What is Logic?

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The term “logic” comes from the Greek word “logos,” which has many translations including word, reason, order, etc. Logic is the philosophical study of correct reasoning, specifically of the rules and methods that distinguish correct reasoning from incorrect reasoning.

In logic, reasoning is the act of drawing a conclusion from given premises, or what is referred to as “inference.” On the other hand, a set of premises together with a conclusion is what is called an “argument.” Logic studies whether the reasoning or inference in an argument is correct or incorrect; meaning, whether the premises support its conclusion or not.

Logic has been studied since antiquity. Early approaches include Aristotelian and Stoic logic in Europe (4th c. BC), Mohism in China (5th c. BC), and Nyaya in India (1st c. AD). In the Western world, Aristotelian logic was considered the main system of logic until it was replaced in the 19th century by modern formal logic, based on the works of George Boole (1815-1864) and Gottlob Frege (1848–1925). Today, the most commonly used system is classical logic, which consists of propositional logic and first-order logic.

Types of Logic

The study of logic includes both formal and informal logic. Traditionally, formal logic is considered the dominant field, with some logicians restricting the study of logic only to formal logic.

A. Formal Logic

Formal logic, as its name suggests, uses a formal approach to studying reasoning. This means that it focuses on the structure—or “form”—of an argument, independent of its topic and content, in order to determine whether it is valid or not. In doing so, it substitutes an argument’s elements with symbols so that it can examine its form more concisely and clearly. Because it uses symbols, formal logic is also called “symbolic logic.”

Some scholars argue that formal logic is concerned only with deductive reasoning; that is, with arguments whose conclusion necessarily follows from its premises; while other scholars include inductive reasoning.

An Example

To better understand how formal logic works, here’s an example. Suppose we have the following argument:

If it rains, then the ground is wet.
It rains.
Therefore, the ground is wet.

This is an example of what is called in logic a “conditional argument.” Here we have three propositions or claims: the first two are called “premises” while the third is called “conclusion.”

To analyze the form of this argument, we can substitute its elements with the following symbols:
  • The antecedent (If it rains) with the small letter “p”
  • The consequent (then the ground is wet) with the small letter “q”
  • The expression “if-then” with “⊃” (a horseshoe symbol)
  • And the expression “therefore” with “∴” (three dots)
We then get the following:

p ⊃ q
q
∴ p

If we apply the logical rule known as “modus ponens” (which states that if the antecedent in a conditional argument [in this case “if it rains”] is true, then its consequent [“then the ground is wet”] is also true), we will see that the argument is valid, meaning that its conclusion logically follows from its premises.

B. Informal Logic

Unlike formal logic, informal logic uses a non-formal—or non-structural—approach to studying reasoning. It was developed in order to address the difficulties in applying formal logic to everyday reasoning, or to what are called “natural language arguments.” As such, it focuses on the soundness and effectiveness of everyday discourse, such as that found in conversations, the internet, advertising, education, and political debates. It deals with issues such as how to identify and evaluate everyday arguments, validity, fallacies, biases, the rhetorical aspects of arguing, etc.

Despite its growing popularity, informal logic is criticized as too context-dependent and subjective. This is because natural language arguments are in themselves context-dependent, and thus are often ambiguous, as people use different ways to communicate, such as facial expressions, gestures, and pictures. 

References

Assadian, Bahram et al.. Introduction to Philosophy: Logic. Edited by Benjamin Martin. Accessed December 21, 2024. https://press.rebus.community/intro-to-phil-logic/.

Groarke, Leo. "Informal Logic." The Stanford Encyclopedia of Philosophy. Last modified July 16, 2021. Accessed December 26, 2024. https://plato.stanford.edu/archives/spr2024/entries/logic-informal/.

Hintikka, J. J.. "Philosophy of Logic." Encyclopedia Britannica. Last modified January 25, 2019. Accessed December 18, 2024. https://www.britannica.com/topic/philosophy-of-logic.

Hughes, G. and Morton Schagrin. “Formal logic.” Encyclopedia Britannica. Last modified November 19, 2024. Accessed December 24, 2024. https://www.britannica.com/topic/formal-logic.

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