Sunday, July 20, 2009 Gregorian Calendar
Hijrah 1430 Rajab 25
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NECESSARY & SUFFICIENT CONDITIONS
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by: Jam bin Javi
Let us examine the following statements:
To be Malay is to be Muslim.
IF one is (a) Malay, THEN one is (a) Muslim.
If one is Malay, then, NECESSARILY, one is Muslim.
To be Muslim is a NECESSARY CONDITION to be Malay.
To be Malay is a SUFFICIENT CONDITION to be Muslim.
All Malays are Muslims. But not all Muslims are Malays.
Important notions or concepts that must be noted in the above consideration are:
- CONDITION (to be Malay = "Malay-ness" & to be Muslim = "Muslim-ness")
- The terms IF & THEN and the whole CONDITIONAL statement "If _, then _."
- NECESSITY/NECESSARY CONDITION
- SUFFICIENCY/SUFFICIENT CONDITION
A graphical tool taught in grade school math may help one's understanding.
Using a modified Venn Diagram:
For simplicity, the diagram does not include a so-called UNIVERSAL SET, a third bigger square that should enclose both squares. The MEMBERS of our sets are portrayed as individual points or items rather than as plane areas. We are dealing with INDIVIDUAL HUMANS and the UNIVERSAL SET should be the set of HUMANS. From the diagram, it is easy to see that all INDIVIDUALS who are (found or located) within the square for Malays are also within the square for Muslims, meaning, ALL Malays are Muslims. If one is Malay, then one is Muslim.But not all Muslims are Malays because there are INDIVIDUALS that are outside the square for Malays and yet are within the square for Muslims, meaning, there are Muslims who are not Malay or, EQUIVALENTLY, NOT ALL Muslims are Malays.
Actually, the presentation is an oversimplified account since the notion of an individual representing or exemplifying an attribute/property or a condition is more complicated than as given. In this case, a single or lone individual exemplifies the attribute or condition of Malayness or Muslimness or both. But, how does Muslimness or Malayness relate to one's being an individual? Can't an individual be a half or just 1/4 Muslim or Malay? And what does it mean to be BOTH Muslim AND Malay? In the diagram, an individual stick-figure represents a unit Malay or a unit Muslim and this is the smallest item which cannot be broken down or analyzed further.
In the mathematical language of SET THEORY, one says that "the SET of Malays forms a SUBSET of the SET of Muslims". A set is a mathematical notion - a group of objects or individuals all together conceived as a single entity - a COLLECTION with each member exemplifying a common attribute of all the other members of the set. Another subset of the set of MUSLIMS may be the set of ARABS, or the set of MOORS.
To satisfy the condition of Malayness is to belong to the class or set of Malays
To satisfy the condition of Muslimness is to belong to the class or set of Muslims
CONDITION of MALAYness = To BE MALAY = To be a MEMBER of/To BELONG to the CLASS or SET of MALAYS
CONDITION of MUSLIMness = To BE MUSLIM = To be a MEMBER of/To BELONG to the CLASS or SET of MUSLIMS
To be Malay is a sufficient condition to be Muslim and to be Muslim is a necessary condition to be Malay. Being Malay guarantees being Muslim. Alternatively,
One cannot be Malay if one is not Muslim.
" " " " unless one is Muslim.
ADDED: 081209
Condition A is necessary for condition B if its FALSITY or NON-OCCURENCE guarantees the FALSITY or NON-OCCURENCE of condition B.
Condition A is sufficient for condition B if its TRUTH or OCCURENCE guarantees the TRUTH or OCCURENCE of condition B.
Necessity and sufficiency are CONVERSE. That a condition A suffices for another condition B
also means that condition B is necessary for condition A.
EXERCISE: Contemplate the case for ARABS or MOORS instead of MALAYS.
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TO BE CONTINUED/EMENDED
