Re: mathematical language

From: Mitch Harris (harrisq_at_tcs.inf.tu-dresden.de)
Date: 12/12/04 

Date: 12 Dec 2004 16:46:47 GMT

Lester Zick <lesterDELzick@worldnet.att.net> wrote:
>
>The definition I used is just the dictionary definition.

A mathematical dictionary? Regular definitions are notoriously confusingly
different from the mathematical ones.

However you seem to have placed a lot of extra nontraditional semantics on
the word tautology, just like has already been done by logicians. So
you're struggling against a (very successful and much older) tradition.

>Given a particular proposition, p, is
>p true or false? If we take a proposition such as p "car", meaning "it
>is a car", is the proposition true or false?If we combine propositions
>to form t:[car][not car] we form a tautological proposition which
>covers all possibilities. The halves referred to are just parts of the
>tautological proposition, positive and negative parts. I call the
>positive half or part an empirical observation.

So, for you, are all propositions of the form "t:[x][not x]"?
How do you "combine" propositions?
Can you give some more examples of propositions (as you think of them)?

>>>(Conversely, circular logic such as "it is a car because it
>>>is a car" includes no logical possibility and is considered always
>>>false for this reason.)
>>
>>the commonly accepted way to rewrite this sentence is as "P->P"
>>which is (also commonly accepted to be) a tautology.
>
>For what it's worth, I'm trying to avoid specialized notation whether
>commonly accepted or not.

Why? It makes things clearer. Everybody agrees on the notation so then
everybody can speak without being misunderstood.

>I realize the notation I've adopted seems
>pretty specialized, but it's easy enough to explain in plain language
>without resort to commonly accepted formalisms.

It should be easy enough, but so far in the case of
discussions using your language, it is obviously -not- easy in plain
language.

>For a given tautology of the
>form t:[subject][not subject] there is a negative part [not subject]
>and a non negative or positive part [subject]. I consider the non
>negative or positive part to be the same as what we call an empirical
>observation and the negative part to be a logical observation.

Nothing here matches up with anything I can conjure in may imagination.
How can positive correspond to empirical and negative to logical?
If true is positive and false is negative, aren't these both logical?

Mitch

Relevant Pages

  • Re: mathematical language
    ... >The definition I used is just the dictionary definition. ... the word tautology, just like has already been done by logicians. ... is the proposition true or false?If we combine propositions ... but it's easy enough to explain in plain language ...
    (comp.theory)
  • Re: Godels comments about the "true reason" for incompleteness
    ... why not formally admit propositions ... arbitrary Q. Obviously there is an implied quantification over Q, ... letters of the object language). ... refutable in PA and as confirmed by the supposed undecidability of S. ...
    (sci.logic)
  • Re: A missing definition in "Gödels Proof" by Nagel & Newman (open letter)
    ... he defined a proof to be any finite sequence ... "Every tautology itself shows that it is a tautology." ... The propositions of logic are tautologies. ... logical propositions out of others by mere _symbolic rules_. ...
    (sci.logic)
  • Re: Multiple-Attribute Keys and 1NF
    ... propositions that state "'Green and yellow' contains 'Green'" ... name--the attribute names correspond to free variables in a predicate: ... The person named Brian speaks the language English ...
    (comp.databases.theory)
  • Re: Can propositions be classified into type-n?
    ... propositions be classified into any in Chomsky hierarchy? ... Items that can be placed in the Chomsky hierarchy are languages (which ... usually defined using a grammar or machine). ... The language of PC is context free. ...
    (comp.theory)