On 12/15/2022 10:40 AM, Skep Dick wrote:
> On Thursday, 15 December 2022 at 18:27:13 UTC+2, olcott wrote:
>> On 12/15/2022 10:23 AM, Skep Dick wrote:
>>> On Thursday, 15 December 2022 at 18:11:52 UTC+2, olcott wrote:
>>>> On 12/15/2022 6:12 AM, Skep Dick wrote:
>>>>> On Wednesday, 14 December 2022 at 22:19:47 UTC+2, olcott wrote:
>>>>>> On 12/14/2022 1:49 PM, Skep Dick wrote:
>>>>>>> On Wednesday, 14 December 2022 at 21:46:27 UTC+2, olcott wrote:
>>>>>>>> On 12/14/2022 1:39 PM, Skep Dick wrote:
>>>>>>>>> How do you plan to traverse an infinite set in finite time?
>>>>>>>> That may place in in (b).
>>>>>>>
>>>>>>> You'd have to exhaust the search to place it in (b)...
>>>>>> If an exhaustive search is required and not possible in finite time then
>>>>>> this counts as (b).
>>>>> No, it doesn't. It counts as (c).
>>>>>
>>>>> You don't know whether an "exhaustive" search is required. The search-termination condition may be satisfied on the very next element; or never.
>>>> (a) Truth-bearer
>>>> 1. True
>>>> 2. False
>>>> (b) Not a truth bearer
>>>> (c) As yet undetermined whether (a); or (b)
>>>> If we know that an exhaustive search is required then it counts as (b).
>>>> If we don't know whether or not an exhaustive search is required then it
>>>> counts as (c).
>>> Idiot. Here is a Turing machine that will halt if ZFC is inconsistent.
>>>
>>> https://turingmachinesimulator.com/shared/vgimygpuwi
>>>
>>> Is the statement "ZFC is inconsistent" (a), (b); or (c)?
>> It took me an hour to write the part that you skipped.
>
> Shame.
>
> Are you going to address the question or are you going to bullshit your way out again?

The part that you skipped was the most important essence of my point and
you simply changed the subject.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Thursday, 15 December 2022 at 18:46:16 UTC+2, olcott wrote:
> On 12/15/2022 10:40 AM, Skep Dick wrote:
> > On Thursday, 15 December 2022 at 18:27:13 UTC+2, olcott wrote:
> >> On 12/15/2022 10:23 AM, Skep Dick wrote:
> >>> On Thursday, 15 December 2022 at 18:11:52 UTC+2, olcott wrote:
> >>>> On 12/15/2022 6:12 AM, Skep Dick wrote:
> >>>>> On Wednesday, 14 December 2022 at 22:19:47 UTC+2, olcott wrote:
> >>>>>> On 12/14/2022 1:49 PM, Skep Dick wrote:
> >>>>>>> On Wednesday, 14 December 2022 at 21:46:27 UTC+2, olcott wrote:
> >>>>>>>> On 12/14/2022 1:39 PM, Skep Dick wrote:
> >>>>>>>>> How do you plan to traverse an infinite set in finite time?
> >>>>>>>> That may place in in (b).
> >>>>>>>
> >>>>>>> You'd have to exhaust the search to place it in (b)...
> >>>>>> If an exhaustive search is required and not possible in finite time then
> >>>>>> this counts as (b).
> >>>>> No, it doesn't. It counts as (c).
> >>>>>
> >>>>> You don't know whether an "exhaustive" search is required. The search-termination condition may be satisfied on the very next element; or never.
> >>>> (a) Truth-bearer
> >>>> 1. True
> >>>> 2. False
> >>>> (b) Not a truth bearer
> >>>> (c) As yet undetermined whether (a); or (b)
> >>>> If we know that an exhaustive search is required then it counts as (b).
> >>>> If we don't know whether or not an exhaustive search is required then it
> >>>> counts as (c).
> >>> Idiot. Here is a Turing machine that will halt if ZFC is inconsistent.
> >>>
> >>> https://turingmachinesimulator.com/shared/vgimygpuwi
> >>>
> >>> Is the statement "ZFC is inconsistent" (a), (b); or (c)?
> >> It took me an hour to write the part that you skipped.
> >
> > Shame.
> >
> > Are you going to address the question or are you going to bullshit your way out again?
> The part that you skipped was the most important essence of my point and
> you simply changed the subject.
Bullshit. The subject remains exactly as before.

Which category does "ZFC Is inconsistent" belong to: (a), (b); or (c)?

On 12/15/2022 10:49 AM, Skep Dick wrote:
> On Thursday, 15 December 2022 at 18:46:16 UTC+2, olcott wrote:
>> On 12/15/2022 10:40 AM, Skep Dick wrote:
>>> On Thursday, 15 December 2022 at 18:27:13 UTC+2, olcott wrote:
>>>> On 12/15/2022 10:23 AM, Skep Dick wrote:
>>>>> On Thursday, 15 December 2022 at 18:11:52 UTC+2, olcott wrote:
>>>>>> On 12/15/2022 6:12 AM, Skep Dick wrote:
>>>>>>> On Wednesday, 14 December 2022 at 22:19:47 UTC+2, olcott wrote:
>>>>>>>> On 12/14/2022 1:49 PM, Skep Dick wrote:
>>>>>>>>> On Wednesday, 14 December 2022 at 21:46:27 UTC+2, olcott wrote:
>>>>>>>>>> On 12/14/2022 1:39 PM, Skep Dick wrote:
>>>>>>>>>>> How do you plan to traverse an infinite set in finite time?
>>>>>>>>>> That may place in in (b).
>>>>>>>>>
>>>>>>>>> You'd have to exhaust the search to place it in (b)...
>>>>>>>> If an exhaustive search is required and not possible in finite time then
>>>>>>>> this counts as (b).
>>>>>>> No, it doesn't. It counts as (c).
>>>>>>>
>>>>>>> You don't know whether an "exhaustive" search is required. The search-termination condition may be satisfied on the very next element; or never.
>>>>>> (a) Truth-bearer
>>>>>> 1. True
>>>>>> 2. False
>>>>>> (b) Not a truth bearer
>>>>>> (c) As yet undetermined whether (a); or (b)
>>>>>> If we know that an exhaustive search is required then it counts as (b).
>>>>>> If we don't know whether or not an exhaustive search is required then it
>>>>>> counts as (c).
>>>>> Idiot. Here is a Turing machine that will halt if ZFC is inconsistent.
>>>>>
>>>>> https://turingmachinesimulator.com/shared/vgimygpuwi
>>>>>
>>>>> Is the statement "ZFC is inconsistent" (a), (b); or (c)?
>>>> It took me an hour to write the part that you skipped.
>>>
>>> Shame.
>>>
>>> Are you going to address the question or are you going to bullshit your way out again?
>> The part that you skipped was the most important essence of my point and
>> you simply changed the subject.
> Bullshit. The subject remains exactly as before.
>
> Which category does "ZFC Is inconsistent" belong to: (a), (b); or (c)?

That is off topic, the topic is Gödel and Tarski.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Thursday, 15 December 2022 at 19:13:14 UTC+2, olcott wrote:
> On 12/15/2022 10:49 AM, Skep Dick wrote:
> > On Thursday, 15 December 2022 at 18:46:16 UTC+2, olcott wrote:
> >> On 12/15/2022 10:40 AM, Skep Dick wrote:
> >>> On Thursday, 15 December 2022 at 18:27:13 UTC+2, olcott wrote:
> >>>> On 12/15/2022 10:23 AM, Skep Dick wrote:
> >>>>> On Thursday, 15 December 2022 at 18:11:52 UTC+2, olcott wrote:
> >>>>>> On 12/15/2022 6:12 AM, Skep Dick wrote:
> >>>>>>> On Wednesday, 14 December 2022 at 22:19:47 UTC+2, olcott wrote:
> >>>>>>>> On 12/14/2022 1:49 PM, Skep Dick wrote:
> >>>>>>>>> On Wednesday, 14 December 2022 at 21:46:27 UTC+2, olcott wrote:
> >>>>>>>>>> On 12/14/2022 1:39 PM, Skep Dick wrote:
> >>>>>>>>>>> How do you plan to traverse an infinite set in finite time?
> >>>>>>>>>> That may place in in (b).
> >>>>>>>>>
> >>>>>>>>> You'd have to exhaust the search to place it in (b)...
> >>>>>>>> If an exhaustive search is required and not possible in finite time then
> >>>>>>>> this counts as (b).
> >>>>>>> No, it doesn't. It counts as (c).
> >>>>>>>
> >>>>>>> You don't know whether an "exhaustive" search is required. The search-termination condition may be satisfied on the very next element; or never.
> >>>>>> (a) Truth-bearer
> >>>>>> 1. True
> >>>>>> 2. False
> >>>>>> (b) Not a truth bearer
> >>>>>> (c) As yet undetermined whether (a); or (b)
> >>>>>> If we know that an exhaustive search is required then it counts as (b).
> >>>>>> If we don't know whether or not an exhaustive search is required then it
> >>>>>> counts as (c).
> >>>>> Idiot. Here is a Turing machine that will halt if ZFC is inconsistent.
> >>>>>
> >>>>> https://turingmachinesimulator.com/shared/vgimygpuwi
> >>>>>
> >>>>> Is the statement "ZFC is inconsistent" (a), (b); or (c)?
> >>>> It took me an hour to write the part that you skipped.
> >>>
> >>> Shame.
> >>>
> >>> Are you going to address the question or are you going to bullshit your way out again?
> >> The part that you skipped was the most important essence of my point and
> >> you simply changed the subject.
> > Bullshit. The subject remains exactly as before.
> >
> > Which category does "ZFC Is inconsistent" belong to: (a), (b); or (c)?
> That is off topic, the topic is Gödel and Tarski.
Bullshit. It's on-topic.

Is "ZFC is inconsistent" a truth-bearer or not?

On 12/15/2022 1:05 PM, Skep Dick wrote:
> On Thursday, 15 December 2022 at 19:13:14 UTC+2, olcott wrote:
>> On 12/15/2022 10:49 AM, Skep Dick wrote:
>>> On Thursday, 15 December 2022 at 18:46:16 UTC+2, olcott wrote:
>>>> On 12/15/2022 10:40 AM, Skep Dick wrote:
>>>>> On Thursday, 15 December 2022 at 18:27:13 UTC+2, olcott wrote:
>>>>>> On 12/15/2022 10:23 AM, Skep Dick wrote:
>>>>>>> On Thursday, 15 December 2022 at 18:11:52 UTC+2, olcott wrote:
>>>>>>>> On 12/15/2022 6:12 AM, Skep Dick wrote:
>>>>>>>>> On Wednesday, 14 December 2022 at 22:19:47 UTC+2, olcott wrote:
>>>>>>>>>> On 12/14/2022 1:49 PM, Skep Dick wrote:
>>>>>>>>>>> On Wednesday, 14 December 2022 at 21:46:27 UTC+2, olcott wrote:
>>>>>>>>>>>> On 12/14/2022 1:39 PM, Skep Dick wrote:
>>>>>>>>>>>>> How do you plan to traverse an infinite set in finite time?
>>>>>>>>>>>> That may place in in (b).
>>>>>>>>>>>
>>>>>>>>>>> You'd have to exhaust the search to place it in (b)...
>>>>>>>>>> If an exhaustive search is required and not possible in finite time then
>>>>>>>>>> this counts as (b).
>>>>>>>>> No, it doesn't. It counts as (c).
>>>>>>>>>
>>>>>>>>> You don't know whether an "exhaustive" search is required. The search-termination condition may be satisfied on the very next element; or never.
>>>>>>>> (a) Truth-bearer
>>>>>>>> 1. True
>>>>>>>> 2. False
>>>>>>>> (b) Not a truth bearer
>>>>>>>> (c) As yet undetermined whether (a); or (b)
>>>>>>>> If we know that an exhaustive search is required then it counts as (b).
>>>>>>>> If we don't know whether or not an exhaustive search is required then it
>>>>>>>> counts as (c).
>>>>>>> Idiot. Here is a Turing machine that will halt if ZFC is inconsistent.
>>>>>>>
>>>>>>> https://turingmachinesimulator.com/shared/vgimygpuwi
>>>>>>>
>>>>>>> Is the statement "ZFC is inconsistent" (a), (b); or (c)?
>>>>>> It took me an hour to write the part that you skipped.
>>>>>
>>>>> Shame.
>>>>>
>>>>> Are you going to address the question or are you going to bullshit your way out again?
>>>> The part that you skipped was the most important essence of my point and
>>>> you simply changed the subject.
>>> Bullshit. The subject remains exactly as before.
>>>
>>> Which category does "ZFC Is inconsistent" belong to: (a), (b); or (c)?
>> That is off topic, the topic is Gödel and Tarski.
> Bullshit. It's on-topic.
>
> Is "ZFC is inconsistent" a truth-bearer or not?

I would trash ZFC and instead have an axiom: ∀x ∉ x
This is derived from an inheritance hierarchy that specifies no physical
or abstract thing x can totally contain itself.

The inheritance hierarchy of all knowledge would have no place to put
misconceptions the derive incoherence.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/14/2022 12:33 PM, Skep Dick wrote:
> On Wednesday, 14 December 2022 at 21:08:17 UTC+2, Jeff Barnett wrote:
>> On 12/14/2022 5:55 AM, Skep Dick wrote:
>>
>> <NIP>
>>
>>> "Part of the whole is as big as the whole" sure sounds crazy in English.
>>
>> Not to a mathematician! Only to a bad skeptic.
> Perhaps only to a bad mathematician, but not to a good skeptic?
>
>> A good mathematician says that's an interesting "definition", explores
>> the concept, and discovers amazing ideas and instances.
> That sounds no different to a drug addict chasing a high.
>
> I tend to find it quite annoying that I can make two spheres out of one; but I can't do that with any physical resources.
> So I much prefer to do my thinking in linear logic. Where resource-boundedness is a thing.
>
>> A good skeptic believes the "definition" useless because nothing should
>> satisfy it, explores the concept because it interests him, and is
>> (secretly) delighted to find his initial impression was wrong.
> Indeed, that sounds like escapism to me.
>
>> Try being a good little skeptic not an Olcott. You'll have more fun.
> I don't know how to be any better at skepticism than to reject your entire paradigm.
>
> Maths is useful. Even when it's not fun.

Sounds like you will never accept, know, or appreciate much about the
beauty of ideas in mathematics and abstract relations. That's a pity.
Most mathematicians I know are just that for the sake of enjoyment and
consider themselves quite fortunate to be able to call that enjoyment
work and be paid for it. Of course some of those results eventually
support some engineering or accounting concerns but that typically was
not the original intent. The concepts just seemed interesting at the
time and the mathematician explored in the same way a child becomes
fascinated when he observes and interesting pattern in the surface of
his sand box. I think you should play more.
--
Jeff Barnett

On Thursday, 15 December 2022 at 21:45:11 UTC+2, olcott wrote:
> On 12/15/2022 1:05 PM, Skep Dick wrote:
> > On Thursday, 15 December 2022 at 19:13:14 UTC+2, olcott wrote:
> >> On 12/15/2022 10:49 AM, Skep Dick wrote:
> >>> On Thursday, 15 December 2022 at 18:46:16 UTC+2, olcott wrote:
> >>>> On 12/15/2022 10:40 AM, Skep Dick wrote:
> >>>>> On Thursday, 15 December 2022 at 18:27:13 UTC+2, olcott wrote:
> >>>>>> On 12/15/2022 10:23 AM, Skep Dick wrote:
> >>>>>>> On Thursday, 15 December 2022 at 18:11:52 UTC+2, olcott wrote:
> >>>>>>>> On 12/15/2022 6:12 AM, Skep Dick wrote:
> >>>>>>>>> On Wednesday, 14 December 2022 at 22:19:47 UTC+2, olcott wrote:
> >>>>>>>>>> On 12/14/2022 1:49 PM, Skep Dick wrote:
> >>>>>>>>>>> On Wednesday, 14 December 2022 at 21:46:27 UTC+2, olcott wrote:
> >>>>>>>>>>>> On 12/14/2022 1:39 PM, Skep Dick wrote:
> >>>>>>>>>>>>> How do you plan to traverse an infinite set in finite time?
> >>>>>>>>>>>> That may place in in (b).
> >>>>>>>>>>>
> >>>>>>>>>>> You'd have to exhaust the search to place it in (b)...
> >>>>>>>>>> If an exhaustive search is required and not possible in finite time then
> >>>>>>>>>> this counts as (b).
> >>>>>>>>> No, it doesn't. It counts as (c).
> >>>>>>>>>
> >>>>>>>>> You don't know whether an "exhaustive" search is required. The search-termination condition may be satisfied on the very next element; or never.
> >>>>>>>> (a) Truth-bearer
> >>>>>>>> 1. True
> >>>>>>>> 2. False
> >>>>>>>> (b) Not a truth bearer
> >>>>>>>> (c) As yet undetermined whether (a); or (b)
> >>>>>>>> If we know that an exhaustive search is required then it counts as (b).
> >>>>>>>> If we don't know whether or not an exhaustive search is required then it
> >>>>>>>> counts as (c).
> >>>>>>> Idiot. Here is a Turing machine that will halt if ZFC is inconsistent.
> >>>>>>>
> >>>>>>> https://turingmachinesimulator.com/shared/vgimygpuwi
> >>>>>>>
> >>>>>>> Is the statement "ZFC is inconsistent" (a), (b); or (c)?
> >>>>>> It took me an hour to write the part that you skipped.
> >>>>>
> >>>>> Shame.
> >>>>>
> >>>>> Are you going to address the question or are you going to bullshit your way out again?
> >>>> The part that you skipped was the most important essence of my point and
> >>>> you simply changed the subject.
> >>> Bullshit. The subject remains exactly as before.
> >>>
> >>> Which category does "ZFC Is inconsistent" belong to: (a), (b); or (c)?
> >> That is off topic, the topic is Gödel and Tarski.
> > Bullshit. It's on-topic.
> >
> > Is "ZFC is inconsistent" a truth-bearer or not?
> I would trash ZFC and instead have an axiom: ∀x ∉ x
> This is derived from an inheritance hierarchy that specifies no physical
> or abstract thing x can totally contain itself.
>
> The inheritance hierarchy of all knowledge would have no place to put
> misconceptions the derive incoherence.
I didn't ask you whether ZFC contains itself.

I asked you whether "ZFC is inconsistent" is a truth-bearer.

On 12/15/2022 2:03 PM, Skep Dick wrote:
> On Thursday, 15 December 2022 at 21:45:11 UTC+2, olcott wrote:
>> On 12/15/2022 1:05 PM, Skep Dick wrote:
>>> On Thursday, 15 December 2022 at 19:13:14 UTC+2, olcott wrote:
>>>> On 12/15/2022 10:49 AM, Skep Dick wrote:
>>>>> On Thursday, 15 December 2022 at 18:46:16 UTC+2, olcott wrote:
>>>>>> On 12/15/2022 10:40 AM, Skep Dick wrote:
>>>>>>> On Thursday, 15 December 2022 at 18:27:13 UTC+2, olcott wrote:
>>>>>>>> On 12/15/2022 10:23 AM, Skep Dick wrote:
>>>>>>>>> On Thursday, 15 December 2022 at 18:11:52 UTC+2, olcott wrote:
>>>>>>>>>> On 12/15/2022 6:12 AM, Skep Dick wrote:
>>>>>>>>>>> On Wednesday, 14 December 2022 at 22:19:47 UTC+2, olcott wrote:
>>>>>>>>>>>> On 12/14/2022 1:49 PM, Skep Dick wrote:
>>>>>>>>>>>>> On Wednesday, 14 December 2022 at 21:46:27 UTC+2, olcott wrote:
>>>>>>>>>>>>>> On 12/14/2022 1:39 PM, Skep Dick wrote:
>>>>>>>>>>>>>>> How do you plan to traverse an infinite set in finite time?
>>>>>>>>>>>>>> That may place in in (b).
>>>>>>>>>>>>>
>>>>>>>>>>>>> You'd have to exhaust the search to place it in (b)...
>>>>>>>>>>>> If an exhaustive search is required and not possible in finite time then
>>>>>>>>>>>> this counts as (b).
>>>>>>>>>>> No, it doesn't. It counts as (c).
>>>>>>>>>>>
>>>>>>>>>>> You don't know whether an "exhaustive" search is required. The search-termination condition may be satisfied on the very next element; or never.
>>>>>>>>>> (a) Truth-bearer
>>>>>>>>>> 1. True
>>>>>>>>>> 2. False
>>>>>>>>>> (b) Not a truth bearer
>>>>>>>>>> (c) As yet undetermined whether (a); or (b)
>>>>>>>>>> If we know that an exhaustive search is required then it counts as (b).
>>>>>>>>>> If we don't know whether or not an exhaustive search is required then it
>>>>>>>>>> counts as (c).
>>>>>>>>> Idiot. Here is a Turing machine that will halt if ZFC is inconsistent.
>>>>>>>>>
>>>>>>>>> https://turingmachinesimulator.com/shared/vgimygpuwi
>>>>>>>>>
>>>>>>>>> Is the statement "ZFC is inconsistent" (a), (b); or (c)?
>>>>>>>> It took me an hour to write the part that you skipped.
>>>>>>>
>>>>>>> Shame.
>>>>>>>
>>>>>>> Are you going to address the question or are you going to bullshit your way out again?
>>>>>> The part that you skipped was the most important essence of my point and
>>>>>> you simply changed the subject.
>>>>> Bullshit. The subject remains exactly as before.
>>>>>
>>>>> Which category does "ZFC Is inconsistent" belong to: (a), (b); or (c)?
>>>> That is off topic, the topic is Gödel and Tarski.
>>> Bullshit. It's on-topic.
>>>
>>> Is "ZFC is inconsistent" a truth-bearer or not?
>> I would trash ZFC and instead have an axiom: ∀x ∉ x
>> This is derived from an inheritance hierarchy that specifies no physical
>> or abstract thing x can totally contain itself.
>>
>> The inheritance hierarchy of all knowledge would have no place to put
>> misconceptions the derive incoherence.
> I didn't ask you whether ZFC contains itself.
>
> I asked you whether "ZFC is inconsistent" is a truth-bearer.

The problem with verifying the consistency of ZFC is that it depends
upon insufficient or incorrect understandings about the size of infinite
sets. My infinitesimal number system seems to provide the means to count
the geometric points on a number line, thus disputing the assumption
that reals are not countable.

The point of this thread is to show that when mathematics is defined to
have a consistent foundational basis that inconsistency ceases to exist
because it can no longer be expressed.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Skep Dick <skepdick22@gmail.com> writes:

> On Thursday, 15 December 2022 at 14:19:44 UTC+2, Ben Bacarisse wrote:
>> Skep Dick <skepd...@gmail.com> writes:
>>
>> > On Thursday, 15 December 2022 at 03:20:24 UTC+2, richar...@gmail.com wrote:
>> >> On 12/14/22 8:19 AM, Skep Dick wrote:
>> >> > On Wednesday, 14 December 2022 at 14:24:00 UTC+2, richar...@gmail.com wrote:
>> >> >> And yes, they are all the "same size" because you can make the bijection
>> >> >> between them, even though "logic" seems to say that one is bigger than
>> >> >> another.
>> >> > In other news...
>> >> >
>> >> > [0,2..] ∪ [1,3..] ↔ ℕ
>> >> >
>> >> > SIZE([0,2..]) + SIZE([1,3..]) = SIZE(ℕ)
>> >> > SIZE([0,2..]) = SIZE([1,3..])
>> >> > SIZE([0,2..]) = SIZE(ℕ)
>> >> > SIZE([1,3..]) = SIZE(ℕ)
>> >> >
>> >> > Houston, we have a problem!
>> >>
>> >> And whats the problem.
>> >>
>> >> Since all the SIZEs are "Countable Infinite", there is no problem,
>> >> because of the derived rules of mathematics of infinities.
>> >>
>> >> There is no problem that x + x = x, if x is an infinity.
>> >
>> > The problem is (x + x = x) ↔ (x + x - x = x - x) ↔ ( x = x - x) ↔ (x = 0)
>>
>> Seriously? You think every quantity must follow the rules you learned
>> as a child? Of course I know you don't think so, so I'm wondering what
>> your point it. Just chatting?
>
> My point is that there is no point.

That's another way of saying you'd like to have a chat.

--
Ben.

On 12/15/22 8:05 AM, Skep Dick wrote:
> On Thursday, 15 December 2022 at 15:00:53 UTC+2, richar...@gmail.com wrote:
>> And with that sort of base, you can know nothing, so your system becomes
>> worthless.
>
> What is the objective arbiter for "worth" ?
>

That it can generate something you value.

Since a system that can't actually show anything can't generate
anything, it can't generate anything of value.

On 12/15/22 8:04 AM, Skep Dick wrote:
> On Thursday, 15 December 2022 at 14:59:36 UTC+2, richar...@gmail.com wrote:
>> Nope, because in mathematics with infinites you don't have those properties.
>>
>> That is one of the problems with infinities.
>>
>> You are assuming that all the properties of the finite numbers hold,
>> which they don't.
>
> Where's the objective arbiter on such things?

That they generate contradictions, and thus make the system worthless
due to the power of the principle of explosion, since there can be no
actual information or knowledge in such a system.

On 12/14/2022 7:05 PM, Richard Damon wrote:
> On 12/14/22 12:25 PM, olcott wrote:
>> On 12/14/2022 11:02 AM, Skep Dick wrote:
>>> On Wednesday, 14 December 2022 at 18:06:22 UTC+2, olcott wrote:
>>>> On 12/14/2022 9:24 AM, Skep Dick wrote:
>>>>> On Wednesday, 14 December 2022 at 16:21:35 UTC+2, wyni...@gmail.com
>>>>> wrote:
>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>> <=> Valid(φ) ↔ TRUE
>>>>>>
>>>>>> Valid(φ) is a tautology.
>>>>>> This explains why you think your H is correct.
>>>>> It's only a tautology in systems in which excluded middle holds.
>>>>>
>>>> All expressions of formal or natural language are
>>>> (a) True
>>>> (b) False
>>>> (c) Not a truth bearer
>>> Lets try that again...
>>>
>>> (a) Truth-bearer
>>>      1. True
>>>      2. False
>>> (b) Not a truth bearer
>>> (c) As yet undetermined whether (a); or (b)
>>
>>
>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>> If the only way to determine that the above is true is to test every
>> element of the set of natural numbers then it may be (c).
>>
>
> So you accept that some statement might be neither a Truth-Bearer or not
> a Truth-Beared?
>
> Or are you just conflating KNOWLEDGE with TRUTH.
>

Every expression of language is either true / false or not a truth bearer.

> The Truth of a statement doesn't change just because we find the proof
> for it.

Until an expression of language can be correctly determined to be true
or false it is not an element of the set of knowledge.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/14/2022 7:08 PM, Richard Damon wrote:
> On 12/14/22 9:48 AM, olcott wrote:
>> On 12/14/2022 8:21 AM, wij wrote:
>>> On Sunday, December 11, 2022 at 9:59:47 AM UTC+8, olcott wrote:
>>>> Theorem 1.
>>>> Every valid logical expression is provable. Equivalently, every logical
>>>> expression is either satisfiable or refutable.
>>>> https://plato.stanford.edu/entries/goedel/#ComThe
>>>>
>>>> The conventional definition of incompleteness:
>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>
>>>> Should actually be written as:
>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>> thus abolishing Incompleteness.
>>>    Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>> <=> Valid(φ) ↔ TRUE
>>>
>>
>> *Correction*
>>   True(φ) ↔ (T ⊢ φ)
>> ¬True(φ) ↔ (T ⊬ φ)
>> False(φ) ↔ (T ⊢ ¬φ)
>
> Which since you say Godel's G is ¬True but also not False.
>
> Since G is a statement of the form T ⊬ x, that means that since G is
> ¬True, that T ⊬ x, and since G is ¬False we have that ¬(T ⊢ ¬φ)
>
> Which means that (T ⊬ ¬x) and from the previous (T ⊬ x)
>
> Thus either Provability (since that is the sort of statement x is) isn't
> a truth bearer, or x is a statement that can neither be proven or
> disproven.
>

Because the Gödel incompleteness theorem forms an exact isomorphism of
Tarski's undefinability theorem any refutation of Tarski is a refutation
of Gödel. The formalized Liar paradox is an exact isomorphism:

(3) x ∉ Provable if and only if x ∈ True.
~Provable(x) ↔ True(x).
x is true if and only if x is unprovable

https://liarparadox.org/Tarski_275_276.pdf

G ↔ (F ⊬ G)
G is true if and only if G is unprovable in F

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/14/2022 7:10 PM, Richard Damon wrote:
> On 12/14/22 10:22 AM, olcott wrote:
>> On 12/13/2022 8:38 PM, Richard Damon wrote:
>>> On 12/13/22 10:56 AM, olcott wrote:
>>>> On 12/12/2022 8:31 PM, Richard Damon wrote:
>>>>> On 12/12/22 8:51 PM, olcott wrote:
>>>>>> On 12/12/2022 6:29 PM, Richard Damon wrote:
>>>>>>> On 12/12/22 10:44 AM, olcott wrote:
>>>>>>>> On 12/12/2022 7:05 AM, Richard Damon wrote:
>>>>>>>>> On 12/11/22 3:38 PM, olcott wrote:
>>>>>>>>>> On 12/11/2022 1:45 PM, Skep Dick wrote:
>>>>>>>>>>> On Sunday, 11 December 2022 at 21:41:07 UTC+2, olcott wrote:
>>>>>>>>>>>> On 12/11/2022 1:29 PM, Skep Dick wrote:
>>>>>>>>>>>>> On Sunday, 11 December 2022 at 21:11:02 UTC+2, olcott wrote:
>>>>>>>>>>>>>> On 12/11/2022 11:46 AM, Skep Dick wrote:
>>>>>>>>>>>>>>> On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
>>>>>>>>>>>>>>>> On 12/11/2022 10:39 AM, Skep Dick wrote:
>>>>>>>>>>>>>>>>> On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott
>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>> On 12/11/2022 9:21 AM, Skep Dick wrote:
>>>>>>>>>>>>>>>>>>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott
>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>>>>>>>>>>>>>>>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2,
>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>>>>>>>>>>>>>>> So which one is it?
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> The disjunction requires a valid proof.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Unless φ is provable or refutable φ is not a logic
>>>>>>>>>>>>>>>>>>>> expression.
>>>>>>>>>>>>>>>>>>> ERGO!!!
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> 1 to n is NOT a logic expression. Because logic
>>>>>>>>>>>>>>>>>>> expressiong (e.g the sort of things you are referring
>>>>>>>>>>>>>>>>>>> to when you say "φ") DON'T contain free variables.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Using my MTT one can construct an 1,2,3,4...n ary
>>>>>>>>>>>>>>>>>> logic expression using
>>>>>>>>>>>>>>>>>> a slightly adapted FOL syntax.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨
>>>>>>>>>>>>>>>>> (T ⊢ ¬φ))
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> the expression "1,2,3,4...n" is **NOT** a valid logic
>>>>>>>>>>>>>>>>> expression!
>>>>>>>>>>>>>>>> Only because you did not encode it correctly: ∃n ∈ ℕ
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Furthermore, Sir.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation#The_interpretation
>>>>>>>>>>>>>>> A proof of P ∨ Q is either <0,a> where a is a proof o P
>>>>>>>>>>>>>>> or <1,b> where b is a proof of Q.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Sir. You can interpret <0,a> and <1, b> through the
>>>>>>>>>>>>>>> semantics of the usual Either-monad. Sir.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Where Left and Right are the usual projections: Left<a,b>
>>>>>>>>>>>>>>> ↔ a and Right<a,b> ↔ b
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> https://hackage.haskell.org/package/category-extras-0.52.0/docs/Control-Monad-Either.html
>>>>>>>>>>>>>> Is_a_Theorem_of_T(φ) 0 1 0 1
>>>>>>>>>>>>>> Is_a_Theorem_of_T(¬φ) 0 0 1 1
>>>>>>>>>>>>>> ∨ 0 1 1 1
>>>>>>>>>>>>> *sigh* Moron. What is confusing you about the sentence
>>>>>>>>>>>>> "Disjunctions require proof"?
>>>>>>>>>>>>>
>>>>>>>>>>>>> The ∨ operator is a disjunction.. It's not enough to tell
>>>>>>>>>>>>> us that P or Q is a theorem. That claim is incomplete.
>>>>>>>>>>>>>
>>>>>>>>>>>>> In order to complete the claim you need to provide us with
>>>>>>>>>>>>> the additional information telling us **which one** (P or
>>>>>>>>>>>>> Q) holds!
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>> The truth table already has the fully semantics of all of
>>>>>>>>>>>> that and you
>>>>>>>>>>>> know this thus are only playing deceptive head games.
>>>>>>>>>>> One more time for the slow kid in the room...
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I am establishing the epistemological foundation inheritance
>>>>>>>>>> hierarchy
>>>>>>>>>> (upper ontology) of analytical truth itself. Every logic
>>>>>>>>>> system must be
>>>>>>>>>> derived from this foundation or it is incorrect by definition.
>>>>>>>>>
>>>>>>>>> Soure of this?
>>>>>>>>>
>>>>>>>>> Why do things need to be based on a foundation that didn't
>>>>>>>>> exist when they were founded?
>>>>>>>>>
>>>>>>>>> Seems untruthful to me.
>>>>>>>>>
>>>>>>>>> You don't seem to understand what Epistemology is about, it
>>>>>>>>> isn't about "Truth", but "Knowledge", which are different things.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Not really, truth includes things that are unknown, yet the only
>>>>>>>> way
>>>>>>>> that we know any analytic expressions of language are true is we
>>>>>>>> understand the semantic connections that define their meaning. The
>>>>>>>> entirely body of semantic truth is true on the basis of semantic
>>>>>>>> tautology.
>>>>>>>
>>>>>>> Right, and since the rules of a system create a "Reality", there
>>>>>>> are some statements that are EMPIRICALLY true that can't be
>>>>>>> analytically proven (they require the application of an unbounded
>>>>>>> number of rules, while an analytic proof needs a bounded number
>>>>>>> of steps).
>>>>>>>
>>>>>>
>>>>>> You don't seem to understand the difference between empirical
>>>>>> (verified with sense organs) and analytical verified based on the
>>>>>> meaning of expressions of language.
>>>>>
>>>>> No, YOU don't seem to understand the difference between Knowledge,
>>>>> Truth that has been verified, and Actual Truth.
>>>>>
>>>>
>>>> knowledge ⊂ truth
>>>
>>> Right, so some Truth is not part of Knowledge, and even some CAN'T be
>>> known (or it might get pulled into the proper sub-set), and thus some
>>> Truth is unprovable.
>>>
>>> You just ADMITTED that your claim that all Truth must be Provable is
>>> incorrect.
>>>
>>
>> Every undecidable proposition is merely semantically incoherent and
>> nothing more. Every truth is provable including truth where one or
>> more of the steps of the proof are currently unknown.
>>
>
> Nope. That is just your failure to understand what it Truth, and are
> confusing it with Knowledge.
>
> Your definition lead to inconsistencies like ending up with statements
> for which no proof exists but are not Unprovable.
>

On 12/14/2022 7:12 PM, Richard Damon wrote:
> On 12/14/22 10:27 AM, olcott wrote:
>> On 12/13/2022 8:38 PM, Richard Damon wrote:
>>> On 12/13/22 10:56 AM, olcott wrote:
>>>> On 12/12/2022 8:31 PM, Richard Damon wrote:
>>>>> On 12/12/22 8:51 PM, olcott wrote:
>>>>>> On 12/12/2022 6:29 PM, Richard Damon wrote:
>>>>>>> On 12/12/22 10:44 AM, olcott wrote:
>>>>>>>> On 12/12/2022 7:05 AM, Richard Damon wrote:
>>>>>>>>> On 12/11/22 3:38 PM, olcott wrote:
>>>>>>>>>> On 12/11/2022 1:45 PM, Skep Dick wrote:
>>>>>>>>>>> On Sunday, 11 December 2022 at 21:41:07 UTC+2, olcott wrote:
>>>>>>>>>>>> On 12/11/2022 1:29 PM, Skep Dick wrote:
>>>>>>>>>>>>> On Sunday, 11 December 2022 at 21:11:02 UTC+2, olcott wrote:
>>>>>>>>>>>>>> On 12/11/2022 11:46 AM, Skep Dick wrote:
>>>>>>>>>>>>>>> On Sunday, 11 December 2022 at 19:16:05 UTC+2, olcott wrote:
>>>>>>>>>>>>>>>> On 12/11/2022 10:39 AM, Skep Dick wrote:
>>>>>>>>>>>>>>>>> On Sunday, 11 December 2022 at 17:33:27 UTC+2, olcott
>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>> On 12/11/2022 9:21 AM, Skep Dick wrote:
>>>>>>>>>>>>>>>>>>> On Sunday, 11 December 2022 at 17:11:05 UTC+2, olcott
>>>>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>>>> On 12/11/2022 8:44 AM, Skep Dick wrote:
>>>>>>>>>>>>>>>>>>>>> On Sunday, 11 December 2022 at 15:53:29 UTC+2,
>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> Valid(φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>>>>>>>>>>>>>>> So which one is it?
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> The disjunction requires a valid proof.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Unless φ is provable or refutable φ is not a logic
>>>>>>>>>>>>>>>>>>>> expression.
>>>>>>>>>>>>>>>>>>> ERGO!!!
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> 1 to n is NOT a logic expression. Because logic
>>>>>>>>>>>>>>>>>>> expressiong (e.g the sort of things you are referring
>>>>>>>>>>>>>>>>>>> to when you say "φ") DON'T contain free variables.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Using my MTT one can construct an 1,2,3,4...n ary
>>>>>>>>>>>>>>>>>> logic expression using
>>>>>>>>>>>>>>>>>> a slightly adapted FOL syntax.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Idiot. By **your very own rule**: Valid(φ) ↔ ((T ⊢ φ) ∨
>>>>>>>>>>>>>>>>> (T ⊢ ¬φ))
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> the expression "1,2,3,4...n" is **NOT** a valid logic
>>>>>>>>>>>>>>>>> expression!
>>>>>>>>>>>>>>>> Only because you did not encode it correctly: ∃n ∈ ℕ
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Furthermore, Sir.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation#The_interpretation
>>>>>>>>>>>>>>> A proof of P ∨ Q is either <0,a> where a is a proof o P
>>>>>>>>>>>>>>> or <1,b> where b is a proof of Q.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Sir. You can interpret <0,a> and <1, b> through the
>>>>>>>>>>>>>>> semantics of the usual Either-monad. Sir.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Where Left and Right are the usual projections: Left<a,b>
>>>>>>>>>>>>>>> ↔ a and Right<a,b> ↔ b
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> https://hackage.haskell.org/package/category-extras-0.52.0/docs/Control-Monad-Either.html
>>>>>>>>>>>>>> Is_a_Theorem_of_T(φ) 0 1 0 1
>>>>>>>>>>>>>> Is_a_Theorem_of_T(¬φ) 0 0 1 1
>>>>>>>>>>>>>> ∨ 0 1 1 1
>>>>>>>>>>>>> *sigh* Moron. What is confusing you about the sentence
>>>>>>>>>>>>> "Disjunctions require proof"?
>>>>>>>>>>>>>
>>>>>>>>>>>>> The ∨ operator is a disjunction.. It's not enough to tell
>>>>>>>>>>>>> us that P or Q is a theorem. That claim is incomplete.
>>>>>>>>>>>>>
>>>>>>>>>>>>> In order to complete the claim you need to provide us with
>>>>>>>>>>>>> the additional information telling us **which one** (P or
>>>>>>>>>>>>> Q) holds!
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>> The truth table already has the fully semantics of all of
>>>>>>>>>>>> that and you
>>>>>>>>>>>> know this thus are only playing deceptive head games.
>>>>>>>>>>> One more time for the slow kid in the room...
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I am establishing the epistemological foundation inheritance
>>>>>>>>>> hierarchy
>>>>>>>>>> (upper ontology) of analytical truth itself. Every logic
>>>>>>>>>> system must be
>>>>>>>>>> derived from this foundation or it is incorrect by definition.
>>>>>>>>>
>>>>>>>>> Soure of this?
>>>>>>>>>
>>>>>>>>> Why do things need to be based on a foundation that didn't
>>>>>>>>> exist when they were founded?
>>>>>>>>>
>>>>>>>>> Seems untruthful to me.
>>>>>>>>>
>>>>>>>>> You don't seem to understand what Epistemology is about, it
>>>>>>>>> isn't about "Truth", but "Knowledge", which are different things.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Not really, truth includes things that are unknown, yet the only
>>>>>>>> way
>>>>>>>> that we know any analytic expressions of language are true is we
>>>>>>>> understand the semantic connections that define their meaning. The
>>>>>>>> entirely body of semantic truth is true on the basis of semantic
>>>>>>>> tautology.
>>>>>>>
>>>>>>> Right, and since the rules of a system create a "Reality", there
>>>>>>> are some statements that are EMPIRICALLY true that can't be
>>>>>>> analytically proven (they require the application of an unbounded
>>>>>>> number of rules, while an analytic proof needs a bounded number
>>>>>>> of steps).
>>>>>>>
>>>>>>
>>>>>> You don't seem to understand the difference between empirical
>>>>>> (verified with sense organs) and analytical verified based on the
>>>>>> meaning of expressions of language.
>>>>>
>>>>> No, YOU don't seem to understand the difference between Knowledge,
>>>>> Truth that has been verified, and Actual Truth.
>>>>>
>>>>
>>>> knowledge ⊂ truth
>>>
>>> Right, so some Truth is not part of Knowledge, and even some CAN'T be
>>> known (or it might get pulled into the proper sub-set), and thus some
>>> Truth is unprovable.
>>>
>>> You just ADMITTED that your claim that all Truth must be Provable is
>>> incorrect.
>>>
>>>
>>>>
>>>>> You seem to think we need to be Omniscient.
>>>>>
>>>>>>
>>>>>>> Again, you confuse KNOWING that something is true, with it BEING
>>>>>>> true.
>>>>>>>
>>>>>>>>
>>>>>>>>> Yes, we can only KNOW something to be true by either PROVING it
>>>>>>>>> (analytical Truth) or OBSERVING it (Synthetic Truth), but it
>>>>>>>>> can be True but unknown.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Analytic expressions of language are verified as completely true
>>>>>>>> entirely based on their meaning. In other words they are
>>>>>>>> semantic tautologies.
>>>>>>>
>>>>>>> VERIFIED, not ARE. Again, confustion of Knowledge with Truth.
>>>>>>>
>>>>>>
>>>>>> The only reason that analytic expressions are true is that they
>>>>>> are semantic tautologies.
>>>>>
>>>>> No. Analytic proofs can be based on the use of Emperical Facts, which
>>>>
>>>> Empirical(x) ≡ ¬Analytical(x)
>>>> Empirical(x) requires sense data for the sense organs.
>>>
>>> Nope, you are confusing Empirical KNOWLEDGE with Empirical TRUTH.
>>>
>>> You same old problem.
>>>
>>> You are also forgetting that "Senses" go beyond the "organs" and
>>> include the mind, and aids that extend our senses.
>>
>> My definitions are a stipulated clarification to the analytic versus
>> synthetic distinction. Analytic truth is the set of expressions of
>> language that can be verified as true on the basis of their meaning
>> without relying on any sense data from the sense organs.
>>
>> I am seeing my KJV bible on my TV table right now relies on my
>> eyesight and it thus not an analytic expression of language.
>
>
> Which means you just stipulated that you are not working on the ACTUAL
> Halting Problem,

On 12/14/2022 7:17 PM, Richard Damon wrote:
> On 12/14/22 10:36 AM, olcott wrote:
>> On 12/13/2022 8:38 PM, Richard Damon wrote:
>>> On 12/13/22 10:56 AM, olcott wrote:
>>> Unless an expression of language is a semantic tautology is it not an
>>>> analytic expression of language.
>>>
>>> Nope, analytic expressions don't need to be a tautology.
>>>
>>> For instance, Cats and Dogs are in distinct animal groups can be a
>>> true analytical expression. its Truth is dependent on the implied
>>> meaning of some of the terms, so it is NOT a Tautology, which must be
>>> true in ALL models of the system.
>>
>> <sarcasm>
>> Yes maybe there is a possible world where the feline animal of a cat
>> is also an office building. This makes perfect sense to me. When this
>> cat sits on your lap and purrs you are crushed by its thousands of
>> tons of weight.
>> </sarcasm>
>>
>
> Nope, you show you lack of understanding. You don't seem to understand
> the difference between a universal statement and a statment of existance.
>
> This shows your ignorance. You logic if FULL of these sorts of Fallacies.
>
> If the context is Feline vs Canine, there are in different groups.
>
> If the context is Animal vs Vegetable, there are NOT in different groups.
>
> Since the model we are working in matters, it is not a Tautology.
>
>

That a cat is an animal is a Haskell Curry elementary theorem of
English, thus making it true by definition, thus a tautology.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/14/2022 7:19 PM, Richard Damon wrote:
> On 12/14/22 10:39 AM, olcott wrote:
>> On 12/13/2022 8:38 PM, Richard Damon wrote:
>>> On 12/13/22 10:56 AM, olcott wrote:
>
>>>>
>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>> If this requires counting all the way to infinity to verify then it is
>>>> not a tautology. If it is possible to verify in finite time then it
>>>> is a
>>>> tautology.
>>>>
>>>
>>> So, your definition of an analytical expression says there are
>>> expression that you can't tell if they ARE analytical expressions,
>>> and thus you don't know if you can talk about them?
>>>
>>> Seems like A pretty weak system.
>> Every expression of language that does not require any sense data from
>> the sense organs to verify that it is true is an analytic expression
>> of language. That you are stuck in rebuttal mode is a form of dishonesty.
>>
>> That you disagree with stipulated definitions is an example of
>> dishonesty.
>>
>
> The problem is that you try to stipluate definitions that aren't actuall
> part of the field.
>

The "field" that I am talking about is my creation of the foundation of
analytical truth.

> You keep trying to stipulate that only things that are KNOWN are True,
> which isn't a correct statement.
>

So we are back to the possibility that cats are actually office
buildings and thus not animals?

Haskell Curry elementary theorems of English are tautologies.

> That just proves you are not working in the right field.

A am establishing the brand new field of the correct foundation of
analytical truth.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/14/2022 7:20 PM, Richard Damon wrote:
> On 12/14/22 9:41 AM, olcott wrote:
>> On 12/14/2022 8:18 AM, wij wrote:
>>> On Wednesday, December 14, 2022 at 8:24:00 PM UTC+8,
>>> richar...@gmail.com wrote:
>>>> On 12/14/22 1:47 AM, Skep Dick wrote:
>>>>> On Wednesday, 14 December 2022 at 05:48:49 UTC+2,
>>>>> richar...@gmail.com wrote:
>>>>>> Simple example, the even counting numbers are a sub-set of the
>>>>>> counting
>>>>>> numbers, as you can divide the counting numbers into the even
>>>>>> counting
>>>>>> numbers and the odd counting numbers.
>>>>>>
>>>>>> But, the even counting numbers is of the same size as the counting
>>>>>> numbers as you can map any counting numbrer n to and even number e by
>>>>>> the mapping of e = 2n.
>>>>> Eeeeeh, that's only true if you assume the usual ordering on ℕ.
>>>>> It's not generally true in other structures containing the same
>>>>> elements.
>>>>>
>>>>> Take the infinite stream of even numbers: [0,2,4,...)
>>>>> Take the infinite stream of odd numbers: [1,3,5,...)
>>>>> Prefix the odd with the even such that all even numbers are <1 e.g
>>>>> : 0,2,4,..., 1,3,5,...
>>>>>
>>>>> Now tell me about e=2n
>>>>>
>>>> First, you aren't allowed to count numbers with two ... embedded in the
>>>> sequence (at least by the classic rules, if you want to do it you need
>>>> to define the rules and show they are consistent).
>>>>
>>>> And yes, they are all the "same size" because you can make the
>>>> bijection
>>>> between them, even though "logic" seems to say that one is bigger than
>>>> another.
>>> What does "same size" mean? If the 'size' cannot add, subtract, ....
>>> olcott is partly correct that "Everyone that has been debating me on
>>> this forum
>>> does so entirely on the basis of learn-by-rote dogma."
>>> You just recite and think as the text-book tells what to say and how
>>> to think.
>>> I don't think you really understand what you say (esp. those big
>>> words and logic).
>>>
>>
>> Yes, the philosophical foundation of mathematics and logic is derived
>> from the philosophical foundation of analytic truth and are arranged
>> in an inheritance hierarchy knowledge ontology such that math and
>> logic inherit these two properties:
>
> Note, you siad KNOWLEDGE.

Truth - unknown = knowledge. (its not that hard)

>>
>> (1) Expressions of (formal or natural) language that are stipulated to
>> have the semantic value of Boolean true. Same idea as Haskell Curry
>> elementary theorems or natural language verified facts.
>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>
>> (2) Expressions derived by applying truth preserving operations to (1)
>> or the output of (2). AKA provability
>
> thus, you are talking about KNOWLEDGE, not TRUTH.

Truth - unknown = knowledge. (its not that hard)

>>
>> Every element of the set of analytic knowledge is established as a
>> semantic tautology. This converts all undecidable propositions into
>> semantically incorrect expressions of language.
>
> No, it doesn't.
>
> Undecided propositions are just undecided, and perhaps are NEVER
> decidable, and thus unknowable. Mathematics accepts that.

(3) x ∉ Provable if and only if x ∈ True.
~Provable(x) ↔ True(x).
x is true if and only if x is unprovable

https://liarparadox.org/Tarski_275_276.pdf

G ↔ (F ⊬ G)
G is true if and only if G is unprovable in F

Self-contradictory expressions of language are not truth bearers.
True and unprovable are just like morbidly obese and grossly
underweight.

The conventional definition of incompleteness:
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

Undecidable[math] actually means semantically incoherent.
Wittgenstein boiled this down to it barest essence:

'True in Russell's system' means, as was said: proved
in Russell's system; and 'false in Russell's system'
means: the opposite has been proved in Russell's system
https://www.liarparadox.org/Wittgenstein.pdf

He never quite said this directly yet it was implied:
Valid(T, φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))

Wittgenstein was no mere learned-by-rote mathematician or logician that
can only dogmatically obey the rules. His specialty was determining the
foundations of math and logic, thus re-examining these rules to see if
they are consistent.

> You may not, but that is because you are an idiot.
>
>>
>>>> The fact that a proper subset of a set, which meets the requirements of
>>>> being "within" the full set, ends up being just as large as the full
>>>> set, is what shows that the whole can be a subset of itself.
>>>>
>>>> It is a classical fact that infinity breaks a number of "obvious"
>>>> properties. This is one reason the Number System like the Naturals, and
>>>> the Reals don't include infinity as a normal "value", but just a limit
>>>> that things approach, but the sets with it included are considered
>>>> to be
>>>> a DIFFERENT number system. The adding of infinity needs some careful
>>>> extra definition and the lose of some classical properties that no
>>>> longer hold.
>>
>

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/14/2022 7:20 PM, Richard Damon wrote:
> On 12/14/22 9:18 AM, wij wrote:
>> On Wednesday, December 14, 2022 at 8:24:00 PM UTC+8,
>> richar...@gmail.com wrote:
>>> On 12/14/22 1:47 AM, Skep Dick wrote:
>>>> On Wednesday, 14 December 2022 at 05:48:49 UTC+2,
>>>> richar...@gmail.com wrote:
>>>>> Simple example, the even counting numbers are a sub-set of the
>>>>> counting
>>>>> numbers, as you can divide the counting numbers into the even counting
>>>>> numbers and the odd counting numbers.
>>>>>
>>>>> But, the even counting numbers is of the same size as the counting
>>>>> numbers as you can map any counting numbrer n to and even number e by
>>>>> the mapping of e = 2n.
>>>> Eeeeeh, that's only true if you assume the usual ordering on ℕ. It's
>>>> not generally true in other structures containing the same elements.
>>>>
>>>> Take the infinite stream of even numbers: [0,2,4,...)
>>>> Take the infinite stream of odd numbers: [1,3,5,...)
>>>> Prefix the odd with the even such that all even numbers are <1 e.g :
>>>> 0,2,4,..., 1,3,5,...
>>>>
>>>> Now tell me about e=2n
>>>>
>>> First, you aren't allowed to count numbers with two ... embedded in the
>>> sequence (at least by the classic rules, if you want to do it you need
>>> to define the rules and show they are consistent).
>>>
>>> And yes, they are all the "same size" because you can make the bijection
>>> between them, even though "logic" seems to say that one is bigger than
>>> another.
>> What does "same size" mean? If the 'size' cannot add, subtract, ....
>> olcott is partly correct that "Everyone that has been debating me on
>> this forum
>> does so entirely on the basis of learn-by-rote dogma."
>> You just recite and think as the text-book tells what to say and how
>> to think.
>> I don't think you really understand what you say (esp. those big words
>> and logic).
>
> When dealing with possible infinite sets, one definition of "same size"
> is that there can be a bijection made between the two sets, i.e. you can
> build a one-to-one mapping between the sets such that EVERY element in
> one set is mapped to PRECISELY a unique element in the other. If that
> can be done, then the sets are defined to be the same size.
>
> Note, there may be other mappings between the sets that have left overs
> on one side or the other (even an infinite number of them), but if a
> bijection exists, then they are the same size.
>
> This definition also works for finite sets.
>
> Note also, that when you get into infinities, many (if not most) of the
> comfortable rules we are used to just
>
> This IS a field that I have studied (an not just learned by rote) over
> the many years of my life.
>

If you did not actively examine the philosophical foundations of the
notion of analytic truth itself and make sure that all of the rules of
math and logic are consistent with these foundations then you merely
have learned-by-rote knowledge of these things.

Addendum you could not have possibly have done this because the
philosophical foundations of the notion of analytic truth itself have
never previously been correctly established

> I wil also note that I have a minor learning disability that makes it

Please elaborate on this I really want to have much more empathy for you.

> very hard to learn things "by rote", but I need to have at least good
> understanding of WHY things work the way they do to remember them.
>

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/15/22 10:37 PM, olcott wrote:
> On 12/14/2022 7:17 PM, Richard Damon wrote:
>> On 12/14/22 10:36 AM, olcott wrote:
>>> On 12/13/2022 8:38 PM, Richard Damon wrote:
>>>> On 12/13/22 10:56 AM, olcott wrote:
>>>> Unless an expression of language is a semantic tautology is it not an
>>>>> analytic expression of language.
>>>>
>>>> Nope, analytic expressions don't need to be a tautology.
>>>>
>>>> For instance, Cats and Dogs are in distinct animal groups can be a
>>>> true analytical expression. its Truth is dependent on the implied
>>>> meaning of some of the terms, so it is NOT a Tautology, which must
>>>> be true in ALL models of the system.
>>>
>>> <sarcasm>
>>> Yes maybe there is a possible world where the feline animal of a cat
>>> is also an office building. This makes perfect sense to me. When this
>>> cat sits on your lap and purrs you are crushed by its thousands of
>>> tons of weight.
>>> </sarcasm>
>>>
>>
>> Nope, you show you lack of understanding. You don't seem to understand
>> the difference between a universal statement and a statment of existance.
>>
>> This shows your ignorance. You logic if FULL of these sorts of Fallacies.
>>
>> If the context is Feline vs Canine, there are in different groups.
>>
>> If the context is Animal vs Vegetable, there are NOT in different groups.
>>
>> Since the model we are working in matters, it is not a Tautology.
>>
>>
>
> That a cat is an animal is a Haskell Curry elementary theorem of
> English, thus making it true by definition, thus a tautology.
>

So, you still don't understand the statement.

YOU FAIL.

The Statement: "Cats and Dogs are in distinct animal groups" is a
statement that can be a true analytical expression but can't be a Tautology.

IF the Animal Groups in question are Feline vs Canine, it is true.

If the Animal Groups in question are Mammilian, it is false.

Thus, it is NOT a Tautology, but could be true.

On 12/15/2022 10:18 PM, Richard Damon wrote:
> On 12/15/22 10:37 PM, olcott wrote:
>> On 12/14/2022 7:17 PM, Richard Damon wrote:
>>> On 12/14/22 10:36 AM, olcott wrote:
>>>> On 12/13/2022 8:38 PM, Richard Damon wrote:
>>>>> On 12/13/22 10:56 AM, olcott wrote:
>>>>> Unless an expression of language is a semantic tautology is it not an
>>>>>> analytic expression of language.
>>>>>
>>>>> Nope, analytic expressions don't need to be a tautology.
>>>>>
>>>>> For instance, Cats and Dogs are in distinct animal groups can be a
>>>>> true analytical expression. its Truth is dependent on the implied
>>>>> meaning of some of the terms, so it is NOT a Tautology, which must
>>>>> be true in ALL models of the system.
>>>>
>>>> <sarcasm>
>>>> Yes maybe there is a possible world where the feline animal of a cat
>>>> is also an office building. This makes perfect sense to me. When
>>>> this cat sits on your lap and purrs you are crushed by its thousands
>>>> of tons of weight.
>>>> </sarcasm>
>>>>
>>>
>>> Nope, you show you lack of understanding. You don't seem to
>>> understand the difference between a universal statement and a
>>> statment of existance.
>>>
>>> This shows your ignorance. You logic if FULL of these sorts of
>>> Fallacies.
>>>
>>> If the context is Feline vs Canine, there are in different groups.
>>>
>>> If the context is Animal vs Vegetable, there are NOT in different
>>> groups.
>>>
>>> Since the model we are working in matters, it is not a Tautology.
>>>
>>>
>>
>> That a cat is an animal is a Haskell Curry elementary theorem of
>> English, thus making it true by definition, thus a tautology.
>>
>
> So, you still don't understand the statement.
>
> YOU FAIL.
>
> The Statement: "Cats and Dogs are in distinct animal groups" is a
> statement that can be a true analytical expression but can't be a
> Tautology.
>

In mathematical logic, a tautology (from Greek: ταυτολογία) is a formula
or assertion that is true in every possible interpretation.
https://en.wikipedia.org/wiki/Tautology_(logic)

> IF the Animal Groups in question are Feline vs Canine, it is true.
>
> If the Animal Groups in question are Mammilian, it is false.
>
> Thus, it is NOT a Tautology, but could be true.

A cat is always an animal and never an office building. That mammals are
also animals still does not turn a cat into an office building.

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 12/15/22 10:31 PM, olcott wrote:
> On 12/14/2022 7:10 PM, Richard Damon wrote:

>> Nope. That is just your failure to understand what it Truth, and are
>> confusing it with Knowledge.
>>
>> Your definition lead to inconsistencies like ending up with statements
>> for which no proof exists but are not Unprovable.
>>
>
> True/false/not a truth bearer/currently unknown

"Currently Unknown" is NOT a valut of Truth, but Knowledge.

>
> Inconsistencies are screened out as not elements of the set of truth in
> the correction to the foundation of analytical truth that I propose.
>

You are confusing Truth with knowledge.

You admit you are not all-knowing, so you are showing your ignoorance
when you claim that Knowledge == Truth.

Since you are proving you don't know the difference between the two, you
have disqualified yourself in the field.

On 12/15/22 10:34 PM, olcott wrote:
> On 12/14/2022 7:12 PM, Richard Damon wrote:

>> Which means you just stipulated that you are not working on the ACTUAL
>> Halting Problem,
>
> I am talking about the definition of the term {analytical} as in the
> analytic versus empirical distinction.
>
>
>

Since the Halting Problem isn't about such a distinction, ait shows you
don't know what you are talking about.

On 12/15/22 10:40 PM, olcott wrote:
> On 12/14/2022 7:19 PM, Richard Damon wrote:
>> On 12/14/22 10:39 AM, olcott wrote:
>>> On 12/13/2022 8:38 PM, Richard Damon wrote:
>>>> On 12/13/22 10:56 AM, olcott wrote:
>>
>>>>>
>>>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>>> If this requires counting all the way to infinity to verify then it is
>>>>> not a tautology. If it is possible to verify in finite time then it
>>>>> is a
>>>>> tautology.
>>>>>
>>>>
>>>> So, your definition of an analytical expression says there are
>>>> expression that you can't tell if they ARE analytical expressions,
>>>> and thus you don't know if you can talk about them?
>>>>
>>>> Seems like A pretty weak system.
>>> Every expression of language that does not require any sense data
>>> from the sense organs to verify that it is true is an analytic
>>> expression of language. That you are stuck in rebuttal mode is a form
>>> of dishonesty.
>>>
>>> That you disagree with stipulated definitions is an example of
>>> dishonesty.
>>>
>>
>> The problem is that you try to stipluate definitions that aren't
>> actuall part of the field.
>>
>
> The "field" that I am talking about is my creation of the foundation of
> analytical truth.
>
>> You keep trying to stipulate that only things that are KNOWN are True,
>> which isn't a correct statement.
>>
>
> So we are back to the possibility that cats are actually office
> buildings and thus not animals?

Nope, you are just showing your lack of comprension.

>
> Haskell Curry elementary theorems of English are tautologies.
>
>> That just proves you are not working in the right field.
>
> A am establishing the brand new field of the correct foundation of
> analytical truth.
>

Nope, because you are defining it in a way that you are requiring
Mathematics to be based on it, but make it so that it can't be.

You are showing your stupidity.

On 12/15/22 10:59 PM, olcott wrote:
> On 12/14/2022 7:20 PM, Richard Damon wrote:
>> On 12/14/22 9:41 AM, olcott wrote:
>>> On 12/14/2022 8:18 AM, wij wrote:
>>>> On Wednesday, December 14, 2022 at 8:24:00 PM UTC+8,
>>>> richar...@gmail.com wrote:
>>>>> On 12/14/22 1:47 AM, Skep Dick wrote:
>>>>>> On Wednesday, 14 December 2022 at 05:48:49 UTC+2,
>>>>>> richar...@gmail.com wrote:
>>>>>>> Simple example, the even counting numbers are a sub-set of the
>>>>>>> counting
>>>>>>> numbers, as you can divide the counting numbers into the even
>>>>>>> counting
>>>>>>> numbers and the odd counting numbers.
>>>>>>>
>>>>>>> But, the even counting numbers is of the same size as the counting
>>>>>>> numbers as you can map any counting numbrer n to and even number
>>>>>>> e by
>>>>>>> the mapping of e = 2n.
>>>>>> Eeeeeh, that's only true if you assume the usual ordering on ℕ.
>>>>>> It's not generally true in other structures containing the same
>>>>>> elements.
>>>>>>
>>>>>> Take the infinite stream of even numbers: [0,2,4,...)
>>>>>> Take the infinite stream of odd numbers: [1,3,5,...)
>>>>>> Prefix the odd with the even such that all even numbers are <1 e.g
>>>>>> : 0,2,4,..., 1,3,5,...
>>>>>>
>>>>>> Now tell me about e=2n
>>>>>>
>>>>> First, you aren't allowed to count numbers with two ... embedded in
>>>>> the
>>>>> sequence (at least by the classic rules, if you want to do it you need
>>>>> to define the rules and show they are consistent).
>>>>>
>>>>> And yes, they are all the "same size" because you can make the
>>>>> bijection
>>>>> between them, even though "logic" seems to say that one is bigger than
>>>>> another.
>>>> What does "same size" mean? If the 'size' cannot add, subtract, ....
>>>> olcott is partly correct that "Everyone that has been debating me on
>>>> this forum
>>>> does so entirely on the basis of learn-by-rote dogma."
>>>> You just recite and think as the text-book tells what to say and how
>>>> to think.
>>>> I don't think you really understand what you say (esp. those big
>>>> words and logic).
>>>>
>>>
>>> Yes, the philosophical foundation of mathematics and logic is derived
>>> from the philosophical foundation of analytic truth and are arranged
>>> in an inheritance hierarchy knowledge ontology such that math and
>>> logic inherit these two properties:
>>
>> Note, you siad KNOWLEDGE.
>
> Truth - unknown = knowledge. (its not that hard)

So Truth is greater that Knowledge, so rules of knowledge don't limit truth,

We can change that formula to Truth = Knowlege + Unknown, and thus we
have shown that some truth isn't known, and it turns out, is unknowable.
>
>>>
>>> (1) Expressions of (formal or natural) language that are stipulated to
>>> have the semantic value of Boolean true. Same idea as Haskell Curry
>>> elementary theorems or natural language verified facts.
>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>
>>> (2) Expressions derived by applying truth preserving operations to (1)
>>> or the output of (2). AKA provability
>>
>> thus, you are talking about KNOWLEDGE, not TRUTH.
>
> Truth - unknown = knowledge. (its not that hard)

See above.

>
>>>
>>> Every element of the set of analytic knowledge is established as a
>>> semantic tautology. This converts all undecidable propositions into
>>> semantically incorrect expressions of language.
>>
>> No, it doesn't.
>>
>> Undecided propositions are just undecided, and perhaps are NEVER
>> decidable, and thus unknowable. Mathematics accepts that.
>
> (3) x ∉ Provable if and only if x ∈ True.
>     ~Provable(x) ↔ True(x).
> x is true if and only if x is unprovable

and if x is false, it can't be proven either.

Thus x must be unprovable, and thus the statement is true but unprobable.

>
> https://liarparadox.org/Tarski_275_276.pdf
>
> G ↔ (F ⊬ G)
> G is true if and only if G is unprovable in F
>
> Self-contradictory expressions of language are not truth bearers.
> True and unprovable are just like morbidly obese and grossly
> underweight.

What is self-contradictory?

What is wrong with G being True but Unprovable?

>
>
> The conventional definition of incompleteness:
> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>
> Undecidable[math] actually means semantically incoherent.
> Wittgenstein boiled this down to it barest essence:
>
>    'True in Russell's system' means, as was said: proved
>     in Russell's system; and 'false in Russell's system'
>     means: the opposite has been proved in Russell's system

Which is a false statement.

True is NOT defined to be proven.

KNOWN is defined to be proven.

> https://www.liarparadox.org/Wittgenstein.pdf
>
> He never quite said this directly yet it was implied:
> Valid(T, φ) ↔ ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>
> Wittgenstein was no mere learned-by-rote mathematician or logician that
> can only dogmatically obey the rules. His specialty was determining the
> foundations of math and logic, thus re-examining these rules to see if
> they are consistent.
>
>> You may not, but that is because you are an idiot.
>>
>>>
>>>>> The fact that a proper subset of a set, which meets the
>>>>> requirements of
>>>>> being "within" the full set, ends up being just as large as the full
>>>>> set, is what shows that the whole can be a subset of itself.
>>>>>
>>>>> It is a classical fact that infinity breaks a number of "obvious"
>>>>> properties. This is one reason the Number System like the Naturals,
>>>>> and
>>>>> the Reals don't include infinity as a normal "value", but just a limit
>>>>> that things approach, but the sets with it included are considered
>>>>> to be
>>>>> a DIFFERENT number system. The adding of infinity needs some careful
>>>>> extra definition and the lose of some classical properties that no
>>>>> longer hold.
>>>
>>
>