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Comment

Valid means true in all cases.

Thus, the schema :

Some A are B

 

Some B are C

 

Therefore : Some A are C

is not valid exactly for the reason you have stated :

it becomes true [not valid] if at least one element lies in A ∩ B ∩ C.

Correct..., but if this is not, the argument does not conclude, and this means that the argument form is not valid.

This distinction between true and valid is the core of Hurley's explanation of Rule 4 (and is the core of formal logic, since Aristotle).

Consider the fallacy :

Drawing an affirmative conclusion from a negative premise,

and consider the invalid :

All crows are birds

 

Some wolves are not crows

 

Therefore : Some wolves are birds.

This is a counter-example to the "purported" rule :

it is possible to (validly) conclude in the affermative when a premise is negative.

This means that, from the fact :

if a schema has one premise negative and the conclusion affermative, then it is not valid,

by contraposition we have :

if a schema is valid, then not (one premise negative and the conclusion affermative) i.e. either the conclusion is negative or all the premise must be afermative.

Comment

Valid means true in all cases.

Thus, the schema :

Some A are B

Some B are C

Therefore : Some A are C

is not valid exactly for the reason you have stated :

it becomes true [not valid] if at least one element lies in A ∩ B ∩ C.

Correct..., but if this is not, the argument does not conclude, and this means that the argument form is not valid.

This distinction between true and valid is the core of Hurley's explanation of Rule 4 (and is the core of formal logic, since Aristotle).

Consider the fallacy :

Drawing an affirmative conclusion from a negative premise,

and consider the invalid :

All crows are birds

Some wolves are not crows

Therefore : Some wolves are birds.

This is a counter-example to the "purported" rule :

it is possible to (validly) conclude in the affermative when a premise is negative.

This means that, from the fact :

if a schema has one premise negative and the conclusion affermative, then it is not valid,

by contraposition we have :

if a schema is valid, then not (one premise negative and the conclusion affermative) i.e. either the conclusion is negative or all the premise must be afermative.

Comment

Valid means true in all cases.

Thus, the schema :

Some A are B

Some B are C

Therefore : Some A are C

is not valid exactly for the reason you have stated :

it becomes true [not valid] if at least one element lies in A ∩ B ∩ C.

Correct..., but if this is not, the argument does not conclude, and this means that the argument form is not valid.

This distinction between true and valid is ate the core of Hrley's explanation of Rule 4.

Consider the invalid :

All crows are birds

Some wolves are not crows

Therefore : Some wolves are birds.

This is a counter-example to the "purported" rule :

it is possible to conclude in the negative when both premises are affirmative.

This means that, from the fact : if a schema has all premises affirmative and conclusion negative, then it is not valid, by contraposition we have :

if a schema is valid, then not-(all premises affirmative and conclusion negative) i.e. either some premise is negative or the conclusion is affirmative.

Comment

Valid means true in all cases.

Thus, the schema :

Some A are B

Some B are C

Therefore : Some A are C

is not valid exactly for the reason you have stated :

it becomes true [not valid] if at least one element lies in A ∩ B ∩ C.

Correct..., but if this is not, the argument does not conclude, and this means that the argument form is not valid.

This distinction between true and valid is the core of Hurley's explanation of Rule 4 (and is the core of formal logic, since Aristotle).

Consider the fallacy :

Drawing an affirmative conclusion from a negative premise,

and consider the invalid :

All crows are birds

Some wolves are not crows

Therefore : Some wolves are birds.

This is a counter-example to the "purported" rule :

it is possible to (validly) conclude in the affermative when a premise is negative.

This means that, from the fact :

if a schema has one premise negative and the conclusion affermative, then it is not valid,

by contraposition we have :

if a schema is valid, then not (one premise negative and the conclusion affermative) i.e. either the conclusion is negative or all the premise must be afermative.

Comment

Valid means true in all cases.

Thus, the schema :

Some A are B

Some B are C

Therefore : Some A are C

is not valid exactly for the reason you have stated :

it becomes true [not valid] if at least one element lies in A ∩ B ∩ C.

Correct..., but if this is not, the argument does not conclude, and this means that the argument form is not valid.

Comment

Valid means true in all cases.

Thus, the schema :

Some A are B

Some B are C

Therefore : Some A are C

is not valid exactly for the reason you have stated :

it becomes true [not valid] if at least one element lies in A ∩ B ∩ C.

Correct..., but if this is not, the argument does not conclude, and this means that the argument form is not valid.

This distinction between true and valid is ate the core of Hrley's explanation of Rule 4.

Consider the invalid :

All crows are birds

Some wolves are not crows

Therefore : Some wolves are birds.

This is a counter-example to the "purported" rule :

it is possible to conclude in the negative when both premises are affirmative.

This means that, from the fact : if a schema has all premises affirmative and conclusion negative, then it is not valid, by contraposition we have :

if a schema is valid, then not-(all premises affirmative and conclusion negative) i.e. either some premise is negative or the conclusion is affirmative.