For the interlocutors of PO

[mitch]

At the link,

https://web.stanford.edu/~cgpotts/talks/potts-symsys100-2012-04-26-montague.pdf

there is a slideshow summary about Montague
semantics. As a slideshow, it is not as
explanatory as one might hope. But, in this
case that is a good thing.

Unless one has some curiosity about historical
background, one may skip the earlier slides.

At page 28 is the assertion that the typed
lambda calculus is a particularly important
tool for linguists studying formal semantics.
A number of analyses are given after that
page for topics like conjunction, disjunction,
quantification, and negation. These include
formal expressions using lambda terms. And,
in some cases, there are direct comparisons
with the syntax one expects from typical
formal systems.

Whatever problems Mr. Olcott might have regarding
issues such as "What is a proof?", they are
mirrored within his claims about formal semantics
in natural language.

That should be evident from a cursory examination
of the link. At no time has Mr. Olcott discussed
the lambda calculus when invoking Montague
semantics or reprimanding forum participants for
their lack of knowledge about formal semantics in
linguistics.

mitch

[Ross A. Finlayson]

I wonder that you might speak to the perceived goals
of his stated directions and claims then how they may
be achieved and if not then where due to inconstancy,
incongruency, incomprehensibility, here whether or
not the model or the means are erroneous.

Olcott's take of late on the Liar, well, we all know
that's a feature of the language with self-reference
and negation, its description as a simple prototype
of a falsity was also found underneath in logic in the
notion of the affirmatory logic and quantification's
consequence (Russell's) of the Liar as prototype of
falsity with self-reference and negation.

This was then held up as where logically, what would
be the elements of the language as truisms, affirmatory,
those fundamental models of all objects (including models
of language) has the Liar as a simple derived constant
of languages rich with self-reference and negation,
basically about the Liar's eliminability in the
affirmatory.



Then perhaps otherwise you're talking about various
systems beyond Goedel (that clearly include Goedel
and otherwise the usual regular well-founded apparatus
of "modern mathematics") that find, if singularly,
an extra-ordinary model for theory.


But, these are mine.

[Charlie-Boo]

1. Syntax = Input. Semantics = Output. Consider a computer program whose characters are considered to be “syntax” and whose functions are considered “semantics”. When that program (assume it calculates a function) is simply executed, the values of individual variables and functions are never seen. Only the final value is seen. The only “semantics” is the value produced - the output.

2. A proof is the evaluation of a recursive predicate. But there is more to it. Actually, a decision procedure that searches for a proof or refutation of a sentence is the evaluation of a recursive predicate. A proof is such an evaluation but it refuses to output a value unless it is TRUE. (Proof theory is simpler if our primitive process is deciding rather than proving.)

3. Natural Language semantics = truth in predicate calculus = Set Theory. Programming Languages = Axiomatic Systems = Base of Computing. On top of that, Logic = Set Theory. These studies should be combined to remove duplication and enhance generality.

4. The Liar Paradox has nothing to do with “truth”. Truth concerns determining the state of the universe, which doesn’t include sentences that you haven’t thought of yet. Every person who developed a new system to help explain the Liar needs to study Propositional Calculus – and actually Calculus especially limits.

5. Why is Lambda Calculus different from any other programming language? I once wrote a program to generate lambda expressions, execute them, and determine what function they were computing. It turned out that every function was monotonic! Years later I read they were having a problem representing nonmonotonic functions!

C-B

[mitch]

Mr. Olcott wishes to dispute any oddity arising from
logical studies that force humans to accept
epistemological limitations. He is claiming that
the error lies with admitting forms that lead to
apparent circularities. His goal is to formulate a
theory which excludes these circularities as
ill-formed constructs.

If you look at the fact that he is applying a logic
with three truth values in order to support this
exclusion, you can see that he is confusing apples
and oranges.

The standard approaches are realist in the sense of
only admitting two truth values. The language of
formal systems has been formulated to enforce the
exclusion of cases as a matter of grammatical form.
There is no truth value for "meaningless" in these
systems. Consequently, his criticisms of the results
associated with such systems is misplaced.

He wants to use the expression "not semantically
well-formed" in these contexts when the only notion
of "well-formed" that exists corresponds to the
formation rules designed to enforce a compositional,
two-valued logic.

In order for Mr. Olcott' to succeed, the statement

3 = 2

must be true in standard arithmetic. His remarks
describe an understanding of logic without a
fixed number of truth values.

That is for starters.

mitch

[graham...@gmail.com]

You can use a TRACE program and run the program step by step

>
> 2. A proof is the evaluation of a recursive predicate. But there is more to it. Actually, a decision procedure that searches for a proof or refutation of a sentence is the evaluation of a recursive predicate.

CORRECT!

PROOF is a DETERMINISTIC PROCEDURE, usually not(F) is tested aswell as F

A proof is such an evaluation but it refuses to output a value unless it is TRUE. (Proof theory is simpler if our primitive process is deciding rather than proving.)
>
> 3. Natural Language semantics = truth in predicate calculus = Set Theory. Programming Languages = Axiomatic Systems = Base of Computing. On top of that, Logic = Set Theory. These studies should be combined to remove duplication and enhance generality.
>
> 4. The Liar Paradox has nothing to do with “truth”.



Truth concerns determining the state of the universe

Good Stuff!

, which doesn’t include sentences that you haven’t thought of yet. Every person who developed a new system to help explain the Liar needs to study Propositional Calculus – and actually Calculus especially limits.
>
> 5. Why is Lambda Calculus different from any other programming language? I once wrote a program to generate lambda expressions, execute them, and determine what function they were computing. It turned out that every function was monotonic! Years later I read they were having a problem representing nonmonotonic functions!
>
> C-B

There are no FUNCTION NAMES! lambda <==means==> anonymous


lambda(X,
2X+3)

[Ross A. Finlayson]

It seems like language makes objects into
propositional objects. The apple is green
or red as a green apple or red apple. Apples
(here by varieties or instances) have a Cartesian
product with predicates, here colors or varietals.
Then, for apples X {red, green} there's a natural
inner product with a binary value. But, the outer
product is basically the expansion of all the terms,
i.e. green x apple = green apple. Then, the idea
of a non-binary value for a given apple is only
a consequence of a proposition about a particular
apple of unknown provenance.

Then, the propositional component seems to
include a temporal component. Some green
apples turn red with time. Then, there's always
apples X {red, green} X time, or for other time-
like components. The point here is that the
inner product is eventually of binary values.

Here then the Liar is this "alternating" component,
vis-a-vis discrete and continuous components. A
candiate value reverse itself on confirmation. This
is a difference between values (contingent and
permanent) and objects (concrete and abstract).

Now these objects as concrete have permanent
values and as abstract have contingent values.
Then, a matter for foundations is that fundamentally
the abstract objects are concrete (this then is a strong
platonism about mathematics vis-a-vis logic).

[graham...@gmail.com]

CORRECT! IT ONLY TOOK SCI.LOGIC 15 YEARS TO ACKNOWLEDGE!


PROGRAM A
IF INFINITE-LOOPS(A) THEN BREAK
GOTO A


THEOREM G
G = NOT(PROOF(G))



By bringing up OBJECTIONS to PROGRAM A we succumb to 1000s of ad homs in SCI.LOGIC!

>
> If you look at the fact that he is applying a logic
> with three truth values in order to support this
> exclusion, you can see that he is confusing apples
> and oranges.

Tri-State logic does not help as CHAITANS OMEGA still has
admittedly "UNKNOWN" values.

2 1/2 VALUE LOGIC can solve some problems.

1 = HALTS
2 = LOOPS
[ ] = *processing*

>
> The standard approaches are realist in the sense of
> only admitting two truth values. The language of
> formal systems has been formulated to enforce the
> exclusion of cases as a matter of grammatical form.
> There is no truth value for "meaningless" in these
> systems. Consequently, his criticisms of the results
> associated with such systems is misplaced.

CONSEQUENTLY! Consequently your logic is full of PARADOXES
with real unsolvable mystery anecdotes.

In the real world, CORRECT INITIAL SPECIFICATION OF THE PROBLEM
resolves all paradoxes before you *POORLY* specify them

>
> He wants to use the expression "not semantically
> well-formed" in these contexts when the only notion
> of "well-formed" that exists corresponds to the
> formation rules designed to enforce a compositional,
> two-valued logic.

Then dont confuse SWFF with WFF!

>
> In order for Mr. Olcott' to succeed, the statement
>
> 3 = 2
>
> must be true in standard arithmetic. His remarks
> describe an understanding of logic without a
> fixed number of truth values.
>
> That is for starters.
>
> mitch

I think P.O.'s O.H.P.s for a series of Lectures and the
"Lecture Notes" so far would work just as well on 1st year students,
even if it contradicts all of your notes!


Whatever happened to EXISTENTIAL OVER UNIVERSAL...

THE SET OF ALL SETS!


mitch has dumped all his work and went back to reading TRANSFINITE INCOMPLETE FOR THE SAKE OF MENTIONING ALL(OF IT) NONSENSE

[peteolcott]

The syntax of lambda calculus is too messy, that is why I created MTT.

[peteolcott]

On 5/6/2017 4:53 PM, mitch wrote:
> On 05/06/2017 12:40 PM, Ross A. Finlayson wrote:
>> On Saturday, May 6, 2017 at 7:28:31 AM UTC-7, mitch wrote:
>>> At the link,
>>>

>>

>> I wonder that you might speak to the perceived goals
>> of his stated directions and claims then how they may
>> be achieved and if not then where due to inconstancy,
>> incongruency, incomprehensibility, here whether or
>> not the model or the means are erroneous.
>
> Mr. Olcott wishes to dispute any oddity arising from
> logical studies that force humans to accept
> epistemological limitations. He is claiming that
> the error lies with admitting forms that lead to
> apparent circularities. His goal is to formulate a
> theory which excludes these circularities as
> ill-formed constructs.

// Just to be clear: Oranges ⊂ Type_of_Fruit
∃x ∈ Integers, ∃y ∈ Oranges (x > y)

>
> If you look at the fact that he is applying a logic
> with three truth values in order to support this
> exclusion, you can see that he is confusing apples
> and oranges.
>

True(x) = "∀x ∈ finite strings, ∃Γ ⊂ L (Γ ⊢ x)"
False(x) = "∀x ∈ finite strings, ∃Γ ⊂ L (Γ ⊢ ~x)"
Logic_Proposition(x) = "True(x) ∨ False(x)"

Not really logic with three values at all.

> The standard approaches are realist in the sense of
> only admitting two truth values. The language of
> formal systems has been formulated to enforce the
> exclusion of cases as a matter of grammatical form.
> There is no truth value for "meaningless" in these
> systems. Consequently, his criticisms of the results
> associated with such systems is misplaced.

The key mistake of Kurt Gödel in his GIT and Alfred Tarski in his TUT is that they did not ascertain that their reasoning was on the basis of actual Logic_Proposition(x).

>
> He wants to use the expression "not semantically
> well-formed" in these contexts when the only notion
> of "well-formed" that exists corresponds to the
> formation rules designed to enforce a compositional,
> two-valued logic.

Purely syntactic compositional rules have no basis to detect their insufficiency until after they have been augmented by semantic rules that have been specified syntactically.

>
> In order for Mr. Olcott' to succeed, the statement
>
> 3 = 2
>

I call bullshit on this.

> must be true in standard arithmetic. His remarks
> describe an understanding of logic without a
> fixed number of truth values.

The fixed number of truth values only apply to (Declarative Sentence / Logical Proposition).

It is clear that the following sentence is not declarative: "What time is it?" thus it is clear then neither true nor false applies to it.

It is also clear that no three-valued logic value applies to it.

The question asking about its truth value contains a type mismatch error: "What time is it (true or false)?"

[peteolcott]

"This sentence is not true"
x = "~True(x)"
Minimal Type Theory (MTT) Directed Acyclic Graph (DAG) of Liar Paradox
(1) Negation —> (2) // x is an alias for this node
(2) True —> (1) // cycle indicates error: evaluation infinite loop

No the Liar is an expression that gets stuck in an infinite loop when it is evaluated semantically to determine its truth value.

No one ever noticed this before because prior to Minimal Type Theory these was no way to express the semantics of formal expressions.

[Ross A. Finlayson]

It seems more usual to
make types as the products of arrangements of things
as functions between them also are,
instead of partitioning the space
into disconnected ranges for each type
that then would have all the types structurally
as products anyways, for sensible read-outs
of their values with self-contained context.

[mitch]

On 05/07/2017 01:41 AM, graham...@gmail.com wrote:
>
> In the real world, CORRECT INITIAL SPECIFICATION OF THE PROBLEM
> resolves all paradoxes before you *POORLY* specify them

I have no disagreement with this
statement, Graham.

The paradoxes arise specifically as
analyses challenging beliefs. They
motivate movement from poor specifications
to implementable ones. However, there are
still problems involved with halting. And,
I am unqualified to engage you on that
topic.

One path to the resolution of the
paradoxes had been to develop "formal
languages" separated from their truth
predicates. As we approach a century
of experience with this method, we
avoid the paradoxes.

I would be happy if there is a notion
of "semantically well-formed" that
could be applied. You have accused
me of conflating that with "well-formed"
in the syntactic sense.

Have you seen a coherent explanation
from Mr. Olcott?

Let him choose any language for Peano
arithmetic (a well-known first-order
theory) and demonstrate his method
for sorting syntactically well-formed
formulas into semantically well-formed
formulas and semantically ill-formed
formulas. Mr. Percival has been repeatedly
asking for him to provide this procedure.

If you think you can explain MTT on
his behalf, then show us how his statements
lead to an effective procedure that can
be generally applied. That is all anyone
wants to see. All Mr. Olcott manages to
do is to cut and paste a handful of statements
that correspond to a single instance of some
parsed formulas.

There is, apparently, no general procedure.

mitch

[mitch]

You really do not understand the consequences
of your own statements.

You can neither prove nor disprove the finite
string,

aoifjaosfaoc[hweheipweiotu0woutwnviimcm[wehwweoixjvnrp9uwo

It is in your domain. It has no truth value.

mitch

[mitch]

And lied about Montague grammar.

mitch

[mitch]

On 05/07/2017 01:41 AM, graham...@gmail.com wrote:
>
>

> mitch has dumped all his work
>

Correct.

One of the problems with mathematics is
the complexity of the work involved.

I have concluded that it is effectively
impossible to explain myself to others
with interests in this field.

In defense of Mr. Olcott you claimed
that it took courage to write a new
logic.

With respect to quantificational logic, I
developed logical axioms similar to those
for negative free logic in order to formalize
mathematical objects as fictions related by
hypotheticals. There had been mistakes
before, but they are cleaned up now. And, I
needed this logic specifically to address
the introduction of a self-membered universe
into my set-theoretic axioms.

At a completely different level, I now
have a system of 96 connectives for the
lattice,

http://cmp.felk.cvut.cz/~navara/FOML/beran_no.png

using the 80 triple systems,

http://pottonen.kapsi.fi/sts19/sts15.txt

to augment the sixteen classical connectives.

Each triple system yields a 16x16 product
which yields a 96x96 product when combined
with suitably chosen Latin squares of order
six. The 96 products are then analogues for
what I did with the truth tables for propositional
logic.

Of course, while I have ways of formulating
applicative structures, I have yet no
basis for situating the connectives in the
lattice yet.

Discerning an applicative structure for the
Boolean lattice associated with truth tables
had been a matter of analysis. Its axiomatization
involved 16^3 = 4096 axioms. Each possible
structure for the 96 connectives involves over
800,000 axioms.

It is beyond my ability.

With no one else interested and no benefit
from further work, there is no reason to
proceed.

Courage is a pretty worthless commodity,
Graham. I see it in the physical labor
I expend to pay my bills. I see it in the
mental labor I have expended to understand
the issues in the foundations of mathematics.

mitch

[graham...@gmail.com]

On Sunday, May 14, 2017 at 6:59:07 AM UTC+10, mitch wrote:
> On 05/07/2017 01:41 AM, graham...@gmail.com wrote:
> >
> > In the real world, CORRECT INITIAL SPECIFICATION OF THE PROBLEM
> > resolves all paradoxes before you *POORLY* specify them
>
> I have no disagreement with this
> statement, Graham.

GOOD START! ALL CLEVER POSTS SHOULD BEGIN THIS WAY!!

>
> The paradoxes arise specifically as
> analyses challenging beliefs. They
> motivate movement from poor specifications
> to implementable ones. However, there are
> still problems involved with halting. And,
> I am unqualified to engage you on that
> topic.
>
> One path to the resolution of the
> paradoxes had been to develop "formal
> languages" separated from their truth
> predicates. As we approach a century
> of experience with this method, we
> avoid the paradoxes.

not really, its like a steering lock on the topological landscape
of imaginary total closure under implication. its axiom of infinity
and seperation that whittle down well formed self descriptions

>
> I would be happy if there is a notion
> of "semantically well-formed" that
> could be applied. You have accused
> me of conflating that with "well-formed"
> in the syntactic sense.

we dont know WHAT P.O is constructing.... there seems to be many posters in CONSTRUCTION phase, he did misuse WFF for a time as a lot of paradoxes occur from transitive closure of WFF under implication

>
> Have you seen a coherent explanation
> from Mr. Olcott?

his C+ prover isn't finished yet!

>
> Let him choose any language for Peano
> arithmetic (a well-known first-order
> theory) and demonstrate his method
> for sorting syntactically well-formed
> formulas into semantically well-formed
> formulas and semantically ill-formed
> formulas. Mr. Percival has been repeatedly
> asking for him to provide this procedure.

I doubt P.O. understands the 'combinatorial explosion' issue of semantic construction. one way to see a brick wall stop someone is to sit back and observe

>
> If you think you can explain MTT on
> his behalf, then show us how his statements
> lead to an effective procedure that can
> be generally applied. That is all anyone
> wants to see. All Mr. Olcott manages to
> do is to cut and paste a handful of statements
> that correspond to a single instance of some
> parsed formulas.
>
> There is, apparently, no general procedure.

He's trying a new approach! :-)

Really Mitch... haven't you worked for a company that needs weekly printed reports every board meeting? These posts are GOLD!!!

[peteolcott]

x = "aoifjaosfaoc[hweheipweiotu0woutwnviimcm[wehwweoixjvnrp9uwo"
~Logic_Proposition(x) // thus Gibberish(x)