Definition:Argument Form

From ProofWiki
Jump to navigation Jump to search

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

Retrieved from "https://proofwiki.org/w/index.php?title=Definition:Argument_Form&oldid=696996"