Archive for the 'Logic' Category

The Logical Necessity of the Oxford Comma

by Jason Stotts

I detest when people don’t use the “Oxford Comma,” which, sadly, is no longer used even by Oxford.  For those who don’t know, it’s the last comma in a set before the “and.”

Let’s say you want to talk about three separate things, you would write it thus: A, B, and C. Logically, you’d be talking about the set of the three where each is independent of the other {A,B,C}.  Now, you could also talk about three things where not all three are separate and you would write it thus: A, B and C.  Logically, you’d be talking about the set {A,B&C}, where A is discrete while B and C are conjoined.  This is not the same thing at all!

What if A, B, and C were all themselves sets of two variables?  I would write it: A and Z, B and Y, and C and X. Which is logically {A&Z, B&Y, C&X}  Without the Oxford comma, I’d have the mess of: A and Z, B and Y and C and X.  This is, perhaps, because who really knows, represented as: {A&Z, B&Y&C&X} and since in logic you can transpose variables that are conjoined, A&B is the same as B&A, I might be talking about {A&Z, B&X&Y&C}.  This is all logically the same.  But if we put values onto those variables, you can imagine the problems that might arise!  Thus, the Oxford Comma is logically necessary.

Commas are very important and they shouldn’t be treated lightly, otherwise you could end up with:

Let’s eat mother!

Instead of:

Let’s eat, mother!

Or, to use a problem that the Oxford Comma might create:

And if you don’t understand the problem, please stop reading my blog.  It is much too advanced for you.

Informal Fallacies

by Jason Stotts

One of the best ways to improve the clarity of your thinking and arguing is to learn the informal fallacies.  A fallacy is an error of reasoning whereby your conclusion does not follow from your premises.  Importantly, it is not that the content of the premise is false (that is its own issue), but that you have not correctly reasoned from the premises to the conclusion.

There are two different kinds of fallacies: formal fallacies and informal fallacies.  The distinction is whether the fallacy is a function of the form of the argument (formal) or the content of the argument (informal).  While the formal fallacies are important, the informal fallacies are more often committed and show up frequently in arguments.  For that reason, I’m posting this list of some of the more common informal fallacies to help people to try to think and reason better.

Appeal to Force (ad Baculum) – arguing (implicitly or explicitly) that if a person does not accept your conclusion, he will be harmed.  Obviously, just because you can compel someone to assent to your conclusion, does not make it true.

Appeal to Pity (ad Misericordiam) – attempting to support a conclusion by appealing to pity.

Appeal to the People (ad Populum) – an argument that appeals to what other people think and/or do in order to attempt to justify it’s conclusion.  The “bandwagon” technique is an example of this where it is argued that “everyone else is doing X, you should too.”

Argument against the Person (ad Hominem) – attacking a person instead of addressing his arguments.  This fallacy has a number of different instances, including: ad hominem abusive (attaking a person directly), ad hominem circumstantial (discrediting a person based on their situation), and tu quoque (attacking the other person as hypocritical, literally means “you too”).

Accident – misapplying a general rule to a particular case.

Straw Man – distorting an opponent’s position and then showing the weaker position to be false, while claiming you have actually disproved the opponents position.

Missing the Point – when a conclusion is drawn from premises that actually warrant a different conclusion.

Red Herring – changing the subject during the argument in order to distract the other person.

Appeal to Ignorance – having premises that entail that no conclusion can be drawn and then drawing a conclusion anyway.

Hasty Generalization – generalizing from an inadequate sample to the entire group.  For example, “this particular cat is black, therefore all cats are black.”

False Cause – an argument that depends on a causal connection that does not actually exist.

Begging the Question – assuming the conclusion is true and using it as proof of the conclusion or reasoning in a circle.

False Dichotomy – using an inexhaustive dichotomy as a premise.  For example, if I were to say: “my wife is either at the store or at home, she’s not at home, therefore she’s at the store” this would be invalid because she could be many other places.  In order to make an argument of this kind, the dichotomy must exhaust all possibilities.

Equivocation – using a key term in two different senses to justify an argument.

Composition – arguing that because the parts have an attribute, the whole must have it as well.  For example, if one were to argue that “hydrogen and oxygen are both gases, water is two parts hydrogen and one part oxygen, therefore water is a gas.”

Division – arguing that because a whole has a property, its parts must have it as well.  For an example, just reverse the water argument above.

I strongly recommend reading a good book on Logic to get a better understanding of the issues.  In my undergrad, I used Hurley’s A Concise Introduction to Logic and thought that it did a very nice job.  I used it in order to refresh my memory for the above, but don’t blame Hurley for a poor formulation since it’s all my take on it.  There’s also a website called “The Nizkor Project” that seems to have a good list of informal fallacies.

Ideally, though, you can spot fallacies by just making sure your conclusion actually does follow from your premises and that your premises are relevant to your conclusion.