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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Newsgroups | comp.theory, sci.lang.semantics |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) |
| Followup-To | comp.theory |
| Date | 2020-07-24 23:49 +0100 |
| Organization | A noiseless patient Spider |
| Message-ID | <87zh7ojzp8.fsf@bsb.me.uk> (permalink) |
| References | (6 earlier) <6MednYs8F9v7qYvCnZ2dnUU7-R3NnZ2d@giganews.com> <87lfjcmg9p.fsf@bsb.me.uk> <ntCdnWze3_XLxYXCnZ2dnUU7-QvNnZ2d@giganews.com> <87tuxzkswv.fsf@bsb.me.uk> <fJqdnUz0O-u4iYbCnZ2dnUU7-aHNnZ2d@giganews.com> |
Cross-posted to 2 groups.
Followups directed to: comp.theory
olcott <NoOne@NoWhere.com> writes:
> On 7/22/2020 6:54 PM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>>> Try reading page 57 of Mendelson first. I'll answer any reasonable
>>>> questions you might have about that page.
>>>
>>> I have a hard copy of edition 4 and and PDF copy of edition 6. I
>>> assume you mean edition 6.
>>
>> 4th I think. Anyway, the page where the concept of an interpretation
>> is introduced.
> I think that I totally understand this:
> Page 58 fourth edition Mendelson
> The super script ^n in a name means its number of arguments
> The subscript _i in a name makes this name unique
>
> Definition
> Let L be a first-order language. An interpretation M of L consists of
> the following ingredients.
>
> a. A nonempty set D, called the domain of the interpretation.
>
> My understanding: [The set of elements (integers, humans ...) that can
> be assigned to the free variables]
Not just the free variables. Lets take D = ℕ and use the usual infix
notation with variables that don't have subscripts. The formula
x < y
has two free variables and is satisfied by some assignment and not for
others. The sentence
∀x∀y x < y
has no free variables but is false (in this interpretation) because
(informally) x < y is not the case for every assignment that could be
made. Mendelson starts with this rather informal, intuitive notion but
then makes it technically watertight by explaining how you deal with
sentences like this on the pages that follow.
> b. For each predicate letter A^n_j of L, an assignment of an n-place
> relation (A^n_j)^M in D.
>
> My understanding: [selects the subset of n-tuples of D that satisfy
> this relation]
If that wording help you, fine. Technically (A^n_j)^M /is/ a set of
n-tuples. If D is ℕ and we use the usual interpretation of <, then < is
just a set of pairs: {(0, 1), (0, 2), ... (1, 2), (1, 3), ... } with a
funny-looking name.
> My understanding: [predicates are functions that evaluate to Boolean]
Take care here. That's programmer language. The interpretation of a
predicate is a set of pairs. There's not really any evaluation and
there is definitely no need for a predicate to be computable. See the
next comment for why the distinction actually helps.
> c. For each function letter f^n_j of L, an assignment of an n-place
> operation (f^n_j)^M in D (that is, a function from D^n into D).
>
> My understanding: [functions evaluate to non _Boolean]
More to be wary of here. If the interpretation domain is {true, false}
or includes {true, false} then functions can "evaluate" to something you
might call _Boolean. (I don't know exactly what you mean by _Boolean.)
And that's fine. There is no confusion with predicates because they are
not functions and you can't mix functions and predicates in arbitrary
ways.
And again, there is no need for functions to be computable.
> My understanding: [father_of(x) would evaluate to a unique constant
> element of the set of humans]
I would use use "evaluate". And there is no need for unique -- the
definition of a function does not permit f(x) to be anything by one
thing. And the term "constant" is part of the syntax of the language.
It has no meaning here. If the domain is the set H of humans (not very
well-defined but let's let that slip) then father_of(x) is an element of
H.
It's unfortunate you picked an example function with the same name as
Mendelson's example predicate (see below). I hope your example does not
confuse you.
> My estimate: [functions must always evaluate to elements of D]
Yes, that's explicitly in the text.
> d. For each individual constant a_i of L, an assignment of some fixed
> element (a_i)^M of D. According to Wikipedia 0-ary functions are also
> considered to be constants.
It's the other way round. Some authors don't bother with constants but
instead permit 0-ary functions to serve the same purpose.
> My estimate: [constants are unique elements of D]
> Given such an interpretation, variables are thought of as ranging over
> the set D, and ¬, ⇒ and quantifiers are given their usual
> meaning. Remember that an n-place relation in D can be thought of as a
> subset of D^n, the set of all n-tuples of elements of D. For example,
> if D is the set of human beings, then the relation “father of” can be
> identified with the set of all ordered pairs 〈x, y〉 such that x is
> the father of y.
>
> My understanding: [if there are n human beings then there are n^2 2-tuples]
>
> This is where my understanding drops off. I can't see how his
> notation translates from the subset of n-tuples of D that satisfy
> n-ary relation_i.
First, are you ok with this informal notation of whether a formula is
can be satisfied, and of whether a sentence is true or false, in some
interpretation? I ask because the technical definition is harder to
understand than the idea. You may no need to go though every technical
details provided you grasp the intuitive idea.
To be sure, I would insist that a student do exercises 2.10 and 2.11.
Can you do them?
> Page 59 fourth edition Mendelson
> For a given interpretation of a language L, a wf of L without free
> variables (called a closed wf or a sentence) represents a proposition
> that is true or false, whereas a wf with free variables may be
> satisfied (i.e., true) for some values in the domain and not satisfied
> (i.e., false) for the others.
>
> Satisfiability will be the fundamental notion, on the basis of which
> the notion of truth will be defined. Moreover, instead of talking
> about the n-tuples of objects that satisfy a wf that has n free
> variables, it is much more convenient from a technical standpoint to
> deal uniformly with denumerable sequences. What we have in mind is
> that a denumerable sequence s = (s1, s2, s3, ...) is to be thought of
> as satisfying a wf B that has xj1, xj2 ,..., xjn as free variables
> (where j1 < j2 < ... < jn)
>
> if the n-tuple <sj1, sj2 ,..., sjn> .satisfies B in the usual
> sense. For example, a denumerable sequence (s1, s2, s3, ...) of
> objects in the domain of an interpretation M will turn out to satisfy
> the wf A21(x2, x5) if and only if the ordered pair, <s2, s5> is in the
> relation (A21)M assigned to the predicate letter A21 by the
> interpretation M.
>
> Let M be an interpretation of a language L and let D be the domain of
> M. Let Σ be the set of all denumerable sequences of elements of D. For
> a wf B of L, we shall define what it means for a sequence s = (s1, s2,
> ...) in Σ to satisfy B in M. As a preliminary step, for a given s in Σ
> we shall define a function s* that assigns to each term t of L an
> element s*(t) in D.
This is just quoting with no questions. I guess your question is what
it all means, but that is much better discussed after you grasp the
informal notion because it is all simply detailed text to explain the
simple idea.
But to get you started, the basic idea is that a sequence (an infinite
sequence) from the domain is used to provide values for the variables in
a formula. So (1, 0, 0, 2, 34, 7, 89, ...) assigns 1 to x_1, 0 to x_2
and so on. For any one formula there will be infinitely many irrelevant
values, but it turns out to be simpler to define it like this.
--
Ben.
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Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) André G. Isaak <agisaak@gm.invalid> - 2020-07-21 11:01 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-21 19:54 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) André G. Isaak <agisaak@gm.invalid> - 2020-07-21 19:23 -0600
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Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-23 00:54 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-23 21:12 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Kaz Kylheku <793-849-0957@kylheku.com> - 2020-07-24 16:31 +0000
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-24 12:40 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Jeff Barnett <jbb@notatt.com> - 2020-07-24 12:06 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-24 13:26 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-24 11:38 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-24 14:05 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-24 12:33 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-24 14:42 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Kaz Kylheku <793-849-0957@kylheku.com> - 2020-07-26 15:05 +0000
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-24 19:57 +0100
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Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Jeff Barnett <jbb@notatt.com> - 2020-07-24 14:43 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-24 16:00 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) David Kleinecke <dkleinecke@gmail.com> - 2020-07-24 15:38 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-24 17:45 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) David Kleinecke <dkleinecke@gmail.com> - 2020-07-24 15:57 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-24 16:11 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-24 15:52 -0700
Re: Simply defining G"odel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) R Kym Horsell <kym@kymhorsell.com> - 2020-07-24 19:02 +0000
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-26 10:27 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-26 10:36 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-26 10:39 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-24 20:20 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-24 14:37 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-25 00:13 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-24 19:25 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-24 12:02 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-24 23:49 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-24 18:49 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-25 02:28 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Jeff Barnett <jbb@notatt.com> - 2020-07-24 22:18 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) David Kleinecke <dkleinecke@gmail.com> - 2020-07-24 21:58 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Jeff Barnett <jbb@notatt.com> - 2020-07-25 01:46 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) David Kleinecke <dkleinecke@gmail.com> - 2020-07-25 10:31 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-25 12:04 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Jeff Barnett <jbb@notatt.com> - 2020-07-25 14:45 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-26 00:51 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Jeff Barnett <jbb@notatt.com> - 2020-07-25 22:46 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-26 12:10 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-25 22:53 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-26 20:46 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-26 16:42 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-26 15:46 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-26 22:46 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-27 00:28 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-26 17:05 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-27 02:52 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-27 00:30 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-27 00:33 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-26 22:39 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-27 14:12 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-27 12:23 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-27 23:41 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) André G. Isaak <agisaak@gm.invalid> - 2020-07-27 17:37 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-27 19:08 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) André G. Isaak <agisaak@gm.invalid> - 2020-07-27 19:57 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-27 21:14 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) André G. Isaak <agisaak@gm.invalid> - 2020-07-27 20:45 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-27 21:55 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) André G. Isaak <agisaak@gm.invalid> - 2020-07-27 22:58 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 00:07 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) André G. Isaak <agisaak@gm.invalid> - 2020-07-27 23:16 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 00:38 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) André G. Isaak <agisaak@gm.invalid> - 2020-07-28 00:05 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 10:00 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) André G. Isaak <agisaak@gm.invalid> - 2020-07-28 21:32 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 22:44 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-28 02:01 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-27 20:45 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-28 03:11 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-27 21:16 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-28 03:24 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-27 21:44 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-28 17:33 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 11:40 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 11:46 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-28 22:58 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 17:13 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-29 00:51 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 21:05 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-29 12:04 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-29 12:42 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-29 20:24 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-29 15:38 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-30 01:31 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-30 10:29 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-30 17:45 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-31 10:55 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-28 17:50 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 11:57 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-28 20:30 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 14:38 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-28 22:52 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 17:09 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-29 01:00 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 21:29 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-29 15:47 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-29 13:20 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-29 12:13 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-29 15:16 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-29 14:43 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-29 22:37 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-29 18:34 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-30 02:01 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-31 10:34 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-01 01:48 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-01 10:58 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-01 21:24 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-01 15:33 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-02 00:24 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-02 09:51 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-02 17:29 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-03 09:41 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-03 17:39 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-08-02 18:04 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) André G. Isaak <agisaak@gm.invalid> - 2020-08-01 23:19 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-29 16:33 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-29 13:31 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) David Kleinecke <dkleinecke@gmail.com> - 2020-07-29 12:02 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-29 14:57 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-29 22:47 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) David Kleinecke <dkleinecke@gmail.com> - 2020-07-29 15:33 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-29 20:50 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-29 18:51 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-30 02:38 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-31 10:36 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-01 00:47 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-01 01:30 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-01 12:55 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-01 10:45 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-01 20:28 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-01 15:10 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-02 00:11 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-02 09:43 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-02 17:20 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-03 09:39 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-03 17:46 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-30 00:28 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 23:31 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-29 16:43 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-29 14:02 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-30 00:36 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-29 21:44 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) André G. Isaak <agisaak@gm.invalid> - 2020-07-29 21:50 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) André G. Isaak <agisaak@gm.invalid> - 2020-07-29 21:55 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-31 10:48 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-31 12:45 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-31 14:55 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-31 13:13 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-31 16:16 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) David Kleinecke <dkleinecke@gmail.com> - 2020-07-31 14:42 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-31 18:16 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-31 14:44 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Jeff Barnett <jbb@notatt.com> - 2020-07-31 14:02 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) André G. Isaak <agisaak@gm.invalid> - 2020-07-31 17:58 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-31 22:33 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-31 10:43 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-30 13:39 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-31 10:51 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-01 00:58 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-01 10:52 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-01 21:02 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-02 09:28 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-02 17:45 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-03 09:46 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-08-03 17:46 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-08-03 13:22 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Andy Walker <anw@cuboid.co.uk> - 2020-07-30 20:35 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) David Kleinecke <dkleinecke@gmail.com> - 2020-07-30 12:57 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-30 17:20 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Andy Walker <anw@cuboid.co.uk> - 2020-07-30 23:24 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) David Kleinecke <dkleinecke@gmail.com> - 2020-07-30 16:30 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Andy Walker <anw@cuboid.co.uk> - 2020-07-31 01:31 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) David Kleinecke <dkleinecke@gmail.com> - 2020-07-30 20:36 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-31 00:12 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-30 20:41 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-30 17:10 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) David Kleinecke <dkleinecke@gmail.com> - 2020-07-30 16:31 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-30 20:50 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) David Kleinecke <dkleinecke@gmail.com> - 2020-07-30 20:40 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-31 01:34 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-28 10:41 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 12:51 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Kaz Kylheku <793-849-0957@kylheku.com> - 2020-07-28 08:23 +0000
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-28 09:20 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-26 13:00 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-26 22:45 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-27 16:17 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-27 23:51 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-26 22:46 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) olcott <NoOne@NoWhere.com> - 2020-07-27 17:14 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V33 (Mendelson Satisfiability) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-28 00:22 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-24 15:57 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-25 00:03 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V31 (Semantically Incorrect Defined) olcott <NoOne@NoWhere.com> - 2020-07-24 19:10 -0500
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