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The forms of the statement and its types — Philosophy STD 12 Arts — Question

Gujarat BoardEnglish MediumSTD 12 ArtsPhilosophyThe forms of the statement and its types5 Marks
Question
Explain the actual method of determining the type of form for a statement.
✓

Answer

  • The form of the form for the statement is determined by constructing a fact sheet.
  • If the $‘F’$ value appears in all the rows of the last column representing the form in the truth table of the form for the statement, then it is the ‘meaningful’ form for the statement. This means that all the substitutions for the form $A$ for the statement are true.
  • If the $‘F’$ value appears in all the rows of the last column representing the form in the verification table of the form for the statement, then it is a ‘self$-$disturbing’ form for the statement. This means that all substitutions for that form of statement are untrue.
  • If the value of $'T'$ in some rows of the last column and the value of $'F'$ in some rows is more than the representation of that form in the fact sheet of the form for the statement, then it is the 'parayat' form for the statement. This means that some of the substitutions for the statement are true and some of the substitutions are false.
  • Here are some examples of how to determine the type of form for a statement directly from the fact sheet:
$(i)$ Form for statement: $(p\ \&\ r)\ \&\ (p\ V\ q)$
Truth table
  $1$ $2$ $3$ $4$ $5$ $6$
$p$ $q$ $r$ $p\ \&\ r$ $p\ v\ q$ $(p\ \&\ r)\ \&\ (p\ V\ q)$
$1$ $T$ $T$ $T$ $T$ $T$ $T$
$2$ $T$ $T$ $F$ $F$ $T$ $T$
$3$ $T$ $F$ $T$ $T$ $T$ $T$
$4$ $T$ $F$ $F$ $F$ $T$ $T$
$5$ $F$ $T$ $T$ $F$ $T$ $T$
$6$ $F$ $T$ $F$ $F$ $T$ $T$
$7$ $F$ $F$ $T$ $F$ $F$ $T$
$8$ $F$ $F$ $F$ $F$ $F$ $T$
  $1, 3 (\&)$ $1, 2 (v)$ $4, 5 (\rightarrow)$
Determining the type of form for the statement: Looking at the fact sheet above, it will be seen that the form given for the statement is represented in column no$.6.$ All rows in this column are $‘T’.$ This means that all the substitutions of this form for the statement are true, so it is assumed that the form for the statement is 'tadevarthaka'.
$(ii)$ Form for statement: $(p\ \&\ \sim\ q)\ \&\ (p\ \rightarrow \ q)$
Truth table:
  $1$ $2$ $3$ $4$ $5$ $6$
$p$ $q$ ~ $q$ $p \& \sim q$ $p\rightarrow q$ $(p\ \&\ \sim\ q)\ \&\ (p\ \rightarrow\ q)$
$1$ $T$ $T$ $F$ $F$ $T$ $F$
$2$ $T$ $F$ $T$ $T$ $F$ $F$
$3$ $F$ $T$ $F$ $F$ $T$ $F$
$4$ $F$ $F$ $T$ $T$ $T$ $F$
  $2 (\sim )$ $1,3 (\&)$ $1, 2(\rightarrow)$ $4, 5(\&)$
Decision of the type of form for the statement: Looking at the fact sheet above, it will be seen that the form given for the statement is represented in column $6.$ All rows in this column have an $'F'.$ This means that all substitutions for this form of statement are untrue. So it is clear that this form of statement is 'self-defeating'.
$(iii)$ Form for statement: $p \rightarrow [\sim q v (p \rightarrow r)]$
Truth table:
  $1$ $2$ $3$ $4$ $5$ $6$ $7$
$p$ $q$ $r$ $\sim q$ $p \rightarrow r$ $[\sim\ q\ v\ (p\ \rightarrow\ r)$ $p\ \rightarrow\  [\sim\ q\ v\ (p\  \rightarrow\ r)]$
$1$ $T$ $T$ $T$ $F$ $T$ $T$ $T$
$2$ $T$ $T$ $F$ $F$ $F$ $F$ $F$
$3$ $T$ $F$ $T$ $T$ $T$ $T$ $T$
$4$ $T$ $F$ $F$ $T$ $F$ $T$ $T$
$5$ $F$ $T$ $T$ $F$ $T$ $T$ $T$
$6$ $F$ $T$ $F$ $F$ $T$ $T$ $T$
$7$ $F$ $F$ $T$ $T$ $T$ $T$ $T$
$8$ $F$ $F$ $F$ $T$ $T$ $T$ $T$
  $2(\sim )$ $1, 3(\rightarrow)$ $4,5 (v)$ $1, 6 (\rightarrow)$
Decision of the type of form for the statement: Looking at the above fact sheet, it will be seen that the form given for the statement is represented in column $7.$ Looking at all the rows of this column, it will be clear that it has $‘T’$ in the first, third, fourth, fifth, sixth, seventh and eighth rows. And the second row has $‘F’.$ This means that some of the substitutions for this form of statement are true. While some substitutions are untrue. So it is clear that this form of statement is 'parayat'.

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