Studying Logic: - simple guidelines for Muslim students

Thursday 31 January 2019 Adnaan Raja·

This note is adapted from a series of exchanges I had with a student who agreed to share them for wider benefit.

There seems to be some confusion about the nature of classical Islamic Logic (henceforth IL) and how it relates to the wider and non-religious subject of Logic. While those who fail to understand its true role in Islamic thought disregard it as a relic of the past, many who are not acquainted with more recent developments in Logic believe IL to be the final or at least the most powerful or useful form of Logic. Both sentiments are, quite simply, gross mistakes.

This post will answer 2 key questions:

1. What is Islamic Logic?

2. How should you study Logic?

What is Islamic Logic?

To answer this question, we need to explore the different types of Logic and how they relate to each other. There are many Logics, but the following three are the most prevalent and possibly the most important:

i. Propositional Logic (henceforth PL)

PL treats propositions as whole sentences without concerning about the content or micro bits of the statement. For this reason, it is sometimes referred to as sentential logic. Have a look at these examples:

Khalid is dreaming.

PL will not consider the individual terms of this statement, viz. the subject (Khalid) and the predicate (is dreaming); instead, it will treat it as a single macro, atomic unit. Practically, a statement like this is then represented with a single letter, say P, instead of one letter for the subject and another for the predicate.

PL works by considering the relationships between whole propositions instead of dealing with the relationships between individual units of a given proposition as explained above. These sentence-to-sentence relationships include:

- Disjunction (or)

- Conjunction (and)

- Equivalence (if and only if)

PL is therefore perfectly equipped to work with arguments such as:

If Khalid is dreaming (P) then he is asleep (Q)

Khalid is dreaming (P)

Therefore, he is asleep (Q)

In notation form:P>QPQ

PL can operate these statements because they have an if relationship. However, if we are facing an argument or set of statements which lack these relationships, we will need to resort to a different type of Logic. To use a classical example:

Every human is mortal

Socrates is a human

Therefore, Socrates is a mortal

Each of the statements in this argument lacks the type of relationships that PL deals with: there is no and-relationship, or if-relationship, or any other type for that matter. This is where Categorical Logic comes in.

ii. Categorical Logic (henceforth CL)

Before we proceed, it is this type of Logic which we find in classical Islamic books. In other words, Islamic Logic is essentially CL. Instead of treating statements as atomic or macro units, CL deals with individual terms of a given statement. For this reason, it is sometimes referred to as Term Logic.

Khalid is dreaming is broken into its constituent parts by CL. Additionally, quantifiers are among the additional operators that CL provides in contrast to PL. Now, we can work with propositions such as:

Every human is mortal

Every H is M

∀h (M(h))

iii. Predicate Calculus (henceforth PC)

PC is the combination of PL and CL and is a powerful form of logic which can handle an extensive range of statements and arguments. It is also termed First Order Logic and is the Logic we teach as part of the Critical Thinking in Islam unit at ISNAD Institute. It is more complex than PL and CL and utilities sets and variables to great use.

How should you study Logic?

My advice to Muslims wanting to pursue this wonderful subject is that they start off by studying propositional Logic. The constant use of truth tables, which form the backbone of PL, can be somewhat tedious though. Our mantiq books do not really deal with this so you will have to find an alternative course somewhere. You can skip this step and go straight into studying categorical logic via a classical Islamic text such as Isagoge. Usually, our Islamic mantiq texts have a first chapter about the nature of knowledge (Isagoge is an exception). Such an initial chapter is essentially an introduction to Islamic Epistemology and although not fundamental to the study of Logic, it provides a useful theoretical framework for the Islamic view of Logic.

However, teachers usually keep students bereft of developments in PL which are not found in Islamic texts. A successful course will ensure the accurate use of English equivalents to communicate the concepts from these classical books while also informing learners about more recent developments. For example; instead of simply listing the four types of categorical propositions, the teacher could utilize the square of opposition to explain the relationships between these propositions, include relevant Venn diagrams, and introduce Bertrand Russel’s critique of this specific topic in Logic.

Some traditional books, like Mirqat, also have a chapter on modal logic. However, these chapters tend to be basic and ultimately outdated. Modal logic has been greatly developed since Ibn Sina pioneered it all those centuries ago. Modal logic is especially useful in dialectics as it provides operators to deal with contingency, possibility, etc.Then, a serious student, should really take a course on Predicate Calculus – it was one of the best decisions I ever made in terms of education - and a system of modern Modal Logic such as Kripke Semantics. By following these guidelines, you will be well equipped to not only engage with Islamic texts but also be converse with current trends in Logic.

Beyond this, higher order logics are mostly useful for mathematics and physics and offer little practical use in our study of Islamic disciplines such as Aqida or Fiqh. As for informal logic and informal fallacies; you do not need a course on that. It’s straight forward stuff. Get a good book on it, a cup of tea, and you will master them in no time!

In summary:

Step 1: Propositional Logic/truth tables

Step 2: Categorical Logic/ some epistemology from the Islamic perspective

Step 3: Predicate Calculus/modern Modal Logic (essential for Aqida)

So: our Classical Islamic Logic is not outdated (except for the ML part) yet it is not enough for a serious student of the sacred knowledge given the current climate.

Much more could be said about the joys and scope of logic - but this is all for now!I hope this has shed some light on the matter.

Stay logical.

Adnaan Raja