Re: LOGIC WITHOUT QUANTIFIERS

From	Jim Burns <james.g.burns@att.net>
Newsgroups	sci.logic
Subject	Re: LOGIC WITHOUT QUANTIFIERS
Date	2019-09-22 19:52 -0400
Organization	A noiseless patient Spider
Message-ID	<f80566ec-bfc0-eaa9-c984-5715bb20cc30@att.net> (permalink)
References	<e9d73774-f8f8-4723-bcad-a9338d26ab5c@googlegroups.com>

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On 9/22/2019 11:29 AM, grahamcooper7@gmail.com wrote:

> USE  @->  FOR *ALWAYS* IMPLIES
> 
> For every number there is a bigger number
> Ax Ey y>x
> 
> xeN  @->  y>x

There are two kinds of quantifiers that we make
a lot of use of, 'forall' and 'exists'.

'forall x, P(x)' is the strongest claim we can make
about the objects in our domain, and
"exists x, P(x)'is the weakest claim we can make
about the objects in our domain.

When we wish to negate a strong claim, like
"All dogs have fleas", we don't need more than a weak
claim, "At least one dog does not have fleas."
And the other way around. We really need both.

How does one write the "at least one" part of
"Always, for x in N, at least one y in N, y > x"?

I don't know enough to say for sure, but it seems
to me that we need some form of quantifier to
distinguish a bare-minimal negation, like
"At least one dog does not have fleas"
from maximal negation, like
"All dogs do not have fleas".

> Definition of SUBSET
> subset(S,T)
> <-
> Ax xeS -> xeT
> 
> subset(S,T)
> <-
> xeS  @->  xeT
> 
> Induction Formula
> 0eN & (An neN -> s(n)eN)  ->  An neN
> 
> 0eN & (neN  @->  s(n)eN)  @->  meN
> 
>

Thread

LOGIC WITHOUT QUANTIFIERS grahamcooper7@gmail.com - 2019-09-22 08:29 -0700
  Re: LOGIC WITHOUT QUANTIFIERS Python <python@invalid> - 2019-09-22 17:32 +0200
    Re: LOGIC WITHOUT QUANTIFIERS grahamcooper7@gmail.com - 2019-09-22 08:54 -0700
  Re: LOGIC WITHOUT QUANTIFIERS Jim Burns <james.g.burns@att.net> - 2019-09-22 19:52 -0400
    Re: LOGIC WITHOUT QUANTIFIERS grahamcooper7@gmail.com - 2019-09-22 17:17 -0700
      Re: LOGIC WITHOUT QUANTIFIERS Jim Burns <james.g.burns@att.net> - 2019-09-22 21:41 -0400
        Re: LOGIC WITHOUT QUANTIFIERS Khong Dong <khongdongphong@gmail.com> - 2019-09-23 08:51 -0700
          Re: LOGIC WITHOUT QUANTIFIERS Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-23 20:04 +0100
            Re: LOGIC WITHOUT QUANTIFIERS Khong Dong <khongdongphong@gmail.com> - 2019-09-23 12:17 -0700
              Re: LOGIC WITHOUT QUANTIFIERS Khong Dong <khongdongphong@gmail.com> - 2019-09-23 13:28 -0700
                Re: LOGIC WITHOUT QUANTIFIERS Khong Dong <khongdongphong@gmail.com> - 2019-09-23 15:42 -0700
      Re: LOGIC WITHOUT QUANTIFIERS Fred <Fred@nowhere.invalid> - 2019-09-23 08:17 +0100
        Re: LOGIC WITHOUT QUANTIFIERS Peter Percival <peterxpercival@hotmail.com> - 2019-09-23 12:56 +0100
        Re: LOGIC WITHOUT QUANTIFIERS grahamcooper7@gmail.com - 2019-09-23 18:56 -0700
  Re: LOGIC WITHOUT QUANTIFIERS Dan Christensen <Dan_Christensen@sympatico.ca> - 2019-09-23 10:20 -0700
    Re: LOGIC WITHOUT QUANTIFIERS grahamcooper7@gmail.com - 2019-09-23 14:14 -0700
      Re: LOGIC WITHOUT QUANTIFIERS George Greene <greeneg@email.unc.edu> - 2019-09-23 17:38 -0700
        Re: LOGIC WITHOUT QUANTIFIERS grahamcooper7@gmail.com - 2019-09-23 17:50 -0700
      Re: LOGIC WITHOUT QUANTIFIERS George Greene <greeneg@email.unc.edu> - 2019-09-23 17:39 -0700
        Re: LOGIC WITHOUT QUANTIFIERS grahamcooper7@gmail.com - 2019-09-23 17:48 -0700
      Re: LOGIC WITHOUT QUANTIFIERS Dan Christensen <Dan_Christensen@sympatico.ca> - 2019-09-23 20:20 -0700
      Re: LOGIC WITHOUT QUANTIFIERS Dan Christensen <Dan_Christensen@sympatico.ca> - 2019-09-23 20:25 -0700
      Re: LOGIC WITHOUT QUANTIFIERS Dan Christensen <Dan_Christensen@sympatico.ca> - 2019-09-23 20:28 -0700
        Re: LOGIC WITHOUT QUANTIFIERS grahamcooper7@gmail.com - 2019-09-23 22:16 -0700
          Re: LOGIC WITHOUT QUANTIFIERS Dan Christensen <Dan_Christensen@sympatico.ca> - 2019-09-24 06:26 -0700
            Re: LOGIC WITHOUT QUANTIFIERS grahamcooper7@gmail.com - 2019-09-24 07:08 -0700
              Re: LOGIC WITHOUT QUANTIFIERS Dan Christensen <Dan_Christensen@sympatico.ca> - 2019-09-24 09:18 -0700
                Re: LOGIC WITHOUT QUANTIFIERS grahamcooper7@gmail.com - 2019-09-24 15:48 -0700
                Re: LOGIC WITHOUT QUANTIFIERS Dan Christensen <Dan_Christensen@sympatico.ca> - 2019-09-24 20:42 -0700
              Re: LOGIC WITHOUT QUANTIFIERS Fred <Fred@nowhere.invalid> - 2019-09-25 13:58 +0100
                Re: LOGIC WITHOUT QUANTIFIERS grahamcooper7@gmail.com - 2019-09-25 07:54 -0700
                Re: LOGIC WITHOUT QUANTIFIERS Fred <Fred@nowhere.invalid> - 2019-09-25 16:26 +0100

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