Philosophy core problem solutions

Solution to Problem 1 – Conceptual coherence#

$$ C = \frac{T_f}{τ_r}. $$

If $$τ_r$$ increases, the denominator increases, so $$C$$ decreases.

Answer: Coherence decreases.

Solution to Problem 2 – Ethical weight#

$$ E = ΛΘ D_6. $$

If $$Θ$$ doubles:

$$ Θ' = 2Θ, \quad E' = Λ(2Θ)D_6 = 2E. $$

Answer: Ethical weight doubles.

Solution to Problem 3 – Argument strength#

$$ S = X \sqrt{τ_r}. $$

If $$τ_r$$ quadruples:

$$ τ_r' = 4τ_r, \quad S' = X \sqrt{4τ_r} = 2X\sqrt{τ_r} = 2S. $$

Answer: Argument strength doubles.