Socrates is Mortal
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Theorem
- $(1): \quad$ All humans are mortal.
- $(2): \quad$ Socrates is human.
- $(3): \quad$ Therefore Socrates is mortal.
Variant
- $(3): \quad$ Therefore Socrates is mortal.
Proof
Let $x$ be an object variable from the universe of rational beings.
Let $\map H x$ denote the propositional function $x$ is human.
Let $\map M x$ denote the propositional function $x$ is mortal.
Let $S$ be a proper name that denotes Socrates.
The argument can then be expressed as:
\(\text {(1)}: \quad\) | \(\ds \forall x: \, \) | \(\ds \map H x\) | \(\implies\) | \(\ds \map M x\) | ||||||||||
\(\ds \therefore \ \ \) | \(\ds \map H S\) | \(\implies\) | \(\ds \map M S\) | Universal Instantiation | ||||||||||
\(\text {(2)}: \quad\) | \(\ds \map H S\) | \(\) | \(\ds \) | |||||||||||
\(\text {(3)}: \quad\) | \(\ds \therefore \ \ \) | \(\ds \map M S\) | \(\) | \(\ds \) | Modus Ponendo Ponens |
That is:
- Socrates is mortal.
$\blacksquare$
Also presented as
The subject of this syllogism varies.
For example, 1993: Richard J. Trudeau: Introduction to Graph Theory presents it as Plato.
Historical Note
The syllogism Socrates is Mortal appears first to have been presented by Aristotle.
Sources
- 1951: Willard Van Orman Quine: Mathematical Logic (revised ed.) ... (previous) ... (next): Introduction
- 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $1$ Introduction: Logic and Language: $1.2$: The Nature of Argument
- 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $4$: Propositional Functions and Quantifiers: $4.2$: Proving Validity: Preliminary Quantification Rules
- 1993: Richard J. Trudeau: Introduction to Graph Theory ... (previous) ... (next): $1$. Pure Mathematics: Games