Exploring Philosophy: Argument Analysis - Validity and Soundness

Validity

Logic is very useful when it comes to argument analysis because it is easy to confirm validity with logic. Normally, people think a valid argument equates to a correct argument. Unfortunately, that is incorrect. Let us examine this argument:

      1. All dogs are dinosaurs
      2. I have a pet dog.
      C. I have a pet dinosaur.

Many people will immediately think this argument is invalid because of the false claim made in [1]. However, this is a valid argument. An argument is valid when supposing all the premises are true, it is impossible for the conclusion to be false. Let that sink in. In my last post, I mentioned that logic concerns itself with the movement and consequences of facts, not the establishment of facts. As you can see, this plays a large role in validity. We do not question whether dogs are dinosaurs, we suppose it were true and look at the consequences. It is the work of a zoologist to confirm it as true or false. I should note that if there is even one case where all the premises are true and the conclusion is false, then it is not a valid argument. For it to be valid, it must be impossible for the conclusion to be false.

Now you might be thinking, “well that’s dumb. Validity doesn’t tell us much about the real world then. An argument can be valid but not applicable to the real world”. You are correct in thinking that there might be some “flaws” in this definition of validity. In response, I would once again direct you to the nature of logic. The goal is not to create facts, but to see how facts behave. Secondly, I would like to introduce the notion of soundness.

Soundness

Soundness is most likely what you thought validity was before reading this post. An argument is sound if and only if [1] the argument is valid, [2] All of its premises are true. Now we can start to see the real world applications. What much of argument has to offer is to persuade other parties, which is why we want to construct sound arguments. However, testing for soundness is quite difficult. We normally start off by examining an argument’s validity. This is because no external knowledge is required. It is possible to declare an argument invalid within the argument itself. Proving that a premise is wrong usually requires extensive empirical knowledge.

For example, take the argument:
      1. The average human hearing range is 30 kHz to 46 kHz.
      2. The frequency range of a guitar spans from 10 kHz to 20 kHz.
      C. The average human can hear a guitar.

This argument is not sound because it is [1] it is invalid [2] the premises are true. We can easily see that if we suppose the premises are true, the range of the guitar does not fall within the range of human hearing. Therefore, humans would not be able to hear the guitar. It is much easier to show that the argument is unsound through these means rather than knowing the range of humans and guitars.
*Note that soundness plays a huge role in completeness and provability in logical systems. However, we have not yet discussed propositional logic, much less metalogical implications.

Hopefully this post will help you form stronger arguments and pinpoint the weaknesses in the arguments against you.

I was debating whether to put this as an entry of Exploring Philosophy or Analytic Philosophy. I considered the latter because as we will see later on, symbolic logic ties into validity almost seamlessly. However, I chose the former because argument analysis is important for all schools of thought. It is important to justify your thinking in all disciplines, not just philosophy. In that sense, validity is in no way limited to analytic philosophy

Thanks and stay rational everybody.

The philosopher of science is not much interested in the thought processes which lead to scientific discoveries; he looks for a logical analysis of the completed theory, including the establishing its validity. That is, he is not interested in the context of discovery, but in the context of justification.
                        ― Hans Reichenbach