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JimmyRay

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- Thread starter JimmyRay
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JimmyRay

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rygar

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my analysis might be a bit rusty, but here's what i remember.

the first meditation deals with how we can't trust our senses because we might be dreaming. however, our sense of logic is intact.

the second meditation deals with how we can't trust our logic either, because we may be being controlled by an evil demon (many analogies have been made to The Matrix, if you've seen it)

the third meditation... is not worth reading, IMHO. it's a crappy "proof" of god's existence, that contradicts his earlier meditations. however, many scholars believe he only added this proof of god's existence due to pressure from the church. keep in mind, he lived around the same time as galileo, who was sentenced to house arrest for contradicting the church. this is further supported by the enscription on his gravestone, which translates to "he who hides well, lives well". sneaky bastard!

i haven't read any of the other meditations.

anyway, i think it's the second one that states the famous "Cogito ergo sum", or, "I think therefore I am". his philosophy was that you can doubt that I exist, or you can doubt that the Earth exists... you can doubt pretty much anything. However, it's hard to justify doubting doubt. If you doubt doubt exists, there is still doubt! a better phrasing of his words might be to say "Doubt exists.", and that's all we can prove. make of it what you will.

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JimmyRay

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Icebreaker, so a proof is based on ASSUMPTIONS, which are self evident... ? Maybe I don't understand this but If its based on assumptions, is it really proving anything?

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Different assumptions allow you to prove different things. The key is finding the logical assumptions that are self-evident. If something you're trying to prove is not self-evident, then break it down, look at it and see if you can spot any ambiguities in the components -- anything that can be refuted, or anything that simply doesn't make sense; if so, break them down further until you arrive at the fundamental parts of the argument which are self-evident while eliminating the flawed ones. If you can rebuild your original argument with these, then your proof has merit.

How well you can break them down and analyse them determines how rigorous your proof is. This applies to any field.

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Paul Wilson

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But surely, an assumption is mearly speculation or 'what you think something will be' and 'what you think something will be' is most definitely speculation.Icebreaker said:

IMO, Rygars post makes the most sense. We can only doubt everything - except doubt itself - as doubting something is doubt.

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If you assume nothing, then you can prove nothing.

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JimmyRay

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Nothing can be proven then, except doubt... ?

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Selfless

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Everything is an illusion, except that that creates the illusion.

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Jameson

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MHB

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Selfless

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rygar

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but does that mean it's not worth trying?

i don't think that's true. there is a long list of major philosophers that covered these issues.

do you really need something to be 100% justified to take it as fact? if it's not conclusive, does that mean it's a mere speculation? maybe justification is a sliding scale, and not a dichotomy?

i guess to me, i have that small spot in my head that says "yeah, descarte is right, we can't prove anything"... but it's overshadowed by a plethora of inductive evidence that states elsewise. so if i can't justify induction (which no one can, by the way), i guess I'm screwed.

but I'm not going to sweat over it, because the world i live in is all i have to go by!

sure, i guess it's true that a lot of evidence used to "prove" something would be based on inductive premises, but if it's all i have to go by, i'll take it over nothing!

- #13

moving finger

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Descartes' best quote (to my mind) is :rygar said:read decartes meditations!

...a better phrasing of his words might be to say "Doubt exists.", and that's all we can prove. make of it what you will.

If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things.

Rene Descartes, Discours de la Méthode. 1637

MF

- #14

moving finger

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I agree that all "proofs" ride on the back of assumptions (or axioms). There is no proof in existence which does not somewhere assume something.Icebreaker said:

Different assumptions allow you to prove different things. The key is finding the logical assumptions that are self-evident. If something you're trying to prove is not self-evident, then break it down, look at it and see if you can spot any ambiguities in the components -- anything that can be refuted, or anything that simply doesn't make sense; if so, break them down further until you arrive at the fundamental parts of the argument which are self-evident while eliminating the flawed ones. If you can rebuild your original argument with these, then your proof has merit.

How well you can break them down and analyse them determines how rigorous your proof is. This applies to any field.

I think one can sum up "truth" in one phrase : "logical consistency"

I believe our world must be logically consistent (ie we could not be living in a logically inconsistent world).

This means that whatever view we have of "truth" or "reality", we must always endeavour to ensure that it remains logically consistent.

Aside from this - anything is possible!

The only question that remains is : Is there more than one possible logically consistent world?

MF

- #15

moving finger said:The only question that remains is : Is there more than one possible logically consistent world?

Well, to give a mathematical example: non-Euclidean geometry.

- #16

<<<GUILLE>>>

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First, I can ussume something, it doesn't mean that you have prove it. I can assume that E=mc^3 but it isn't it's E=mc^2 and only the fact that I ssume that it is the first equation, it doesn't mean it's correct.

Secondly, someone said up there that everything is an illision except that that created the illusion. Well, that leads to paradox...If everything is an illusion except, and only except that that creates the illusion, then the illusion itself isn't an illusion, contradicting it's own meaning, but if the illusion is an illusion, it is contradicting the statement.

Thridly, here we are asked if it is possible to prove, and if this is able, how to prove and why this is to proof. Not about what most people are talking which is about what proving is. But let's define proof, maybe this is ok: the demonstration of something. It can be via many ways, it can be proof or disproof, it can be proving something true... Now, if proving is the demonstration of something, how can we demosntrate something? Really, I'm not sure that we actually can. We know what it is, and it's nature, but we can do it because most probably it is something that depends on nature. If any of you knows how to prove and why that is a prove, please tel me because that I really don't know.

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moving finger

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which is an example of a geometry; not (with respect) an example of a logically consistent world.Icebreaker said:Well, to give a mathematical example: non-Euclidean geometry.

MF

- #18

selfAdjoint

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moving finger said:which is an example of a geometry; not (with respect) an example of a logically consistent world.

MF

And the non-euclidean geometry of Lorentzian spacetime. This is not proposed as a logically self-consistent world? Not a model but an assertion that this is the way the world really is? (I know there are objections to this from the particle physics community, but Freeman Dyson, for example, isn't persuaded by them).

- #19

moving finger

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No, it is proposed as the "geometry" of a logically self-consistent world.selfAdjoint said:And the non-euclidean geometry of Lorentzian spacetime. This is not proposed as a logically self-consistent world? Not a model but an assertion that this is the way the world really is? (I know there are objections to this from the particle physics community, but Freeman Dyson, for example, isn't persuaded by them).

The map is not the territory.

And the geometry is not the entirety of the world.

The world is not asserted to be non-Euclidean; even if the "geometry of the world" may be asserted to be non-Euclidean.

MF

- #20

JimmyRay

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Our views on reality must be consistant because there is no real way of proving anything.. so we have to follow some model? And make it logical?

Also you agreed that all proofs are based on assumptions... Does that make them proofs? Is proof meant to be based on assumption or does proof mean no assumption?

- #21

inquire4more

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Also, we always have axioms in any system. These axioms are, well, really assumptions, but assumptions we hold to be self-evident. That is, there will probably be wide-ranging agreement as to their truth. These are necessary. The moment we throw away all assumptions, our foundation, so to speak, we lose our construction. We need some "ground" to proceed from. But, keep in mind, these are not arbitrarily chosen assertions, they are well-accepted. Something akin to "There is a number one." and "For every number, there is a successor." We generally all see the truth of such statements.

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inquire4more

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- #23

moving finger

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See post #14 of this thread.JimmyRay said:Moving finger, I was following you up until you said logical consistency... What exactly do you mean by this?

proofs normally adhere to the rules of logic.JimmyRay said:Our views on reality must be consistant because there is no real way of proving anything.. so we have to follow some model? And make it logical?

in logic, "proof" usually means : take one or more axioms, work on them with a set of inference rules, and from that derive an inference (sometimes called a conclusion).JimmyRay said:Also you agreed that all proofs are based on assumptions... Does that make them proofs? Is proof meant to be based on assumption or does proof mean no assumption?

It's a bit like axioms are the ingredients, the inference rules are the recipe, and the conclusion is the pudding.

As far as I am aware, it is not possible to prove anything unless one starts with axioms (but I will gladly be proven wrong!)

In other words, you can't make pudding without the ingredients; but even if you take the ingredients but don't follow the recipe, you end up with a mess instead of pudding.

MF

- #24

moving finger

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a world is not the same as a geometry.inquire4more said:Ok, I'm not really clear where the difference exists between a consistent world and a consistent geometry. Let's assume for sake of argument our geometry is Euclidean (it's probably not, but bear with me). There may well be a universe which is spherical in geometry (or of some other such non-Euclidean geometry). This universe, world, whatever, would indeed be self-consistent, at least as concerns its geometry.

a Euclidean geometry is a geometry. it is not a "world".

a Euclidean geometry may be a self-consistent geometry, but it does not follow from this that a world based on a Euclidean geometry is a self-consistent world.

MF

- #25

selfAdjoint

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moving finger said:No, it is proposed as the "geometry" of a logically self-consistent world.

The map is not the territory.

And the geometry is not the entirety of the world.

The world is not asserted to be non-Euclidean; even if the "geometry of the world" may be asserted to be non-Euclidean.

MF

Absolutely wrong. GR is/was proposed as the world; the geometry IS the physics, get off your little Korzybski podium and look at what Einstein actually says! GR is NOT the map (so it is claimed by its proponents) it is the TERRITORY in reality.

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inquire4more

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moving finger said:a world is not the same as a geometry.

a Euclidean geometry is a geometry. it is not a "world".

a Euclidean geometry may be a self-consistent geometry, but it does not follow from this that a world based on a Euclidean geometry is a self-consistent world.

MF

Then please, explain to me what you mean by the term "world." You've given one instance of what a world is not, namely a geometry. I'm not sure I agree with this, but that's not relevant. What exactly, then, is this world you refer to? I can't but help think of it as the geometry of the universe. I guess this is just where mathematicians differ from everyone else. For us, so often, the map is the territory. It does not merely describe the thing, it is the thing. At any rate, what is "world?" Sorry about my digression there.

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JimmyRay

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lol... okay I understand the axioms...

Whats Euclidean geometry :( .

Whats Euclidean geometry :( .

- #28

inquire4more

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JimmyRay said:lol... okay I understand the axioms...

Whats Euclidean geometry :( .

No worries mate. That's just the regular old geometry you learned in junior-high or high-school. The geometry of the rigid x-y-z axes (I won't bother to generalize it here). Where the interior angles of a triangle sum to [tex]\pi [/tex] radians, or 180 degrees, and all is right with the world.

- #29

JimmyRay

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Also, is gravity an axiom, or a proof? Because, it's self-evident but there's nothing to assume...I can see how the number 1 is an axiom because you have to assume it exists since it's abstract... But what about gravity? It is easily seen...

- #30

inquire4more

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JimmyRay said:

Also, is gravity an axiom, or a proof? Because, it's self-evident but there's nothing to assume...I can see how the number 1 is an axiom because you have to assume it exists since it's abstract... But what about gravity? It is easily seen...

No, Euclidean geometry is completely self-consistent. As are non-Euclidean geometries. Key phrase here is self-consistent. May not be consistent with other models or conceptions of geometry, but self-consistent. That is, you do not arrive at any false statements in the geometry when proceeding logically from the axioms of that geometry. Gravity an axiom or a proof? I don't really understand your question, sorry. Gravity exists. I am sure one of the physicists here would be able to give you some idea of just what it is. I'm sorry that I can't really help you there.

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