Finding an Arguments Validity Using the Mood and Figure

How It All Works

In order to determine the validity of an argument, you first must find the mood and figure of the argument; the order this process follows is Mood → Figure → validity.

Mood

The mood is an arrangement of the following letters A, E, I, and O, which stand for variations of the form called categoricals, which follows the following chart:

A :	All S are P
E :	No S are P
I :	Some S are P
O :	Some S are not P

The way we use the chart above is by replacing S and P with the terms used in an argument; an example of this is replacing S and P with the terms “Athenian” and “Greek,” so an example of form A would be “All Athenians are Greek.”
Here is an example of categoricals being used in a full argument:
- All Athenians are Greek. | A (All S are P)
- Some humans are not Athenians. | O (Some S are not P)
- So, some humans are not Greek.| O (Some S are not P)
  - Putting the categoricals together makes AOO, which is what we call our “mood.”
Let’s look at another example.
- All sentient creatures are rights-holders. | A (All S are P)
- All animals are sentient. | A (All S are P)
- So all animals are rights holders. | A (All S are P)
  - Putting the categoricals together makes AAA which is the mood for this given argument.

How to Find the Figure

In the simplest explanation, you can find the figure by identifying where the middle term is positioned in an argument in the first and second sentences; the middle term can be explained as a recurring term in an argument that does not show in the conclusion of an argument.
There are four kinds of figures, and they are broken down in the following chart.

Figure 1:	When the middle term is on the left in the first premise and on the right in the second premise.
Figure 2:	When the middle term is on the right in both the first and second premises.
Figure 3:	When the middle term is on the left in both the first and second premises.
Figure 4:	When the middle term is on the right in the first premise and on the left in the second premise.

The way we use the chart above is by finding the middle term in both the first and second premise and using their position to see which figure they belong to.
Here is an example of finding the middle term and finding its figure; we will underline the middle term for simplicity.
- All Athenians are Greek.
- Some humans are not Athenians.
- So some humans are not Greek.
  - In this argument, the middle term was “Athenians,” located on the left in the first premise and on the right in the second premise, making it figure 1.
Let’s look at another example.
- All liars are self-deceived people.
- All liars are wicked people.
- So, all wicked people are self-deceived people.
  - In this argument, the middle term was “liars,” located on the left in both the first and second premises, making it figure 3.

Using the Mood and Figure to Find Validity

We determine validity by locating the arguments figure on the top of the following chart and then searching for the arguments mood in the figures column; if you cannot find your mood in your figures column, then your argument is invalid.
- An argument’s mood can fall in a column that states “… must refer,” and if this happens, for example, if it landed in the “minor term must refer column,” you would write “Valid only if the minor term refers.”

Figures / Validity	Figure 1	Figure 2	Figure 3	Figure 4
15 Valid forms	AAA \| EAE \| AII \| EIO	AOO \| AEE \| EAE \| EIO	OAO \| IAI \| AII \| EIO	AEE \| IAI \| EIO
Minor term must refer	AAI \| EAO	AEO \| EAO		AEO
Middle term must refer			AAI \| EAO	EAO
Major term must refer				AII

Here is an example of finding the validity of your argument using the chart above:
- All Athenians are Greek. | A (All S are P)
- Some humans are not Athenians. | O (Some S are not P)
- So, some humans are not Greek.| O (Some S are not P)
- Mood: AOO, Figure: 1
  - By looking at the figure 1 column, we can see the mood AOO is not inside that column, making this argument invalid.
Let’s look at another example:
- All meaningful activities are worth doing well. (All S are P)
- Some hobbies are not things worth doing well. O (Some S are not P)
- So, some hobbies are not meaningful activities. O (Some S are not P)
- Mood: AOO, Figure: 2
  - By looking at the figure 2 column, we can see the mood AOO is inside the column, making this argument valid.
Let’s look at an “… must refer” example:
- No gin drinkers are Russian speakers E (No S are P)
- All English miners are gin drinkers A (All S are P)
- So, some English miners are not Russian speakers. O (Some S are not P)
- Mood: EAO, Figure: 1
  - By looking at the figure 1 column, we can see the mood EAO is inside the column but intersects with “Minor term must refer,” which means this argument is “valid only if the minor term refers.”

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Finding an Arguments Validity Using the Mood and Figure

How It All Works

In order to determine the validity of an argument, you first must find the mood and figure of the argument; the order this process follows is Mood → Figure → validity.

Mood

The mood is an arrangement of the following letters A, E, I, and O, which stand for variations of the form called categoricals, which follows the following chart:

A :	All S are P
E :	No S are P
I :	Some S are P
O :	Some S are not P

The way we use the chart above is by replacing S and P with the terms used in an argument; an example of this is replacing S and P with the terms “Athenian” and “Greek,” so an example of form A would be “All Athenians are Greek.”
Here is an example of categoricals being used in a full argument:
- All Athenians are Greek. | A (All S are P)
- Some humans are not Athenians. | O (Some S are not P)
- So, some humans are not Greek.| O (Some S are not P)
  - Putting the categoricals together makes AOO, which is what we call our “mood.”
Let’s look at another example.
- All sentient creatures are rights-holders. | A (All S are P)
- All animals are sentient. | A (All S are P)
- So all animals are rights holders. | A (All S are P)
  - Putting the categoricals together makes AAA which is the mood for this given argument.

How to Find the Figure

In the simplest explanation, you can find the figure by identifying where the middle term is positioned in an argument in the first and second sentences; the middle term can be explained as a recurring term in an argument that does not show in the conclusion of an argument.
There are four kinds of figures, and they are broken down in the following chart.

Figure 1:	When the middle term is on the left in the first premise and on the right in the second premise.
Figure 2:	When the middle term is on the right in both the first and second premises.
Figure 3:	When the middle term is on the left in both the first and second premises.
Figure 4:	When the middle term is on the right in the first premise and on the left in the second premise.

The way we use the chart above is by finding the middle term in both the first and second premise and using their position to see which figure they belong to.
Here is an example of finding the middle term and finding its figure; we will underline the middle term for simplicity.
- All Athenians are Greek.
- Some humans are not Athenians.
- So some humans are not Greek.
  - In this argument, the middle term was “Athenians,” located on the left in the first premise and on the right in the second premise, making it figure 1.
Let’s look at another example.
- All liars are self-deceived people.
- All liars are wicked people.
- So, all wicked people are self-deceived people.
  - In this argument, the middle term was “liars,” located on the left in both the first and second premises, making it figure 3.

Using the Mood and Figure to Find Validity

We determine validity by locating the arguments figure on the top of the following chart and then searching for the arguments mood in the figures column; if you cannot find your mood in your figures column, then your argument is invalid.
- An argument’s mood can fall in a column that states “… must refer,” and if this happens, for example, if it landed in the “minor term must refer column,” you would write “Valid only if the minor term refers.”

Figures / Validity	Figure 1	Figure 2	Figure 3	Figure 4
15 Valid forms	AAA \| EAE \| AII \| EIO	AOO \| AEE \| EAE \| EIO	OAO \| IAI \| AII \| EIO	AEE \| IAI \| EIO
Minor term must refer	AAI \| EAO	AEO \| EAO		AEO
Middle term must refer			AAI \| EAO	EAO
Major term must refer				AII

Here is an example of finding the validity of your argument using the chart above:
- All Athenians are Greek. | A (All S are P)
- Some humans are not Athenians. | O (Some S are not P)
- So, some humans are not Greek.| O (Some S are not P)
- Mood: AOO, Figure: 1
  - By looking at the figure 1 column, we can see the mood AOO is not inside that column, making this argument invalid.
Let’s look at another example:
- All meaningful activities are worth doing well. (All S are P)
- Some hobbies are not things worth doing well. O (Some S are not P)
- So, some hobbies are not meaningful activities. O (Some S are not P)
- Mood: AOO, Figure: 2
  - By looking at the figure 2 column, we can see the mood AOO is inside the column, making this argument valid.
Let’s look at an “… must refer” example:
- No gin drinkers are Russian speakers E (No S are P)
- All English miners are gin drinkers A (All S are P)
- So, some English miners are not Russian speakers. O (Some S are not P)
- Mood: EAO, Figure: 1
  - By looking at the figure 1 column, we can see the mood EAO is inside the column but intersects with “Minor term must refer,” which means this argument is “valid only if the minor term refers.”