Change this invalid argument into a valid argument.  all students are brilliant,she is brilliant,so she is a student.  

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

A valid argument is one in which the conclusion must be true if the premises are both true.  In this invalid argument, you have a conclusion that does not have to follow from the premises.

Your premises are:

  • All students are brilliant.
  • She is brilliant.

Your conclusions is:

  • Therefore she is a student.

But there could be other types of brilliant people -- your premises do not preclude that possibility.

To make this argument valid, simply change the first premise.  If you change the first premise as follows, then the conclusion will have to be true and the argument will be valid.

  • Only students are brilliant.

Since she is a student and only students are brilliant, she must be a student.  This is a valid argument.

manataoscar's profile pic

manataoscar | College Teacher | (Level 1) eNoter

Posted on

Error: Incorrect Reversal.

All students are brillants can be translated into: If you are a student, then you are brillant. There is an error consisting in reversing the two terms of the syllogism without negating them.

Correct Reversal should read: If you are not brillant, then you are not a student: the two terms must be reversed and then negated in order to reach a valid conclusion.

All students are brillant: in other words, if you belong to the category of students then you also belong to the large category of brillant people.

However, there are some people belonging to the category of "brillant" personnes who are note students; therefore the correct statement should be:All students are brillant; she is a brillant person but she may not be a student.

All students are brillant

 

manataoscar's profile pic

manataoscar | College Teacher | (Level 1) eNoter

Posted on

Error: Incorrect Reversal.

All students are brillants can be translated into: If you are a student, then you are brillant. There is an error consisting in reversing the two terms of the syllogism without negating them.

Correct Reversal should read: If you are not brillant, then you are not a student: the two terms must be reversed and then negated in order to reach a valid conclusion.

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