Prove a point exists

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James_S_Saint said:
We all know that. You are missing the point.
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Argumentum ad populum
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                                                                  Originally Posted by **eucharisteo**                     [forums.catholic-questions.org/images/buttons_khaki/viewpost.gif](http://forums.catholic-questions.org/showthread.php?p=5763274#post5763274)                 
             *Argumentum ad populum*
Huh? What does popular belief have to do with anything stated? :confused:
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Sorry, I just thought I was lost before. Now I’m really lost. 😊
 
Main Entry: point
Pronunciation: \ˈpȯint
Function: noun
Etymology: Middle English, partly from Anglo-French, prick, dot, moment, from Latin punctum, from neuter of punctus, past participle of pungere to prick; partly from Anglo-French pointe sharp end, from Vulgar Latin *puncta, from Latin, feminine of punctus, past participle — more at pungent
Date: 13th century
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4 a : a geometric element that has zero dimensions and a location determinable by an ordered set of coordinates
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If you can “see” (identify) a location, you have seen a point by the above definition. 🙂
 
Can’t we prove a point in topology exists by making transformations from the real number line to a topological space and use a proof for the irrational numbers as a step by step process where each irrational number occupies a single infinitely small distance along the line.

Using cuts to divide the line to prove the irrational numbers may exists. Then using induction to find that they must exist. then the limit to corresponds to any irrational number much corresponds to a limit on topological space that corresponds to a point?

I’m just throwing out quick ideas. Seems doable.
 
StillWondering said:
and use a proof for the irrational numbers as a step by step process where each irrational number occupies a single infinitely small distance along the line.
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How would you do that exactly?? Irrational numbers do NOT have real existence. That is why they are called “irrational”. :confused:
 
StillWondering said:
Can’t we prove a point in topology exists by making transformations from the real number line to a topological space and use a proof for the irrational numbers as a step by step process where each irrational number occupies a single infinitely small distance along the line.

Using cuts to divide the line to prove the irrational numbers may exists. Then using induction to find that they must exist. then the limit to corresponds to any irrational number much corresponds to a limit on topological space that corresponds to a point?

I’m just throwing out quick ideas. Seems doable.
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This sounds familiar
 
Give me a break, I KNOW what the term means. I am asking what was stated that had anything to do with popular belief. :rolleyes:
 
James_S_Saint said:
Give me a break, I KNOW what the term means. I am asking what was stated that had anything to do with popular belief. :rolleyes:
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Here’s a break…Hey Joey. …give the guy a break…

I mean you said “everyone here knows”… that falls under the same category as Argumentum ad populum

I’m just pointing it out. No need to get defensive about it. Just trying to get along to the point of rational thinking, not fallacious thinking. It’s best to refrain from such uses when trying to prove, I’m sure you know this, but I have to state it for my sake. No need to go down the wrong path on this. I pointed something odd with ByzCat and then you. Just trying to spread the wealth. 😉

BTW: Joey, is actually Fr. Joey, my children’s godfather and my friend from the seminary.
 
Well, can I suggest being a little bit more considerate and think about the usage before you interject presumption of fallacy. The statement was not an argument. At worst it would be an unfounded assertion. But the usage was not a part of any argument anyway. It was merely explanation concerning someone being “off-course” from the argument being presented. :o
 
James_S_Saint said:
Well, can I suggest being a little bit more considerate and think about the usage before you interject presumption of fallacy. The statement was not an argument. At worst it would be an unfounded assertion. But the usage was not a part of any argument anyway. It was merely explanation concerning someone being “off-course” from the argument being presented. :o
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No need for you to apologize. I’m just trying to do my part on the confusion here.
 
James_S_Saint said:
I object a bit of your use of the word “accident” in place of “effect”, but all you have said then is that your proof requires physical effect and that limits anything to only what can be sensed. So by your proof method, a point cannot be proven (along with a great many other rational things).

You have limited existence and Reality to only that which can be physically sensed. Thus logic, in your world, cannot be proven to exist at all. But of course, that means that nothing you observe (perceive) is really anything at all, because without inherent logic, nothing can be perceived.
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I see what you are saying but my main point is that you can not prove an abstract thought exists when it only exists in your mind.
 
ByzCath said:
I see what you are saying but my main point is that you can not prove an abstract thought exists when it only exists in your mind.
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My point was that if your abstract thought refers to something that you can point at, even though you cannot see it, then you have still proven that the concept (in your mind) really refers to something in the real world == exists.

In the long run, all existence is determined by your mind’s concern of it even though that seems like I’m saying that if you don’t concern yourself with it, it doesn’t exist, I am not saying that.

Your mind is actually NOT yours to dictate existence to. All your conscious mind can do is provide ordered categories for relevant concerns about existence. Thus your conscious mind, by merely declaring that a category is open and defining that category as something that you can point to in the outside “real” world, establishes that the category is valid and hence refers to an “existence” (ei. something that has effect). Even a “blank space” has affect. The blank space exists. Just as the point exists.
 
StillWondering said:
Can’t we prove a point in topology exists by making transformations from the real number line to a topological space and use a proof for the irrational numbers as a step by step process where each irrational number occupies a single infinitely small distance along the line.

Using cuts to divide the line to prove the irrational numbers may exists. Then using induction to find that they must exist. then the limit to corresponds to any irrational number much corresponds to a limit on topological space that corresponds to a point?

I’m just throwing out quick ideas. Seems doable.
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A “point” in topology is just a member of the defining set of a space. So as long as that set is nonempty, then a point exists therein.

In geometry, a “point” is typically given by an ordered n-tuple, usually a pair or triple. The same goes for it that goes for topology–that is, for any metric space, if the underlying set is nonempty, then a member thereof exists and is termed a point.

Of course, this mathematical notion of existence has nothing to do with physical existence.
 
eucharisteo said:
I took a course in college many years ago. We discussed this topic for a week. Can you prove that a point exists.
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In math, I don’t believe the existence of “point” can be proven. Point is an axiom or postulate. An axiom is a starting assumption from which propositions are logically derived. Axioms are not derived by principles of deduction or demonstrable by formal proofs. There is nothing that a point logically follows from, and therefore its existence cannot be proven.
 
James_S_Saint said:
How would you do that exactly?? Irrational numbers do NOT have real existence. That is why they are called “irrational”. :confused:
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Are you confusing “irrational” with “imaginary”?

The ratio of the circumference of a circle to its diameter (d) is a real, irrational number (π if d=1). The length of the hypotenuse of an isosceles right triangle with leg lengths of 1 is also real and irrational (√2).
 
itinerant1 said:
In math, I don’t believe the existence of “point” can be proven. Point is an axiom or postulate. An axiom is a starting assumption from which propositions are logically derived. Axioms are not derived by principles of deduction or demonstrable by formal proofs. There is nothing that a point logically follows from, and therefore its existence cannot be proven.
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Well…

Any metric space is constructed from axioms and definitions. So, for example, in Harvey Blau’s Foundations of Plane Geometry (2nd ed), we have the following axioms of incidence (p54):

I1. There are at least two different lines.
I2. Each line contains at least two different points.

Neither of these axioms explicitly state that a point exists in the space. However, from axiom I1 we have the existence of line l, and from axiom I2 we have a point A in l.

So, the existence of a point in Blau’s plane is easily proved from these two axioms. However, they are not proved to exist in any physical sense.
 
hatsoff said:
Well…

Any metric space is constructed from axioms and definitions. So, for example, in Harvey Blau’s Foundations of Plane Geometry (2nd ed), we have the following axioms of incidence (p54):

I1. There are at least two different lines.
I2. Each line contains at least two different points.

Neither of these axioms explicitly state that a point exists in the space. However, from axiom I1 we have the existence of line l, and from axiom I2 we have a point A in l.

So, the existence of a point in Blau’s plane is easily proved from these two axioms. However, they are not proved to exist in any physical sense.
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That was going to be my original response, though I would not have stated as clearly as you did.

However, my second thought was that line assumes the existence point (point being logically prior to line), and therefore any argument to prove the existence of point from the existence of line implicitly presupposes what it attempts to show. Hence that argument does not hold.

What say you?
 
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