Suppose the proposition is a conditional statement, and its form is: if P, then Q. Here the first part is the antecedent and the latter is consequent. Fallacies are a flaw in the argument, involving wrong reasoning; sometimes they are deliberately made to influence or mislead readers or listeners. (Affirming the Antecedent)
In this conditional statement “If he studied, then he received a good grade.” The first part (If…) is marked as an antecedent, and the second part (then…) is marked as consequent.
In this case, two valid inferences can be drawn, and two invalid inferences can be drawn-but only if we assume that the relationship expressed in the hypothesis is true. If the relationship is not established, no effective inference can be drawn. Let’s now look whether affirming the antecedent is a valid inference or not?
What is a conditional statement?
A conditional statement can be defined by the following truth table:
| P | Q | if P then Q |
| True | True | True |
| True | False | False |
| False | True | True |
| False | False | True |
Assuming the truth of a hypothetical proposition, it is possible to draw two valid and two invalid inferences:
| Valid Inference | Invalid inference |
| Affirming the Antecedent | Denying the Consequent |
| Affirming the Consequent | Denying the Antecedent |
What is meant by affirming the antecedent?
The first valid inference is called affirming the antecedent, which involves making valid arguments because the antecedent is true, so the consequent is also true.
Let’s take this example to understand this valid inference:
“If she wore her coat, then she will not be cold.”
Therefore because it is true that she does wear her coat, then it will also be true that she will not be cold. In the Latin term for this, modus ponens is often used.
Any argument in this form is valid because it only shows what is implicit in the meaning of the hypothesis. This premise indicates that the true value of p is sufficient to satisfy the true value of q. If we then assume that p is true, we can conclude that q is also true.
What is the use of Direct Reasoning?
Direct reasoning is also related to the modus ponens or affirming the antecedent. When solving problems, the “use direct reasoning” strategy is almost always used in combination with other strategies.
Direct reasoning is used to draw valid conclusions from a series of statements. Generally, the form of sentences involving direct reasoning is “if A then B”. Once the statement is proved to be true, as long as statement A is true, statement B will be true.
Quick Read: Mictlantecuhtli: God of Death (Aztec Religion)
Patterns of Usage
The use of Direct Reasoning strategy may be appropriate when:
- A proof is required.
- A statement of the form “If…then…” is involved.
- You see a statement that you want to imply from a collection of known conditions.
How to know when a conditional statement is affirming the antecedent?
Affirm the antecedent part of the hypothesis directly, and proceed directly from there to the conclusion. The contradictory proof assumes that the hypothesis is correct, and the conclusion is false and continues until the previous hypothesis or proof is forged.
The proof of the opposite is a direct proof of the theorem, which means that the conclusion is considered to be wrong and the proof proceeds directly until the assumption is proved to be wrong.
Sometimes it is difficult to distinguish it from proof by contradiction because some people use the same framework in both types.
Is Modus ponens a Rule of Inference?
Modus Ponens is a deductive argument form and is a rule of inference. It can be abridged as “P implies Q and P are true, therefore Q must be true.”
The form of ponens usage is similar to syllogism, with two premises and a conclusion:
If P, then Q.
The first premise is a conditional (“if-then”) statement, where P means Q. The second premise is to assert that P (which is the premise of the conditional statement) is the case. From these two premises, it can be logically concluded that the conditional result Q must also be the case.
Examples of parameters suitable for modus ponens:
If today is Tuesday, then John will go to work.
Today is Tuesday.
Therefore, John will go to work.
This parameter is valid, but it has nothing to do with whether any statement in the parameter is true. To make the way of committing a crime a reasonable argument, the premise of any real instance of the conclusion must be true.
An argument can be valid, but if one or more premises are false, it is unreasonable. If a parameter is valid and all premises are true, the parameter is correct. For example, John may go to work on Wednesday.
In this case, John’s reason for working (because it is Wednesday) is incorrect. This argument is only valid on Tuesday (when John is at work), but valid every day of the week.
Propositional arguments using conventional methods are considered deductions.
Conclusion
Affirming the antecedent means a valid inference and this is required to understand what the logical deductions are and are they related with the direct reasoning.
By understanding the difference between necessary and sufficient conditions, you can help understand how and why the conditional statements are important to know. You can also read the inference rules to learn more.
People Also Ask (FAQs)
What does affirming the antecedent mean?
Affirming the antecedent is the principle that whenever a conditional statement and its antecedent are given to be true its consequent may be validly inferred as if it’s Tuesday this must be Belgium and its Tuesday so this must be Belgium.
Is affirming the antecedent valid?
Yes, affirming the antecedent is a valid inference. Affirming the antecedent of a conditional and concluding its consequent is a validating form of argument, usually called “modus ponens” in propositional logic.
What is an antecedent in critical thinking?
An antecedent is the first part of a conditional statement) if p, then q.), the component that begins with the word if. Cogent argument. A strong inductive argument with all true premises.
What is disjunction critical thinking?
It is true when p is true, or when q is true, or when p and q are both true; it is false when both p and q are false. For example, ‘Either Mac Did it or Bud did.’ This statement is true if either or both of its component statements, or disjuncts, is true.”
What is the argument form known as Modus Ponens?
Modus ponens (sometimes abbreviated as MP) says that if one thing is true, then another will be. It then states that the first is true. The conclusion is that the second thing is true.