Inferential density#

Inferential density measures how much the arguments in a debate have constrained the space of coherent positions, which indicates how free agents are in their choice of an admissible belief system in light of the debate.

Consider how the debate consisting of just one argument, \((a\land b) \implies c\) has \(2^3-1\) coherent and complete truth-value assignments. The one that is missing assigns False to \(c\) but True to \(a\) and \(b\). Betz ([Betz2013], p. 44) gives a general formula for calculating this density of a debate \(\tau\), \(D(\tau)\) with a sentene pool of length \(n\) and a space of complete on coherent positions \(\Gamma(\tau)\):

\[D(\tau) := \frac{n-\log_2 (|\Gamma(\tau)|)}{n}\]

Density offers a time-indepent measure of progress in debates, a reliable alternative to the number of introduced arguments. A debate in which the arguments impose rather few constraints on the available complete and coherent positions will have a low density; a debate in which this influence is high, the debate’s density will be high as well. However, while the density generally rises with number of arguments, not every argument renders a previously coherent position incoherent. And so, not every argument contributes to density equally, and some won’t change it at all.

Base.density()[source]#: Return the dialectical density of the Debate object, as defined by Betz ([Betz2013] , pp. 44–49).

Tip

Density is returned as a fraction. If you prefer integers, try float(tau1.density()).