Propositional Logic
Propositional logic, formalized by the Stoic philosopher Chrysippus, is the branch of logic that deals with the truth-functional relationships between propositions and the valid inferences, such as modus ponens and modus tollens, that can be derived from them.
THE IDEA
Propositional Logic
There is a tradition of reasoning with propositions or sentences in the West that goes back to Aristotle as well but received its first serious treatment with the Stoic philosopher Chrysippus (ca. 280–205 BCE). Whereas categorical logic deals with the attributes of categories of things and what can be inferred from the relationships between and among these things, propositional logic concerns the attributes of claims (propositions, sentences) and the reasoning possible when claims are related to one another.
Among others, Chrysippus noted these pieces of correct reasoning:
- If the 1st, then the 2nd. But, the 1st. Therefore, the 2nd. (Modus Ponens)
- If the 1st, then the 2nd. But, not the 2nd. Therefore, not the 1st. (Modus Tollens)
- Either the 1st or the 2nd. But not the 1st. Therefore, the 2nd. (Disjunctive Syllogism)
Examples of these arguments:
Disjunctive Syllogism: There are only two ways for me to get to work – either Highway 1 or Main St. Highway 1 is closed due to construction. So, I have to take Main St. to work today.
Modus Tollens: If my client committed the crime, then he would have been in Chicago. But he wasn't in Chicago (check the gas receipts, GPS, and witness testimony). Therefore, my client did not commit the crime.
Constructive Dilemma: If it’s raining we’ll stay inside, and if it’s snowing we’ll go outside to play. It’s either raining or snowing. Hence, we’ll either stay inside or go outside to play.
When to use it
Software Debugging: Using Modus Tollens to narrow down bugs. 'If the bug is in Module A, the database will show error X. The database does not show error X. Therefore, the bug is not in Module A.'
Legal argumentation: distinguish a valid deductive form from the separate question of whether its premises are established.
Everyday Decision Making: Systematically evaluating 'if-then' scenarios to avoid fallacious reasoning.
Mathematics: Proving theorems by constructing rigorous chains of logical deduction.
FROM THEORY TO EVERYDAY LIFE
In practice
Commute Route (Disjunctive Syllogism)
There are only two ways for me to get to work – either Highway 1 or Main St. Highway 1 is closed due to construction. Therefore, I have to take Main St. to work today.
Legal Alibi (Modus Tollens)
If my client committed the crime, then he would have been in Chicago. He was not in Chicago. Therefore, my client did not commit the crime.
A MOMENT TO REFLECT
Put it to work.
Think of a recent argument. Does it fit one of the valid forms here? If it uses another form, how would you check whether the conclusion follows?
How does understanding Modus Tollens ('If A then B, not B, therefore not A') help in designing scientific experiments or debugging software?
Why is it important to distinguish between 'If P then Q, Q, therefore P' (affirming the consequent) and 'If P then Q, P, therefore Q' (Modus Ponens)?
Often confused with
References
- Propositional Logic (Stoic Logic) — Chrysippus (-280)
CONTINUE THE CONVERSATION
Source texts
- Bad Arguments 100 of the Most Important Fallacies in Western Philosophy (Steven Barbone, Michael Bruce)