Wittigenstein (Early) was heavily influenced by Russel and the early logical positivists generally truly believed that we could get all this stuff licked and finished with the right application of clarity, logic and precision.
Noble aims. I once read that Gene Roddenberry was a very strong proponent of logical positivism, showing up in his work, which also influenced me growing up with Star Trek.
Yet, it has its empty spaces and the chasms that it can’t cross.
An analogy. Let us make logic a sharp pencil.
We now have a space on paper to fill in with logic.
With the sharp pencil, and no overlapping, can you perfectly color the space with an even set of strokes at an even speed with no changes of pressure to result in a space whose tone, hue and color is identical to that of a single line of a given pressure?
But even in that real world example, it will not be easy and likely close to impossible.
I made up this analogy on the fly just now, but it illustrates (pun intended) the difficulties with a very clear, logical positivist outlook when one attempts to apply it universally.
It can’t be.
It can do a fine job. It is pragmatic and useful and I wouldn’t take that away from it. My tendencies are towards logical positivism and humanism in general.
However, the gaps will remain, the pencil breaks, the paper rips and to me, it’s important to keep that in mind while drawing logical conclusions from premises, when attempting to speak unambigously and with perfect-as-possible clarity and precision.