The idea of "truth tables" originated in the 19th century, independently with British George Boole (1815-1864) and American Charles S. Peirce (1839-1914). Not aware of their work, it was set forth in the 20th century by Austrian British, Ludwig Wittgenstein (1889-1951). These tables tainned popularity after Polish-American, Emil W.Post (1897-1954), used such tables to give a model-theoretic proof of the completeness theorem for statement logic.

Following this, Claude Shannon adapted these tables for computer logic circuits.

And Roman Sikorski and Helena Rasiowa, in their unique work, The Mathematics of Metamathematics, show that indicator tables represent a kind of "matrix algebra".

In contrast to the axiom-theorem-proof procedure, these combinatorial tables provide (Do I alone see this?) a measure-theoretic method (indmeasuring) for proving theses of logic and mathematics.

• Head columns by labels for each independent statement.
• Given n statements, the total number of assignments of T, F ("true", "false") valuations for these n statements is 2ⁿ. The 2ⁿ rows below these column headings (with these statements and their connectives) are filled with these T, F assignments.
• The connectives of statement logic are:
  • negation, denoted Ø: if a statement has a "T" valuation, its negation is "F", and conversely.
  • conjunction (and), denoted &: "T" if, and only if, all conjunctands are evaluated as "T", otherwise "F".
  • disjunction (inclusive or), denoted OR: "F" if, and only if, all disjunctands are evaluated as "F", otherwise "T".
  • conditional ("if_, then_"), denoted Þ: "F" if, and only if, precedent ("if_") is evaluted as "T" and consequent ("then _") is evaluated as "F", otherwise "T".
  • biconditional ("if, and only if"), denoted Û: "F" if, and only if precedent and consequent do not agree in truth-valuations, otherwise "T".
• Whenever a connective appears in the argument, its table-column evaluates it by the above rules.
• If all entries in the concluding column are "T", then the argument is valid, otherwise invalid.

For example, the most powerful logical proof is known by the Latin label, "modus ponens (MP)". All of statement logic (zeroth order predicate logic) can be proven by this method alone. Given independent statement, A,B, the MP argument runs:

            ((A Þ B) & A) Þ B

We display its truth table proof:

TRUTH-TABLE PROOF OF MODUS PONENS (MP)

A	B	A Þ B	(A Þ B) & A	((A Þ B) & A) Þ B
F	F	T	F	T
F	T	T	F	T
T	F	F	F	T
T	T	T	T	T

Please note that the last column (conclusion of the MP argument) contains all "T" valuations, measuring MP as valid.

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Later, "T, F", were respectively replaced by "1,0", especially to calculate logic circuits in a computer. Still later, this "truth table" became known as "an indicator table". With this replacment the above table becomes:

TRUTH-TABLE PROOF OF MODUS PONENS (MP)

A	B	A Þ B	(A Þ B) & A	((A Þ B) & A) Þ B
0	0	1	0	1
0	1	1	0	1
1	0	0	0	1
1	1	1	1	1

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This suggested to me the notion of creating the new measure of "ballot" to sum the (1,0) measures of each column. The previous table appears with ballot in the last row:

TRUTH-TABLE PROOF OF MODUS PONENS (MP)

BALLOT	A	B	A Þ B	(A Þ B) & A	((A Þ B) & A) Þ B
-	0	0	1	0	1
-	0	1	1	0	1
-	1	0	0	0	1
-	1	1	1	1	1
BALLOT	2	2	3	1	4

Given the ballot measure, I normalized it by division with the total number of possibilities, to obtain another logical measure: verdibility, which relates to statements in the way that probability measure relates to events: (verdibilty : statements :: probability : events).

The previous table, with a column for verdibility, becomes:
-

TRUTH-TABLE PROOF OF MODUS PONENS (MP)

BALLOT	VERDIBIITY	A	B	A Þ B	(A Þ B) & A	((A Þ B) & A) Þ B
-	-	0	0	1	0	1
-	-	0	1	1	0	1
-	-	1	0	0	0	1
-	-	1	1	1	1	1
BALLOT	-	2	2	3	1	4
-	VERDIBILITY	1/2	1/2	3/4	1/4	1

Thus, the verdibility measure of a validity is 1; of an invalidity, less than 1.

In wildcatpage.htm , I show how the verdibility measure can be applied via a formula for computing it, along with several theorems which follow from this formula. This file also has a hyperlink to a verdibility calculator -- unique in all the world.

Then, following the terrorism of Sept. 11, 2001, I realized that my verdibility measure could be transformed into a security measure for evaluating suspicious observations and what they might "tipoff". This is ONLINE at http://.../securab.htm .

Both of my measures fill a vacuum in the literature. As I note elsewhere ONLINE:

		Those who know seldom care.
		Those who care rarely know.
		When KNOW meets CARE,
		And teams with DARE,
		Then Mt. Constipation will blow!

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The above history shows the nature and power of the indicator measure, and calls attention to the general neglect of it, particularly by the Mathematical Establishment.