How to Understand Syllogisms
Recognize how a syllogism makes an argument., Determine the three parts of a syllogism., Determine the minor and major terms., Look for categorical terms., Understand the distribution of terms in a syllogism., Identify an enthymeme.
Step-by-Step Guide
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Step 1: Recognize how a syllogism makes an argument.
To understand syllogisms, you need to familiarize yourself with several terms often used when discussing formal logic.
At the most basic level, a syllogism is the simplest sequence of a combination of logical premises that lead to a conclusion.
A premise is a proposition that is used as evidence in an argument.
A conclusion is asserted by the logical result of an argument based on the relationship of the stated premises.Consider the conclusion of a syllogism to be the “thesis” of an argument.
In other words, the conclusion is the point proven by the premises. -
Step 2: Determine the three parts of a syllogism.
Recall that a syllogism includes a major premise, a minor premise, and a conclusion.
Jumping into an example: “All humans are mortal” might function as a major premise, and would stand as a generally accepted fact. “David Foster Wallace is a human” might follow as a minor premise.Notice that the minor premise is more specific, and immediately relates to the major premise.
If each of the prior statements are considered valid, the logical conclusion would be “David Foster Wallace is mortal.” , Both the minor and major premises of a syllogism must have one term in common with the conclusion.
The term that is in both the major premise and the conclusion is the major term, which forms the predicate of the conclusion – in other words, it states something about the subject of the conclusion.
The term shared by the minor premise and the conclusion is the minor term, which will be the subject of the conclusion.Consider the example: “All birds are animals.
Turkey vultures are bird.
All turkey vultures are animals.” Here, “animal” is the major term, as it is in both the major premise and is the predicate of the conclusion. “Turkey vulture” is the minor term, as it is in the minor premise and is the subject of the conclusion.
Notice that there is also a categorical term shared by the two premises, in this case “bird.” This is called the middle term, and is of immense importance in determining the figure of the syllogism, which is addressed in a later step. , If you’re preparing for a logical reasoning test, or simply want to better understand syllogisms in general, note that most syllogism you will encounter will be categorical.
This means that they will rely on reasoning akin to: “If ____ are/are not , then ____ are/are not ”Another way to think of the logical sequence employed by categorical syllogisms is that they all employ the logical sequence of “Some/all/no _____ is/isn’t ______.” , There are four different types of propositions that can be made by each of the three parts of a syllogism.
Think of how they differ in terms of how they each distribute – or don’t distribute – any categorical term.
Consider a categorical terms to be “distributed” only if all individual members of that category are accounted for in the term.
For example, in the premise "all men are mortal"
the term "men" is distributed, as every member belonging to that category is accounted for – in this case, as mortal.
Note how each of the four different types of propositions distributes (or does not distribute) the terms:
In "All X are Y" propositions, the subject (X) is distributed.
In "No X are Y" propositions, both the subject (X) and the predicate (Y) are distributed.
In "Some X are Y" propositions, neither the subject nor the predicate are distributed.
In "Some X are not Y" propositions, the predicate (Y) is distributed. , Enthymemes, aside from having another really hard to pronounce name, are simply compressed syllogisms.
Another way to think of an enthymeme is as a one-sentence syllogism, which may help you recognize both how and why syllogisms are a convenient reasoning device.In specific terms, enthymemes disregard the major premise and combine the minor premise with the conclusion.
For instance, consider the syllogism: “All dogs are canine.
Lola is a dog.
Lola is a canine.” The enthymeme of this same logical sequence would be: “Lola is a canine because she’s a dog.” Another example of an enthymeme is “David Foster Wallace is mortal because he is human.” -
Step 3: Determine the minor and major terms.
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Step 4: Look for categorical terms.
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Step 5: Understand the distribution of terms in a syllogism.
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Step 6: Identify an enthymeme.
Detailed Guide
To understand syllogisms, you need to familiarize yourself with several terms often used when discussing formal logic.
At the most basic level, a syllogism is the simplest sequence of a combination of logical premises that lead to a conclusion.
A premise is a proposition that is used as evidence in an argument.
A conclusion is asserted by the logical result of an argument based on the relationship of the stated premises.Consider the conclusion of a syllogism to be the “thesis” of an argument.
In other words, the conclusion is the point proven by the premises.
Recall that a syllogism includes a major premise, a minor premise, and a conclusion.
Jumping into an example: “All humans are mortal” might function as a major premise, and would stand as a generally accepted fact. “David Foster Wallace is a human” might follow as a minor premise.Notice that the minor premise is more specific, and immediately relates to the major premise.
If each of the prior statements are considered valid, the logical conclusion would be “David Foster Wallace is mortal.” , Both the minor and major premises of a syllogism must have one term in common with the conclusion.
The term that is in both the major premise and the conclusion is the major term, which forms the predicate of the conclusion – in other words, it states something about the subject of the conclusion.
The term shared by the minor premise and the conclusion is the minor term, which will be the subject of the conclusion.Consider the example: “All birds are animals.
Turkey vultures are bird.
All turkey vultures are animals.” Here, “animal” is the major term, as it is in both the major premise and is the predicate of the conclusion. “Turkey vulture” is the minor term, as it is in the minor premise and is the subject of the conclusion.
Notice that there is also a categorical term shared by the two premises, in this case “bird.” This is called the middle term, and is of immense importance in determining the figure of the syllogism, which is addressed in a later step. , If you’re preparing for a logical reasoning test, or simply want to better understand syllogisms in general, note that most syllogism you will encounter will be categorical.
This means that they will rely on reasoning akin to: “If ____ are/are not , then ____ are/are not ”Another way to think of the logical sequence employed by categorical syllogisms is that they all employ the logical sequence of “Some/all/no _____ is/isn’t ______.” , There are four different types of propositions that can be made by each of the three parts of a syllogism.
Think of how they differ in terms of how they each distribute – or don’t distribute – any categorical term.
Consider a categorical terms to be “distributed” only if all individual members of that category are accounted for in the term.
For example, in the premise "all men are mortal"
the term "men" is distributed, as every member belonging to that category is accounted for – in this case, as mortal.
Note how each of the four different types of propositions distributes (or does not distribute) the terms:
In "All X are Y" propositions, the subject (X) is distributed.
In "No X are Y" propositions, both the subject (X) and the predicate (Y) are distributed.
In "Some X are Y" propositions, neither the subject nor the predicate are distributed.
In "Some X are not Y" propositions, the predicate (Y) is distributed. , Enthymemes, aside from having another really hard to pronounce name, are simply compressed syllogisms.
Another way to think of an enthymeme is as a one-sentence syllogism, which may help you recognize both how and why syllogisms are a convenient reasoning device.In specific terms, enthymemes disregard the major premise and combine the minor premise with the conclusion.
For instance, consider the syllogism: “All dogs are canine.
Lola is a dog.
Lola is a canine.” The enthymeme of this same logical sequence would be: “Lola is a canine because she’s a dog.” Another example of an enthymeme is “David Foster Wallace is mortal because he is human.”
About the Author
Tyler Garcia
Tyler Garcia has dedicated 6 years to mastering sports and recreation. As a content creator, Tyler focuses on providing actionable tips and step-by-step guides.
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