The Problem and the Method - rbjones/HoLoTruth GitHub Wiki
Wittgenstein's philosophy, and his conception of language, fell into two phases. In the first, manifest in his "Tractatus Logico-Philosophicus" his conception of language was derived from the new formal notations devised by Frege and Russell primarily for the purpose of achieving rigour in mathematics. He then came to recognise that this model of language did not accommodate the great variety in how language is used.
Though his first narrow conception of language did not encompass all, the kind of language it describes is of particular importance to science. We will call this "propositional" language, it is the kind of language with which this project is principally concerned. Its importance derives from its ability to provide objective knowledge of the nature and state of the world, which can be recorded and re-used in places and at times very different to those in which is was first encountered. Using this kind of knowledge, it is possible to predict how the world and artefacts in it will behave in situations which we have not yet encountered. We are therefore empowered to take steps to mitigate the consequences of accidents of nature, and to design tools and architect buildings which will be effective and safe. Underlying this kind of science and engineering there is propositional knowledge, and underlying the predictive capabilities it supports there is deduction.
The deductive cloud is intended to hold and to reason using this kind of knowledge, and the primary requirement for philosophical underpinning is to give an account of propositional language, how it can be represented and exploited deductively.
This is an enterprise which can be related to just some aspects of Wittgenstein's Tractatus, and it therefore demands not great tomes of broad ranging philosophical doctrine, but rather, a compact and clear account of the special kinds of language involved, the ways in which they related to our world, and the ways in which they can be effectively exploited in the deductive cloud.
Simplicity and precision are key to the logical fundamentals, and the principal method adopted here for giving a minimalistic philosophical account suitable for our purposes may be understood through an analogy with the idea of feeding the Universe through the eye of a needle.
The problem to be solved by this analogy is what I call "the problem of regress in the semantics of language". This is the problem that in order to define the meaning of some language we must use language, but for the definition to make sense, we need to define the language in which it was given, and then the language in which that definition was given. We therefore require either an infinite regression of language definitions, or some "meta-circularity" (the definition directly or indirectly given in the language itself).
Of course, it is known that meta-circular definitions may have more than one fixed point, and therefore do not by themselves suffice to fix a language but the combination of a meta-circular definition with a careful description in a small and relatively unambiguous portion of natural language will suffice for our purposes. This small and unambiguous portion of natural language is the eye of our needle. Through this eye we will pull a language at first very simple, but powerful, abstract HOL. This language will by incremental conservative extension grow to provide for the formalisation of mathematics, science, engineering, and any other kind of propositional knowledge. Though the underlying abstract language in all these domains is formal, and therefore precise enough to support long chains of rigorous deduction, concrete presentations can be in whatever form best suits its intended audience, even through the ubiquitous chat-bot.