Thursday, March 23, 2006

An Example of "Bad Logic": Human Cloning

I was asked recently, via email, to provide an example of "bad logic." In fact, here's the full text of the email:
I need about a paragraph's worth of a dumb logical or tautological
argument, the kind that a self important logic student in a senior seminar might spew out in his term paper. Anything come to mind? Thanks. -jv
If you care to read and/or critique my response, read on.
Here, in it's full and complete form, is my response:
Not totally sure what you're asking for but I'll do my best...

1) I'm going to interpret "dumb logical" as meaning "logically unsound" and "tautological" as, well, "tautological." So, before we get to what you’re looking for, a little in the way of definitions:

2) Soundness: An argument is logically sound if and only if the argument is valid AND all of its premises are true.

Of course for this to make any sense we need the following definition:

3) Validity: An argument is logically valid if and only if when its premises are true its conclusion cannot be false.

The following is an example of a valid argument form:

I) If A then B
III) Therefore B

Note that this argument is valid regardless of what you substitute for A and B. So if I say

I) If I can type a sentence then John will give me $1,000,000.
II) I can type a sentence.
III) John will give me $1,000,000.

that is a logically valid argument. However, as is readily apparent, it is not a logically sound argument because all of the premises are not true, namely the first one. On a side note, if it turns out that all of the premises are true please let me know immediately – I’ll send you my address.

Now we get to the last key term…

3) Tautology: A statement (different from an argument, which is composed of several statements) is a tautology that is truth-functionally valid. That means that regardless of the truth of its variables, the statement itself is always true. Or, to put it more colloquially, a tautology is an argument that is trivially true. So, an example:

I) A or not A

Or, in words:

I) The Raven is black or the Raven is not-black.

Notice that tautologies or more or less independent of the logical validity or soundness of an argument. An argument can be logically sound (which implies logical validity) and contain a tautology, it just probably won’t be a very meaningful argument. For example:

I) The sky is blue.
II) If the sky is blue then either the sky is blue or the sky is not blue.
III) Therefore, the sky is blue.

This argument has a logically sound form, and it also contains a tautology (II). As you notice, it’s not all that compelling.

This leads me to the final point…

4) What you want:

I assume that what you want is not for me to give you one sentence examples of unsound or tautological arguments. What I’m not too clear on is what you do want…

Do you want an example of a “bad” argument (where “bad” means either “unsound” or “tautological” or both) that might show up in a college classroom? Do you have a topic or a prompt?

In case you don’t, here’s an example I came up with that you might find useful.

5) Example: Human Cloning

The development of genetic sciences is proceeding with astonishing speed. Sooner or later it may become possible to clone human beings. If this happens, cloning of human beings should be banned. Why? Because allowing the cloning human beings would create a host of nightmare scenarios – children harvested for organs, armies of warrior clones trained to feel no pain or remorse, an inexhaustible supply of Dick Cheneys – that everybody would agree must be stopped at all costs. Therefore, human cloning should be banned.

Notice that if you break this argument down you get the following argument (more or less, there are some interpretative questions here):

I) Either cloning will be possible or cloning will not be possible (“Sooner or later it may become possible to clone human beings”).
II) If cloning is possible it should be banned (“If this happens, cloning of human beings should be banned”).
III) Therefore, human cloning should be banned (“Therefore, human cloning should be banned”).

or, to use symbols:

I) Either A or not A
II) If A then C
III) Therefore, C

Notice, first and foremost, that all the “meat” of the argument – the stuff about Cheney and whatnot – adds nothing to the logical structure of the argument. It simply is an elaboration on the “If A then C” premise above. That is, “If cloning is possible it should be banned because ….”. This is important for getting you to believe that premise II is a true premise, but it doesn’t change the logical form.

And looking at the logical form we see an argument that a) contains a tautology, which is usually a bad sing and b) is neither logically sound nor logically valid.

1) The tautology is obvious – it’s premise (I).
2) The argument is invalid because all the premises (I and II) may be true and the conclusion may yet be false. That is, it might never prove possible to clone human beings, which means that the conclusion would not follow despite the (arguable) truth of both premises.
3) The argument is unsound because the truth of all the premises has not been demonstrated. The first premise is true because it is a tautology. The second premise, on the other hand, is not necessarily true. There has been support given (the Cheney line) but it is hardly compelling or convincing support.

Thus you have an argument that is logically flawed in several ways and yet, despite this, might conceivably be employed. Usually horrible arguments like this are surrounded by slightly more padding, and are slightly more difficult to unpack and expose, but this is, in my opinion, a reasonable representation of arguments against cloning that are in fact made. And, for what its worth, made by persons more eminent than mere college students at that.


Whew. Not certain if I got that entirely correct, so anybody who wants to provide feedback will be warmly welcomed.


Anonymous photostream said...

Whew indeed.

You could add that the art of unbundling this sort of argument is to spot the sentence containing a belief masquerading as a fact.

In your example the 'if A then C' statement of which you say "is not necessarily true. There has been support given (the Cheney line) but it is hardly compelling or convincing support." is obviously the belief statement.

Whilst you were presenting a detailed deconstruction of the argument for the purpose of answering the question, in practice it is faster to home in on the belief statement.

Fri Mar 24, 03:14:00 PM EST  
Blogger Tim Kanwar said...

Quite correct. While I was trying to demonstrate a point for my friend (and perhaps I belabored it), in practice, one of the quickest and easiest methods of deconstructing a specious argument is to do exactly what you suggest.

And, unfortunately, it's all too easy to find examples of pure belief statements masquerading as "facts" or knowledge. If only that was limited to academic exercises...

Sat Mar 25, 11:07:00 AM EST  
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Fri Nov 20, 04:44:00 PM EST  

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