Part 1: Introduction to Logic
Part II: Term Logic
Part III: Aristotle’s Logic of Propositions
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Part II: Examples

Let’s return to some more examples of imperfect arguments. First, we will look at two instances that show how helpful it can be to take commonly expressed arguments and recast them in the premise-conclusion form. Consider the following sequence of statements:

1. It’s pretty obvious that all snakes are animals. Think about it. What’s a snake? It’s a reptile, right? I mean, not just a single snake, all of the snakes. You take any snake and it’s a reptile. But then what’s a reptile? Again, all the reptiles, not just a single one, you get it. Take any reptile – is it not an animal? Of course it’s an animal! So, all snakes are animals.

This is an unclear way to make an argument, at least compared to a formally structured one, with premises and conclusions clearly stated. But, in everyday life, we don’t always formalize our arguments before making them. This is not to say that formalized arguments are more correct or that our common way of speaking  is defective. But, formalizing arguments does make it easier for us to characterize what is going wrong (or not) in an inference. The previous paragraph is just a roundabout way to express the following argument:

Premise 1 (P1): All snakes are reptiles.

Premise 2 (P2): All reptiles are animals.

Conclusion (C): All snakes are animals.

Reducing to this premise-conclusion form is a useful tool to parse out what is really going on in an argument. Now let’s consider another argument:

2. It’s pretty obvious that all tables are chairs. Think about it. What’s a table? It’s a piece of furniture, right? I mean, not just a single table, all of the tables. You take any table and it’s a piece of furniture. But then what’s a piece of furniture? Again, all the pieces of furniture, not just a single one, you get it. Take any piece of furniture – is it not a chair? Of course it’s a chair! So all tables are chairs.

If someone expressed this to us, we might be tempted to say, “That’s not an argument!” While that is a common response to particularly faulty reasoning, from a logical perspective, it’s not correct. The above paragraph is an argument, albeit a bad one – we can see just how bad it is when we reduce it to premise-conclusion form:

Premise 1 (P1): All tables are pieces of furniture.

Premise 2 (P2): All pieces of furniture are chairs.

Conclusion (C): All tables are chairs.

From this reduction, we can see what is wrong with the argument – the second premise is false

The point is that all arguments have a well-defined set of features, and any sequence of statements that fits them counts as an argument. Of course, not all sequences of statements are arguments. Consider the following:

3. A self-taught musician, [Julian] Bream learned playing to radio dance bands with the lute his father bought from a sailor on London’s Charing Cross Road in 1947. As a child prodigy, his early recitals led to him being “acknowledged as one of the most remarkable artists of the post-war era”, according to the Royal Academy of Music. After studying piano and composition at the Royal College of Music, and completing national service, he became one of the most prolific and best-selling recording artists in classical music.”

(BBC News, Julian Bream: Classical Guitarist Dies Aged 87, 2020)

This sequence of statements does use some language that is frequently employed in argumentation, and each declarative statement taken on its own is capable of being true or false. However, there is no discernible logical connection between them – there is no conclusion reached by drawing  inferences from premises. So, this cannot be called an argument.  It is merely a sequence of claims about the life of a beloved classical guitarist.

[Activity]: We have mentioned that declarative sentences are a basic element of logical arguments. Recall that declarative sentences can be either true, or false. Considering this, do you think that statements such as questions or exclamations can be evaluated from a logical perspective? Why or why not? Explain your answer in your own words.