Cecily Zamora
A syllogism is a type of logical argument that uses deductive reasoning to arrive at a conclusion based on two propositions assumed to be true. Deductive reasoning uses facts, definitions, and accepted properties to draw conclusions. The word syllogism comes from the Ancient Greek syllogismos, meaning conclusion, inference. Syllogisms can be represented using a three-line structure, with the first two lines forming the major and minor premises, and the third line forming the conclusion. For example: All mammals are animals. All elephants are mammals. Therefore, all elephants are animals. The law of syllogism, also known as the hypothetical syllogism, is a specific type of syllogism that expresses the transitivity of implication or the conditional. For example, if a=b and b=c, then a=c.
| Characteristics | Values |
|---|---|
| Definition | A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. |
| Structure | Syllogisms are usually represented in a three-line form. |
| Example | All men are mortal. Socrates is a man. Therefore, Socrates is mortal. |
| Fallacies of Invalid Patterns | Undistributed middle, illicit treatment of the major term, illicit treatment of the minor term, exclusive premises, affirmative conclusion from a negative premise. |
| Law of Syllogism | The law of syllogism is a specific case of the transitive property. |
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What You'll Learn
Law of Syllogism vs. Transitive Property
The law of syllogism and the transitive property are both forms of deductive reasoning. Deductive reasoning relies on validity and soundness. A proof that is sound will always be valid, but a valid proof is not always sound.
The transitive property of equality states that if one thing is equal to a second, and the second is equal to a third, then the first is equal to the third. For example, if A = B, and B = C, then A = C. Equality is not the only relation that is transitive. Other binary relations, such as the "less than" relation between numbers, also have the transitive property.
The law of syllogism is a specific case of the transitive property. It is a method of reasoning by drawing a conclusion from two premises. The first, major premise shares something with a second, minor premise, which leads to a conclusion. For example, "If you use our product, your hair will be shiny." "If your hair is shiny, you will have lots of friends." "Therefore, if you use our product, you will have lots of friends." Syllogisms can also be used in geometry, for example, "If it rains today, then I better buy Band-Aids" because "If it rains today, then my dog will get wet, and once inside, he'll shake the water off, which will get the cat wet. If the cat gets wet, then she'll get angry and scratch me."
While the law of syllogism and the transitive property are similar, they are not identical. The transitive property deals with equality, whereas the law of syllogism deals with implication. For example, if Team A beats Team B and Team C, it does not necessarily follow that Team A will beat Team C. However, it can be said that Team A beating Teams B and C implies that they are as good as those teams, which is an example of the law of syllogism.
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Modus Ponens and Modus Tollens
A syllogism is a type of logical argument that uses deductive reasoning to arrive at a conclusion based on two propositions assumed to be true. In other words, a syllogism is a three-part argument with two premises and one conclusion.
The law of syllogism, also known as the hypothetical syllogism, is a specific type of syllogism. Syllogisms use modus ponens, modus tollens, and the law of syllogism to arrive at a conclusion. Modus ponens and modus tollens are logical truths and are, therefore, implications that appear self-evidently true.
Modus ponens is a type of inference drawn from a hypothetical proposition. It is a valid argument form that ensures that when both premises are true, the conclusion must also be true. It can be represented as:
Premise 1: If A, then B
Premise 2: A
For example, "If it is a car, then it has wheels. It is a car. Therefore, it has wheels."
Modus tollens is another valid argument form that operates by denying the consequent. Its structure is as follows:
Premise 1: If A, then B
Premise 2: Not B
For example, "If it snows, then the roads are slippery. The roads are not slippery. Therefore, it did not snow."
In summary, modus ponens and modus tollens are two types of inferences or argument forms that can be drawn from hypothetical propositions. They are both valid forms of reasoning, ensuring that when the premises are true, the conclusion follows necessarily.
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Categorical Syllogisms
A syllogism is a kind of logical argument that uses deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its simplest form, a syllogism consists of two true premises (propositions or statements) that validly imply a conclusion, or the main point that the argument aims to convey.
For example, consider the following argument: "All chipmunks are Republicans. Some Republicans are golfers. Therefore, some chipmunks are golfers." This argument meets the conditions of a categorical syllogism: it has three propositions, there are exactly three classes involved (chipmunks, Republicans, and golfers), and each of the three classes occurs in exactly two of the propositions.
The logical form of a categorical syllogism is determined by two features: its mood and its figure. The mood of a syllogism is determined by the types of categorical propositions contained in the argument and the order in which they occur. In the above example, the mood of the argument is IAI. There are 64 possible moods, created by combining the letters A, E, I, and O into unique three-letter combinations.
The validity of a categorical syllogism can be determined using Venn diagrams. By drawing three overlapping circles to represent the three variables or elements in the argument, we can use shading and labels to represent Universal and Existential statements and evaluate the truth or falsehood of the argument.
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Universal Syllogisms
A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form, defined by Aristotle in his 350 BC book "Prior Analytics", a deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise) and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
The traditional type of syllogism is the categorical syllogism, in which both premises and the conclusion are simple declarative statements that are constructed using only three simple terms between them, each term appearing twice (as a subject and as a predicate). An example of this is: "All men are mortal; no gods are mortal; therefore no men are gods." The argument in such syllogisms is valid because it would not be possible to assert the premises and deny the conclusion without contradicting oneself.
The word syllogism is sometimes used to refer generally to any argument that uses deductive reasoning. Syllogisms can be represented using a three-line structure, in which A, B, and C stand for the different terms. In a syllogism, the more general premise is called the major premise, and the more specific premise is called the minor premise. The conclusion joins the logic of the two premises.
A universal syllogism is a syllogism in which the conclusion is a universal proposition. In other words, a universal syllogism is a type of syllogism where both premises are universal, and therefore, so is the conclusion.
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Disjunctive Syllogisms
A syllogism is a three-part logical argument, based on deductive reasoning, in which two premises are combined to arrive at a conclusion. In its simplest form, a syllogism can be represented as: All A are B. All C are A. Therefore, all C are B.
Disjunctive syllogism is closely related to hypothetical syllogism, which is another rule of inference involving a syllogism. It is also related to the law of noncontradiction, one of the three traditional laws of thought.
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Frequently asked questions
A syllogism is a three-part logical argument, based on deductive reasoning, in which two premises are combined to arrive at a conclusion.
"All mammals are animals. All elephants are mammals. Therefore, all elephants are animals."
The law of syllogism is a specific case of the transitive property. It is the expression of the transitivity of the implication.
A syllogism is a type of logical argument that applies deductive reasoning to arrive at a conclusion. The law of syllogism is a type of syllogism, also known as a hypothetical syllogism.
If p equals q and p is true, then q is true. For example, if an ostrich is the largest living bird, then, as a bird, it is flightless.
