# What does Tarka shastra say about consistency in accepting statements in Pramana?

Tarka shastra is ancient-day 'Logic'. Lack of contradiction is one of the key pillars to establish any point of view. Below is an example.

A book written by author X, 5000 years ago, states "A+B = 5. B+C = 1000"

None of us met X. None of us know the values of A, B & C. None of us have any easily verifiable historical proof (like photographs) of X.

Now, suppose there are 4 persons - Shyamu, Somu, Karthik & Kumar.

1. Shyamu says "I believe both A+B=5, and B+C=1000, because I trust author X which is because my elders trust him, just like their elders before them..".

2. Somu says "I believe A+B=5 because it's written in the book. But I don't believe B+C=1000, because it just seems unlikely according to my thinking".

3. Karthik says "I believe B+C=1000 because it's written in the book. But I don't believe A+B=5, because it just seems unlikely according to my thinking".

4. Kumar says "I neither believe A+B=5, nor B+C=1000, because I don't trust author X because I think for myself and don't care what elders say"

IMO, persons 1 & 4 - Shyamu & Kumar are both scientifically consistent, even though they have opposite viewpoints.
But 2 & 3 - Somu & Karthik are not consistent, because they pick & choose according to their convenience/intellect/trust.

What does Tarka shastra say about sources of truth (Pramana) and logical consistency in accepting statements in that Pramana.