Structure of Arguments
Arguments consist of two parts: premises and conclusions.
A premise is an assertion, or an assumption, that provides reason and support for the argument. In common terms, we might think of premises as the statements we make in an argument to prove our overall point. In a well-developed argument the premises will be related to one another, building on each other to develop a strong line of thought to its final outcome.
A conclusion is the final outcome of the argument; it is the overall point the argument intends to prove. A single argument can only have a single conclusion, and the conclusion of a well-structured argument is one that logically derives from the given premises.
Arguments can be mapped as follows:
P1 All mammals have fur
P2 Cats have fur
C1 Therefore, cats are mammals
The above example demonstrates how arguments are structured. A premise is given. Then a second premise is given, which builds from the first premise. The premises form a complete thought and lead to a conclusion. The conclusion evaluates the given premises and expresses an overall point regarding the argument.
Logical Validity
Arguments are of no value if they are nonsensical. An argument that is obviously flawed or nonsensical is unconvincing and easily overcome. The first step to developing a believable argument is to structure the argument in a way that it is logically valid.
A logically valid argument is one that is structured so that the following is true:
1. The conclusion can be logically derived from the premises. This means the conclusion must come from, and relate to, the given premises. If the premises and conclusion of an argument are unrelated, the argument is not valid.
2. If the given premises are true then the given conclusion must also be true. If an argument is formed such that the premises could be true but the conclusion could be false, then the argument is invalid.
Example of a Valid Argument
P1 All mammals have fur
P2 Cats have fur
C1 Therefore, cats are mammals
The above argument is logically valid. The first premise establishes a characteristics of mammals. The second premise establishes that cats possess the mammalian characteristic. Then the conclusion completes the thought that cats are mammals, given the previous premises. The conclusion follows from the premises, and if the premises can be proven true the conclusion will also be proven true.
Example of an Invalid Argument
P1 All mammals have fur
P2 Cats have fur
C1 Therefore, cats are carnivores
This example is a logically invalid argument, because the conclusion is unrelated to the premises. Also, even if the premises are true the conclusion could be false. This argument begins with premises that build on an idea of proving or disproving whether cats are mammals. Then, the conclusion goes in a different direction of defining whether cats eat meat. Since the premises never address dietary habits of mammals, the conclusion does not relate to the premises. Based on the given premises it could be true that mammals have fur, and it could be true that cats have fur, but it could be false that cats are carnivores.
Logical Validity is Not Truth
An important consideration of logical validity is that validity does not equal truth. It is possible for a logically valid argument to be false. The characteristic of a logically valid argument is that if the premises are true then the conclusion will also be true. The premises don’t actually have to be proven true for the argument to be valid; it’s only the form and structure of the argument that determine its validity. The fact that an argument can have logical validity yet still be false is why we must be careful to test things (which we will explore later), and it is the basis of such warnings as:
For I want you to know how great a struggle I have for you and for those at Laodicea and for all who have not seen me face to face, that their hearts may be encouraged, being knit together in love, to reach all the riches of full assurance of understanding and the knowledge of God’s mystery, which is Christ, in whom are hidden all the treasures of wisdom and knowledge. I say this in order that no one may delude you with plausible arguments. For though I am absent in body, yet I am with you in spirit, rejoicing to see your good order and the firmness of your faith in Christ.
Therefore, as you received Christ Jesus the Lord, so walk in him, rooted and built up in him and established in the faith, just as you were taught, abounding in thanksgiving.
See to it that no one takes you captive by philosophy and empty deceit, according to human tradition, according to the elemental spirits of the world, and not according to Christ. (Colossians 2:1-8, ESV)
In the letter to the Colossians, Paul tells of the struggles he endured as a teacher. Paul devoted himself to fully teaching and preaching the word of God, serving as a mentor to believing disciples, and urging everyone to spiritual knowledge and maturity. As we read into chapter two, we see Paul’s warning for believers to be on guard against arguments that sound plausible but are deceptive. Paul cautioned the Colossian people not to be fooled by empty philosophy that deviates from the truth of Jesus.
A plausible, fine-sounding, argument is one that is logically valid. A plausible argument that deceives people is one that is logically valid but untrue. We face these types of logically valid deceptions both inwardly and outwardly. Inwardly, we are exposed to doctrines that sound reasonable but deviate from the truth of scripture. Outwardly, we face antagonists who attempt to break our faith by developing arguments as convincingly as possible. The answer to fine-sounding arguments is to first examine the argument for validity then to test the premises for truth.
Logical Soundness
It’s not enough to form valid arguments. We want to move towards understanding truth, and logically valid arguments can be untrue. So we start by forming logically valid arguments as our basis for reasoning, but then we must test our arguments for truth.
A logically sound argument is one that meets the following conditions:
1. The argument must be logically valid.
2. All premises in the argument must be proven true.
A logically valid argument is structured so that if the premises are true then the conclusion must be true. A logically sound argument proves the valid argument is actually true; the premises are proven true and, therefore, the conclusion is proven true.