First, be familiar with the vocabulary of syllogism.
1, how to demonstrate the realization of syllogism.
To understand syllogism, you need to be familiar with several terms that are often used when discussing formal logic. At the most basic level, syllogism is the simplest sequence of logical premise combinations leading to conclusions. The premise is the proposition used as evidence in the argument. The conclusion is asserted by the logical result of the argument based on the premise relationship.
Take the conclusion of syllogism as the "proposition" of argument. In other words, the conclusion is the point of premise proof.
2. Determine the three parts of syllogism.
Recall that syllogism includes major premise, minor premise and conclusion. For example, "everyone will die" may be a major premise and will become a universally accepted fact. "David Foster Wallace is a man" can be used as a minor premise.
Please note that the minor premise is more specific and directly related to the major premise.
If each of the previous statements is considered to be correct, the logical conclusion will be "David Foster Wallace will die".
3. Determine the minor and major projects.
The minor premise and major premise of syllogism must have the same items as the conclusion. At the same time, the term in the major premise and conclusion is a big term, which constitutes the predicate of the conclusion-in other words, it states something about the theme of the conclusion. Minor premise and conclusion * * * Some items are minor items and will be the subject of conclusion.
Consider this example: "All birds are animals. The Turkish vulture is a bird. All Turkish vultures are animals. "
Here, "animal" is a big term, because it is both a major premise and a predicate of the conclusion.
"Turkish vulture" is a small term, because it is the subject of the conclusion in the minor premise.
Please note that these two premises also enjoy a classification and terminology, in this case, a "bird". This is called the middle term, which is very important for determining the figure of syllogism, and the following steps will be solved.
Step 4 find classifications and terms
If you are preparing for the logical reasoning exam, or just want to better understand syllogism, please note that most syllogisms you will encounter are classified. This means that they will rely on reasoning like this: "If _ _ _ is/is not [a member of a certain category], then _ _ _ is/is not [also a member of this category/a member of a different category]".
Another way to consider the logical order of syllogism classification is that they all adopt the logical order of "part/whole/no _ _ _ _ yes/no _ _ _ _".
5. Understand the distribution of terms in syllogism.
Each of the three parts of syllogism can put forward four different types of propositions. Think about the differences between them when assigning (or not assigning) any categories and terms. A category term is considered "distributed" only when all individual members of the category are included in the category. For example, under the premise that "everyone will die", the word "person" is assigned, because every member belonging to this category is counted-in this case, as a mortal. Notice how four different types of propositions allocate (or not allocate) terms:
In the proposition "Everything X is Y", the subject (X) is distributed.
In the proposition "No X is Y", both the subject (X) and the predicate (Y) are distributed.
In the proposition "A certain X is Y", the subject and predicate are not distributed.
In a proposition that X is not Y, the predicate (Y) is distributed.
Step 6 identify a thyme
Enthymemes, except for another name that is difficult to pronounce, is just a compressed syllogism. Another way to understand roots is a one-sentence syllogism, which can help you realize how and why syllogism is a convenient reasoning tool.
Specifically, rhyming does not consider the major premise, but combines the minor premise with the conclusion.
For example, consider a syllogism: "All dogs are dogs. Lola is a dog. Lola is a dog. " The rhythm of the same logical sequence is: "Lola is a dog because she is a dog."
Another example of rhythm is "David Foster Wallace is mortal because he is human."
Thirdly, identify invalid syllogism.
1, distinguishing validity from rationality.
Logically valid syllogism is a syllogism in which the premise must contain the conclusion, because the premise cannot be true and the conclusion cannot be false. However, if the premise of an effective syllogism is false, it may actually be untrue. This is called imperfect syllogism. A reasonable syllogism is an effective syllogism with real premises. A reasonable syllogism is faithful, and a true proposition needs a true conclusion.
For example, consider a syllogism: "All dogs can fly. Fido is a dog. Fido can fly. " This syllogism is logically established, but because the major premise is not established, the conclusion is obviously inaccurate and syllogism is unreliable.
The structure of syllogism argument-the reasoning of argument itself-is what you should evaluate when evaluating the logical validity of syllogism. When evaluating robustness, you are evaluating its effectiveness and the factual accuracy of the premise.
2. Looking for invalid language talent.
When determining validity, observe the positive or negative nature of premises and conclusions. Please note that if any premise is negative, then the conclusion must be negative. If both premises are affirmative, then the conclusion must be affirmative. If you don't follow any of these rules, you already know that syllogism is invalid.
In addition, at least one of the two premises of syllogism must be positive, because an effective conclusion cannot be drawn from two negative premises. For example, "no pencil is a cat, some cats are not pets, so some pets are not pencils" has a true premise and a true conclusion, but it is invalid because there are two negative premises. If you change your position, you will come to an absurd conclusion that some pets are pencils.
In addition, at least one premise of an effective syllogism must contain the full name form. If both premises are special, then no effective conclusion can be drawn. For example, "some cats are black" and "some black things are tables" is a special proposition, and it cannot be concluded that "some cats are tables".
You usually simply know without thinking that a syllogism that violates one of the rules is invalid because it may sound illogical.
3. Be skeptical about conditional syllogism.
Conditional syllogism is hypothetical, and their conclusions are not always valid, because they depend on an unconfirmed condition, that is, the premise is true. Conditional syllogism will include reasoning based on "If _ _ _, then _ _". These syllogisms are invalid when there are other factors that may contribute to the conclusion.
For example, "If you eat Jolly Ranchers every day, you are at risk of developing diabetes. Sterling doesn't eat Happy Wanderers every day. Sterling is not at risk of diabetes. "
This syllogism is invalid for several reasons. Among them, Sterling may eat a lot of Jolly Rangers a few days a week-but not every day-which still puts him at risk of diabetes. Or, Sterling may eat cakes every day, which will definitely put him at risk of diabetes.
4. Pay attention to the fallacy of syllogism
Syllogism can allow wrong arguments to imply incorrect conclusions. Consider this example: "Jesus walked on water. Green lizard lizard walks on the water. The green lizard lizard is Jesus. " This conclusion is not necessarily correct, because the middle term-in this case, "the ability to walk on water"-is not distributed in the conclusion.
For another example, "all dogs like food" and "John likes food" do not logically mean "John is a dog". These are called undistributed intermediate fallacies, in which the terms connecting two phrases are never completely distributed.
Also beware of the fallacy of illegal occupation. For example, consider: "All cats are animals. No dog is a cat. No dog is an animal. " This is invalid because the premise that "animals" are not distributed-not all animals are cats, but the conclusion depends on this hint.
The same is true for minors who violate the law. For example, "All cats are mammals. All cats are animals. All animals are mammals. " This is invalid because not all animals are cats, and the conclusion depends on this invalid hint.
Third, determine the form and figure of the outspoken syllogism.
1, identify the proposition type
If every premise of syllogism is considered valid, then the conclusion may also be valid. However, the validity of logic also depends on the form and image of syllogism, both of which depend on the proposition of syllogism. In category syllogism, four different types of propositions are used to form premises and conclusions.
The "A" proposition puts forward the full name affirmation, for example, "All [classifications or specific terms] are [different classifications or specific terms]". For example, "All cats are cats".
The "e" proposition puts forward the opposite: universal negation. For example, "no [classification of specific terms] means [different classification or specific terms]." More specifically, "no dog is a cat."
The "I" proposition contains a concrete positive definiteness, which involves an item in the premise. For example, "some cats are black."
The "O" proposition, on the other hand, contains a specific negative qualification. For example, "some cats are not black."
2. Identify the tone of syllogism according to the proposition of syllogism.
By determining which of the four propositions to use, we can simplify syllogism into three letters to help determine whether it is an effective form of a specific syllogism diagram. Different syllogism graphics will be described in the following steps. Now, as long as you know that you can mark every part of syllogism-including every premise and conclusion-according to the types of propositions they put forward to identify the emotions of syllogism.
For example, consider an outspoken syllogism in AAA tone: "All X's are Y's. All y is z, so all x is z.
Mood only refers to the types of propositions used in standard sequence syllogism-major premise, minor premise and conclusion-and it may be the same for two different forms according to the form of syllogism discussed.
3, determine the "figure" of syllogism
The case of syllogism is determined by whether the middle term is the subject or predicate in the premise. Recall that the subject is the content of the sentence and the predicate is the word applied to the subject of the sentence.
In the first case syllogism, the middle term acts as the subject in the major premise and the predicate in the minor premise: "All birds are animals. All parrots are birds. All parrots are animals. "
In the second case syllogism, the middle term acts as a predicate in the major premise and a predicate in the minor premise. For example, "No fox is a bird. All parrots are birds. No parrot is a fox. "
In the third case syllogism, the middle term is the subject in the major premise and the subject in the minor premise. For example, "All birds are animals. All birds will die. Some mortals are animals. "
In the fourth case syllogism, the middle term acts as the predicate in the major premise and the subject in the minor premise. For example, "No bird is a cow. All cows are animals. Some animals are not birds. "
4. Identify the effective form of syllogism.
Although there are 256 mathematically possible forms of syllogism-because each part of syllogism has four possible variants (A/E/I/O) and four different forms of syllogism-only 19 is logically effective.
For the first case syllogism, the effective forms are AAA, EAE, AII and EIO.
For the second lattice syllogism, the effective forms are EAE, AEE, EIO and AOO.
For the third case syllogism, the effective forms are AAI, IAI, AII, EAO, OAO and EIO.
For the fourth lattice syllogism, the effective forms are AAI, AEE, IAI, EAO and EIO.