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Definition:
A hypothetical proposition is a conditional statement which takes the form: if P
then Q. Examples would include:
If he studied, then he received a good grade.
If we had not eaten, then we would be hungry.
If she wore her coat, then she will not be cold.
In all three statements, the first part (If...) is labeled the antecedent and the second part (then...) is labeled the consequent. In such situations, there are two valid inferences which can be drawn and two invalid inferences which can be drawn - but only when we assume that the relationship expressed in the hypothetical proposition is true. If the relationship is not true, then no valid inferences can be drawn.
A hypothetical statement can be defined by the following truth table:
| P | Q | if P then Q |
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
Assuming the truth of a hypothetical proposition, it is possible to draw two valid and two invalid inferences:
The first valid inference is called affirming the antecedent, which involves making the valid argument that because the antecedent is true, then the consequent is also true. Thus: because it is true that she wore her coat, then it is also true that she will not be cold. The Latin term for this, modus ponens, is often used.
The second valid inference is called denying the consequent, which involves making the valid argument that because the consequent is false, then the antecedent is also false. Thus: she is cold, therefore she did not wear her coat. The Latin term for this, modus tollens, is often used.
The first invalid inference is called affirming the consequent, which involves making the invalid argument that because the consequent is true, then the antecedent must also be true. Thus: she is not cold, therefore she must have worn her coat. This is sometimes referred to as a fallacy of the consequent.
The second invalid inference is called denying the antecedent, which involves making the invalid argument because the antecedent is false, then therefore the consequent must also be false. Thus: she did not wear her coat, therefore she must be cold. This is sometimes referred to as a fallacy of the antecedent.
Understanding how and why the above two invalid inferences occur can be aided by understanding the difference between necessary andsufficient conditions. You can also read the rules of inference to learn more.
Also Known As: none
Alternate Spellings: none
Common Misspellings: none
Related Resources:
What is an Argument?
It helps to know what, exactly, an argument is before you can critique one and tell what is wrong with it. Sometimes, people say they are making arguments when they are not!How do you critique an argument?
Assuming that we have established that we have an actual argument, the next step is to examine it for validity. There are two points on which an argument might fail: its premises or its inferences.What is a Fallacy?
Fallacies are defects in an argument - other than false premises - which cause an argument to be invalid, unsound or weak. By understanding what fallacies are, you can avoid making them and more easily detect them in the work of others.Index of Fallacies
Known logical fallacies listed in categories and explained as to why they are defects in arguments as opposed to valid reasoning. Examples are included so that you can better see what is happening.
