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Oh, OK. Tell me, how many elephants are on your head just now?
What does that have to do with an abstract concept?
Oh, OK. Tell me, how many elephants are on your head just now?
You're the one who said numbers are just an abstract. So, why not prove it out by letting "one" elephant sit on your head and then report back to us?
Failure to do so is an admission that "zero" and "one" are not abstract after all.
Sure. I have ten thousand hairs on my head but zero dinosaurs. Why is that abstract? It's pretty concrete, even if what happens to not be on my head at the moment is a hat.
Please calamity stop now, this subject is clearly above your level, you are embarrassing yourself.
No, it's abstract...what kind of dinosaurs don't you have on your head? It's like the old joke: Jean-Paul Sartre sits in a café and says "I'd like a coffee without cream." The waitress says, "Mes excuses, Monsieur, we have no cream. Would you like your coffee without milk instead?" The whole point of the joke is that absence is an abstraction.
There is a difference between having 1 hat on your head, having 2 hats on your head, and having 1 dinosaur on your head.
There is no difference between having zero hamsters and zero dinosaurs. So both are meaningless by themselves.
Zero is no more or less abstract than any other number. Likewise with infinity, with the only exception being infinity happens to be the next number, on through infinity.
Anything can "exist" in the mind only. Ideas exist. Not all ideas have something outside of the mind that correspond in reality. We are able to make things up.
True, although this doesn't explain how they exist in the mind. Is this a part of reality? If so, they do exist in reality.
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True, although this doesn't explain how they exist in the mind. Is this a part of reality? If so, they do exist in reality.
Anyway, the point is most mathematicians believe mathematical objects, like infinity, do exist outside the human mind, hence they are objective and not created by the human mind. You seem to be taking some sort of mathematical constructivist position without arguing for it. If you say that abstract mathematical concepts are entirely subjective, you have to explain how they can have the seemingly objective qualities and uses they are put to in mathematics, and how we can know what seem to be their objective, abstract properties.
But having 5 horses is not an abstraction. Having zero horses or -5 horses is an abstract idea. Absolute zero is an abstract idea. Infinity is an abstract idea. God is an abstract idea.
Infinity is not the next number. Infinity doesn't represent a number. Infinity is an absolutely meaningless idea. Whatever you think of it is not enough. Likewise, absolute zero is meaningless. The fact that you exist to contemplate zero is proof that zero does not exist.
Math does not exist independent of human beings. Math was created, not discovered. It is a tool that has some usefulness in helping to describe reality. It is not part of reality outside of human thought.
Math does not exist independent of human beings. Math was created, not discovered. It is a tool that has some usefulness in helping to describe reality. It is not part of reality outside of human thought.
How do you know that this line of reasoning is accurate? THe conclusions that something exists conceptually does not mean it is part of reality. What do you mean 'part of reality'?? To me, 'reality' is something that physically exists, and can be examined, or the effects of it can be examined indirectly.
I did not use the term real here originally. But your definition of reality seems strange. Are concepts unreal then?
The first definition isn't really a philosophical definition of the real. Besides, those definitions rely on equally contentious terms, like substance, existence, being.
Let's put it this way, if concepts are unreal, does that mean they lack all being? If I think of the abstract concept of a triangle, does it that concept - either in itself or as a mental event - nothing at all?
Or take a term like a married bachelor and our concept of a triangle? Are they equally unreal?
The first definition isn't really a philosophical definition of the real. Besides, those definitions rely on equally contentious terms, like substance, existence, being.
Let's put it this way, if concepts are unreal, does that mean they lack all being? If I think of the abstract concept of a triangle, does it that concept - either in itself or as a mental event - nothing at all?
Or take a term like a married bachelor and our concept of a triangle? Are they equally unreal?
A married bachelor is an oxymoron. The concept of a triangle is conceptual.. We can take that conception, and create objects using that shape.. but calling that shape is a 'triangle' is conceptual. Just like saying 'that cloud is in the shape of a cow;'
I'm not sure what this has to do with the claim that the conceptual is unreal? The triangle is not quite the same as the cloud, as one is an abstract mathematical entity (the concept of a triangle is abstract and universal, not individual and particular like material things - it applies to all triangles, whatever shape or size, location or material) and also has properties that seem objective and necessary.
seem?? You have to apply the concept to something else to make it objective. It is merely a tool to describe an object. It can be used to describe an object, but in and of itself, it has no existence except conceptually.
This is not the view of most mathematicians. Mathematical entities seem to have objective properties - they are not depend upon human arbitrariness, for example exhibiting necessary relationships (that seem to hold in all possible worlds). In this sense some concept certainly seem objective.
What mathematicians can't do is physically show me a number. They can only use a number or numbers as a descriptive quality of something that exists objectively, or they can use it in a purely conceptual way.
I'm not sure what the relevance is here. What does purely conceptual mean? Is it unreal? And does that mean the same as nothing at all? If not, what is the difference?
It does not exist in reality. It is not objective. YOu can't touch it, you can't detect it. It can be used to describe something.. as a symbol. Other than that, you are just trying to analyse things beyond which there is any meaning.
No, because I am not entertaining your irrelevant point.So, you are not willing to test your hypothesis. I should have known.