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Polysyllogisms & the Sorites
Categorical syllogisms can be “chained together” to form more complex argumentation. Each syllogism is connected in a chain. One syllogism’s conclusion becomes a premise of the next syllogism. The conclusion to that may become a premise to another syllogism, etc.
Polysyllogisms are precisely that! They are interconnected syllogisms.
A valid polysyllogism requires that every syllogism that composes it be valid.
So, we start with a categorical syllogism. It contains premises P1 and P2. With those we arrive at some conclusion, C1. And next we add another premise, P3. With C1 and P3, assuming everything works validly by following the rules of categorical syllogisms, we arrive at a new conclusion, C2. Add another premise, P4. And then we can reach C3. Etc.
Given a starting syllogism, there will be limits to what the next syllogism can be in order to form a valid polysyllogism.
A cool fact that’s not as discussed as often as it should be is that this can go on infinitely! C1, C2, C3, …, Cn. For example, with syllogisms of the first figure with an AAA mood. These don’t need to logically terminate; they could go on forever. This is assuming validity remains throughout. To be sure, this is a theoretical observation, not strictly a practical observation.
Take, for example, a syllogism in the second figure with an AEE mood. How could that starting point produce an infinite polysyllogism? Here’s a challenge question to consider!
It’s actually not too bad… Recognize that the new premise must be affirmative.
In turns out, the second syllogism would either have to be in the first figure with the mood EAE or the second syllogism, while remaining in the second figure, would have to be the in the mood EAE. If the latter, it can continue that way, theoretically, forever. If the former, it is possible to move back-and-forth between the first figure and the second figure, theoretically, forever.
A Basic Example of a Polysyllogism. . .
All men are mortal.
All Catholics are men.
Therefore, all Catholics are mortal.
But all popes are Catholic.
Therefore, all popes are mortal.
The above polysyllogism consists of two syllogisms, both of which happen to be of the first figure (and are Barbara syllogisms). Notice that the major term of the first syllogism is also the major term of the second syllogism (i.e., mortal). Also, the minor term of the first syllogism becomes the middle term of the second syllogism (i.e., Catholic).
In practice such a series will stop at an individual. Let’s expand that polysyllogism! So, the next proposition with the above example might be: “Jorge Bergoglio is a pope.” Combined with the previous proposition; ergo, “Jorge Bergoglio is mortal.”
Once again, notice that the major term remains constant (i.e., mortal).
The previous minor term becomes the middle term (i.e., pope).
Another Example of a Polysyllogism. . .
All philosophers are contemplative.
No member of congress is contemplative.
Hence, no member of congress is a philosopher.
All in this room are contemplative.
Hence, nobody in this room is a member of congress.
Sorites!
Sorites are a type of shortened or abridged polysyllogism.
Many middle terms are “linked” together in an easy to follow way.
Sorites are in the first figure.
The first proposition’s predicate term becomes the subject of the second proposition. The second proposition’s predicate terms becomes the subject term of the third proposition. Etc. The conclusion’s subject is the same as the first proposition’s subject.
Basic Example of a Sorites. . .
Socrates is a man.
All men are animals.
All animals are living beings.
All living beings are substances.
Therefore, Socrates is a substance.
This example has many middle terms: men, animals, and living beings. It’s composed of syllogisms of the first figure.
And notice that it’s actually an abridged polysyllogism. . .
Socrates is a man.
All men are animals.
[Therefore, Socrates is an animal.]
All animals are living beings.
[Therefore, Socrates is a living being.]
All living beings are substances.
Therefore, Socrates is a substance.
As constituted, there really are two “special” rules for sorites. Only the last premise can be negative (to get a negative conclusion). And only the first premise can be particular (to get a particular conclusion).
Additional Examples. . .
Complete the polysyllogism.
Example 1: “Some theologians are not arrogant. All theologians have an obligation to be virtuous. This implies that some of those who have an obligation to be virtuous are not arrogant. And all of those who have an obligation to be virtuous can help produce a more just society.” Therefore . . .
Complete the sorites argument.
Example 2: “Some people are very hard working. All hard working people are focused. People who are focused can accomplish a lot. And people who can accomplish a lot can contribute a lot to their community.” Therefore. . . .
Figure out the missing major premise of the sorites argument.
Example 3: “__________ . All citizens of Cook County are Illinoisans. All Illinoisans are Midwesterners and all Midwesterns are Americans. Ergo, all Chicagoans are Americans.”
***
Example 1 has the conclusion “Thus, some of those who can help produce a more just society are not arrogant.” Example 2 has the conclusion “Thus, some people contribute a lot to their community.” Example 3 is missing the major premise “All Chicagoans are citizens of Cook County.”