Copyright (C) 2018 Dennis Joe Darland
For every person at any time, there will a set of ideas he has. This set cannot be precisely determined – checking it takes time and it changes with time (uncertainty principle). For many of those ideas, there will be words the person shares (how I will say later) with other people. Also, for many of those ideas, there are (mostly external to the person) objects. For any meaningful word, a person has an idea (or ideas), but that idea need not correspond to an object. (phlogiston, the ether, various gods). Also, there will be objects for which there is no idea or name. For example most elementary particles. (Particular ones – not types of them). Also, almost all real numbers cannot be represented in a finitary language – not just by individual signs of the language – but by any finite combination of them.
A person almost always learns to connect a word due to a causal chain going back to a christening of the word, This creates a R|S link between the word and the object the person learns that it represents. If “Bill” P|R|S Bill, then “Bill” P|R the_persons_idea_of_Bill and the_persons_idea_of_Bill S Bill. Here P|R is a relation for a person at a time between a word and an idea, and S is a relation between ideas and objects.
We have an innate ability to learn language, but need the correct experience to realize that ability.
Logic is formalized in signs. From particular sentences, we generalize. From “Spot is a dog”, we form the representation of “dog(Spot)”. And thus we get the idea of a predicate dog^x and a object Spot. From these ideas, we get the ideas of objects – a universal dogness and a particular Dog.
Some consequences:
There will be objects (e.g. real numbers) for which there is no idea or words. This also means in PM, there are real numbers for which there is no predicative function to define the corresponding class. We can define real numbers in general but not most specific ones. This means the Axiom of Reducibility is false.
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