Here's a famous quote from John von Neumann: "in mathematics, you don't understand things, you just get used to them."

That quote can be used to undestand what's going on in the never ending debate in this newsgroup over whether Cantor's theory of infinity belongs in mathematics.

There are two sides to the debate:

1) Mathematics is, by definition, the game that mathematicians choose to play, and if you want status and respect in the mathematics community, you just have to get used to it. And Cantor's theory is part of the game. If you question it, you're a crank.

2) The whole purpose of mathematics, and in fact, in any honest academic discipline, it to gain an understanding of the real world. And to "understand" mathematics means to understand how mathematics is connected to our search for an understanding of the real world. And Cantor's theory of infinity has no role to play in our understanding the real world. So "get used to it" is simply bad advice.

There seem to be some people in the debate who are caught in the middle. They seem to take on a confused mixture of both views, and they end up muddying the waters, so to speak.

Anyways, for what it's worth, some thirty years ago, back when serious mathematicians participated in sci.math discussions, one mathematician who was known to be especially bright, seemed to understand my reasons for arguing that Cantor's theory of infinity doesn't truly belong in mathematics, but then he kept twisting my arguments around, making it impossible to argue with him. And then he suggested I should be criticizing von Neumann instead of Cantor. So I guess he saw problem, but didn't see any option other than to "get used to it".

So that's the way it is!

On Tuesday, August 10, 2021 at 11:39:11 PM UTC-4, david...@gmail.com wrote:
> Here's a famous quote from John von Neumann: "in mathematics, you don't understand things, you just get used to them."
>
> That quote can be used to undestand what's going on in the never ending debate in this newsgroup over whether Cantor's theory of infinity belongs in mathematics.
>

Do you have a problem with the notion of an infinite set?

Dan

onsdag 11 augusti 2021 kl. 05:39:11 UTC+2 skrev david...@gmail.com:
> Here's a famous quote from John von Neumann: "in mathematics, you don't understand things, you just get used to them."
>
> That quote can be used to undestand what's going on in the never ending debate in this newsgroup over whether Cantor's theory of infinity belongs in mathematics.
>
> There are two sides to the debate:
>
> 1) Mathematics is, by definition, the game that mathematicians choose to play, and if you want status and respect in the mathematics community, you just have to get used to it. And Cantor's theory is part of the game. If you question it, you're a crank.
>
> 2) The whole purpose of mathematics, and in fact, in any honest academic discipline, it to gain an understanding of the real world. And to "understand" mathematics means to understand how mathematics is connected to our search for an understanding of the real world. And Cantor's theory of infinity has no role to play in our understanding the real world. So "get used to it" is simply bad advice.
>
> There seem to be some people in the debate who are caught in the middle. They seem to take on a confused mixture of both views, and they end up muddying the waters, so to speak.
>
> Anyways, for what it's worth, some thirty years ago, back when serious mathematicians participated in sci.math discussions, one mathematician who was known to be especially bright, seemed to understand my reasons for arguing that Cantor's theory of infinity doesn't truly belong in mathematics, but then he kept twisting my arguments around, making it impossible to argue with him. And then he suggested I should be criticizing von Neumann instead of Cantor. So I guess he saw problem, but didn't see any option other than to "get used to it".
>
> So that's the way it is!

actually there is only 1 side, and then there are the cranks like you.

Dan Christensen wrote:

> On Tuesday, August 10, 2021 at 11:39:11 PM UTC-4, david...@gmail.com
> wrote:
>> Here's a famous quote from John von Neumann: "in mathematics, you don't
>> understand things, you just get used to them."
>> That quote can be used to undestand what's going on in the never ending
>> debate in this newsgroup over whether Cantor's theory of infinity
>> belongs in mathematics.
>
> Do you have a problem with the notion of an infinite set?

ohh really?? Moderna just made $4B with big B on "vaccines", just after
they NEVER sold anything in their entire capitalist existence.

On Wednesday, 11 August 2021 at 11:39:11 UTC+8, david...@gmail.com wrote:
> Here's a famous quote from John von Neumann: "in mathematics, you don't understand things, you just get used to them."
>
> That quote can be used to undestand what's going on in the never ending debate in this newsgroup over whether Cantor's theory of infinity belongs in mathematics.
>
> There are two sides to the debate:
>
> 1) Mathematics is, by definition, the game that mathematicians choose to play, and if you want status and respect in the mathematics community, you just have to get used to it. And Cantor's theory is part of the game. If you question it, you're a crank.
>
> 2) The whole purpose of mathematics, and in fact, in any honest academic discipline, it to gain an understanding of the real world. And to "understand" mathematics means to understand how mathematics is connected to our search for an understanding of the real world. And Cantor's theory of infinity has no role to play in our understanding the real world. So "get used to it" is simply bad advice.
>
> There seem to be some people in the debate who are caught in the middle. They seem to take on a confused mixture of both views, and they end up muddying the waters, so to speak.
>
> Anyways, for what it's worth, some thirty years ago, back when serious mathematicians participated in sci.math discussions, one mathematician who was known to be especially bright, seemed to understand my reasons for arguing that Cantor's theory of infinity doesn't truly belong in mathematics, but then he kept twisting my arguments around, making it impossible to argue with him. And then he suggested I should be criticizing von Neumann instead of Cantor. So I guess he saw problem, but didn't see any option other than to "get used to it".
>
> So that's the way it is!

The important thing is to be aware of it. I had just started a New conversation
https://groups.google.com/g/sci.math/c/yuQ7Sx9UnVM
'Cardinality' of ℝ is greater than ℵ1,ℵ2,ℵ3,...

On Tuesday, 10 August 2021 at 23:39:11 UTC-4, david...@gmail.com wrote:
> Here's a famous quote from John von Neumann: "in mathematics, you don't understand things, you just get used to them."

A fool is known by his words. John von Neumann's most laughable derivation of number using set theory is exhibit 1.

>
> That quote can be used to undestand what's going on in the never ending debate in this newsgroup over whether Cantor's theory of infinity belongs in mathematics.
>
> There are two sides to the debate:
>
> 1) Mathematics is, by definition, the game that mathematicians choose to play, and if you want status and respect in the mathematics community, you just have to get used to it. And Cantor's theory is part of the game. If you question it, you're a crank.
>
> 2) The whole purpose of mathematics, and in fact, in any honest academic discipline, it to gain an understanding of the real world. And to "understand" mathematics means to understand how mathematics is connected to our search for an understanding of the real world. And Cantor's theory of infinity has no role to play in our understanding the real world. So "get used to it" is simply bad advice.
>
> There seem to be some people in the debate who are caught in the middle. They seem to take on a confused mixture of both views, and they end up muddying the waters, so to speak.
>
> Anyways, for what it's worth, some thirty years ago, back when serious mathematicians participated in sci.math discussions, one mathematician who was known to be especially bright, seemed to understand my reasons for arguing that Cantor's theory of infinity doesn't truly belong in mathematics, but then he kept twisting my arguments around, making it impossible to argue with him. And then he suggested I should be criticizing von Neumann instead of Cantor. So I guess he saw problem, but didn't see any option other than to "get used to it".
>
> So that's the way it is!

On Wednesday, August 11, 2021 at 8:05:19 AM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:

> A fool is known by his words.

Yup...

STUDENTS BEWARE: Don't be a victim of JG's fake math

JG here claims to have a discovered as shortcut to mastering calculus without using limits. Unfortunately for him, this means he has no workable a definition of the derivative of a function. It blows up for functions as simple f(x)=|x|. Or even f(x)=0. As a result, he has had to ban 0, negative numbers and instantaneous rates of change rendering his goofy little system quite useless. What a moron!

Forget calculus. JG has also banned all axioms because he cannot even derive the most elementary results of basic arithmetic, e.g. 2+2=4. Such results require the use of axioms, so he must figure he's now off the hook. Again, what a moron!

Even at his advanced age (60+?), John Gabriel is STILL struggling with basic, elementary-school arithmetic. As he has repeatedly posted here:

"There are no points on a line."
--April 12, 2021

"Pi is NOT a number of ANY kind!"
--July 10, 2020

"1/2 not equal to 2/4"
--October 22, 2017

“1/3 does NOT mean 1 divided by 3 and never has meant that”
-- February 8, 2015

"3 =< 4 is nonsense.”
--October 28, 2017

"Zero is not a number."
-- Dec. 2, 2019

"0 is not required at all in mathematics, just like negative numbers."
-- Jan. 4, 2017

“There is no such thing as an empty set.”
--Oct. 4, 2019

“3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)
--Oct. 22, 2019

No math genius our JG, though he actually lists his job title as “mathematician” at Linkedin.com. Apparently, they do not verify your credentials.

Though really quite disturbing, interested readers should see: “About the spamming troll John Gabriel in his own words...” (lasted updated March 10, 2020) at https://groups.google.com/forum/#!msg/sci.math/PcpAzX5pDeY/1PDiSlK_BwAJ

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog a http://www.dcproof.wordpress.com

On Tuesday, August 10, 2021 at 11:39:11 PM UTC-4, david...@gmail.com wrote:
> Here's a famous quote from John von Neumann: "in mathematics, you don't understand things, you just get used to them."
>
> That quote can be used to understand what's going on in the never ending debate in this newsgroup over whether Cantor's theory of infinity belongs in mathematics.

Sounds to me as not so much some deep philosophical thought as an irritated brush-off to me. I wouldn't read too much into it.

Dan

On Tuesday, August 10, 2021 at 11:39:11 PM UTC-4, david...@gmail.com wrote:
> Here's a famous quote from John von Neumann: "in mathematics, you don't understand things, you just get used to them."
>

This posting at MSE may help you: https://math.stackexchange.com/questions/11267/what-are-some-interpretations-of-von-neumanns-quote

Dan

Dan Christensen wrote:

> On Tuesday, August 10, 2021 at 11:39:11 PM UTC-4, david...@gmail.com
> wrote:
>> Here's a famous quote from John von Neumann: "in mathematics, you don't
>> understand things, you just get used to them."
>>
>>
> This posting at MSE may help you:

Come on, use your brain. It's impossible for a "virus" to make it through
the air, from China to america, europe and canada. The oxygen in air is
highly reactive. End of story.

On 8/11/2021 2:04 PM, Dusty Ordonez wrote:

> Come on, use your brain. It's impossible for a "virus" to make it through
> the air, from China to america, europe and canada. The oxygen in air is
> highly reactive. End of story.
>

OK, nymshifter, so the flu, measles and the common cold are just
figments of our imaginations. Gotcha.

Michael Moroney wrote:

> On 8/11/2021 2:04 PM, Dusty Ordonez wrote:
>
>> Come on, use your brain. It's impossible for a "virus" to make it
>> through the air, from China to america, europe and canada. The oxygen
>> in air is highly reactive. End of story.
>>
>>
> OK, nymshifter, so the flu, measles and the common cold are just
> figments of our imaginations. Gotcha.

No hombrero, those are home grown, part of the immune system, without
which you cannot evolve, you cannot exists. Bio probes particles are
putten out, to test the environment, temp, humidity etc, then inhaled
back, in order to adapt. Use your brain one more time, if applicable.
Without bio-probes you couldn't even adapt from summer to winter. You are
such a pussy, don't understand physics and anything.

On 8/10/2021 10:39 PM, David Petry wrote:
>
> Here's a famous quote from John von Neumann: "in mathematics, you don't understand things, you just get used to them."

he was having a bad day.

>

>
> There are two sides to the debate:
>
> 1) Mathematics is, by definition, the game that mathematicians choose to play,

wrong.

<snip crap>

On 8/10/2021 11:39 PM, David Petry wrote:

> Here's a famous quote from John von Neumann:
> "in mathematics, you don't understand things,
> you just get used to them."
>
> That quote can be used to undestand what's going on
> in the never ending debate in this newsgroup over
> whether Cantor's theory of infinity belongs in mathematics.

If I remember correctly, you, David Petry, challenged the rest
of sci.math to explain the non-binary nature of quantifiers.
I'm not sure when you issued your challenge. Let's just say
it was well after the Battle of Agincourt. It's possible you
recognize the post of yours I'm sort-of remembering.

I'd like to try my hand at explaining that now.

Suppose that there are these individuals in which we are
interested. There are variables x,y,z,... which refer to
one of these interesting individuals.

Without more information, we do not know which one of these
individuals x refers to, y refers to, z refers to, ...
For each interesting individual, it is _possible_ that
x refers to it. ("Possible" carries a lot of weight here.)

Suppose that there is a predicate P(x) on these individuals.
That is, for each individual, if x refers to it,
P(x) is true xor false.

There are four statements that can be made about P(x) and
the individual x refers to. Two are true, two are false.

| It is possible that P(x) is false.
| It is not possible that P(x) is false.
| It is possible that P(x) is true.
| It is not possible that P(x) is true.

There are four cases to consider.

| It is not possible that P(x) is false.
| It is possible that P(x) is true.

| It is possible that P(x) is false.
| It is not possible that P(x) is true.

| It is possible that P(x) is false.
| It is possible that P(x) is true.

| It is not possible that P(x) is false.
| It is not possible that P(x) is true.

If any interesting individuals at all exists, the fourth case
never holds. It would be possible for x to refer to that
individual, and, because either P(x) is true or false,
one of those possible-statements would be false.

So, we can simplify our considerations by eliminating the
fourth case.
For the same reason, we have

| If it is not possible that P(x) is false,
| then it is possible that P(x) is true.

| If it is not possible that P(x) is true,
| then it is possible that P(x) is false.

and we can remove some clauses as redundant.

Our new-and-improved version, for a non-empty domain
of interesting individuals, is

| It is not possible that P(x) is false.

| It is not possible that P(x) is true.

| It is possible that P(x) is false.
| It is possible that P(x) is true.

----
We can introduce notation.
| exists x, P(x)
for
| It is possible (that x refers to an individual such that) P(x).

| forall x, P(x)
for
| It is not possible (that x refers ... ) ~P(x).

Thus,
| ( forall x, P(x) ) iff ( not exists x, ~P(x))

Lemmas.

| if ( forall x, P(x) ), then P(b)

| ( forall x,( Q or P(x) ) ) iff ( Q or, forall x, P(x) )

That's basically everything we need to know about quantifiers.

David Petry was thinking very hard :
> Here's a famous quote from John von Neumann: "in mathematics, you don't
> understand things, you just get used to them."
>
> That quote can be used to undestand what's going on in the never ending
> debate in this newsgroup over whether Cantor's theory of infinity belongs in
> mathematics.
>
> There are two sides to the debate:
>
> 1) Mathematics is, by definition, the game that mathematicians choose to
> play, and if you want status and respect in the mathematics community, you
> just have to get used to it. And Cantor's theory is part of the game. If
> you question it, you're a crank.
>
> 2) The whole purpose of mathematics, and in fact, in any honest academic
> discipline, it to gain an understanding of the real world. And to
> "understand" mathematics means to understand how mathematics is connected to
> our search for an understanding of the real world. And Cantor's theory of
> infinity has no role to play in our understanding the real world. So "get
> used to it" is simply bad advice.
>
> There seem to be some people in the debate who are caught in the middle.
> They seem to take on a confused mixture of both views, and they end up
> muddying the waters, so to speak.
>
> Anyways, for what it's worth, some thirty years ago, back when serious
> mathematicians participated in sci.math discussions, one mathematician who
> was known to be especially bright, seemed to understand my reasons for
> arguing that Cantor's theory of infinity doesn't truly belong in mathematics,
> but then he kept twisting my arguments around, making it impossible to
> argue with him. And then he suggested I should be criticizing von Neumann
> instead of Cantor. So I guess he saw problem, but didn't see any option
> other than to "get used to it".
>
> So that's the way it is!

It is too bad that you feel that way.

Sergio wrote:

> On 8/10/2021 10:39 PM, David Petry wrote:
>>
>> Here's a famous quote from John von Neumann: "in mathematics, you
>> don't understand things, you just get used to them."
>
> he was having a bad day.

even fauci is banned from youtube and facebook, for saying the manned
moon landing 1969 was fake.

On 8/11/2021 4:40 PM, Dusty Ordonez wrote:
> Sergio wrote:
>
>> On 8/10/2021 10:39 PM, David Petry wrote:
>>>
>>> Here's a famous quote from John von Neumann: "in mathematics, you
>>> don't understand things, you just get used to them."
>>
>> he was having a bad day.
>
> even fauci is banned from youtube and facebook, for saying the manned
> moon landing 1969 was fake.
>

fauci is a commie for sure,

On Wednesday, August 11, 2021 at 1:01:25 PM UTC-7, Jim Burns wrote:

> If I remember correctly, you, David Petry, challenged the rest
> of sci.math to explain the non-binary nature of quantifiers.
> I'm not sure when you issued your challenge. Let's just say
> it was well after the Battle of Agincourt. It's possible you
> recognize the post of yours I'm sort-of remembering.

That doesn't ring a bell at all. Not at all.

The only thing remotely related to that is a claim I made that "vacuous" should be added to "true" and "false" as possible truth values for propositions.

My claim was that if you have a statement "for all x, P(x) -> Q(x)", and then you find out that "for all x, not( P(x))" is true, you must admit that the first proposition is vacuous. That is, mathematics, like science, is all about prediction, and if a statement makes no predictions, then it is vacuous.

But is that what you're thinking of?

On 8/12/2021 3:15 PM, David Petry wrote:
> On Wednesday, August 11, 2021 at 1:01:25 PM UTC-7,
> Jim Burns wrote:

>> If I remember correctly, you, David Petry, challenged the rest
>> of sci.math to explain the non-binary nature of quantifiers.
>> I'm not sure when you issued your challenge. Let's just say
>> it was well after the Battle of Agincourt. It's possible you
>> recognize the post of yours I'm sort-of remembering.
>
> That doesn't ring a bell at all. Not at all.
>
> The only thing remotely related to that is a claim I made that
> "vacuous" should be added to "true" and "false" as possible
> truth values for propositions.
>
> My claim was that if you have a statement
> "for all x, P(x) -> Q(x)",
> and then you find out that
> "for all x, not( P(x))" is true,
> you must admit that the first proposition is vacuous.
> That is, mathematics, like science, is all about prediction,
> and if a statement makes no predictions, then it is vacuous.
>
> But is that what you're thinking of?

That's not what I am thinking of.
Perhaps my recollection is actually of a different poster.
(I note that you don't always post about falsifiability etc.)

> and if a statement makes no predictions, then it is vacuous.

Consider a prediction that some set is empty.
Is this vacuous?

For example, we could predict that the set of fundamental
particles going into and coming out of an interaction which
show a change in parity is the empty set.
(Shorter: that parity is conserved.)

It's a prediction. It's a falsifiable prediction, which we know
in the most useful way: it' been falsified.

On Wednesday, August 11, 2021 at 1:01:25 PM UTC-7, Jim Burns wrote:
> On 8/10/2021 11:39 PM, David Petry wrote:
>
> > Here's a famous quote from John von Neumann:
> > "in mathematics, you don't understand things,
> > you just get used to them."
> >
> > That quote can be used to undestand what's going on
> > in the never ending debate in this newsgroup over
> > whether Cantor's theory of infinity belongs in mathematics.
> If I remember correctly, you, David Petry, challenged the rest
> of sci.math to explain the non-binary nature of quantifiers.
> I'm not sure when you issued your challenge. Let's just say
> it was well after the Battle of Agincourt. It's possible you
> recognize the post of yours I'm sort-of remembering.
>
> I'd like to try my hand at explaining that now.
>
> Suppose that there are these individuals in which we are
> interested. There are variables x,y,z,... which refer to
> one of these interesting individuals.
>
> Without more information, we do not know which one of these
> individuals x refers to, y refers to, z refers to, ...
> For each interesting individual, it is _possible_ that
> x refers to it. ("Possible" carries a lot of weight here.)
>
> Suppose that there is a predicate P(x) on these individuals.
> That is, for each individual, if x refers to it,
> P(x) is true xor false.
>
> There are four statements that can be made about P(x) and
> the individual x refers to. Two are true, two are false.
>
> | It is possible that P(x) is false.
> | It is not possible that P(x) is false.
> | It is possible that P(x) is true.
> | It is not possible that P(x) is true.
>
> There are four cases to consider.
>
> | It is not possible that P(x) is false.
> | It is possible that P(x) is true.
>
> | It is possible that P(x) is false.
> | It is not possible that P(x) is true.
>
> | It is possible that P(x) is false.
> | It is possible that P(x) is true.
>
> | It is not possible that P(x) is false.
> | It is not possible that P(x) is true.
>
> If any interesting individuals at all exists, the fourth case
> never holds. It would be possible for x to refer to that
> individual, and, because either P(x) is true or false,
> one of those possible-statements would be false.
>
> So, we can simplify our considerations by eliminating the
> fourth case.
> For the same reason, we have
>
> | If it is not possible that P(x) is false,
> | then it is possible that P(x) is true.
>
> | If it is not possible that P(x) is true,
> | then it is possible that P(x) is false.
>
> and we can remove some clauses as redundant.
>
> Our new-and-improved version, for a non-empty domain
> of interesting individuals, is
>
> | It is not possible that P(x) is false.
>
> | It is not possible that P(x) is true.
>
> | It is possible that P(x) is false.
> | It is possible that P(x) is true.
>
> ----
> We can introduce notation.
> | exists x, P(x)
> for
> | It is possible (that x refers to an individual such that) P(x).
>
> | forall x, P(x)
> for
> | It is not possible (that x refers ... ) ~P(x).
>
> Thus,
> | ( forall x, P(x) ) iff ( not exists x, ~P(x))
>
> Lemmas.
>
> | if ( forall x, P(x) ), then P(b)
>
> | ( forall x,( Q or P(x) ) ) iff ( Q or, forall x, P(x) )
>
> That's basically everything we need to know about quantifiers.

Before impredicativity, that's covering cases,
then there's also that in terms and as is well explored
in the logic usual notions like bridge or
transfer, indicates cases where when
"expression's limited to the terms",
they still have what are their truth values.

I.e. it is usually a bonus or sputnik.

Besides those kinds of cases then are as along
the lines of differentiating as along
for-each/for-any/for-every/for-all,
for indicating where in terms there is disambiguation
of quantifiers, in the least terms, in the terms.

On 8/12/2021 9:12 PM, Ross A. Finlayson wrote:
> On Wednesday, August 11, 2021 at 1:01:25 PM UTC-7,
> Jim Burns wrote:
>> On 8/10/2021 11:39 PM, David Petry wrote:

>>> Here's a famous quote from John von Neumann:
>>> "in mathematics, you don't understand things,
>>> you just get used to them."
>>>
>>> That quote can be used to undestand what's going on
>>> in the never ending debate in this newsgroup over
>>> whether Cantor's theory of infinity belongs in mathematics.
>> If I remember correctly, you, David Petry, challenged the rest
>> of sci.math to explain the non-binary nature of quantifiers.
>> I'm not sure when you issued your challenge. Let's just say
>> it was well after the Battle of Agincourt. It's possible you
>> recognize the post of yours I'm sort-of remembering.
>>
>> I'd like to try my hand at explaining that now.
>>
>> Suppose that there are these individuals in which we are
>> interested. There are variables x,y,z,... which refer to
>> one of these interesting individuals.
>>
>> Without more information, we do not know which one of these
>> individuals x refers to, y refers to, z refers to, ...
>> For each interesting individual, it is _possible_ that
>> x refers to it. ("Possible" carries a lot of weight here.)
>>
>> Suppose that there is a predicate P(x) on these individuals.
>> That is, for each individual, if x refers to it,
>> P(x) is true xor false.
>>
>> There are four statements that can be made about P(x) and
>> the individual x refers to. Two are true, two are false.
>>
>> | It is possible that P(x) is false.
>> | It is not possible that P(x) is false.
>> | It is possible that P(x) is true.
>> | It is not possible that P(x) is true.
>>
>> There are four cases to consider.
>>
>> | It is not possible that P(x) is false.
>> | It is possible that P(x) is true.
>>
>> | It is possible that P(x) is false.
>> | It is not possible that P(x) is true.
>>
>> | It is possible that P(x) is false.
>> | It is possible that P(x) is true.
>>
>> | It is not possible that P(x) is false.
>> | It is not possible that P(x) is true.
>>
>> If any interesting individuals at all exists, the fourth case
>> never holds. It would be possible for x to refer to that
>> individual, and, because either P(x) is true or false,
>> one of those possible-statements would be false.
>>
>> So, we can simplify our considerations by eliminating the
>> fourth case.
>> For the same reason, we have
>>
>> | If it is not possible that P(x) is false,
>> | then it is possible that P(x) is true.
>>
>> | If it is not possible that P(x) is true,
>> | then it is possible that P(x) is false.
>>
>> and we can remove some clauses as redundant.
>>
>> Our new-and-improved version, for a non-empty domain
>> of interesting individuals, is
>>
>> | It is not possible that P(x) is false.
>>
>> | It is not possible that P(x) is true.
>>
>> | It is possible that P(x) is false.
>> | It is possible that P(x) is true.
>>
>> ----
>> We can introduce notation.
>> | exists x, P(x)
>> for
>> | It is possible (that x refers to an individual such that) P(x).
>>
>> | forall x, P(x)
>> for
>> | It is not possible (that x refers ... ) ~P(x).
>>
>> Thus,
>> | ( forall x, P(x) ) iff ( not exists x, ~P(x))
>>
>> Lemmas.
>>
>> | if ( forall x, P(x) ), then P(b)
>>
>> | ( forall x,( Q or P(x) ) ) iff ( Q or, forall x, P(x) )
>>
>> That's basically everything we need to know about quantifiers.
>
> Before impredicativity, that's covering cases,
> then there's also that in terms and as is well explored
> in the logic usual notions like bridge or
> transfer, indicates cases where when
> "expression's limited to the terms",
> they still have what are their truth values.
>
> I.e. it is usually a bonus or sputnik.
>
> Besides those kinds of cases then are as along
> the lines of differentiating as along
> for-each/for-any/for-every/for-all,
> for indicating where in terms there is disambiguation
> of quantifiers, in the least terms, in the terms.

I'm just letting you know I read your post.
I don't even have a guess at what you're saying.
I might not even be able to diagram your sentences.

torsdag 12 augusti 2021 kl. 21:16:04 UTC+2 skrev david...@gmail.com:
> On Wednesday, August 11, 2021 at 1:01:25 PM UTC-7, Jim Burns wrote:
>
>
> > If I remember correctly, you, David Petry, challenged the rest
> > of sci.math to explain the non-binary nature of quantifiers.
> > I'm not sure when you issued your challenge. Let's just say
> > it was well after the Battle of Agincourt. It's possible you
> > recognize the post of yours I'm sort-of remembering.
> That doesn't ring a bell at all. Not at all.
>
> The only thing remotely related to that is a claim I made that "vacuous" should be added to "true" and "false" as possible truth values for propositions.
>
> My claim was that if you have a statement "for all x, P(x) -> Q(x)", and then you find out that "for all x, not( P(x))" is true, you must admit that the first proposition is vacuous. That is, mathematics, like science, is all about prediction, and if a statement makes no predictions, then it is vacuous.
>
> But is that what you're thinking of?

Mathematics is not about making predictions in nature, I have told you this!

On Thursday, August 12, 2021 at 9:37:03 PM UTC-7, Jim Burns wrote:
> On 8/12/2021 9:12 PM, Ross A. Finlayson wrote:
> > On Wednesday, August 11, 2021 at 1:01:25 PM UTC-7,
> > Jim Burns wrote:
> >> On 8/10/2021 11:39 PM, David Petry wrote:
>
> >>> Here's a famous quote from John von Neumann:
> >>> "in mathematics, you don't understand things,
> >>> you just get used to them."
> >>>
> >>> That quote can be used to undestand what's going on
> >>> in the never ending debate in this newsgroup over
> >>> whether Cantor's theory of infinity belongs in mathematics.
> >> If I remember correctly, you, David Petry, challenged the rest
> >> of sci.math to explain the non-binary nature of quantifiers.
> >> I'm not sure when you issued your challenge. Let's just say
> >> it was well after the Battle of Agincourt. It's possible you
> >> recognize the post of yours I'm sort-of remembering.
> >>
> >> I'd like to try my hand at explaining that now.
> >>
> >> Suppose that there are these individuals in which we are
> >> interested. There are variables x,y,z,... which refer to
> >> one of these interesting individuals.
> >>
> >> Without more information, we do not know which one of these
> >> individuals x refers to, y refers to, z refers to, ...
> >> For each interesting individual, it is _possible_ that
> >> x refers to it. ("Possible" carries a lot of weight here.)
> >>
> >> Suppose that there is a predicate P(x) on these individuals.
> >> That is, for each individual, if x refers to it,
> >> P(x) is true xor false.
> >>
> >> There are four statements that can be made about P(x) and
> >> the individual x refers to. Two are true, two are false.
> >>
> >> | It is possible that P(x) is false.
> >> | It is not possible that P(x) is false.
> >> | It is possible that P(x) is true.
> >> | It is not possible that P(x) is true.
> >>
> >> There are four cases to consider.
> >>
> >> | It is not possible that P(x) is false.
> >> | It is possible that P(x) is true.
> >>
> >> | It is possible that P(x) is false.
> >> | It is not possible that P(x) is true.
> >>
> >> | It is possible that P(x) is false.
> >> | It is possible that P(x) is true.
> >>
> >> | It is not possible that P(x) is false.
> >> | It is not possible that P(x) is true.
> >>
> >> If any interesting individuals at all exists, the fourth case
> >> never holds. It would be possible for x to refer to that
> >> individual, and, because either P(x) is true or false,
> >> one of those possible-statements would be false.
> >>
> >> So, we can simplify our considerations by eliminating the
> >> fourth case.
> >> For the same reason, we have
> >>
> >> | If it is not possible that P(x) is false,
> >> | then it is possible that P(x) is true.
> >>
> >> | If it is not possible that P(x) is true,
> >> | then it is possible that P(x) is false.
> >>
> >> and we can remove some clauses as redundant.
> >>
> >> Our new-and-improved version, for a non-empty domain
> >> of interesting individuals, is
> >>
> >> | It is not possible that P(x) is false.
> >>
> >> | It is not possible that P(x) is true.
> >>
> >> | It is possible that P(x) is false.
> >> | It is possible that P(x) is true.
> >>
> >> ----
> >> We can introduce notation.
> >> | exists x, P(x)
> >> for
> >> | It is possible (that x refers to an individual such that) P(x).
> >>
> >> | forall x, P(x)
> >> for
> >> | It is not possible (that x refers ... ) ~P(x).
> >>
> >> Thus,
> >> | ( forall x, P(x) ) iff ( not exists x, ~P(x))
> >>
> >> Lemmas.
> >>
> >> | if ( forall x, P(x) ), then P(b)
> >>
> >> | ( forall x,( Q or P(x) ) ) iff ( Q or, forall x, P(x) )
> >>
> >> That's basically everything we need to know about quantifiers.
> >
> > Before impredicativity, that's covering cases,
> > then there's also that in terms and as is well explored
> > in the logic usual notions like bridge or
> > transfer, indicates cases where when
> > "expression's limited to the terms",
> > they still have what are their truth values.
> >
> > I.e. it is usually a bonus or sputnik.
> >
> > Besides those kinds of cases then are as along
> > the lines of differentiating as along
> > for-each/for-any/for-every/for-all,
> > for indicating where in terms there is disambiguation
> > of quantifiers, in the least terms, in the terms.
> I'm just letting you know I read your post.
> I don't even have a guess at what you're saying.
> I might not even be able to diagram your sentences.

The marvel that is a diagram of a sentence as into
its parts of speech as according to grammar and
vocabulary, ..., doesn't necessarily lend itself to
a usual medium of non-graphical text, but I can only
assure you that that there is at least one right reading.

Thanks though I appreciate it, about the depth of terms.

The point though is that there is not a "mathematical madness",
just plain mental exercise what results in a fair abstraction.

Even as to what's "paradoxical but true".

(Excuse me that's a sentence fragment , as for as in
narrative "... even as to what's paradoxical but true".
It's only a recent affectation and as for style it's poor.)

I thank you for reminding about the diagramming of
speech: being able to diagram any grammatical
sentence is an excellent exercise in command of language.

That in this particular milieu terms collide or conflate,
for example a singular/plural distinction in the collective,
makes for that's probably the most usual subtlety.

On 8/13/2021 1:10 AM, Ross A. Finlayson wrote:
> On Thursday, August 12, 2021 at 9:37:03 PM UTC-7, Jim Burns wrote:
>> On 8/12/2021 9:12 PM, Ross A. Finlayson wrote:
>>> On Wednesday, August 11, 2021 at 1:01:25 PM UTC-7,
>>> Jim Burns wrote:
>>>> On 8/10/2021 11:39 PM, David Petry wrote:
>>
>>>>> Here's a famous quote from John von Neumann:
>>>>> "in mathematics, you don't understand things,
>>>>> you just get used to them."
>>>>>
>>>>> That quote can be used to undestand what's going on
>>>>> in the never ending debate in this newsgroup over
>>>>> whether Cantor's theory of infinity belongs in mathematics.
>>>> If I remember correctly, you, David Petry, challenged the rest
>>>> of sci.math to explain the non-binary nature of quantifiers.
>>>> I'm not sure when you issued your challenge. Let's just say
>>>> it was well after the Battle of Agincourt. It's possible you
>>>> recognize the post of yours I'm sort-of remembering.
>>>>
>>>> I'd like to try my hand at explaining that now.
>>>>
>>>> Suppose that there are these individuals in which we are
>>>> interested. There are variables x,y,z,... which refer to
>>>> one of these interesting individuals.
>>>>
>>>> Without more information, we do not know which one of these
>>>> individuals x refers to, y refers to, z refers to, ...
>>>> For each interesting individual, it is _possible_ that
>>>> x refers to it. ("Possible" carries a lot of weight here.)
>>>>
>>>> Suppose that there is a predicate P(x) on these individuals.
>>>> That is, for each individual, if x refers to it,
>>>> P(x) is true xor false.
>>>>
>>>> There are four statements that can be made about P(x) and
>>>> the individual x refers to. Two are true, two are false.
>>>>
>>>> | It is possible that P(x) is false.
>>>> | It is not possible that P(x) is false.
>>>> | It is possible that P(x) is true.
>>>> | It is not possible that P(x) is true.
>>>>
>>>> There are four cases to consider.
>>>>
>>>> | It is not possible that P(x) is false.
>>>> | It is possible that P(x) is true.
>>>>
>>>> | It is possible that P(x) is false.
>>>> | It is not possible that P(x) is true.
>>>>
>>>> | It is possible that P(x) is false.
>>>> | It is possible that P(x) is true.
>>>>
>>>> | It is not possible that P(x) is false.
>>>> | It is not possible that P(x) is true.
>>>>
>>>> If any interesting individuals at all exists, the fourth case
>>>> never holds. It would be possible for x to refer to that
>>>> individual, and, because either P(x) is true or false,
>>>> one of those possible-statements would be false.
>>>>
>>>> So, we can simplify our considerations by eliminating the
>>>> fourth case.
>>>> For the same reason, we have
>>>>
>>>> | If it is not possible that P(x) is false,
>>>> | then it is possible that P(x) is true.
>>>>
>>>> | If it is not possible that P(x) is true,
>>>> | then it is possible that P(x) is false.
>>>>
>>>> and we can remove some clauses as redundant.
>>>>
>>>> Our new-and-improved version, for a non-empty domain
>>>> of interesting individuals, is
>>>>
>>>> | It is not possible that P(x) is false.
>>>>
>>>> | It is not possible that P(x) is true.
>>>>
>>>> | It is possible that P(x) is false.
>>>> | It is possible that P(x) is true.
>>>>
>>>> ----
>>>> We can introduce notation.
>>>> | exists x, P(x)
>>>> for
>>>> | It is possible (that x refers to an individual such that) P(x).
>>>>
>>>> | forall x, P(x)
>>>> for
>>>> | It is not possible (that x refers ... ) ~P(x).
>>>>
>>>> Thus,
>>>> | ( forall x, P(x) ) iff ( not exists x, ~P(x))
>>>>
>>>> Lemmas.
>>>>
>>>> | if ( forall x, P(x) ), then P(b)
>>>>
>>>> | ( forall x,( Q or P(x) ) ) iff ( Q or, forall x, P(x) )
>>>>
>>>> That's basically everything we need to know about quantifiers.
>>>
>>> Before impredicativity, that's covering cases,
>>> then there's also that in terms and as is well explored
>>> in the logic usual notions like bridge or
>>> transfer, indicates cases where when
>>> "expression's limited to the terms",
>>> they still have what are their truth values.
>>>
>>> I.e. it is usually a bonus or sputnik.
>>>
>>> Besides those kinds of cases then are as along
>>> the lines of differentiating as along
>>> for-each/for-any/for-every/for-all,
>>> for indicating where in terms there is disambiguation
>>> of quantifiers, in the least terms, in the terms.
>> I'm just letting you know I read your post.
>> I don't even have a guess at what you're saying.
>> I might not even be able to diagram your sentences.
>
> The marvel that is a diagram of a sentence as into
> its parts of speech as according to grammar and
> vocabulary, ..., doesn't necessarily lend itself to
> a usual medium of non-graphical text, but I can only
> assure you that that there is at least one right reading.
>
> Thanks though I appreciate it, about the depth of terms.
>
> The point though is that there is not a "mathematical madness",
> just plain mental exercise what results in a fair abstraction.
>
> Even as to what's "paradoxical but true".
>
> (Excuse me that's a sentence fragment , as for as in
> narrative "... even as to what's paradoxical but true".
> It's only a recent affectation and as for style it's poor.)
>
> I thank you for reminding about the diagramming of
> speech: being able to diagram any grammatical
> sentence is an excellent exercise in command of language.
>
> That in this particular milieu terms collide or conflate,
> for example a singular/plural distinction in the collective,
> makes for that's probably the most usual subtlety.
>

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