Definition:Argument Form
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Definition
An argument form is a collation of symbols which contains statement variables such that:
- when statements are used to replace statement variables (the same statement replacing the same statement variable throughout), the result is a logical argument.
Specific Form
The specific form of a given logical argument is that argument form from which the logical argument results from replacing each distinct statement variable by a different simple statement.
Examples
Socrates is Mortal
The Socrates is Mortal argument is as follows:
- $(1): \quad$ All humans are mortal.
- $(2): \quad$ Socrates is human.
- $(3): \quad$ Therefore Socrates is mortal.
The argument form is:
- $\forall x: \paren {\map M x \implies \map F x}$
- $\map M a$
- $\therefore \map F a$
In this context:
- $\map M x$ means: $x$ is a human
- $\map F x$ means: $x$ is mortal
- $a$ is a specific instance of $x$.
The following arguments have the same form:
- $(1): \quad$ All men are mortal.
- $(2): \quad$ Alfred is a man.
- $(3): \quad$ Therefore Alfred is mortal.
- $(1): \quad$ All dogs are four-legged.
- $(2): \quad$ Rover is a dog.
- $(3): \quad$ Therefore Rover is four-legged.
Also known as
An argument form is also known as a logical form by some writers, but the latter term is imprecise and is also found to mean statement form.
Sources
- 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): Chapter $\text I$ Introductory: $2$. The Use of Symbols
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $1$ The Nature of Logic
- 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2$ Arguments Containing Compound Statements: $2.3$: Argument Forms and Truth Tables
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): logic
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): logic