Source: Image of Socrates, Creative Commons, http://bit.ly/29ZntMM;
Hi, I'm Glenn. This ethics tutorial will cover evaluating the structure of an argument. Let's look at a couple of ideas to keep in mind and then cover the topics for the tutorial.
Things to keep in mind for this tutorial are the definition of argument, what inferences are about, the form of inferences, and the classification of inferences.
This tutorial will cover two main areas. We will look at the distinctions between valid and invalid arguments. And here, we will focus on arguments that are deductive. And second, we will look at the distinctions between strong and weak arguments. And there, we will focus on inductive arguments.
Key terms are, valid-- a deductive argument whose premises logically guarantee their conclusion. Invalid-- a deductive argument in which the premises do not logically guarantee their conclusion. Strong-- an inductive argument in which the premises render the conclusion probable. Weak-- an inductive argument in which the premises do not render the conclusion probable.
First, let's look at valid and invalid arguments. It's important to remember that validity only applies to deductive arguments. And only an argument, an entire argument, can be valid or invalid.
In philosophy and logic, we have to be very specific about this. A premise, a statement, a conclusion, an idea, an opinion, a point of view-- none of these are valid or invalid. Only an argument, and specifically, only a deductive argument can be valid or invalid.
What validity does is it determines whether or not the conclusion follows from the premises. If an argument is valid, then the conclusion does necessarily follow from the premises. It is inconceivable for it not to follow from the premises.
However, this does not guarantee the truth of the conclusion. That is only achieved when a deductive argument is valid and it has true premises. Let's look at two quick examples-- one of valid deductive argument and one of an invalid deductive argument.
First is the valid argument. If I go to the opera, I'll be bored. I went to the opera. Therefore, I was bored.
Given the structure of the argument, the form entails the conclusion. And the conclusion, therefore, necessarily follows from the premises, and it is valid.
Next is an invalid argument. All dogs are mammals. All cats are animals. Therefore, all dogs are animals.
This seems OK because the premises are true. However, it is invalid. And that is because of its structure. And we'll be able to see this by a method called counter-example by providing substitution instances for each of the terms and seeing how true premises can lead to a false conclusion and thus show it to be invalid.
So we can do this by first identifying its structure, creating a false conclusion, filling in the content with substitution instances so the premises are shown to be true leading to a false conclusion. This will reveal it as invalid. So let's look at the structure of our argument we just used.
The structure is all A are B, all C are D, and all A are D. To show the invalidity of this argument, we substitute by first coming up with a false conclusion. For example, all dogs are reptiles.
Then we fill in the corresponding letters in the premises. All dogs are B, and all C are reptiles. Now we add a couple of other words for B and C to make the premises true, leading to a false conclusion. All dogs are mammals, all lizards are reptiles, and all dogs are therefore reptiles. This argument has the exact same structure as the original. And because we can show it leading from true premises to a false conclusion, we therefore determine that it is invalid.
Let's look at three more examples of deductive arguments that are invalid and see how we can show them to be invalid by using the method of counter-example. As you can see in the three examples, each of them initially looks OK. Going to the opera and being bored, not being able to watch TV, and deducing that musicians are brilliant all seem to reasonably come from the premises. However, when we isolate the structure of each of them and then use substitutions for those letters, we can see that we can create, in each case, examples of the identical structure of the argument and show them to go from true premises to a false conclusion. And because we can do that, all three of these examples are invalid arguments.
When we talk of strong and weak arguments, we are referring to inductive arguments. Remember that inductive arguments are based upon probability. And so a strong inductive argument is one where it is improbable for the premises to be true and the conclusion to be false.
The strength is based upon the truth of the premises and the conclusion and not necessarily on its structure as we looked at in deductive arguments. There are, therefore, no counter-examples for inductive arguments. We have to use a different method.
And that method for evaluating the strength of inductive arguments is based upon the truth and the degree of certainty that we can identify in the premises. Let's look at two examples to see how they operate. First, all meteorites found to this day are audio recordings. Therefore, the next meteorite found will be an audio recording.
Given that the premise is true, this is a strong argument. However, it does contain a false premise and therefore a false conclusion. It is not a particularly great argument. However, if the premise is true, if we assume it to be true, it is strong because the conclusion does follow with a very high degree of probability.
A second example-- coffee cups and diamonds are both made of atoms. Diamonds are very valuable. Therefore, coffee cups are very valuable.
This is an argument by analogy. And while the first by the premises are true-- both things are made of atoms and diamonds are valuable-- the analogy does not hold very strongly because coffee cups are not necessarily very valuable. So we can see that this is a weak inductive argument. In summary, we looked at the distinctions between valid and invalid arguments under the category of deductive arguments and the distinctions between strong and weak arguments that are inductive.
A deductive argument in which the premise(s) do not logically guarantee their conclusion
An inductive argument in which the premises render the conclusion probable
A deductive argument whose premise(s) logically guarantee their conclusion
An inductive argument in which the premises do not render the conclusion probable