An Aristotelian approach

A long, long time ago, in a country far, far away, a wisdom lover was wondering how things could be defined meaningfully: in a way that would be sound (what is defined corresponds to what we want to define), complete (all the aspects of the thing we want to define are accounted for in our definition), and actionable (to be useful, this style of definition should be reusable). This country far, far away was ancient Greece, the name of this wisdom lover was Aristotle, and he structured definitions with four “causes” – one about the constituents of the thing we want to define (the material cause), one about what has to be done to these constituents to make this thing (the efficient cause), one about the methods used to operate on these constituents (the formal cause), and one about what this thing is for (the final cause).

Brief reminder of Aristotle’s four causes

Aristotle’s four causes are stated as follows:

• Material cause:
  • what is the object of discourse?
  • what are we talking about?
• Efficient cause:
  • action: what is done to it?
  • actor: who does it?
• Formal cause:
  • which methods are used to do that?
• Final cause:
  • towards what use / what goal?
  • why is this done?
  • what for (in English) / pourquoi (in French) / hvorfor (in Danish) / warum (in German)

A first example

The sentence “To make a dish, a cook operates over the ingredients according to the recipe.” includes all four causes:

• “To make a dish” is the final cause,
• “a cook operates” is the efficient cause (the cook is the actor, and operating is the action),
• “over the ingredients” is the material cause, and
• “according to the recipe” is the formal cause.

A second example

The sentence “Using a toothbrush, Michael Scofield unhinges the prison door to escape.” also includes all four causes:

• “Using a toothbrush” is the formal cause,
• “Michael Scofield unhinges” is the efficient cause (Michael Scofield is the actor, and unhinging is the action),
• “the prison door” is the material cause (with door as the subject and prison as the predicate), and
• “to escape” is the final cause.

Interlude

Anton: Wait. Michael Scofield isn’t an actor, he is a character. Wentworth Miller is the actor who play this character.

Pablito: That is correct. I just checked on Wikipedia.

Alfrothul: I am reasonably sure that it’s not the point.

Dana: Right. You guys are crossing levels of reality. Can we move on to the next example?

Anton: Sure.

A third example

Ditto for “My program computes a function over discrete data to predict the weather.”:

• “My program computes” is the efficient cause,
• “a function” is the formal cause,
• “over discrete data” is the material cause (with data as the subject and discrete as the predicate), and
• “to predict the weather” is the final cause.

A fourth example

Ditto for “My recognition algorithm for infinite strings operates in linear time.”: the goal is to recognize, the action is an algorithm, this algorithm operates on infinite strings, and methodologically it proceeds in linear time, i.e., in a time that is proportional to the size of the given strings.

Halcyon: Is this an invitation for critical reading or what?

Mimer: Yup.

Dana: They mean strings that are arbitrarily long.

The fourth wall (courteously): Mind your step.

Dana: Thank you.

Exercise 01

1. Write a few sentences where Aristotle’s four causes are visible.
2. Write a few paragraphs where Aristotle’s four causes are visible, each cause in a separate sentence.

Anton: So we need to do what?

Mimer (patiently): You need to write several sentences and several paragraphs.

Alfrothul: Several sentences and several paragraphs about what?

Mimer: Any topic you fancy.

Dana: And we write them how?

Mimer: In a way such that Aristotle’s four causes are visible.

Pablito: Er... Why do we need to do this?

Mimer: To acquire control over your narratives. “I code, therefore I don’t need to think” is no way to go.

René Descartes: This is getting interesting. Do you guys need a chairperson?

Mimer: Mr. Descartes, thanks for stopping by!

Food for thought

What is the point of the little dialogue in Exercise 01?

Less is more

Sometimes, one cause is enough:

• Material cause:

  Question: What is this rock?

  Answer: Granite.

  Anton: What is this liquid?

  Alfrothul: Helium.

  Halcyon: This is so cool!

  Question: What is this liquid?

  Answer: Water.

• Efficient cause:

  Question: What is this painting?

  Answer: A Picasso.

  Question: What is this car?

  Answer: A Renault.

• Formal cause:

  Question: What is this game?

  Answer: Chess.

  Question: What is this movie about?

  Answer: A love triangle.

  Question: What is this mathematical figure?

  Answer: The lemniscate of Bernoulli.

• Final cause:

  Question: What is a pen?

  Answer: Something for writing or drawing.

  Question: What is a ruler?

  Answer: Something for drawing straight lines or measuring.

  Question: What is a pair of compasses?

  Answer: Something for drawing circles.

Summary

Aristotle’s four causes address aspects of a thing. They can be used to define this thing. They might seem quaint at first, but when encountering a new concept, it is surprisingly fruitful to characterize the four causes of this concept.

More broadly, the present lectures notes follow Aristotle in that they systematically proceed from what is known towards what is unknown (yet), with room enough to grow, freedom enough to make one’s own mistakes, and time enough to learn from these mistakes, without grade penalty.

Mance Rayder: Sounds pretty good to me.

Halcyon (squaring his shoulders): What he said.

Version

Adjusted Mance Rayder’s saying [23 Jan 2023]

Created [10 Jan 2023]