Systematic Philosophy

to know what can be known

Text Format And Numbered Format

The very same argument can be presented in different formats. It can be presented in regular prose, in formal logic or in other ways. Each of these ways has its advantages. But there is one format that stands above the rest, one format that is the clearest and most useful. We call it “numbered format”.

Text format

Arguments are usually presented as big blocks of text. We call this “text format”. Here is an argument presented in text format:

Socrates is composed of particles. How do we know? Socrates is a person. This means that, like all people, he is mortal. Now all mortal things have parts. This and the fact that Socrates is mortal together entail that Socrates has parts. Which parts? His left hand and his right hand, for instance. Or his thoughts and his emotions. Now every thing that has parts is composed of particles. It follows that Socrates is composed of particles.

Numbered format

Take an argument in text format. Strip away absolutely everything but the argument. Express each step in the argument in the form of a statement. Place each step on its own line. Number each of the lines. Put a “Therefore, …” in front of each conclusion. Place bracketed numbers after each conclusion to indicate which steps are meant to entail that conclusion. Wherever possible, put steps some place above the conclusions they are meant to entail. Put the final conclusion at the bottom. Voilà! The argument is now in numbered format.

Performing these operations on the argument above, we get:

  1. Socrates is a person.
  2. All people are mortal.
  3. Therefore, Socrates is mortal. [1,2]
  4. All mortal things have parts.
  5. Therefore, Socrates has parts. [3,4]
  6. All things that have parts are made of particles.
  7. Therefore, Socrates is made of particles. [5,6]

Why we use numbered format

How many steps are there in an argument? Which steps are meant to entail which? Which proposition is the final conclusion? Numbered format makes these things clear instantly. The argument above has seven steps. The first and second are meant to the entail the third. The third and fourth are meant to entail the fifth. The fifth and sixth are meant to entail the seventh. The seventh is the final conclusion. These features constitute the structure of the argument and they are conveyed with crystal clarity.

Now look at the text argument above. Eleven sentences. How many propositions? Nine… maybe. We might say more or less, depending on how we interpret some of the sentences. How many propositions are actually part of the argument? Are all of the relevant propositions explicitly stated or are some tacitly implied? Which propositions entail which? Compared to numbered format, an argument in text format looks like a big jumble of words.

After a while, this is what text format feels like.

Why do we use numbered format? It cuts away everything inessential. It exhibits the structure of an argument clearly and concisely. It makes it easy to check arguments for transparent validity. And we can easily see what numbered arguments are saying as well. This is not true for arguments stated purely in formal logic.

Numbered format is the best we have. That is why we use it.

A checklist for numbered format

  • Has every step in the argument been expressed in the form of a statement?
  • Has every step been put on its own line?
  • Has every step been given its own number?
  • Does every line with a conclusion begin “Therefore, …”?
  • Does every line with a conclusion end with bracketed numbers that indicate the steps that are meant to entail that conclusion?
  • As far as is possible, does every line occur above any lines it is supposed to entail?
  • Does the final conclusion occur at the bottom?
  • Has absolutely everything else been stripped away?

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Written by Geoff Anders

May 19, 2011 at 10:50 am

Posted in Uncategorized

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