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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 and has the following form:
If P, therefore Q.
Not P.
Therefore, Not Q.
A practical example of this would be:
If Roger is a Democrat, then he is liberal. Roger is not a Democrat, therefore he must not be liberal.
Because this is a formal fallacy, anything written with this structure will be wrong, no matter what terms you use to replace P and Q with.
Understanding how and why the above two invalid inferences occur can be aided by understanding the difference between necessary and sufficient conditions. You can also read the rules of inference to learn more.
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Related Resources:
What is the Logic and the Philosophy of Language?
The two fields Logic and the Philosophy of Language are often treated separately, but they are nevertheless close enough that they are presented together here. Logic is the study of methods of reasoning and argumentation, both proper and improper. The Philosophy of Language, on the other hand, involves the study of how our language interacts with our thinking.
What is Philosophy?
What is philosophy? Is there any point in studying philosophy, or is it a useless subject? What are the different branches of philosophy - what's the difference between aestheitcs and ethics? What's the difference between metaphysics and epistemology?
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