Stephen and Jerry LRC, I changed the subject line of this note to replace "related systems" with "Musement", which is closer to the word 'Spiel' in Wittgenstein's 'Sprachspiel' than to the word 'game' in 'language game'.
Stephen, if you lost my previous note, just look at the copy that is included at the end of your note. But your poem raises some issues: SCR
The words are from my Kindle book Tractatus which is clearly related to Wittgenstein.
Yes. But in the preface to his _Logical Investigations_, Wittgenstein himself apologized for the "grave mistakes" (schwere Irrtümer) in the Tractatus. He also credited Frank Ramsey, who had studied Peirce, with helping him realize those mistakes. See Nubiola's article: http://www.iupui.edu/~arisbe/menu/library/aboutcsp/nubiola/SCHOLAR.HTM At the end of his article, Nubiola wrote
Hookway was able to show that Peirce, Ramsey, and the later Wittgenstein not only agreed that the vagueness and indeterminacy of the meaning of predicates is benign and tolerable, but all three are to be found defending vagueness, which "is, rather, a virtue-- something in the absence of which we would simply be unable to say, or think, or do the things we want."
SCR
I would recognize a division between any contrived or explicit or mathematical or scientific language that is logically consistent and what I would call normal language or some such phrase.
Frege and Russell might say that, but definitely not Peirce. First, it makes a sharp distinction where Peirce insisted on continuity. Second, it denigrates ordinary language and privileges formal logic in a way that he never did and never would. For example, "Logicians have too much neglected the study of vagueness, not suspecting the important part it plays in mathematical thought." (CP 5.505) In fact, Peirce explicitly said "logical analysis" has "moderate fertility", and he called musement "open conversation with yourself... illustrated, like a lecture, with diagrams and with experiments":
There is no kind of reasoning that I should wish to discourage in Musement; and I should lament to find anybody confining it to a method of such moderate fertility as logical analysis. Only, the Player should bear in mind that the higher weapons in the arsenal of thought are not playthings but edge-tools... It is, however, not a conversation in words alone, but is illustrated, like a lecture, with diagrams and with experiments.
http://www.commens.org/dictionary/term/musement In another passage on that web page, he compared musement to science:
If one’s observations and reflections are allowed to specialize themselves too much, the Play will be converted into scientific study; and that cannot be pursued in odd half hours.
In 1908, after he had long experience in defining words for the Century Dictionary and Baldwin's encyclopedia, Peirce wrote
Men who are given to defining too much inevitably run themselves into confusion in dealing with the vague concepts of common sense. They generally make the matter worse by erroneous, not to say absurd, notions of the function of reasoning. (CP 6.496-497)
Clarence Irving Lewis, who had studied Peirce's manuscripts in detail, wrote the following comment in a letter to Hao Wang in 1960:
It is so easy... to get impressive "results" by replacing the vaguer concepts which convey real meaning by virtue of common usage by pseudo precise concepts which are manipulable by 'exact' methods — the trouble being that nobody any longer knows whether anything actual or of practical import is being discussed.
For discussion and references, see http://jfsowa.com/pubs/worlds.pdf JLRC
[Music notation] is pragmatically successful despite the linguistic ambiguity of the two temporal reference systems in the notation.
The only vagueness in music notation (when written carefully) is in the words that refer to continuously variable quantities, such as speed (allegro moderato, andante cantabile...) or volume (forte, fortissimo, pianissimo...). In ordinary language, musicians talk about music notation in ordinary language with their colleagues and students. And what they say is sufficiently precise that it can be translated to any notation for logic. For example, see page 27 of http://jfsowa.com/pubs/eg2cg.pdf At the top of that page is a passage in the traditional notation. Beneath it is a translation to a conceptual graph. A good musician can read and play the top diagram at sight, but even with a great deal of practice, the CG would be much harder to read and play. But if the CG were translated to predicate calculus, it would be impossible to play without a great deal of analysis. And any musician who did that analysis would probably translate it to the notation at the top before playing it John
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