Help me understand

1.9999... does not work in reality.

So now you restrict your challenge?
It is a result of fractional representation.
1.999... is no different to 2.
They are 1.999... ways to represent the same thing.
The fraction notation of 0.999... is 1, or 9/9

You are dismissing 1.999...99923 because it does not work in reality, when 1.999... the series you are claiming = 1.99...999 also does not exist in reality.

The only person claiming that is you. 1.999... IS NOT THE SAME AS 1.99...999
Notice how the final one terminates?
That means it doesn't go on forever.
That means it is not 1.999...

So, let us discuss the entirely similar situation: let us put two apples on a table - a sturdy table mind you that would not shake or move the apples or bring in other apples by accident and so on.  Now we then put another two apples on the table, and count those now there - we will likely get the result 4.  We can perform additional experiments like this, but we are fairly confident here that 'adding' works as we think it does. Yes, the results are consistent, and perhaps even corollary, but this is not the same thing as placing two numbers ones on a table and then two more number ones.

Numbers represent things. In this case we have 2 apples, which are represented by the number 2.
We then add more apples, again represented by the number 2.
This gives us 2+2=4.

However, if we did the same procedure with sticks, fingers, line and most things this would show us that sums are completely silly. Look at this figure to see 2+2 = 4, which is similar to your argument:

No, we don't get anything silly out of it.

If this is all we need, as you claim, to show that 2 + 2 = 4 and in your case 5 + 5 + 5 +5 = 20, then this is completely valid reasoning:

2 + 2 + 2 = 4.

Notice how you count two of them twice.
So no, that is nothing like what I am doing.

You have got 2+2, but then 2 extra.
This is not addition.

It is completely invalid reasoning.

Try again.

For similar reasons, your supplied example is not sufficient to show that 2 + 2 = 4 in reality, or that 5 * 4 = 20.

So for similar invalid reasons, i.e. no actual refutation at all.

I do have to ask, though this won't stop me from loving your movies Jack, if you feel that mathematics works in reality, then why are we continuing to work on advancing mathematics?

Just because the math we have works doesn't mean we know everything.

For example, think back to when we didn't have multiplication.
So we have 4 rows of 5.
How many do we have?
Well we have 5 plus 5 plus 5 plus 5.
That isn't all that nice to write out. 4 times 5 would be nicer.

So even though addition works, multiplication is nicer.

It occurs to me it may be helpful for you to have read the previous bits introducing this book:

"... But then, what does the peculiar inexorability of mathematics consist in? - Would not the inexorability with which two follows on and three two be a good example? But presumably this means: follows in the series of cardinal numbers; for in a different series something different follows. And isn't this series just defined by this sequence?


"Is that supposed to mean that it is equally correct whichever way a person counts, and that anyone can count as he pleases?"
- We should presumably not call it 'counting' if everyone said the numbers one after the other anyhow; but of course it is not simply question of a name. For what we call 'counting' is an important part of our life's activities. Counting and calculating are not - eg - simply a pastime. Counting (and that means: counting like *this*) is a technique that is employed dailing in the most various operations of our lives. And that is why we learn to count as we do: with endless practice with merciless exactitude; that is why it is inexorably insisted that we shall all say 'two' after 'one', 'three' after 'two' and so on.

But is this counting only a use then; isn't there also some truth corresponding to this sequence?
The truth is that counting has proved to pay.

"Then do you want to say that 'being true' means: being usable (or useful)?"
No, not that; but that it can't be said of the series of natural numbers any more than of our language -- this it is true, but : that is is usable, and above all, it is used."


In as much as propositions are true in mathematics, they are not true descriptions but rules for reaching similar results. Since they are not 'true', I find it hard to believe they 'work in reality' aside from how they do to be useful.


Edit for formatting that admittedly differs from the book but provides readability.  He goes on to delve in the deeper arguments here until he eventually reaches point 38 cited above.

I find it hard to believe Wittgenstein would be employing 'invalid reasoning' but please share with me why you think its 'invalid.'

In as much as propositions are true in mathematics, they are not true descriptions but rules for reaching similar results. Since they are not 'true', I find it hard to believe they 'work in reality' aside from how they do to be useful.

Mathematics is merely a description of reality.
Yes, there are words and symbols which are used, just like everything else.

The same kind of thing applies to fruits, there are numerous fruits such as apples and oranges. These words have been defined to refer to specific fruits.
Other people could hypothetically have them switched and an apple to them is an orange to us, as some people can hypothetically have a different number system where a three to them is a two to us.

But none of this changes the underlying reality which it is describing. It is merely the placeholders we use to describe things.

Quote from: John Davis on December 10, 2017, 01:58:42 PM

In as much as propositions are true in mathematics, they are not true descriptions but rules for reaching similar results. Since they are not 'true', I find it hard to believe they 'work in reality' aside from how they do to be useful.

Mathematics is merely a description of reality.
Yes, there are words and symbols which are used, just like everything else.

The same kind of thing applies to fruits, there are numerous fruits such as apples and oranges. These words have been defined to refer to specific fruits.
Other people could hypothetically have them switched and an apple to them is an orange to us, as some people can hypothetically have a different number system where a three to them is a two to us.

But none of this changes the underlying reality which it is describing. It is merely the placeholders we use to describe things.

Except it is not describing that underlying reality, except in the way we use it - no more than a poem talking about walking down the path no one goes down reflects an underlying reality. It is only us that gives it a meaning that translates to the real world, and only through use of it as a tool - not a truth. As such, its means for discovering truth or relating truth are also suspect.

To the point though, claiming 1.999....9923 is not valid simply because it does not relate to reality is fallacious. It also fails to show its evidence supporting its original point - that it does not relate to reality. In addition, it ignores very many mathematical nominalists that also happen to be pure mathematicians and their views on the subject.

I find it hard to believe Wittgenstein would be employing 'invalid reasoning' but please share with me why you think its 'invalid.'

I find it extraordinary that you refer to Wittgenstein of all people, I would imagine a man famous for his work in Logical atomism in particular, would not be appealing to one such as yourself as it appears to be at odds with our beliefs

I will not ignore evidence from a globularist, why would I a logical atonomist?

Why would they lie about monsters at the rim? Everyone can look up and see stars, planets, the moon. That makes for a much easier sell than monsters.

"Hey, see that big yellow circle in the sky? We're going on a mission to land on it!"

Or...

"Give me money to protect you from a monster that you've never seen and never will because it lives in a place you can't possibly go!"

first of all, THANK YOU for not ignoring my post like everybody else seems to be doing!

about your answer, it is true that we can see stars etc but be can't see monsters, but the monsters were just an example. What I meant was to create a lie that involved the icy ends of the world and sharing pictures etc with us common people just like they do with the space ones, but in this case it would be less expensive in money, resources and general effort since they would not fake the existence of rockets, satellites etc.

that's what I mean, what does this specific lie about the shape of the earth brings to them? (don't say control over us because this was widely discussed in the first 2-3 pages of this debate)

2+2=4
2 oranges + 2 oranges = 4 oranges
2 apples + 2 swarms of bees = 4 what?

Math is like many things. It is a useful tool, but it shouldn't be followed without thought. We all need to step back and think about what is true, and how we understand truth.

Joe

And cults.

2 apples + 2 swarms of bees = 4 what?

Pre-algebra wasn't your subject, huh?

2+2=4
2 oranges + 2 oranges = 4 oranges
2 apples + 2 swarms of bees = 4 what?

Math is like many things. It is a useful tool, but it shouldn't be followed without thought. We all need to step back and think about what is true, and how we understand truth.

Joe

Nailed it.

Quote from: boydster on December 10, 2017, 10:50:49 AM

Why would they lie about monsters at the rim? Everyone can look up and see stars, planets, the moon. That makes for a much easier sell than monsters.

"Hey, see that big yellow circle in the sky? We're going on a mission to land on it!"

Or...

"Give me money to protect you from a monster that you've never seen and never will because it lives in a place you can't possibly go!"

first of all, THANK YOU for not ignoring my post like everybody else seems to be doing!

about your answer, it is true that we can see stars etc but be can't see monsters, but the monsters were just an example. What I meant was to create a lie that involved the icy ends of the world and sharing pictures etc with us common people just like they do with the space ones, but in this case it would be less expensive in money, resources and general effort since they would not fake the existence of rockets, satellites etc.

that's what I mean, what does this specific lie about the shape of the earth brings to them? (don't say control over us because this was widely discussed in the first 2-3 pages of this debate)

One possible benefit I could think of would be that one of the ancient fellers that said the Earth was round was wrong, but someone in a position of power realized how that belief could be exploited for personal gain.

Just one idea though off the top of my head. I didn't put much time into it; I'm sure you could poke some holes in it if you really wanted to.

Except it is not describing that underlying reality, except in the way we use it - no more than a poem talking about walking down the path no one goes down reflects an underlying reality. It is only us that gives it a meaning that translates to the real world, and only through use of it as a tool - not a truth. As such, its means for discovering truth or relating truth are also suspect.

Just like all words.

To the point though, claiming 1.999....9923 is not valid simply because it does not relate to reality is fallacious.

It isn't valid for several reasons, mainly as it is an infinite series, that ends. That makes no sense at all, and cannot apply to reality.

The only way it makes sense is if the "...." represents some finite number of 9s.

In addition, it ignores very many mathematical nominalists that also happen to be pure mathematicians and their views on the subject.

Such as?

Quote from: Pixie on December 10, 2017, 03:00:19 PM

Quote from: boydster on December 10, 2017, 10:50:49 AM

Why would they lie about monsters at the rim? Everyone can look up and see stars, planets, the moon. That makes for a much easier sell than monsters.

"Hey, see that big yellow circle in the sky? We're going on a mission to land on it!"

Or...

"Give me money to protect you from a monster that you've never seen and never will because it lives in a place you can't possibly go!"

first of all, THANK YOU for not ignoring my post like everybody else seems to be doing!

about your answer, it is true that we can see stars etc but be can't see monsters, but the monsters were just an example. What I meant was to create a lie that involved the icy ends of the world and sharing pictures etc with us common people just like they do with the space ones, but in this case it would be less expensive in money, resources and general effort since they would not fake the existence of rockets, satellites etc.

that's what I mean, what does this specific lie about the shape of the earth brings to them? (don't say control over us because this was widely discussed in the first 2-3 pages of this debate)

One possible benefit I could think of would be that one of the ancient fellers that said the Earth was round was wrong, but someone in a position of power realized how that belief could be exploited for personal gain.

Just one idea though off the top of my head. I didn't put much time into it; I'm sure you could poke some holes in it if you really wanted to.

That's the best answer I got up until now and I accept it. It could have happened as you said and it would actually make sense.

My only argument would be that now government are in deep trouble keeping up the lie of that greedy fellow, but still it could make sense.

2+2=4
2 oranges + 2 oranges = 4 oranges
2 apples + 2 swarms of bees = 4 what?

Math is like many things. It is a useful tool, but it shouldn't be followed without thought. We all need to step back and think about what is true, and how we understand truth.

Yes, you especially.
You have completely misunderstood.

This would be more akin to:
2a+2b.
That does not necessarily equal 4.
It depends entirely upon what you are counting and how you are counting them.

When you have a and b being the same (oranges), you get:
2o+2o=4o.
You can't do that when they are completely different.

Quote from: John Davis on December 10, 2017, 02:13:07 PM

Except it is not describing that underlying reality, except in the way we use it - no more than a poem talking about walking down the path no one goes down reflects an underlying reality. It is only us that gives it a meaning that translates to the real world, and only through use of it as a tool - not a truth. As such, its means for discovering truth or relating truth are also suspect.

Just like all words.

Quote from: John Davis on December 10, 2017, 02:13:07 PM

To the point though, claiming 1.999....9923 is not valid simply because it does not relate to reality is fallacious.

It isn't valid for several reasons, mainly as it is an infinite series, that ends. That makes no sense at all, and cannot apply to reality.

The only way it makes sense is if the "...." represents some finite number of 9s.

Quote from: John Davis on December 10, 2017, 02:13:07 PM

In addition, it ignores very many mathematical nominalists that also happen to be pure mathematicians and their views on the subject.

Such as?

"It isn't valid for many reasons, such as the one I already said which was just debunked."

Quote from: th3rm0m3t3r0 on December 08, 2017, 06:39:37 PM

Quote from: John Davis on December 08, 2017, 05:48:33 PM

I am not playing games. I am not describing a finite and undefined amount of digits by showing the series of 9s ends. I am describe an infinite amount of digits that ends. For example, I could use this notation to say something like 1.999...923.

You are playing games. That's an incredibly abstract way to use that and it doesn't really make much sense. It's like saying, "keep going this straight for an infinite amount of time, then take a right."

This doesn't work in reality.

Why would you have two notations if they do not differ in this way?

Show me any math that works in reality, and I'll give you 100$. I forewarn you that I am a nominalist, so it would not be an easy belief to shake, as it is supported quite well.

Math attempts to describe reality and works quite well in doing so.

Again, what you're saying there is akin to saying, "swim across this infinite body of water, my house is right on the other side."

Quote from: John Davis on December 10, 2017, 09:52:14 AM

Quote from: th3rm0m3t3r0 on December 08, 2017, 06:39:37 PM

Quote from: John Davis on December 08, 2017, 05:48:33 PM

I am not playing games. I am not describing a finite and undefined amount of digits by showing the series of 9s ends. I am describe an infinite amount of digits that ends. For example, I could use this notation to say something like 1.999...923.

You are playing games. That's an incredibly abstract way to use that and it doesn't really make much sense. It's like saying, "keep going this straight for an infinite amount of time, then take a right."

This doesn't work in reality.

Why would you have two notations if they do not differ in this way?

Show me any math that works in reality, and I'll give you 100$. I forewarn you that I am a nominalist, so it would not be an easy belief to shake, as it is supported quite well.

Math attempts to describe reality and works quite well in doing so.

Again, what you're saying there is akin to saying, "swim across this infinite body of water, my house is right on the other side."

Which you have yet to show is invalid.

Quote from: th3rm0m3t3r0 on December 11, 2017, 11:09:12 AM

Quote from: John Davis on December 10, 2017, 09:52:14 AM

Quote from: th3rm0m3t3r0 on December 08, 2017, 06:39:37 PM

Quote from: John Davis on December 08, 2017, 05:48:33 PM

I am not playing games. I am not describing a finite and undefined amount of digits by showing the series of 9s ends. I am describe an infinite amount of digits that ends. For example, I could use this notation to say something like 1.999...923.

You are playing games. That's an incredibly abstract way to use that and it doesn't really make much sense. It's like saying, "keep going this straight for an infinite amount of time, then take a right."

This doesn't work in reality.

Why would you have two notations if they do not differ in this way?

Show me any math that works in reality, and I'll give you 100$. I forewarn you that I am a nominalist, so it would not be an easy belief to shake, as it is supported quite well.

Math attempts to describe reality and works quite well in doing so.

Again, what you're saying there is akin to saying, "swim across this infinite body of water, my house is right on the other side."

Which you have yet to show is invalid.

How do you define the infinite?

Caleb

"It isn't valid for many reasons, such as the one I already said which was just debunked."

Except you are yet to debunk it.
I pointed out why your debunking was wrong. Try again.

Quote from: JackBlack on December 10, 2017, 02:03:19 PM

Quote from: John Davis on December 10, 2017, 01:58:42 PM

In as much as propositions are true in mathematics, they are not true descriptions but rules for reaching similar results. Since they are not 'true', I find it hard to believe they 'work in reality' aside from how they do to be useful.

Mathematics is merely a description of reality.
Yes, there are words and symbols which are used, just like everything else.

The same kind of thing applies to fruits, there are numerous fruits such as apples and oranges. These words have been defined to refer to specific fruits.
Other people could hypothetically have them switched and an apple to them is an orange to us, as some people can hypothetically have a different number system where a three to them is a two to us.

But none of this changes the underlying reality which it is describing. It is merely the placeholders we use to describe things.

Except it is not describing that underlying reality, except in the way we use it - no more than a poem talking about walking down the path no one goes down reflects an underlying reality. It is only us that gives it a meaning that translates to the real world, and only through use of it as a tool - not a truth. As such, its means for discovering truth or relating truth are also suspect.

To the point though, claiming 1.999....9923 is not valid simply because it does not relate to reality is fallacious. It also fails to show its evidence supporting its original point - that it does not relate to reality.

Right here. Also, if your criterion is that 1.9999...9923 does not occur in real life, then neither does 1.9999... as mentioned earlier.

Right here. Also, if you criterion is that 1.9999...9923 does not occur in real life, then neither does 1.9999... as mentioned earlier.

Again, my criterion is that it makes no sense.
You have an infinite sequence, that ends.
It makes as much sense as a square circle.

Meanwhile a sequence of "9"s which doesn't end does make sense. It just keeps on going as 9, with you never reaching the end.

Quote from: th3rm0m3t3r0 on December 11, 2017, 11:09:12 AM

Quote from: John Davis on December 10, 2017, 09:52:14 AM

Quote from: th3rm0m3t3r0 on December 08, 2017, 06:39:37 PM

Quote from: John Davis on December 08, 2017, 05:48:33 PM

I am not playing games. I am not describing a finite and undefined amount of digits by showing the series of 9s ends. I am describe an infinite amount of digits that ends. For example, I could use this notation to say something like 1.999...923.

You are playing games. That's an incredibly abstract way to use that and it doesn't really make much sense. It's like saying, "keep going this straight for an infinite amount of time, then take a right."

This doesn't work in reality.

Why would you have two notations if they do not differ in this way?

Show me any math that works in reality, and I'll give you 100$. I forewarn you that I am a nominalist, so it would not be an easy belief to shake, as it is supported quite well.

Math attempts to describe reality and works quite well in doing so.

Again, what you're saying there is akin to saying, "swim across this infinite body of water, my house is right on the other side."

Which you have yet to show is invalid.

It's obviously invalid because it's self-contradictory. A body of water cannot both be infinite and have something on the other side. Or is your grasp of English as bad as your grasp of reality?
Here, hold this ten pound bowling ball which weighs nine pounds. Then you'll understand.

To those that use 2+2=4 as some infallible proof of Math. The answer is still 'it depends'

Working in base 2, 2+2 = 10+10 (as 2 doesn't exist) and so 10+10=100
Working in base 3, 2+2=11

You can even design a kind of Modulo system to say that 2+2=1!


Math is a classic in that you can spin and bend the rules or make any up to suit an argument. It is not definitive. My math can be different to your math and you saying its wrong, doesn't make it so

Quote from: John Davis on December 11, 2017, 11:11:27 AM

Quote from: th3rm0m3t3r0 on December 11, 2017, 11:09:12 AM

Quote from: John Davis on December 10, 2017, 09:52:14 AM

Quote from: th3rm0m3t3r0 on December 08, 2017, 06:39:37 PM

Quote from: John Davis on December 08, 2017, 05:48:33 PM

I am not playing games. I am not describing a finite and undefined amount of digits by showing the series of 9s ends. I am describe an infinite amount of digits that ends. For example, I could use this notation to say something like 1.999...923.

You are playing games. That's an incredibly abstract way to use that and it doesn't really make much sense. It's like saying, "keep going this straight for an infinite amount of time, then take a right."

This doesn't work in reality.

Why would you have two notations if they do not differ in this way?

Show me any math that works in reality, and I'll give you 100$. I forewarn you that I am a nominalist, so it would not be an easy belief to shake, as it is supported quite well.

Math attempts to describe reality and works quite well in doing so.

Again, what you're saying there is akin to saying, "swim across this infinite body of water, my house is right on the other side."

Which you have yet to show is invalid.

It's obviously invalid because it's self-contradictory. A body of water cannot both be infinite and have something on the other side. Or is your grasp of English as bad as your grasp of reality?
Here, hold this ten pound bowling ball which weighs nine pounds. Then you'll understand.

Are you comfortable saying the universe in infinite? It's not actually infinite, it does have a limit. It just just incomprehensibly large

To a human, a body of water is large, but surmountable. We can measure it.

To an ant that doesn't know the length or perceive an end to it, it could be infinitive

It depends on perception. Infinity is not a number

To those that use 2+2=4 as some infallible proof of Math. The answer is still 'it depends'

Yes, it depends on the meaning given to the words and symbols.
Just like all words will have meaning which depends upon the meaning given to them.

When I say "2" I mean two entities as it is understood in a base 10 number systems, and I mean 4 in a similar way.
Your comment regarding base 2 highlights this.
You need to convert it to base 2, so instead of "2" you have "10" and instead of "4" you have "100".
But the meaning still holds.
You have 10+10=100 in base 2.
In base 3 you still have the "2" and "2", but now "4" is 11.
So you have 2+2=11, in base 3.
The meaning is the same. The representation is different.

Math is not special in this regard.
All forms of communication have the same issue.

We use words and symbols to indicate a meaning, and that only works if people use the same meaning.

Are you comfortable saying the universe in infinite? It's not actually infinite, it does have a limit. It just just incomprehensibly large

The observable universe is finite. The universe itself may be infinite.

It depends on perception. Infinity is not a number

It is a concept.

Would saying "on the other end of an unbounded line through space" be better?

Not going to get involved in the linguistics arguments.

What is sqrt (0.000... 01),  if you allow that ... to be an infinite amount of zeros?

Quote from: Dinosaur Neil on December 11, 2017, 12:43:04 PM

Quote from: John Davis on December 11, 2017, 11:11:27 AM

Quote from: th3rm0m3t3r0 on December 11, 2017, 11:09:12 AM

Quote from: John Davis on December 10, 2017, 09:52:14 AM

Quote from: th3rm0m3t3r0 on December 08, 2017, 06:39:37 PM

Quote from: John Davis on December 08, 2017, 05:48:33 PM

I am not playing games. I am not describing a finite and undefined amount of digits by showing the series of 9s ends. I am describe an infinite amount of digits that ends. For example, I could use this notation to say something like 1.999...923.

You are playing games. That's an incredibly abstract way to use that and it doesn't really make much sense. It's like saying, "keep going this straight for an infinite amount of time, then take a right."

This doesn't work in reality.

Why would you have two notations if they do not differ in this way?

Show me any math that works in reality, and I'll give you 100$. I forewarn you that I am a nominalist, so it would not be an easy belief to shake, as it is supported quite well.

Math attempts to describe reality and works quite well in doing so.

Again, what you're saying there is akin to saying, "swim across this infinite body of water, my house is right on the other side."

Which you have yet to show is invalid.

It's obviously invalid because it's self-contradictory. A body of water cannot both be infinite and have something on the other side. Or is your grasp of English as bad as your grasp of reality?
Here, hold this ten pound bowling ball which weighs nine pounds. Then you'll understand.

Are you comfortable saying the universe in infinite? It's not actually infinite, it does have a limit. It just just incomprehensibly large

To a human, a body of water is large, but surmountable. We can measure it.

To an ant that doesn't know the length or perceive an end to it, it could be infinitive

It depends on perception. Infinity is not a number

I was addressing Davis's crappy dismissal of a metaphor, not the concept of infinity