# Aristotle's syllogism as simple as ABC by new transformed Raval's notations

**Abstract**

Transformed RAVAL NOTATION solves Syllogism problems very quickly and accurately. This method solves any categorical syllogism problem with same ease and is as simple as ABC… In Transformed RAVAL NOTATION, each premise and conclusion is written in abbreviated form, and then conclusion is reached simply by connecting abbreviated premises.NOTATION: Statements (both premises and conclusions) are represented as follows:
Statement Notation
a) All S are P, SS-P
b) Some S are P, S-P
c) Some S are not P, S / PP
d) No S is P, SS / PP
(- implies are and / implies are not)
All is represented by double letters; Some is represented by single letter. No S is P implies No P is S so its notation contains double letters on both sides.
RULES: (1) Conclusions are reached by connecting Notations. Two notations can be linked only through common linking terms. When the common linking term multiplies (becomes double from single), divides (becomes single from double) or remains double then conclusion is arrived between terminal terms. (Aristotle’s rule: the middle term must be distributed at least once)
(2)If both statements linked are having – signs, resulting conclusion carries – sign (Aristotle’s rule: two affirmatives imply an affirmative)
(3) Whenever statements having – and / signs are linked, resulting conclusion carries / sign. (Aristotle’s rule: if one premise is negative, then the conclusion must be negative)
(4)Statement having / sign cannot be linked with another statement having / sign to derive any conclusion. (Aristotle’s rule: Two negative premises imply no valid conclusion)
Syllogism conclusion by Tranformed Raval’s Notation is in accordance with Aristotle’s rules for the same. It is visually very transparent and conclusions can be deduced at a glance, moreover it solves syllogism problems with any number of statements and it is quickest of all available methods. By new Raval method for solving categorical syllogism, solving categorical syllogism is as simple as pronouncing ABC and it is just continuance of Aristotle work on categorical syllogism. It’s believed that Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, it’s claimed that Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle".
Above conclusion is reached at a glance with Raval's Notations (Symbolic Aristotle’s syllogism rules).
Premise:
"No (square that is a quadrangle) is a (rhombus that is a rectangle)"
Raval's Representations:
S – Q, S – Q / Rh – Re, Rh – Re
Premise:
"No (rhombus that is a rectangle) is a (square that is a quadrangle)".
Raval's Representations:
Rh – Re, Rh – Re / S – Q, S - Q
Conclusion:
"No (quadrangle that is a square) is a (rectangle that is a rhombus)"
Raval’s Representations:
Q – S, Q – S / Re – Rh, Re – Rh
As “ Q – S” follows from “S – Q” and “Re – Rh” from “Rh – Re”. Given conclusion follows from the given premises.
Author disregards existential fallacy, as subset of a null set has to be a null set.

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**Added to PP index**

2012-01-10

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