Guides in Symbolizing Statements and Arguments

Submitted by admin on Wed, 10/03/2012 - 05:18
© 2012 byJensen dG. Mañebog
 
IN NATURAL DEDUCTION or providing formal proof for the validity of arguments and other logical operations, symbolizing the argument is the first step. This means correctly translating all the premises and conclusion into symbols. The following are some guides in properly symbolizing statements and arguments:
1. “One to one correspondence”. There must only be one symbol (letter) to be used consistently for each simple statement.
2. Use uppercase letters. Conventionally, capital letters (e.g. A, B, C) are used to symbolize statements.
3. Use the first letter of the subject or the predicate. Unless specified, it is reasonable to choose those letters to represent the whole statement. “Mandy is a student” is thus symbolized as “M”.  But if in an argument, there are statements “Mandy is a student” and “He (Mandy) is an athlete”, they should be symbolized as “S” (for student) and “A” (for athlete), respectively.
4. Use connectives for compound statements and negation sign for negative statements. Between the statements involved, the corresponding symbols for each kind of compound proposition must be used. The commonly used symbols in natural deduction are &,→, and /. Negative statements should be indicated by a negation sign (-) before the statements. Thus, “Edwil is a scholar and Rommel is not a gangster” is symbolized “E&-R”.
5. Use parentheses if and only if necessary. When parentheses will not add anything to the meaning of the symbolized statement, they should not be utilized. “Leo is a professor” should be symbolized “L”, and not “(L)”. Notice, however, that in the following statements, parentheses are necessary:
   1. Either Dindo will sing and Norman will dance or Sieg will recite a poem.
   2. Both Dindo will sing and Norman will dance or Sieg will recite a poem.  

Without parentheses, both statements will be symbolized “D&N/S”. But since the two statements obviously do not mean the same, their respective symbols should not be identical. So there’s a need to differentiate their symbols to correctly represent each statement. The “either…or” phrase in statement 1 indicates that the main operator is the disjunction sign (/) so “D” and “N” should be grouped together disjunctively opposite “S”, thus “(D&N)/S”. In statement 2, the phrase “both…and” suggests that it is basically a conjunction. “D” therefore should be put conjunctively alongside the parenthetically enclosed “N” or “S”, thus “D&(N/S)”. Without parentheses, the symbol “D&N/S” actually means a semantically different statement, “Dindo will sing and Norman will dance or Sieg will recite a poem.”

How to cite this article:
Jensen dG. Mañebog. “Guides in Symbolizing Statements and Arguments” @ www.OurHappySchool.com

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