Honest and finely crafted lines from the co-author of Principia Mathematica. In English: ‘The ‘[Foundational] Principles of Mathematics’.
Is Shūnyam, the ‘Divide’ of ‘True Nothing’ and ‘Not-True Nothing’, a Tautology?
What’s a Tautology?
This subject called Mathematics, in fact it’s larger family, the complex of Analytics that fall under the banner of Logico-Mathematical Method, is erected on multiple pillars.
If they shake an inch the entire structure will swing by a mile. So it’s a good idea to step down with a flashlight and take a look at these foundations every now and then.
The first and most important is the pillar labeled with the little word ‘ Is’ [we will get to it in the Posts, by-and-by]. The second of the pillars is the Principle of Contradiction. A third, often ignored, is the concept of the Tautology.
Here is Professor Bertrand Russell:
‘It is clear that the definition of ‘Logic’ or ‘Mathematics’ must be [newly] sought..[we must] no longer be satisfied [defining] logical propositions as those that follow from the Law of Contradiction..[but] must admit a wholly different class of propositions..[that] all have the characteristic which we
agree..to call Tautology.
For the moment, I do not know how to define ‘Tautology’..I know of none that I feel to be satisfactory, in spite of feeling thoroughly familiar with the characteristic of which a definition is wanted.
At this point, therefore, for the moment, we reach the frontier of knowledge on our backward journey into the logical foundations of Mathematics.’