If there is a probability of faulty inference, then longer inferences are exponentially less likely to be valid, with the length of the valid inference being proportional to logarithm of the process fidelity. Long handwaved inferences can have unbelievably low probability of correctness, and thus be incredibly weak as evidence.
Furthermore, informal arguments very often rely on ‘i can’t imagine an alternative’ in multiple of their steps, and this itself has proven unreliable. It is also too easy to introduce, deliberately or otherwise, a huge number of implicit assumptions all of which must be true for the argument to be valid.
With logarithmic dependence to the fidelity of argument, even dramatically more reliable informal arguments do not lead to dramatically longer inference chains that can be done. One has to use formal methods to produce long inference chains.
If there is a probability of faulty inference, then longer inferences are exponentially less likely to be valid, with the length of the valid inference being proportional to logarithm of the process fidelity. Long handwaved inferences can have unbelievably low probability of correctness, and thus be incredibly weak as evidence.
Furthermore, informal arguments very often rely on ‘i can’t imagine an alternative’ in multiple of their steps, and this itself has proven unreliable. It is also too easy to introduce, deliberately or otherwise, a huge number of implicit assumptions all of which must be true for the argument to be valid.
With logarithmic dependence to the fidelity of argument, even dramatically more reliable informal arguments do not lead to dramatically longer inference chains that can be done. One has to use formal methods to produce long inference chains.