Infinity…… Infinite? Or Finite?

With all my respect TVF, I think your pragmatic view introduces more questions that solves problems. Patrick's question is a real problem that has occupied the lives of scores os philosophers and scientists with no answer todate. Of course, when we refer to perception we do not mean a person specifically but the "collective consiousness". No one in this threads can solve this problem, I guaranty that. You can only take a stand and belong to one of the following camps:

1. Mathematical objects are part of reality
2. Mathematical objects are not a part of reality

Each camp results in different models for the world, a different path to follow, and it is not necessary that the two paths will lead to different conclusions. After all, the objective is the same: To understand the "immediately given".

My own view is that mathematical objects, such as the line, and mathematics as a whole, is just a language that attempts to model the physical world. A line is an arbitrary, and for that purpose very basic, creation of our minds and not necessarily anything that needed to be known for the universe to exist. Therefore, if all humans die, the idea of a line will die with them, since some other creatures may have never consider the line as a necessary element of their knowledge and use, for instance, the ENIL, something different than the LINE.

Zero and infinite are just logical extentions of our severely limited and linearly operating, litle primitive chemical minds. The point is we use the words but we have no clue what they mean. This is an evidence of "creative thinking" attributed only to primitive organisms.

Maybe it is time to move beyond the ideas of zero, infinity, mathematical reality and observer dependence and expand our conception beyond primitive concepts. The problem know is not Zeno's paradox but Meno's paradox, i.e. there is no way to get know something if you do not know what you looking for or what it is. You see, mathematicians solved Zeno's paradox with non-standard analysis but the paradox that remains to be solved is really Meno's.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[makis]: You can only take a stand and belong to one of the following camps:

1. Mathematical objects are part of reality
2. Mathematical objects are not a part of reality<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

My first surprise is that you "switched" the context from real objects or objects that measure reality to mathematical ones. Or maybe I just didn't understand from the outset that we were talking about mathematical objects. If I had, I would not have commented. I would agree that mathematical "lines" exist only in someone's mind.

However, I was referring to physical concepts such as dimensions (length, width, and height in space), each of which is measured by infinite lines. (In the principles of physics, we note that only dimensions, but not objects composed of substance, can be infinite.)

Another example I used was line segments, which can be physical objects. My answer to Zeno's paradoxes requires that all physical objects must be infinitely divisible, so it is more than a mathematical statement to say that a line segment has an infinite number of points within itself.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>My own view is that mathematical objects, such as the line, and mathematics as a whole, is just a language that attempts to model the physical world. A line is an arbitrary, and for that purpose very basic, creation of our minds and not necessarily anything that needed to be known for the universe to exist. Therefore, if all humans die, the idea of a line will die with them, since some other creatures may have never consider the line as a necessary element of their knowledge and use, for instance, the ENIL, something different than the LINE.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I see nothing here I disagree with. We were just talking about different things.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>The problem now is not Zeno's paradox but Meno's paradox, i.e. there is no way to get to know something if you do not know what you looking for or what it is.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I think this claim merely says in different words what I said in <i>Dark Matter...</i>, that if we use inductive reasoning, our descriptions of reality will always remain ambiguous. However, the antidote to that is deductive reasoning, the strength of which is its uniqueness. The Meta Model, for example, pointed up several essential properties of the universe that neither I nor anyone else had considered because they are too subtle to have guessed. But we were able to discover them through a deductive chain of reasoning. Isn't that a violation of "Meno's paradox" (about which I know nothing except the short description you just gave)? -|Tom|-

I see the marvellous arrogance of the anthropic principle beginning to raise its head here. On the one hand the realist, and on the other hand the metaphysicist. Neither the twain shall meet, nor shall they agree on anything, other than a nod from each that there is "something of significance" within each one's doctrine.

Patrick - infinity is a human construct - I explained it's mathematical properties a while back in another thread (I'm tempted to add a long time ago in a galaxy far, far away!). Tom's cited reference is a good exposition of the concept and related ideas. But condense it down and infinity is a label - we use it to define the unknown. It has absolutely no concrete usage in mathematics - no computation or formula works with it as a factor or employs it. I would humbly suggest that, from this viewpoint, you ignore it.

Let's talk about labels. Infinity is a label - a label is a construct of language, and language is a device humans use to communicate feelings, concepts and desires. Which brings us back to the anthropic principle (sort of). We can perceive in a fraction of the electromagnetic spectrum, an equally small portion of the audio range, and so on and so forth with touch and smell, and taste is basically a function of sweet, sour, salt and bitter (based on the receptors on our tongues). We can conceptualise, but as soon as we get to a point where our imagination can't take us, we reach for Infinity; this is our label - we talk of infinity of time (eternity), space and numbers (label system for reality). Consider infinity as that which we cannot conceive - we're limited, but unfortunately, quite arrogant in our belief in our own ability to understand the cosmic all. We've merely dipped our toes in the breakers on the shore of the universe, yet believe we have a model which explains everything.

In an attempt to throw a human net around the universe, we postulated Riemannian space (the folded space concept - in it's simplest form, space folds around on itself and forms a hypersphere, which encapsulates everything), but what lies outside this sphere? And if nothing does, then how can our hypersphere be infinite?

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Patrick - Everything that I perceived uniquely and individually will cease to exist<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

No - it won't. Your memory of perceiving it will. But this is and always will be the case.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote> Patrick - It *may* exist but in what context? Obviously something physical is more easily perceived than the metaphysical.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

But still it exists - this is sheer human arrogance - don't confuse the blessing of being capable of observing something with the very essence of that thing's existence. To test this condition, try telling a friend that their existence is very much a function of your perception of them - they will at worst suggest that your existence is equally dependent on their continued monitoring of your good self. I'd suggest that if you were going to take a mathematical viewpoint of this, then you would cancel each other, and the equation would balance, without need for either's existence.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote> Patrick - On the contrary, I agree with having the guidelines but at what point is it appropriate to question the "realists" "truths"? The "truths" were established by humans therefor they could be inacurrate. If nothing was ever questioned or challenged we would have little if any progression <hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Always question the realists' "truths". But the point is, they're open to observation by all, and can be questioned, and if proven wrong, replaced by a closer approximation to the truth. Metaphysical concepts can't, and remain with one foot firmly planted in the realm of the individual's imagination.

When I was much younger, I suggested to a group of friends that all constructs and naturally occuring objects could be labelled as thermal tubes, because everything had a tubular (topologically speaking) and thermal property, and therefore this must constitute the very essence of the Universe. This is, to use a British expression "Bollocks", but no one came up with a counter-argument. If you want to argue metaphysics, then you can do so infinitely - I wasn't being flippant in my short post above (I don't do flippancy) - that's the point, you don't achieve anything beyond an exposition of your own beliefs. If you want to reveal something about the nature of the universe, then you needs must link your beliefs to something measurable and capable of proof, at least in this forum. Belief without concrete, measurable facts is faith, and that's another story…

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>

I think this claim merely says in different words what I said in <i>Dark Matter...</i>, that if we use inductive reasoning, our descriptions of reality will always remain ambiguous. However, the antidote to that is deductive reasoning, the strength of which is its uniqueness. The Meta Model, for example, pointed up several essential properties of the universe that neither I nor anyone else had considered because they are too subtle to have guessed. But we were able to discover them through a deductive chain of reasoning. Isn't that a violation of "Meno's paradox" (about which I know nothing except the short description you just gave)? -|Tom|-

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let's get some things clear before we proceed. Some scientists use a mix of inductive and deductive reasoning, which is indeed a violation of Meno's paradox, i.e. they are simply in a total vaccum as to what they are looking for. Specifically, the mathematical idea of infinity is based on inductive reasoning. You cannot base the conclusions of deductive reasoning on premises that have been derived inductively because that simple leads, in the bast case, in circular reasoning and in the worse case, in faulty conclusions.

The problem in deductive reasoning is the premises. I repeat the example:

p1: All animals breath
p2: The unicorn is an animal

c: the unicorn breaths

Perfectly correct conclusion with one little problem: What is a unicorn?

In this respect I would say TVF that deductive reasoning is a much more potentially harmfull methodology in the hands of people.

Anyway, Socrates, the teacher of Meno, first time unable in his life to crate a little sofism to solbe the paradox, was driven to invoke the idea of the soul carrying the knowledge and, thereafter God giving the soul, and was forced to drink the conium. <img src=icon_smile.gif border=0 align=middle>

quote:
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You cannot base the conclusions of deductive reasoning on premises that have been derived inductively because that simple leads, in the bast[sic] case, in circular reasoning and in the worse case, in faulty conclusions.
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I must disagree with this quote, because it can only undermine (inadvertantly, perhaps) the usefulness of this forum.

A primary use of inductive reasoning is the use of language.

Meaning cannot be ascribed deductively, but only inductively.

What is the value of "value?" Or the goodness of "good?" One who forms such a question betrays a firm grasp of the concept, and merely pretends to propose a question.

Same with "reality."

The sciences exists in a relationship with inductive foundations. By the time of Aristotle, "metaphysics" was already considered a "hard" science, and it remains so today.

The hard and soft sciences are a part of the same reality, and they have already evolved throught their meeting-point. Let's not be derelict our understanding of science.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>
I must disagree with this quote, because it can only undermine (inadvertantly, perhaps) the usefulness of this forum.

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That's an example of inductive reasoning. Because you disagree, it is not necessary that the usefulness of the forum is undermined. Maybe only as far as you are concerned, but not generalizations please.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>

A primary use of inductive reasoning is the use of language.

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Some accepeted terms below:

Inductive reasoning: from the specific instance to the general theory
Deductive reasoning: from the general theory to predict specific instances

Scientists often develop theories through inductive logic and then test those theories by generating predictions through deductive logic and verifying empirically those predictions.

It's very simple: if the premises used in the deductive process have been derived by inductive thinking and are wrong, you're caught in a circle. That's why TVF adopts a pure deductive approach, a priori theory that must be tested to conform with reality.

Is that so hard to understand, so you will accuse me of underming the usefuleness of the forum?