## Lessons on Causality

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### Re: Lessons on Causality

James S Saint wrote:We aren't talking about imperfect. We are talking about circles having nothing but straight sides. Ask even a child if a circle has straight sides. Assuming that he doesn't merely call you an idiot, see what he says.

This can be interpreted as a circle with straight sides:

It's not a normal "circle" by how people mean but people with common sense understand my point. You're still arguing about the degree by which a shape is considered a circle or not. You've already demonstrated countless times that you refuse to admit a Chiliagon is a circle, and therefore, your position is unreasonable. Further arguing over definitions of circles having sides or "straight sides" is a moot point when you already refused to admit the 1000-sided shape as a circle, which it is, and which people will agree with out of common sense.

As stated before, people identify shapes and geometry out of approximations. Triangles have 3 sides, rectangles 4, hexagons 6, octagons 8, chiliagons 1000, etc. The more sides a shape has, the more 'circle' it becomes.

Those that dispute this fact, you, Arc, Wendy, gib, all of you are simply, wrong.
Urwrongx1000
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### Re: Lessons on Causality

hexagons 6, octagons 8, chiliagons 1000,

What you really meant was circle 6, circle 8, and circle 1000, right?
I AM OFFICIALLY IN HELL!

I live my philosophy, it's personal to me and people who engage where I live establish an unspoken dynamic, a relationship of sorts, with me and my philosophy.

Cutting folks for sport is a reality for the poor in spirit. I myself only cut the poor in spirit on Tues., Thurs., and every other Sat.

WendyDarling
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### Re: Lessons on Causality

I passed 1st grade, unlike you and a few others here.
Urwrongx1000
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### Re: Lessons on Causality

Urwrongx1000 wrote:
James S Saint wrote:We aren't talking about imperfect. We are talking about circles having nothing but straight sides. Ask even a child if a circle has straight sides. Assuming that he doesn't merely call you an idiot, see what he says.

This can be interpreted as a circle with straight sides:

It could also be interpreted as a square with extra sides, as a dog with a few pieces missing, as the King of Cleveland on a good day, as a circle to a blind man....
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Lessons on Causality

as a dog with a few pieces missing

I AM OFFICIALLY IN HELL!

I live my philosophy, it's personal to me and people who engage where I live establish an unspoken dynamic, a relationship of sorts, with me and my philosophy.

Cutting folks for sport is a reality for the poor in spirit. I myself only cut the poor in spirit on Tues., Thurs., and every other Sat.

WendyDarling
Heroine

Posts: 7113
Joined: Sat Sep 11, 2010 8:52 am

### Re: Lessons on Causality

And people who don't think Chiliagons are circles can be interpreted as wrong.
Urwrongx1000
Philosopher

Posts: 1151
Joined: Mon Jun 19, 2017 5:10 pm

### Re: Lessons on Causality

Notice that he's accepted it would be an interpretation.
My thoughts | My art | My music | My poetry

A man convinced against his will is of the same opinion still.
- unknown source

Men must be taught as if you taught them not. And things unknown proposed as things forgot.
- Alexander Pope

Here lies the body of William J, who died maintaining his right of way.
He was right, dead right, as he sped along, but he's just as dead as if he were wrong.
- Boston Transcript

gib
resident exorcist

Posts: 8724
Joined: Sat May 27, 2006 10:25 pm

### Re: Lessons on Causality

I already said it was a matter of approximation pages ago. Some individuals need very specific definition and accuracy, like mathematicians, engineers, and physicists.

To a mathematician, a circle can be defined as (x^2)+(y^2)=r^2

It's okay, you can admit I was right all along, now...
Urwrongx1000
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### Re: Lessons on Causality

Urwrongx1000 wrote:I already said it was a matter of approximation pages ago.

A dog is an approximation of a dog??
A tree is an approximation of a tree??

What is a circle an approximation of?
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Lessons on Causality

I am now waffling. I'm trying to image the points that comprise the circumference of the circle--I'm trying to zoom in with my mind's eye as close as I can to see just a few points (maybe a dozen or so) that are consecutive to each other and try to make out the curvature. I'm having difficulty. I'm finding that the simplest curve I can imagine must consist of at least 3 points. You can't have just 2 points because that would comprise a line (which is problematic in itself given that a circle is not supposed to be composed of lines). But now if these three points make up the smallest curve the circle can have, then it seems curvature is reduced to angles (3 points also make an angle). And furthermore, this angle would have to be so obtuse as to be indistinguishable from a straight line (comprised of the 3 points). Otherwise, you'd be saying the angle is a finite amount (however small) and it would take only a finite number of these angles attached together to form the circle, effectively throwing out the notion that the circle is comprise of infinite points.

^ No doubt, all this is due to the same fact I brought up earlier--that when you're skipping an infinity (from the circle as a whole to its individual points), you're already doing something paradoxical--it shouldn't be a surprise when other paradoxes follow.

Maybe we've been looking at geometry wrong over the past 2,500 years. Maybe we shouldn't say that circles and squares and lines, etc., etc., etc., are made of points, but that points are the smallest geometric entity they can be decomposed into. Points don't "exist" per se on the circumference of the circle but you can mark a point on the circle and say "let that be point A." <-- IOW, we invent points as we need them. As for what the circle (and other geometric shapes) are made of, I'd say segments. Segments can be straight or curved, and they can be infinitely divided, and the result of any such division is just smaller segments. So if you take a quarter of the circle's circumference, that's a segment 1/4 of the circle's circumference in length and half a radian in curvature. But then you can divide that segment in two equal halves, each being an eighth the circle's circumference and a quarter radians, or two unequal halves, .1 radians and .4 radians, or any ratio you want. <-- That's what shapes, lines, and curves are made of. Points end up being, not something these objects divide into, but things used to mark a certain position on these objects. You can then imagine that at that position, you've invented a point (like inventing a border between countries--it's real because we say it's real), and therefore the circle is comprised of that point at that exact location, but that doesn't mean it's got a "neighbouring" point, or that you can count twelve points to the left and be a bit further along the circle's circumference. On either side of the point are segments whose length depends on where you want to mark the other points constituting their other ends. So it's still true that the point constitutes the smallest thing you can decompose the circle into, but unlike segments, they aren't just all "there" before you mark out specific ones.

^ How's that sound to everyone?
My thoughts | My art | My music | My poetry

A man convinced against his will is of the same opinion still.
- unknown source

Men must be taught as if you taught them not. And things unknown proposed as things forgot.
- Alexander Pope

Here lies the body of William J, who died maintaining his right of way.
He was right, dead right, as he sped along, but he's just as dead as if he were wrong.
- Boston Transcript

gib
resident exorcist

Posts: 8724
Joined: Sat May 27, 2006 10:25 pm

### Re: Lessons on Causality

I'm not a fan of points. Lines and sides are practical.

Dogs are approximations of canines, yes.

Trees are approximations of fora and other plantlife, yes.

There are scales of interpretation in terms of accuracy. Wolves are not dogs but huskies are. Same mode of argument.

But a Chiliagon is still a circle.
Urwrongx1000
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### Re: Lessons on Causality

No matter how close one could zoom into a circle there would always be room to zoom in even more. One could however zoom in beyond any individual
point. One could make the point smaller but one could still zoom in beyond it. So for both the point and the zoom it is infinite regress all the way down

If you accept that a circle has points then it must have sides too because sides are made up of points given that they are longer than them. And if it has
infinite sides [ and it does ] then it logically follows that it must have infinite points as well. But there are more points than there are sides even though
both are infinite as Cantor proved that not all infinities are the same
A MIND IS LIKE A PARACHUTE : IT DOES NOT WORK UNLESS IT IS OPEN
surreptitious75

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### Re: Lessons on Causality

Two or more points constitute a line although there is no minimum length that a point can be. And two lines
touching at their edges constitute a side. This proves that circles have both infinite points and infinite sides
A MIND IS LIKE A PARACHUTE : IT DOES NOT WORK UNLESS IT IS OPEN
surreptitious75

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### Re: Lessons on Causality

Two lines touching at their edges can be manipulated so they become a curve. So when that occurs there
is no way of knowing where those edges were and this is another reason why circles have infinite sides as
there are an infinite number of possible places on a curve where that could be. No matter how small it is
A MIND IS LIKE A PARACHUTE : IT DOES NOT WORK UNLESS IT IS OPEN
surreptitious75

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Joined: Sun Aug 27, 2017 5:48 pm

### Re: Lessons on Causality

gib wrote: I'm trying to image the points that comprise the circumference of the circle--I'm trying to zoom in with my mind's eye as close as I can to see just a few points (maybe a dozen or so) that are consecutive to each other and try to make out the curvature. I'm having difficulty. I'm finding that the simplest curve I can imagine must consist of at least 3 points. You can't have just 2 points because that would comprise a line (which is problematic in itself given that a circle is not supposed to be composed of lines). But now if these three points make up the smallest curve the circle can have, then it seems curvature is reduced to angles (3 points also make an angle).

This discourse is now approaching your limits.

Backup. A point is not a physical object or entity. A point is a location, not an entity. There is no such thing as "two consecutive points" in the physical universe. There is always an infinity of points between any and all points, between all locations.

And what that means is that it isn't two points that make up a line, fore there are always an infinity of points between those two. Two points can be used to define a particular line segment by designating the segment's beginning and end locations. Again, the "points" are not a part of the physical line. They are merely locations on the line.

Between any two points on any line, there is a center location/point on the line that is also the center of a 180 degree angle that includes the first two points. No such center points/locations exist on a circumference or curve. That is the difference between the line and the curve or circle.

There can be no lines (3 points on a 180 degree angle) on a geometric circle because EVERY point must be equidistant from a circle center.
Last edited by James S Saint on Tue Oct 03, 2017 9:02 am, edited 1 time in total.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Lessons on Causality

.....................................................................................................

These are points which means they are a physical entity because you can see them
So although a location in spacetime is the definition of a point it is not the only one
This line can be manipulated to make a circle although each point is already a circle
A MIND IS LIKE A PARACHUTE : IT DOES NOT WORK UNLESS IT IS OPEN
surreptitious75

Posts: 466
Joined: Sun Aug 27, 2017 5:48 pm

### Re: Lessons on Causality

surreptitious75 wrote:.....................................................................................................

These are points which means they are a physical entity because you can see them
So although a location in spacetime is the definition of a point it is not the only one
This line can be manipulated to make a circle although each point is already a circle

Those are dots, not geometric points. Geometric points have no width, thus could never be seen.

The smallest possible distance between any two geometric points would be no longer than the points are wide .. which is zero.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Lessons on Causality

A dot and a point are the same thing but I accept that a geometric point is not physical
So this means that a circle can only be composed of physical points not geometric ones
A MIND IS LIKE A PARACHUTE : IT DOES NOT WORK UNLESS IT IS OPEN
surreptitious75

Posts: 466
Joined: Sun Aug 27, 2017 5:48 pm

### Re: Lessons on Causality

surreptitious75 wrote:A dot and a point are the same thing but I accept that a geometric point is not physical
So this means that a circle can only be composed of physical points not geometric ones

A point is a Location, not a dot. A dot is used to represent a point. Or sometimes the center of a dot is said to be the point.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Lessons on Causality

James S Saint wrote:
gib wrote: I'm trying to image the points that comprise the circumference of the circle--I'm trying to zoom in with my mind's eye as close as I can to see just a few points (maybe a dozen or so) that are consecutive to each other and try to make out the curvature. I'm having difficulty. I'm finding that the simplest curve I can imagine must consist of at least 3 points. You can't have just 2 points because that would comprise a line (which is problematic in itself given that a circle is not supposed to be composed of lines). But now if these three points make up the smallest curve the circle can have, then it seems curvature is reduced to angles (3 points also make an angle).

This discourse is now approaching your limits.

Backup. A point is not a physical object or entity. A point is a location, not an entity. There is no such thing as "two consecutive points" in the physical universe. There is always an infinity of points between any and all points, between all locations.

And what that means is that it isn't two points that make up a line, fore there are always an infinity of points between those two. Two points can be used to define a particular line segment by designating the segment's beginning and end locations. Again, the "points" are not a part of the physical line. They are merely locations on the line.

Between any two points on any line, there is a center location/point on the line that is also the center of a 180 degree angle that includes the first two points. No such center points/locations exist on a circumference or curve. That is the difference between the line and the curve or circle.

There can be no lines (3 points on a 180 degree angle) on a geometric circle because EVERY point must be equidistant from a circle center.

I agree wholeheartedly, James. My initial thoughts which you quoted were the result of "zooming in," which as I said earlier, will introduce a whole suite of problems since zooming in to the point where you can actually see individual points is to skip over an entire infinity (allowing for paradoxes allows for more paradoxes). I assume you read on past that point as I dismissed that whole thought experiment on the grounds of these difficulties, and offered the alternative idea that circles (and lines and curves in general) are made of infinitely divisible segments, not points. Points still play a role but you have to invent them as you need them--say, for example, when you mark a point on the circumference of the circle. There's an infinite range of possible locations you could mark a point between any two other points--I agree with that--but I think it's a mistake to say the circle's circumference is made of points.
My thoughts | My art | My music | My poetry

A man convinced against his will is of the same opinion still.
- unknown source

Men must be taught as if you taught them not. And things unknown proposed as things forgot.
- Alexander Pope

Here lies the body of William J, who died maintaining his right of way.
He was right, dead right, as he sped along, but he's just as dead as if he were wrong.
- Boston Transcript

gib
resident exorcist

Posts: 8724
Joined: Sat May 27, 2006 10:25 pm

### Re: Lessons on Causality

gib wrote:circles (and lines and curves in general) are made of infinitely divisible segments, not points... I think it's a mistake to say the circle's circumference is made of points.

That is exactly true. The entire physical universe if made of "segments" or regions ("afflates"), not geometric points.

No matter how small, infinitely small, there is always an infinity of space between any two points. A point has zero width. The smallest space between two points has zero width. So when we add them together, 0+0+0, we get a total distance of zero. Even an infinity of such point pairs will still make only zero distance. A line cannot be built of points. Nor can a volume.

So a circle is made of an infinity of identical curve segments.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Lessons on Causality

Enough of the squabbling and ego-seeking James, this thread is not about you, time to get it back on track:

from a real philosophy forum, not ilp wrote:Causality and Modern Politics:

Liberal-leftists blame nothing, or objects. Conservative-rightists blame victims. But neither side, neither party, blames the cause for the action and event. For example, in light of the recent Las Vegas mass shooting, liberal-leftists immediately repeat their mantra and agenda, "ban guns!" To which the conservative-rightists will defend their base, "you are taking away guns from those who could defend themselves!" But the recent mass-shooting is exceptional. The victims could not defend themselves with guns, as the shooter was at such a vantage point that they could not return fire. Nor do people bring guns to music concerts, or elementary schools, or movie theaters, etc. And hypothetically people should not, ought not, have to bring guns to defend themselves in these 'safe' areas.

Thus most people are missing the point, and not attributing Cause to its rightful place. Liberal-leftists are afraid to blame anybody for wrongness. Conservative-rightists tend not to blame the right people. Thus there is a problem of Justice in the u.s. and western culture. Western culture lacks blame. And it lacks correct and accurate blame (Morality). Who ought to be blamed for events such as these, or throughout life, any types of events. Who ought society point the finger at?

Western society has not developed its sense of Justice, blame, morality, judicial law, etc. Again this is evident by the political base, how liberal-leftists want not "to blame anybody at all". And conservative-rightists are quick to blame the victims. If a desperate bum rapes a woman, then liberal-leftists will say "he was failed and not properly educated by society thus we are all to blame". Conservative-rightists will say, "she should not have dressed so provocatively" and "she should have carried a gun to defend herself".

Both sides can be wrong. And this fact escapes most Westerners, as, much or most or even all of their social "privileges" are built around concepts which protect some from blame, while re-directing blame and causality elsewhere. Spiritually, for pop religion, this means a redirect to godliness or some "grand author". Blame is always redirect to god or satan, a scapegoat. Thus public blame, in events such as these, tend to shift to the political left-right spectrum, or the religious "satanic" scapegoat.

This was done very early in the recent mass shooting, as even the President and other authorities mention "Evil" as the cause.

But, these are mere scape-goating compulsions. Who in Modern discourse, which majority of people, actually blame the shooter, his motivations, and him directly, as the author of his own actions? Who can truly investigate the causes of mass shootings, or 9-11, or any other catastrophe, correctly and accurately? Meanwhile average people, with average intelligence, will ascribe (false) causes to events, or people's motivations, in order to push underlying political agendas?
Urwrongx1000
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### Re: Lessons on Causality

Blaming individuals for actions and events is a very confrontational activity, which requires courage. So when a society becomes cowardly, and fears blaming the perpetrator of a crime, then he has advantage and leverage over others. Also it is dangerous to blame the 'privileged' members of society, as privilege entails an air of authority and degree of prestige such that normal rules and laws do not apply to the upper class (elites). However blame still exists. And there are many social functions in society operating to blame somebody, or something, if not the perpetrator of a crime.

What the West lacks, in my opinion, is morality, wisdom, and justice, lacks maturity which older or ancient countries and nations sometimes retain. Many cultures throughout the world approach the topic of morality differently, according to customs, social hierarchy, traditions, religious mindsets, how to approach life, how to think about the world, etc. Thus one society will find 'blame' in ways that other countries will not. The same applies for individuals. While one person maybe very courageous and outspoken, quick to point the finger and blame somebody, others will be less courageous, silent, and "keep their opinions to themselves". However that doesn't change the fact that person X caused harm Y to person Z. And because people can harm each other so grievously, systems of "justice" and law are put into place and enforced, to prevent the widespread manipulation of harm. If some people are allowed to harm others with impunity, then they will, and so society will become held hostage, captive, to the cruelty of those who are blameless for their crimes and harm of others.

I would like to go much more in depth into thoughts like this, but, this forum really lacks the interaction I require.

Thus I conclude this thread. You can find me elsewhere, if you have the drive and curiosity to do so.

Good riddance.
Urwrongx1000
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### Re: Lessons on Causality

Urwrongx1000 wrote:Enough of the squabbling and ego-seeking

Says the conspicuously defeated egotist.

Urwrongx1000 wrote:What the West lacks, in my opinion, is morality, wisdom, and justice, lacks maturity which older or ancient countries and nations sometimes retain.

Although I wouldn't argue with that.

Urwrongx1000 wrote:And because people can harm each other so grievously, systems of "justice" and law are put into place and enforced, to prevent the widespread manipulation of harm.

Systems of "justice" are not assembled to prevent harm to the populous nor establish any kind of actual justice. They are constructed entirely for the purpose of obtaining and maintaining power and control over the populous. The idea of such systems existing solely to protect the weak or abused is merely a part of its construction. Minority and feminist outcries are the obvious evidence. Long after the minority is no longer the minority and the feminine is no longer at any disadvantage, the outcries continue on and on, because power over all things is their goal, nothing at all to do with justice.

Get your actual causes straight from institutional rhetoric and appearances.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Lessons on Causality

Gib wrote:But then we can define circles in the other context--the geometric context--in which circles adhere to a very specific definition: all points equidistant from the center --> no sides. Here you can't talk about sides that are too small to see because in this context, the definition has nothing to do with visibility or how the object looks from one angle or another, or to one person or another, etc. Here, in this context, it really is black and white--all points on the circumference either are or they are not equidistant to the center. Even if a point is out by an infinitesimal amount, it is out as a fact, and therefore does not adhere to the definition.

What does "all points on the circumference" mean?
You need to ask yourself this question.

What it means is "all the points on the circumference you are focusing on".
You might be focusing on 16 points.
Or you might be focusing on 1024 points.

This means that polygons can meet the definition of circles.
Polygons can have a number of points on their boundary that are equidistant from their center.
If you're focusing on these points and ignoring all other points then they will pass the test.

That's what you are PRETENDING is not the case.

With that establish, we can now move back to the question of cause and responsibility and resolve that puppy!

Nothing can be resolved if people you are talking to do not know how to think.
I got a philosophy degree, I'm not upset that I can't find work as a philosopher. It was my decision, and I knew that it wasn't a money making degree, so I get money elsewhere.
-- Mr. Reasonable

Magnus Anderson
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