# How do complex propositions and Aristotle's logic work?

Is it allowed to create a syllogism with complex propositions?

Here is my example where P is a sequence of actions and M is a final cause.

S = "Cake maker"

P = "Finding of ingredients, making of dough..."

M = "Making of a cake"

(1) Every making of a cake is a finding of ingredients, a making of dough.etc

(2) Every cake maker makes a cake.

(3) Therefore, Every cake maker finds ingredients, makes dough.etc

But I am getting stuck because P isn't one like "Hot" or "Cold" but many like "Green and furry" so i'm not sure whether the proposition can be in a syllogism at all. Anyone know anything about this?

• In A's syllogism there are only the four basic form of statements. And not every valid inference can be symbolized with syllogism. Commented May 1 at 20:18
• But you do not need syllogism here... when you re-write (3) - following Cort's answer - as "for every x (if Cake-maker(x), then Finds ingredients(x))" then you have already (1), because (2) simply states that a Cake-maker is a Cake-maker. Commented May 2 at 10:31

Aristotle's syllogistic approach sometimes requires some word-smithing to get it into the right form.

It's easier if we rephrase the sentences to use "is." Our English word "is" turns out to line up much better with his logic than other verbs. (2) is the easiest to adjust in this way.

(2) Every cake maker is someone who makes a cake.

With this we can confirm that (S) is indeed "Cake maker", and M has shifted slightly to "someone who makes a cake." In modern algebraic notation, MakesCake(person) is clearly a preposition.

So how do we adjust (3) to fit with this? Once again, the cleanest way to do it is to change the language to "is."

(3) Every cake maker is someone who finds ingredients, makes dough, etc.

This makes (P) "someone who finds ingredients, makes dough, etc." which is now a clear preposition over people. In modern notation we might write FindsIngredientsAndMakesDoughAndEtc(person)

Now we can see the Aristotlian syllogism.

Of course, one is free to then tweak the wording and back it out into the original words you sought, but the clearest lines between subjects and propositions is seen by using "is," changing the sentence until it uses that verb.