one may have guessed, is to use coined words (option 1) in order to realize the ideas in the mind. In other words, we will be using regular, spoken language.

 

Aside: Actually, here at Learn Arabic Online, we will be using Option 4. This is because we use written words to indicate on the ideas in the mind, not spoken word, due to the medium of interaction.

 

The Spoken Speech and
What It Indicates

The spoken speech is called the دال (the indicating speech; the tangible realization like the word “president”) and the idea which it represents is known as the مدلول (the indicated idea at the mental level like the idea of president). Subsequent discussions on logic will be with respect to the دال to some extent, and to the مدلول primarily. This will lead into further discussions and eventually into definitions and proofs.

 

1.       Introduction to Classical Logic – introducing the themes of concept and assent and how conspicuous concepts require the study of definitions and how conspicuous assents require the study of proofs

2.       Indication – concepts and assents are at a mental level, but we need to express them using words; this tutorial introduces the idea of simple indication used to indicate on concepts in the mind, and compound indication used to indicate of assent in the mind

3.       Definitions

a.       Simple Indication – moving into the definitions aspect of Logic, this tutorial discusses the simple indication which is used to indicate on concepts in the mind

b.      Indicated Concept – and this tutorial discusses the actual mental concepts themselves

c.       Definitions – putting the simple indication and the indicated concept together culminates in the theory of forming definitions

4.        Proofs

a.       Compound Indication – moving into the proofs aspect of Logic, this tutorial discusses the compound indication which is used to indicate on assent in the mind

b.      Indicated Assent and Modern Logic – and these tutorials discuss the actual mental assent itself

c.       Proofs – putting the compound indication and the indicated assent together culminates in the theory of formulating proofs; a summary of the terminology in this section of Logic has been left to the reader

5.       Logic Reference – a terse set of charts and diagrams as a summary of all Logic related tutorials

 



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