Re: LOGIC WITHOUT QUANTIFIERS

Newsgroups	sci.logic
Date	2019-09-22 17:17 -0700
References	<e9d73774-f8f8-4723-bcad-a9338d26ab5c@googlegroups.com> <f80566ec-bfc0-eaa9-c984-5715bb20cc30@att.net>
Message-ID	<82ef41eb-e34f-4f4b-8f07-2811e48ed9db@googlegroups.com> (permalink)
Subject	Re: LOGIC WITHOUT QUANTIFIERS
From	grahamcooper7@gmail.com

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On Monday, September 23, 2019 at 9:52:05 AM UTC+10, Jim Burns wrote:
> 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.


Yet in predicate logic without quantifiers EXISTS(VAR) is default.




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

the answer is above

xeN  @->  y>x

or even

xeN  @->  yeN & 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".
> 


If 1 dog in a house has fleas, then all dogs in the house have fleas.

fleas(DOG,house)  ->@  fleas(DOG,house)



NOTE: there seems to be 3 symbols

@->         ..... ALWAYS IMPLIES
->@         ..... IMPLIES ALWAYS
@->@


WITHOUT VARIABLES to quantify over, it fits into simple predicate notation (PROLOG, MODUS PONENS)

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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