Logic a very important study in philosophy, as it allows us to assess the truth about the hard questions in life (What is reality? Why are we here? Where did we come from? etc.) along with any other topic to which any kind of observed information is given. Logic is the foundation of reasoning for all fields of science and is what gave birth to the scientific method.
And it is the only way to assess the validity of what’s called an argument. But to answer the question “What is a logical argument?” we would first have to examine what it means to say “logical” and apply that to what an argument is. Hopefully, this will shed some light for you on the matter (and help you finish whatever philosophy homework assignment you may have if you’re here for that).
As redundant as this sounds, a logical argument can simply be defined as an argument that is logical. Yeah, I know that doesn’t help much, but let’s first try to put this into perspective. “Logical” is the adjective form of the word “logic.”
Logic is basically a systematic approach one must take to reach a reasonable conclusion for an argument.
An argument is a claim or a declaration one makes based on any observed evidence of it.
The two are closely connected, but not interchangeable. An argument can be made without following the proper system of logic. (It would be invalid, but still an argument nonetheless.)
In order to figure out if an argument is logical or not, we first need to understand how logic works.
Rules of Logic
Logic consists of two main forms: formal and informal.
Informal logic is a set of rules used to identify what’s called a premise, a prior statement from which a conclusion is drawn. Informal logic uses something called inductive reasoning to form a premise. Inductive reasoning is a method used to draw a conclusion (later used a premise) based on specific observations, which are usually generalized. For example:
- All fire trucks I see are red. [Observation]
- All fire trucks everyone else sees are red. [Observation]
- ∴ All fire trucks must be red. [Premise]
Premises are either observations or assumptions used as evidence to draw a conclusion for the overall argument. This is called deductive reasoning, which is the method of reasoning used in formal logic.
Once two premises are obtained from inductive reasoning, they can be connected sensibly via deductive reasoning by what’s known as an inference. From that inference, a conclusion can be made and the argument is complete. This 3-step argument (premise, premise, conclusion) is known as a syllogism.
(NOTE: The “∴” symbol means “therefore.”)
- Red is my favorite color. [Premise]
- All fire trucks are red. [Premise]
- ∴ All fire trucks are my favorite color. [Conclusion]
A syllogism requires two different kinds of premises: a major premise and a minor premise. The major premise has the predicate of the conclusion in it. The minor premise has the subject of the conclusion. Both premises share a common middle term that gets omitted in the conclusion.
In the example above, “Red is my favorite color” is the major premise, since “[is] my favorite color” appears in the conclusion. “All fire trucks are red” would then be the minor premise, since “all fire trucks” is the subject of the conclusion. “Red” is the middle term that was omitted.
There are many different types of syllogisms used in logic. For now, I’ll just go over the basic kinds: categorical, conditional, and disjunctive.
A categorical syllogism is an inference method that follows this formula:
“All P’s are Q’s. R is P. Therefore, R is Q.”
The major premise, “All P’s are Q’s,” is a general statement in which “P” applies to an entire set of “Q.” The minor premise, “R is P,” refers to something specific about the “P” set or a specific member of that set. “P” is the middle term that is omitted. It works much like the transitive property in math.
- All cars are vehicles. [Premise]
- A Toyota Corolla is a car. [Premise]
- ∴ A Toyota Corolla is a vehicle. [Cat. Syll. 1, 2]
A conditional syllogism is an “if, then” argument that attempts to either validate or reject a statement with some kind of condition, “If P, then Q,” where “P” is a condition that must be satisfied in order for “Q” to be correct. One of two inference methods may be used to draw a conclusion from a conditional syllogism: modus ponens and modus tollens.
A modus ponens refers to the method which validates the consequence “Q” by confirming the condition “P.”
“If P, then Q. P is true. Therefore, Q is true.”
- If the sun is at its highest point in the sky, then it is noon. [Premise]
- The sun is at its highest point in the sky. [Premise]
- ∴ It is noon. [Modes Ponens 1, 2]
The opposite form of this called a modus tollens, which rejects the condition “P” by denying the consequence “Q.”
“If P, then Q. But Q is false. Therefore, P is false.”
- If TJ won the lottery, then he is rich. [Premise]
- But TJ is not rich. [Premise]
- ∴ TJ didn’t win the lottery. [Modes Tollens 1, 2]
(NOTE: This does NOT work by denying the condition, because the consequence is not exclusive to that condition. For this example, if I didn’t win the lottery, that does not necessarily mean I am not rich, since I could be rich by other means.)
A disjunctive syllogism is a form of argument where one of two options is declared true by denying the alternative option. This is also known as “OR elimination.”
“Either P or Q. P is false. Therefore, Q is true.”
- Either the Earth is round or the Earth is flat. [Premise]
- But the Earth is not flat. [Premise]
- ∴ The Earth is round. [Disj. Syll. 1, 2]
Basically, an argument that follows the rules above is a logical argument. If it doesn’t, it is a fallacious argument and is, therefore, considered invalid. There are many times when an argument may appear to be logical when it is, in fact, fallacious, which can be very confusing and/or deceiving.
- All dogs are animals. [Premise]
- Bugs Bunny is an animal. [Premise]
- ∴ Bugs Bunny is a dog. [Conclusion]
This argument attempts to use categorical syllogism, but does so incorrectly. Assuming “dog” is “P” and “animal” is “Q,” the first premise is fine, but the second premise is not in the “R is P” format. Dogs are members of the set of animals, and Bugs Bunny is also in that set, but that doesn’t mean Bugs Bunny is in the set of dogs.
Notice that both premises are correct, yet the conclusion is wrong. This can only happen when the argument is using an improper inference. An argument that does so is called invalid, and is thus a fallacious argument. An argument’s validity has nothing to do with whether the premises are true or false (that would be called “soundness“).
Here’s another example:
- Cars are vehicles. [Premise]
- Trucks are not cars. [Premise]
- ∴ Trucks are not vehicles. [Conclusion]
This argument appears to be logical, but it does not follow the standard syllogistic format “P’s are Q’s. R is P. Therefore, R is Q.” In the first premise, “cars” is being used for “P,” but the second premise uses “not cars” instead. Excluding something from a smaller set (trucks are not cars) does not exclude it from a larger set (trucks are not vehicles).
Deciphering an Argument
Now, obviously, people don’t actually express their arguments so cleanly and visibly like this in everyday speech. It’s up to you to interpret the argument someone tries to make from the type of language they are using. For example, consider this statement:
“Capital punishment is wrong because it’s murder.”
Although not directly mentioned, we can assume, based on the statement’s wording, it implies that murder is wrong. This is enough information to translate into a syllogism, which would look like this:
- Murder is wrong. [Premise]
- Capital punishment is murder. [Premise]
- ∴ Capital punishment is wrong. [Conclusion]
This is a logical argument because it is completely valid. To argue against it, you would have to disagree with at least 1 of its premises.
It’s a bit of a skill to extract arguments like this from regular conversation, but just like all other skills, the more you do it, the easier it becomes. Just remember that any and all verbal arguments can be explained using this logical process.
I hope this explanation was of some use to you. If you ever want to prove a point in a debate, it is vitally important to know how a proper and logical argument is formed so that you can not only create your own, but also identify arguments that aren’t so logical. This is especially true in discussions of things like politics, social issues, and other controversial topics. (gun laws, abortion, capital punishment, euthanasia, etc.)
So, what do you guys think? Do you think you understand the rules of logic well enough to spot a valid argument when you see or hear one? Can you generate one yourself? Let me know in the comments down below.
Until next time,