“(We are) incapable of certain knowledge or absolute ignorance. We are floating in a medium of vast extent, always drifting uncertainly, blown to and fro. Whenever we think we have a fixed point to which we can cling and make fast, it shifts and leaves us behind. If we follow it, it eludes our grasp, slips away, and flees eternally before us. Nothing stands still for us. This is our natural state and yet the state most contrary to our inclinations. We burn with desire to find a firm footing, an ultimate, lasting base on which to build a tower rising up to infinity, but our whole foundation cracks.”
If I wander into a crowded train station and scream “One plus one equals two!” at the top of my lungs, or mutter it to myself, and there is no apparent pair I am gathering together, are my words true? Are they true even if they do not connect with anything or do anything for anyone? If we say they are true in the abstract, is that true in a particular context, or in all contexts?
If Bertrand Russell and Alfred North Whitehead spent over 350 pages in the Principia Mathematica (1910) to prove, with absolute certainty via logic, that one and one make two, was it just as true as it was before? Is it now more certain? How certain are children, compared to Russell’s readers?