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eucharisteo
Guest
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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liquidpele
Guest
I think therefore I am. There, that’s a point.
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Friar_David_O.Carm
Guest
What do you mean? Can you elaborate?
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Shredderbeam
Guest
If you mean a geometrical point, then no. They are abstractions, not real entities.
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eucharisteo
Guest
Topology
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eucharisteo
Guest
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Friar_David_O.Carm
Guest
If you wish to have a discussion that usually means that all parties are talking. You seem to be a little light on your thoughts.
As this Topology is a an area of mathematics, then no, one can not that a points exists as mathematice is an abstraction, as pointed out by Shredderbeam.
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eucharisteo
Guest
Proofs teach you how to think logically
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eucharisteo
Guest
This was “proven” in class
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James_S_Saint
Guest
A geometric point exists by logical declaration.
Declaration for thought cannot be disputed. They are superior to axiom.
“A = A” is a logical declaration, not in need of proof nor presumption. It is to be accepted so as to continue thought within a framework. The framework is always a set of declarations.
The only proof you need is to say, “It exists because I declare it to be a part of my understanding. And in the physical universe, it exists because I distinguish it by its effect.”
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Friar_David_O.Carm
Guest
It is impossible to philosophically prove the existence of an abstraction.
While working a mathematical proof may help you think logically it is not a philosophical issue.
Just like proving the existence of the color red. It can not be done. We have decided collectively that the word (an abstraction) red represents a certain color. It would not be out of the realm of thought to meet a society that has collectively chosen to call that same color something else. Philosophically both are correct.
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eucharisteo
Guest
During the second week of this summer class and after the professor had eaten everyone alive, the class size dropped from 35 to 12. Math is my minor. I did not really need this class but thought if would be fun. It turned out to be a nightmare. You assumption is wrong according to the professor. So now that I want to return for a graduate degree I’m trying to get my mind thinking again. I graduated in 1994 and I’m want to considering getting a math degree instead of an engineering degree, which is irrelevant for the purpose of discussion. I’m just showing my rational reasoning for wanting to discuss this. I also want to study theology since I’m considering the diaconate. I left the seminary in 1980 and would love to go back to what I’ve always wanted to do. I know priests with math and engineering degrees.
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James_S_Saint
Guest
If you are referring to my “assumption”, your professor is in error and wouldn’t be the first.
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Shredderbeam
Guest
You can declare that X exists, but that doesn’t mean that X is an entity in objective reality. X might be a mental abstraction, though, if that’s what you mean.
“A = A” is an axiom, but a point is not an axiom.
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geometer
Guest
The definition of a point is an axiom of geometry, is it not?
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James_S_Saint
Guest
Not really.
If you declare that in your thought construction an item “X” with specific properties is to exist (in thought only at this point), but then you identify something outside yourself, in reality, that happens to exactly fit the description of your declared entity, then you have discovered that your declared entity is real or exists in reality/actuality.
An example;
A tree is an abstract idea first. You then find something that actually fits the category name and description (properties) of “tree”. The category of “tree” always existed from the moment you declared it. You find later that an actual tree has also existed even before you declared it.
The tree really only exists because you declared what you observed to be a tree.
This is a necessary process of a functioning and rational mind. It cannot be avoided even by machines.
In the case of a “point in space”, it is first merely a declaration with specific properties. But those particular properties allow for you to find it in reality immediately. You immediately find an infinite number of them between any 2 objects.
In the case of a point, you do not need to physically see them because their properties are such that visible detection is impossible. Thus they must be deduced. Even though this might sound like a cop-out, in reality ALL knowledge is acquired this exact same way.
You never actually “see” anything. Everything you accept as being seen, is really only a deduction of your mind by it first declaring a category and then deducing that a stimulus pattern fits into that category. This is the nature of ALL sensory and it begins with mere contrast.
But a point in space does not require contrast and thus cannot be seen with an eye of any kind. This was a restriction to the deductive process for visible things, but it is not for things outside any visible potential.
The end result is that you merely have to declare the category and find anything that suits the category and in this case, everywhere represents another item within that category. You have “seen through declaration and deduction” that such things called points actually exist.
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geometer
Guest
People that are deaf dumb and blind know that trees exist. Hellen Keller knew, why limit existence to his declarations?
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James_S_Saint
Guest
There is an elite and very finely technical difference between an axiom and a declaration.
An axiom refers to some thought that is to be accepted before deductive argument begins. A declaration is very similar with one exception.
A declaration is not subject to belief. It is a statement that “in the following argument, this is to be true.” All labels, names, definitions, property assignments, and such are declarations, not axioms.
Every thinking thing MUST declare before it even accepts an axiom (else it wouldn’t even be able to comprehend any axiom proposed).
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geometer
Guest
Well, I have on idea what you are trying to say. Axioms or declarations seem to do exactly the same thing. They set the limits of intuition…
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James_S_Saint
Guest
And without limits, you cannot construct anything including rational thought.
"Nothing is possible until something is impossible."
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