## Quantifier Rules

Quantifiers are symbols in logic such as '' or '' . These symbols means respectively 'for all' and 'there exists'.

The statementmeans that all all objects for all objects with some property, then every individual object has the property.

More precisely, suppose that X is a set of declarative sentences including the sentenceand suppose D is a designator which occurs in a sentence in X. Suppose thatis the sentence obtained by putting D in place of every free occurrence of 'x' in %phi then X thereforeis a valid argument.

Suppose X is the set consisting of the two statements

(1)

Uranium is an element (2)

We may taketo be the statementand D to be 'Uranium' thenis the statement(3)

Therule then states (1) and (2) imply (3).

The statementmeans that you can never create an inconsistency by naming a thing provided the name is not already used for something else.

More precisely suppose that X is a set of declarative sentences among which is a sentence of the formand suppose D is a proper name which occurs somewhere in X. Suppose that that is the sentence got by putting D in place of every free occurrence of 'x' inThencan be added to X without creating an inconsistency.

Suppose X is the set consisting of the three statements:

TheRule states that if X is consistent then so is the set Y consisting of X together with the sentenceIn fact X is inconsistent.