Logic 101: Validity and Soundness

Logic can be one of the most frustrating areas of philosophy. Anyone who has had a class on critical thinking or logic could tell you that they have spent hours and hours working on homework only to come out with a sub-par grade. When a friend of mine suggested to do a few posts on logic, I couldn’t help but to think back to my troublesome logic classes. I’ve created this section to help those learn about basic points in logic that are often confusing to many. Come along, and learn our first topic in Logic 101, Validity and Soundness.

Form of an argument

Arguments follow a particular form and contain two basic components — premises and conclusions. A premise is a statement that supports your conclusion and the conclusion is the thing that you are trying to prove. Here’s an example

  1. I eat when I am hungry
  2. I am hungry
  3. Therefore, I will eat

Statements (1) and (2) are both reasons on why I would eat. They support the idea that is trying to be proven in (3). Since I normally eat when I am hungry and, as it turns out, I am hungry, then it could be logically assumed that I will eat.

Easy right? Now, for the fun stuff.

Validity

An argument is valid if the premises and conclusion follow a logical form. This essentially means that the conclusion logically follows from the premises. Think of it like this, every time you want to figure out if an argument is valid you should think up an imaginary world where anything is possible. Then, ask yourself: if you are able to come up with a situation (in your imaginary world) where if the information in your premises were possible, then, given this information, would the conclusion logically follow from them?. This may be confusing to read at first, since a lot of people misconstrue validity for truth.

Validity and Truth

Like I said above, imagine a made up world where anything can happen. I say this because validity does not entail real truth in any way, WHAT-SO-EVER! Truth entails something that is actual. A true premises, or true conclusion refers to its possibility in reality. This example may help to clear up some confusion.

  1. All whales can fly
  2. Anything that is able to fly can shoot lasers with their mind
  3. All whales can shoot lasers with their minds

This is a valid argument! I’m sure you’re thinking that I’ve lost my mind but it’s true. Even though all the premises are false and the conclusion is also false, the argument is still valid. Why? Like I said before, imagine that whales could fly, now also imagine that anything that could fly could shoot lasers with their mind — got that image? Good. Now, it’s impossible  to think of a world where both of those statements are true and the conclusion is false, right? Since in this world whales can fly, and anything that can fly could shoot lasers with their mind, then a whale which can fly MUST be able to shoot mind lasers! So, validity, as you can see, has no indication of its actual truth in the real world, it just proves that it follows a logical form.

Other forms of valid arguments

As we saw above, arguments can be valid if they have all false premises and a false conclusion. Below are three other examples of logical forms that can be valid given their premises and conclusion are consistent.

False premises, True conclusion

  1. False – My girlfriend’s dog is a rabbit
  2. False – All rabbits are named Butch
  3. True – My girlfriend’s dog is named Butch

Mixed Premises, False Conclusion

  1. True – All alligators lay eggs
  2. False – All eggs are laid from birds
  3. False – All alligators are birds

True Premises True Conclusion

  1. True – All monkeys are primates
  2. True – All primates are mammals
  3. True – All monkeys are mammals

True Premises and False Conclusions

Arguments like these are ALWAYS invalid. Why? Because the sole purpose of an argument is to try to prove your conclusion. If your premises are undoubtedly true and your conclusion is false, then you just completely defeated the purpose of your argument. Here’s an example:

  1. Some birds are cockatiels
  2. All cockatiels are birds
  3. Therefore, all birds are cockatiels

As you can see, where premise (1) and (2) are true statements. The conclusion though is false, all birds are not cockatiels. True premises and a false conclusion is just completely illogical, nothing more.

Soundness

An argument is sound when the conclusion is true and the premises are also true. For soundness, throw the imaginary world out the window and return to the real world. Remember, that all sound arguments must first be proven valid. There are no invalid arguments that are also sound. Let’s take one of the above examples.

  1. All monkeys are primates
  2. All primates are mammals
  3. All monkeys are mammals

This is a sound argument because it is actually true in the real world. The premises are true and so is the conclusion. They logically follow from one another to form a concrete argument that can’t  be denied. Where validity doesn’t have to do with the actual truthfulness of an argument, soundness does.

Conclusion

Learning all of this for the first time in a class is often hard. You usually deal with a professor that teaches validity and soundness as first grade math — something that should be a snap to learn. The truth is, learning these terms takes some work and getting them in your brain quickly is essential to excelling in logic. I’ll be sure to post more on this troublesome topic.

Until then.. Keep thinking, my friends!

Posted in Philosophy.

25 Comments

  1. Premises and conclusions can either be true of false, but evaluating what’s true and false is logic.

  2. Taking a first-year philosophy class, and the “imagine anything is true” imagery gave me an “Ah-ha!” moment… thanks!!

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  6. In a universe which is all illusion (1) to paraphrase – all things made by God are perfect and eternal, therefore all thins in world are only shadows of true and unchangeable reality) any and all thinks born of the imagination in this dream world can be dreamt of. Shakespeare who became enlightened had it right when he mentioned “all things dreamt of in your philosophy”
    I invite any all comments.

    (1) “A Course in Miracles”, written by God Himself.

  7. Interesting and funny argument :P.

    Well, IF God created man in his image, and IF God’s image is invisible, then man, according to the logical sequence, is invisible.

    So, yes — valid!

  8. If only the real world would be valid, its like most of the things we do have no logical valid pattern originating from their cause up until the end result.

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