Soundness and Validity of an Argument

A logical argument can be examined in two ways: soundness and validity. You may have heard these two words used interchangeably, but for someone who may find interest in logic and philosophy, it is important to know the difference between the two terms. Let’s look at how we can determine what a valid argument is and then see how the soundness of an argument will determine how debatable the argument will be.

The validity of a deductive argument is simple: if the premises are true, then the conclusion must be true. Notice that this is a specific definition concerning the relationship between the premises and the conclusion. This rule doesn’t consider whether or not the premises, or the conclusion for that matter, are really true in real life. The validity of an argument isn’t concerned about whether the premises reflect reality- it is only concerned with what would be true if those premises reflected what was real. For example, we could come up with ridiculous premises and still yield a valid argument:

  1. If I flew to school on Monday, then you own 10 unicorns.
  2. I did fly to school on Monday.
  3. Therefore, you own 10 unicorns.

As ludicrous of an argument as this is, it is a valid argument (because it follows the Modus Ponens structure). If the argument is valid, then what is so silly about this it? Well, we all know that unicorns don’t exist in the real world. We also know that since I can’t fly in real life, that I didn’t fly to school on Monday. So, we can reasonably say that the conditional premise 1) in and of itself isn’t really true and premise 2) also doesn’t match reality either. This means that the argument is not a sound argument, even though it is logically valid.

In contrast to the validity of an argument, the soundness of an argument considers whether the premises really reflect the way things are in our own world. We can see by inspection that usually the soundness of a premise is the main focus of debate in any given argument. It is usually easier to determine whether an argument is invalid than it is to determine whether an argument is sound. For example, we can say something like this below:

  1. If objective moral goodness exists, then God exists.
  2. Objective moral goodness does exist.
  3. Therefore, God does exist.

The argument above is simple and valid, however, both premise 1) and premise 2) can and have been debated. Since the argument is valid, the the conclusion is fixed and must be true if 1) and 2) are true. Therefore, 1) and 2) must be proven unsound to attack the argument. For example, someone who doesn’t believe this argument is sound may attack premise 1) by saying that just because objective moral goodness exists, doesn’t mean that it must come from God. Further, one may also object to premise 2) by disagreeing that objective moral goodness really exists.

In closing, it is crucial to remember the distinction between a sound argument and a valid argument. Just because an argument is valid doesn’t mean that it is necessarily sound. When valid arguments are challenged, they are typically attacked by arguing against the soundness of their premises. Therefore, when constructing a valid argument, it is critical to anticipate challenges to the soundness of one’s premises.

The Modus Ponens Argument

The Modus Ponens argumentative form is so common to us as thinkers that it is oftentimes easy to overlook it’s vital importance to our every day reasoning. This argumentative form in it’s original Latin means to “affirm by affirming.” Simply put, this means that we can affirm some kind of conclusion (announce that it is true) by affirming something else. Today let’s look at this structure and one of it’s associated fallacies.

The Modus Ponens structure looks something like this:

  1. If P–>Q
  2. P
  3. Therefore, Q

Premise 1) is what is known as a conditional premise. A conditional premise has two parts: an antecedent and a consequent. Premise 2) is a simple truth assertion. In this case, premise 2) validates the antecedent of the conditional, leading us to conclude that Q is necessarily true. If we affirm the antecedent P, we then affirm Q. Assuming that premise 1) and 2) are really true in real life, let’s look at how this logic plays out:

  1. If you are reading this blog post, then you are on the computer.
  2. You are reading this blog post.
  3. Therefore, you must be on the computer.

A common misapplication of this structure is what is known as affirming the consequent. Let’s examine a similar structure below:

  1. If P–>Q
  2. Q
  3. Therefore, P

Notice the difference in premise 2). Premise 2) affirms the consequent, not the antecedent.  Using the same real life scenarios as above, let’s insert them into this structure and we will see that it is indeed a fallacy.

  1. If you are reading this blog post, then you are on the computer.
  2. You are on the computer.
  3. Therefore, you must be reading this blog post.

Notice that in this case, all we know is that you are on the computer-we don’t know that you are reading this blog specifically. You could be checking the weather, buying plane tickets, or listening to Rick Astley. We simply can’t know what you are doing on the computer. All we know is that you are on it. In this case, it is easy to see that it does not logically follow that you must be reading this blog post, although it is possible. This kind of conclusion is a non-sequitur, which means that the conclusion “does not follow” from the premises.


Deductive Reasoning

Reason can be casually defined as the making sense of things. For as many bad ideas that are out there bouncing around from generation to generation trying to make sense of this world, it is comforting to know that there are some basic rules that can help us understand the way things really are. There is a referee of sorts that keeps ideas in check if we are willing to listen. Reason is governed by the rules of logic.  Fundamentally, there are several types of reasoning: deductive, inductive, and abductive reasoning to name a few; but arguably the most powerful is deductive reasoning. All minds, both great and small, use deductive arguments as we go about our daily lives. Let’s look at the deductive form of reasoning so that we can better understand the structures that we use to think and solve problems.

Deductive reasoning is a kind of thinking that starts with a set of premises and moves towards a concrete conclusion. A set of premises that leads to a conclusion is also known as a syllogism. Deductive syllogisms are arguments that are logically airtight. This means that if the premises of the argument are true, then the conclusion must be necessarily true and there is no amount of reasoning that can change it. The most effective way to argue against a deductive argument is to question the premises of the argument.

For example, a deductive argument might be:

  1. If you are reading this post, then you are on the computer. 
  2. You are reading this post. 
  3. Therefore, you must be on the computer.

or symbolically,

  1. If A—>B
  2. A
  3. Therefore, B. 

Notice that this particular structure is a common valid argumentative form. (We will delve more into this form in the coming days). With this form, thinkers can mix and match any set of premises and, so long as they are true in the real world, the conclusions must be concretely true and can’t be false. In other words, if we accept that premise 1) and premise 2) are really true, then the conclusion must be true. As mentioned earlier, we can only debate the soundness (the real truthfulness) of premise 1) and 2). I would encourage you to think of arguments of your own following this form!

In conclusion, deductive reasoning has immense power and is one of the most commonly used types of reasoning. Because of this power, the usual course of debate shifts to the soundness of the argument’s premises. Therefore, when constructing a deductive argument, one must carefully consider and piece together his premises in such a way that they can withstand the test of a rational charge. One need not be a Roman philosopher to think deductively!


Daniel and the Three Levels of Faith

Daniel 3: 17-18 discusses Daniel’s friends and their unwillingness to bow to King Nebuchadnezzar’s Giant golden Statue.

17″If it be so, our God whom we serve is able* to deliver us from the furnace of blazing fire; and He will** deliver us out of your hand, O king. 18″But even if*** He does not, let it be known to you, O king, that we are not going to serve your gods or worship the golden image that you have set up.”

I love this passage because I think it subtly outlines three levels of Faith, some of which are common, and some extraordinary.

1. God is able
2. God is willing (God will act)
3. But if not…

The first level of faith is that God is able to do something- this is not a hard achievement of faith to have as a Christian. It ought not be a stretch to say that God can do what we ask Him for. In this case, all three of Daniel’s friends knew God was able to save them.

The second level is the confidence that God will do what you are asking of Him (like maybe save you from a fiery furnace that is 7 times hotter than normal). A righteous confidence should come from our ability to discern God’s will through prayer, worship, etc. This level of faith is a bit more challenging because there is more risk involved, but nevertheless, many have it.

The third level of faith is demonstrated by the “but if not” statement. This verse shows the maturity of Shadrach, Meshach, and Abednego and their total commitment to God’s will whether they are consumed by flames or live to worship Him another day. It seems to me that this is a precious, rare kind of faith.

The Market of Values

Are your values for sale?

Eventually, someone will beckon you to exchange your values for an empty promise. For the hedonist, nearly all of his values have a price for pleasure. For the businessman, his word may be worth a golden transaction. For the athlete, the competitive edge could be worth the bargaining of an honest victory. Whoever you are, whatever you do, and wherever you go, someone is vying for your business. Someone is willing to make a deal.

Like an ancient marketplace, we are bombarded with offers in the market of values. The market is loud, distracting, and dusty. It is a never-ending well of discontentment and unrest. In the daylight, there are exchanges of honor for dishonor and the truth for lies. By night, sex for silver is the deal of the day. The market offers a temporal solution for an eternal problem. The finite promises to quench eternal desires.

The flashy bargains fade. The soul has no price in this dark economy. Do not be enamored by the empty promises of the market of values. Cling to the Unchanging, for you are already bought with a price.