1. Introduction
1.1. What is Logic?
Logic is the study of rational argumentation. A belief is rational if we have good reason to believe that it is true. Thus, Logic is the business of evaluating arguments, sorting good ones from bad ones. By using rules and methods, logic helps us evaluate whether conclusions follow necessarily from given premises. It is foundational in disciplines like philosophy, mathematics, and computer science, serving as a tool for effective problem-solving.
1.2. Arguments
In everyday speech, we often use the term 'argument' to describe heated, confrontational exchanges. If you and a friend are having this kind of argument, it usually means things aren't going smoothly between you. In logic, we are not concerned with the emotional, combative type of argument. A logical argument is designed to provide reasons that support a particular conclusion. Here's an example of such an argument:
P1: All humans are mortal.
P2: Socrates is a human.
∴ Socrates is mortal.
The three dots on the last line means 'therefore'. It signifies the conclusion of the argument. The other sentences are called premises. If one believes in the premises, then the argument provides one, a good reason to believe in the conclusion. Thus, we can generalise arguments by defining them as a series of sentences. The sentences at the beginning of the argument are called premises and the sentence at the end of the argument is called conclusion. An argument can have one or more such conclusions.
Arguments can be of two types :
1.2.1. Inductive Arguments
Consider the following argument:
P1: Every swan I have observed so far is white.
P2: I have observed swans in multiple locations and seasons.
∴ all swans are probably white.
This is an inductive argument because it generalises from many cases (all swans are white) to a conclusion about all cases.
1.2.2. DEDUCTIVE ARGUMENTS
A deductive argument is one where the conclusion is logically guaranteed to follow from the premises. In other words, if the premises are true, the conclusion must be true as well.
Consider the argument from section 1.1 :
P1: All humans are mortal.
P2: Socrates is a human.
∴ Socrates is mortal.
This is an example of deductive argument, as the conclusion follows logically from the premises. An argument is deductively valid if and only if it is impossible for the premises to be true and the conclusion false. Consider the following ¹argument :
P1: Oranges are either fruits or musical instruments.
P2: Oranges are not fruits.
∴ Oranges are musical instruments.
The conclusion of this argument is absurd, yet it logically follows from the premises. This is a valid argument because, if the premises were true, the conclusion would necessarily be true. This demonstrates that a deductively valid argument does not need to have true premises or a true conclusion.
1.3. Sentences
Sentences in Logic refer to statements that are capable of expressing a truth value, i.e, statements that are either true or false. However, you should not confuse the concept of a sentence being true or false with the distinction between fact and opinion. In logic, sentences often state facts — like 'The sun rises in the east' or 'Milk is white' — but they can also express opinions, such as 'Cakes are tasty'.
1.3.1. What counts as Sentences In LOGIC?
A question like 'Are you sleepy yet?' is considered an interrogative sentence, but it isn't true or false, so it isn't a logical sentence. However, an answer to that question, such as 'I am not sleepy,' is either true or false, making it a logical sentence. Generally, questions are not considered logical sentences, but answers are. Similarly, 'What is this course about?' isn't a sentence in logic, while 'No one knows what this course is about' is.
Commands, often expressed in the form of imperatives like 'Wake up!' or 'Sit up straight', are not true or false, so they aren't considered logical sentences. However, some commands, like 'You will respect my authority', are either true or false, making them logical sentences.
Exclamations like 'Alas!' aren't true or false, either. We treat a phrase like 'Alas! The man is dead' the same as 'The man is dead,' because the 'Alas' doesn't add any truth value.
2. CONCLUSION
To summarize, Logic is the study of rational argumentation to see if their conclusions follow according to their premises. Good and bad arguments are noted by rules and methods. A logical argument has premises and a conclusion, with premises designed to give a reason to believe in the conclusion. There are two kinds of arguments: inductive, generalizing from particular observation to a more general conclusion; and deductive, which is such that the conclusion follows necessarily from its premises. The sentences of logic are propositions, or statements that are capable of being assigned true or false values; that is, they might be a fact or an opinion. Questions, commands and exclamations are not usually treated as logical sentences unless they can somehow be determined to be true or false, such as answers or some types of imperatives.
3. REFERENCES
1.Magnus, P.D., Button, T., Thomas-Bolduc, A., Zach, R., Trueman, R., & Loftis, J.R. (2019). forall x: Calgary: An introduction to formal logic (p. 8). OpenStax.
Introduction to FORMAL logic: Arguments and Sentences