What Is Your Ontology Of Mathematics?

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What Is Your Ontology Of Mathematics?

What I am asking is: What is the ontological statis of mathematics? Do numbers exists? If so, what IS a number? How do numbers exist?

Explain your Philosophy Of Mathematics. For ideas, here is my Philosophy Of Mathematics:

numbers, their relations, and mathematical propositions are fundementally platonic in nature. What does this mean? This means, that a mathematical proposition such as "there cannot be finitely many prime numbers" exists immaterially and atemporally (not extended in space).

If you want me to defend this view, please ask. OR, if you have questions, please ask.

*waits for todangst to come...* Eye-wink

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Teralek wrote:You know what

Teralek wrote:


You know what amazes me the most about this atheist/theist clash is the desperation people have to protect their most beloved belief on the face of new facts without asking themselves: "Could I be wrong??".

  Of course I could be wrong, that's why I think of myself as an agnostic atheist, ( weak atheism, etc ).  As a former Christian theist I was much more inclined to be dismissive of counter-arguments as my opinions/beliefs were supposedly buttressed by divine revelation and to disagree with me was the same as disagreeing with God.

   Despite Christianity's status as a still functioning religion, the possibility of the Christian God existing is no more compelling than the other god/s of the so-called "myths" of ancient religions....and who defends belief in Zeus, anymore ? 

   http://en.wikipedia.org/wiki/Agnostic_atheism

   http://en.wikipedia.org/wiki/Agnostic_theism


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'Numbers' are our way of

'Numbers' are our way of conceptualizing an aspect of reality that we perceive, which follows from our classifying what we perceive into discrete entities. It a description of a basic feature of a multiplicity of associated discrete objects, ie 'how many of them there are. A number of other creatures are able to recognize different numbers of objects, ie to 'count' up to small numbers.

EDIT: Just saw today a program on Monitor Lizards, where they said that one they have been conducting tests with was able to count to six. They had trained it to wait until it had been fed a given number of items of food before doing some other action.

'Number' exists as a particular pattern of thoughts in a mind, it is a truly 'immaterial' thing, ie, it has no persistence or existence as any kind of 'thing' outside our imaginations.

 

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris

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Chaoslord2004 wrote:What I

Chaoslord2004 wrote:
What I am asking is: What is the ontological statis of mathematics? Do numbers exists? If so, what IS a number? How do numbers exist? Explain your Philosophy Of Mathematics. For ideas, here is my Philosophy Of Mathematics: numbers, their relations, and mathematical propositions are fundementally platonic in nature. What does this mean? This means, that a mathematical proposition such as "there cannot be finitely many prime numbers" exists immaterially and atemporally (not extended in space). If you want me to defend this view, please ask. OR, if you have questions, please ask. *waits for todangst to come...* Eye-wink

Mathematical abstractions do not have any ontological status outside a mind that abstracts. If you believe that they do, then you are making a transcendental argument for the existence of God.

"Scientists animated by the purpose of proving they are purposeless constitute an interesting subject for study." - Alfred North Whitehead


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BobSpence wrote:'Numbers'

BobSpence wrote:

'Numbers' are our way of conceptualizing an aspect of reality that we perceive, which follows from our classifying what we perceive into discrete entities. It a description of a basic feature of a multiplicity of associated discrete objects, ie 'how many of them there are. A number of other creatures are able to recognize different numbers of objects, ie to 'count' up to small numbers.

EDIT: Just saw today a program on Monitor Lizards, where they said that one they have been conducting tests with was able to count to six. They had trained it to wait until it had been fed a given number of items of food before doing some other action.

'Number' exists as a particular pattern of thoughts in a mind, it is a truly 'immaterial' thing, ie, it has no persistence or existence as any kind of 'thing' outside our imaginations.

 


Imagination is material. Unless you want to show me how imagination exists without a brain. 

"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'


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 Yo man! you just

 Yo man! you just resurrected a post two years old after you spent all this time thinking of an answer. 

I think immaterial things exist as well! The pain I feel when you stab me is very real! Imagination is not material, it's an emergent property of the brain. Emergent properties exist. The fact that it cannot be by itself is doesn't say it's material


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Without the brain the

Without the brain the emergent property would not exist, hence the emergent property is material.

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Vastet wrote:Without the

Vastet wrote:
Without the brain the emergent property would not exist, hence the emergent property is material.

Sorry my canadian friend. That's an assumption and you are free to have it given the facts we possess. As I have my own.


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It is as much an assumption

It is as much an assumption that gravity exists. Just because you'd like to believe otherwise does not make it so.

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Teralek wrote: Yo man! you

Teralek wrote:

 Yo man! you just resurrected a post two years old after you spent all this time thinking of an answer. 

And then you went and ignored it!

Quote:

I think immaterial things exist as well! The pain I feel when you stab me is very real!

And material. Pain is produced by sensory neurons. We can identify the processes. They are material.

 

Quote:

Imagination is not material, it's an emergent property of the brain. Emergent properties exist. 

 

Materialism includes emergentism!  Imagination is material. Unless you want to show me how imagination exists without a brain. 

"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'


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Strafio wrote:RandomIdiot

Strafio wrote:

RandomIdiot wrote:
Lastly I know this is an old thread and you may all have moved on from what is written here but I've just found this page, so cheers if you bother to read it.

Funnily enough, I still hold the same position.
Whether the other guys have moved on from their position; they seem to have moved on from the entire site so I can't be sure.
It's a shame really... 3 years on and I still want to know what ChaosLord made of my last post! Eye-wink

 

 

todangst wrote:
Numbers exist in material brains. They are encoded electrochemically, in neurons. They are relational abstractions. Ideas that help sentient beings create relationships between entities, either real or hypothetical. Their existence depends upon the existence of sentient brains. No brains, no numbers. Why do numbers appear "Transcendant"? Because the universe itself transcends the individual brain, the universe impressess itself upon sentient brains in the same fashion.

RandomIdiot wrote:
Making the universe an active principle here seems like superstition. I think we relate to the universe, not it to us. If such a relationship between the universe and brain exists physically then it is by way of our perceptual access to the universe. This seems problematic to me in the following ways:

Seemed like a fair objection to me.
The bit in bold does seem quite strange; claiming that the expanse of the universe gives us the impression of transcendent numbers.
Perhaps if he returned he could elaborate more on what he meant by this.

 

 

What an odd reading. Where do I cite the literal expanse of the universe as the cause?  The point is that the universe is the single constant, the 'substratum' if you will. Sentient brains are capable of generating the same numbers given that they exist in the same universe, with a consistent identity. THe universe could be the size of a closet and still allow for this result. 

 

"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'


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Teralek wrote:I think

Teralek wrote:

I think immaterial things exist as well! The pain I feel when you stab me is very real!

todangst wrote:

And material. Pain is produced by sensory neurons. We can identify the processes. They are material.

 

Ah my friend but this IS what you seem unable to understand! we can know everything that is to know about pain! All the neurons and processes and such but if you never felt pain you would have no clue what REALLY is pain. The Qualia of something is something with an absolute existence in my opinion.

Another example is Mary...

"Mary the colour scientist knows all the physical facts about colour, including every physical fact about the experience of colour in other people, from the behavior a particular colour is likely to elicit to the specific sequence of neurological firings that register that a colour has been seen. However, she has been confined from birth to a room that is black and white, and is only allowed to observe the outside world through a black and white monitor. When she is allowed to leave the room, it must be admitted that she learns something about the colour red the first time she sees it — specifically, she learns what it is like to see that colour."

 

 


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I will never understand

I will never understand theists completely, because of that kind of argument. It says nothing and goes nowhere, yet they seem to think it proves something.

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Vastet wrote:I will never

Vastet wrote:
I will never understand theists completely, because of that kind of argument. It says nothing and goes nowhere, yet they seem to think it proves something.

I believe that people here look at the badge before answering a post... forget the fact that I'm theist. This philosophy is sound and was developed by many who are not theists. This is purely a critic to physicalism nothing else.


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Teralek wrote:Teralek

Teralek wrote:

Teralek wrote:

I think immaterial things exist as well! The pain I feel when you stab me is very real!

todangst wrote:

And material. Pain is produced by sensory neurons. We can identify the processes. They are material.

 

Ah my friend but this IS what you seem unable to understand! we can know everything that is to know about pain! All the neurons and processes and such but if you never felt pain you would have no clue what REALLY is pain. The Qualia of something is something with an absolute existence in my opinion.

Another example is Mary...

"Mary the colour scientist knows all the physical facts about colour, including every physical fact about the experience of colour in other people, from the behavior a particular colour is likely to elicit to the specific sequence of neurological firings that register that a colour has been seen. However, she has been confined from birth to a room that is black and white, and is only allowed to observe the outside world through a black and white monitor. When she is allowed to leave the room, it must be admitted that she learns something about the colour red the first time she sees it — specifically, she learns what it is like to see that colour."

 

 

So Mary does not know "all the physical facts" because what color looks like to her is a physical fact. Knowing how other people see color is not the same as knowing how you are going to see it since viewing color is completely subjective. You posit a scenario where Mary knows all facts except for one, so obviously when she learns that new fact she knows one new thing. That doesn't change that Mary seeing red is a material process and a material process which is different (albeit similar to) John seeing red. 

If, if a white man puts his arm around me voluntarily, that's brotherhood. But if you - if you hold a gun on him and make him embrace me and pretend to be friendly or brotherly toward me, then that's not brotherhood, that's hypocrisy.- Malcolm X


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 Ok then. So explain to me

 Ok then. So explain to me in physical terms what means to subjectively see the red color? Your own words: "...because what color looks like to her is a physical fact"

Please don't say "...when the human eye sees red (and the optic nerve transmits particular types of signals, and the visual cortex processes these signals, etc)." Because that is not actually seing red color.

The "raw sensation of experience" is beyond direct physical observation and at it's core is ineffable. It's the most pure subjective experience that a human can have.

"The hard problem of consciousness may not be solved purely by neuroscience" - David Chalmers

 


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Teralek wrote: Ok then. So

Teralek wrote:

 Ok then. So explain to me in physical terms what means to subjectively see the red color? Your own words: "...because what color looks like to her is a physical fact"

Please don't say "...when the human eye sees red (and the optic nerve transmits particular types of signals, and the visual cortex processes these signals, etc)." Because that is not actually seing red color.

Then what is it? How else do we see color other than our optic nerves and all the activity that happens in our brain to interpret it? Unless you can point to a case where someone was unable to see a color with everything we have identified in our optic system working perfectly there is no reason to believe there is anything else to it and an if we do find such a case it is a very large leap to believe that there is something non-material rather than something material we just have not identified yet.  

 

Teralek wrote:

The "raw sensation of experience" is beyond direct physical observation and at it's core is ineffable. It's the most pure subjective experience that a human can have.

"The hard problem of consciousness may not be solved purely by neuroscience" - David Chalmers

It is only ineffable in that our language is imperfect and it is impossible to perfectly convey meaning and descriptions using it. Just because we are unable to accurately relay our physical experiences to others has no relevance to whether or not those experiences are material. It is a commentary on our ability (or lack thereof) to communicate with others. Such sensations also provide the unique problem that no one else in the world can have the exact same sensation that you have because every brain is unique and doesn't interpret things exactly the same as any other brain.

As such I can read Robert Parker's reviews of wine while sipping on the same vintage, but I will never truly know exactly what he experiences. Perhaps at some point in the distant future we will find a way to experience sensations as they are experienced in someone else's head. However, I think it is a mistake to assign some extra-material influence simply because we don't currently have the technology to really observe a person's consciousness. We know we are technologically limited when it comes to studying the brain and what we have that can measure activity within it is likely going to be considered very crude even in the near future. All you have is a "god of the gaps" argument and while you are not filling it with a tradition deity, there is no reason to believe there is something extra-material. 

 

Edit:

lol I just read the review on the coffee I am drinking,

Quote:

Delicately earthy and tartly fruit-toned. Fresh-cut cedar, chocolate, green grape, plum with a hint of flowers in aroma and cup. Bright, lively acidity; syrupy mouthfeel. Flavor consolidates in a sweet, rich, slightly drying finish.

Just reading the review you wouldn't even know if it was coffee or wine being reviewed. Pretty sure I have read the exact same review for a bottle of wine at some point. The inadequacies of language. 

 

If, if a white man puts his arm around me voluntarily, that's brotherhood. But if you - if you hold a gun on him and make him embrace me and pretend to be friendly or brotherly toward me, then that's not brotherhood, that's hypocrisy.- Malcolm X


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 Here comes God again...

 Here comes God again... I'm just criticizing physicalism not putting a God in the gap... that's the true leap of conclusion...

Clearly we don't interpret this phenomenon in the same way. I say that this stubbornness to say that everything that is real HAS TO BE physical is extremely narrow minded. On top of it Quantum mechanics now shows that particles are not real in classical terms.

There may be a new paradigm we havent found out yet. This is not an empty assertion.

Our language being limited to accurately convey qualia to others it's not saying that it's our fault for having an imperfect language. It is instead saying something deep about qualia. It is saying that there is a Unique "I" forever alone in it's own head. This I is the emergent PERCIEVER of what it's eyes and brain cells can SEE.

How can I define this "I" in words or physical terms? you may ask. I can't! But the wonderful thing is I don't need to! You are experiencing it right now inside your head!! It seems impossible to concieve how can reductionist phenomenons like eletrical impulses in neurons give rise to something like the "I".

One indication that this might be right is the fact that dispite the great complexity of modern computers we are still not able to create a true AI awareness.

If we can someday create AI with classical computers (transistor based) I will truly say: Beyond Saving was right!

In sum there are some hints that there may exist in reality a paradigm which is not physical as we know it.

I have to say that I don't like Occam's Razor, and I don't like it since I saw Contact (the movie). Because it closes my mind to imagination and possibilities and makes me lazy. I preffer Sherlock holmes "when you have eliminated the impossible, whatever remains, however improbablemust be the truth"

... we are getting a bit away from the OP... it's still related nontheless... because deep down we are arguing about the reality of abstractions.


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Teralek wrote:Vastet wrote:I

Teralek wrote:

Vastet wrote:
I will never understand theists completely, because of that kind of argument. It says nothing and goes nowhere, yet they seem to think it proves something.

I believe that people here look at the badge before answering a post... forget the fact that I'm theist. This philosophy is sound and was developed by many who are not theists. This is purely a critic to physicalism nothing else.

The badge may have caused me to label you as a theist more casually, but your argument is faulty regardless.

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Teralek wrote: Here comes

Teralek wrote:

 Here comes God again... I'm just criticizing physicalism not putting a God in the gap... that's the true leap of conclusion...

Clearly we don't interpret this phenomenon in the same way. I say that this stubbornness to say that everything that is real HAS TO BE physical is extremely narrow minded. On top of it Quantum mechanics now shows that particles are not real in classical terms.

There may be a new paradigm we havent found out yet. This is not an empty assertion.

Our language being limited to accurately convey qualia to others it's not saying that it's our fault for having an imperfect language. It is instead saying something deep about qualia. It is saying that there is a Unique "I" forever alone in it's own head. This I is the emergent PERCIEVER of what it's eyes and brain cells can SEE.

How can I define this "I" in words or physical terms? you may ask. I can't! But the wonderful thing is I don't need to! You are experiencing it right now inside your head!! It seems impossible to concieve how can reductionist phenomenons like eletrical impulses in neurons give rise to something like the "I".

One indication that this might be right is the fact that dispite the great complexity of modern computers we are still not able to create a true AI awareness.

If we can someday create AI with classical computers (transistor based) I will truly say: Beyond Saving was right!

In sum there are some hints that there may exist in reality a paradigm which is not physical as we know it.

I have to say that I don't like Occam's Razor, and I don't like it since I saw Contact (the movie). Because it closes my mind to imagination and possibilities and makes me lazy. I preffer Sherlock holmes "when you have eliminated the impossible, whatever remains, however improbablemust be the truth"

... we are getting a bit away from the OP... it's still related nontheless... because deep down we are arguing about the reality of abstractions.

The issue that I have with this argument, is that the proponent never provides an alternative.  You are simply arguing against physicalism, but everything can be explained in terms of physical presence, save certain aspects we do not have the technology for, yet.  However, we can expand from our current knowledge to provide theories on how physicalism explains those odd phenomena.  Those arguing against it, fail to provide this "other" by calling it nonsense terms like "immaterial" or "spiritual" or whatever.  Calling something "not something" without a necessity for its existence, is not an argument or a definition.

Define this immaterial property you are trying to promote and I will listen to your theory.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc


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Alternative is presented, I

Alternative is presented, I believe, in the philosophical zombie argument. In case of conscience and it's raw perceptions.

In case of abstract numbers and the ontology of mathematics perhaps Einstein can clarify: "The most incomprehensible thing about the universe is THAT it is comprehensible."  This is in a peculiar way, telling us something about the ontology of mathematics and that it exists appart from physical reality.

There is no proof of this, it's just an interpretation of the observable reality processed subjectively by a brain...

However I believe that computational science and it's developments might give light to the question of conscience. Basically I think if we can develop conscience with binary microprocessors then Roger Penrose is wrong. But if we can only develop conscience with quantum computing he was right.

I bet he is right.

Finally I just want to say that deep down I feel that physicalist provides no alternative as well given it's strong materialistic sense. (everything that exists HAS to be physical or else does not exist). So basically I can accuse you of the same sin.

We should keep our minds open that's all, even to outrageous possibilities.


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A philosophical argument

A philosophical argument does not equal a viable alternative.

And why should a 'physicalist' provide an alternative? There is no alternative, that's the whole point.

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Vastet wrote:A philosophical

Vastet wrote:
A philosophical argument does not equal a viable alternative. And why should a 'physicalist' provide an alternative? There is no alternative, that's the whole point.

I disagree. The fact that physicalism is not falsifiable actually doesn't help much. Science starts has a philosophical thought and premises and builds up from there. Science gains a lot of points due to it's empirical nature which is very consistent, but that doesn't mean this is the end of the story and there is nothing else.

Penrose work for example shows that some things in the world is not computational, and he says he can prove this mathematically. Meaning that some things are true but cannot be proven by mathematics. And that this relates to consciousness.

I'm not saying that there is a reality forever hidden and appart from measurement. I don't know. What I'm saying is that there are things in reality that might not be recognizable as standard physics... yet. but in the future they can be. Like QM, dispite being weird it is today part of the natural world. Other weird things will come.

I must say that we are actually watching a change in the minds of physicists regarding what the physical world REALLY means. Quantum information theory is gaining a lot of people under it's umbrella. More and more physicists are embracing the idea that reality is not really made of matter but made of information.

http://arxiv.org/abs/1301.1069


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How is physicalism

How is physicalism unfalsifiable?
Science does not start with philosophy. Science starts with observation. Philosophy has very little to do with science.
If there is something else, why has noone ever been able to prove it or even suggest it scientifically in tens of thousands of years? Immaterialism is a red herring at best.

"I don't know. What I'm saying is that there are things in reality that might not be recognizable as standard physics... yet. but in the future they can be. Like QM, dispite being weird it is today part of the natural world. Other weird things will come."

That's 100% "physicalism". Why should anyone bother with non-physicalism when physicalism has worked every single time, and has never failed to explain something given sufficient time?

"I must say that we are actually watching a change in the minds of physicists regarding what the physical world REALLY means. "

That's been happening for thousands of years. The only difference today is the rate of change, which makes perfect sense.

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Vastet wrote:How is

Vastet wrote:
How is physicalism unfalsifiable? Science does not start with philosophy. Science starts with observation. Philosophy has very little to do with science. If there is something else, why has noone ever been able to prove it or even suggest it scientifically in tens of thousands of years? Immaterialism is a red herring at best. "I don't know. What I'm saying is that there are things in reality that might not be recognizable as standard physics... yet. but in the future they can be. Like QM, dispite being weird it is today part of the natural world. Other weird things will come." That's 100% "physicalism". Why should anyone bother with non-physicalism when physicalism has worked every single time, and has never failed to explain something given sufficient time? "I must say that we are actually watching a change in the minds of physicists regarding what the physical world REALLY means. " That's been happening for thousands of years. The only difference today is the rate of change, which makes perfect sense.

Well you are excused for making such a comment, for sure you are not a scientist!

In the foundations of science there is philosophy. There would be no science without philosophy! http://en.wikipedia.org/wiki/Science

The scientific method itself was developed by philosophy! That is the most innacurate comment I've seen from you!

Moreover: "Falsifiability or refutability is the trait of a statement, hypothesis, or theory whereby it could be shown to be false if some conceivable observation were true. In this sense, falsify is synonymous with nullify, meaning not "to commit fraud" but "show to be false". 

Can you, in your mind, imagine a concievable observation that would indicate that physicalism might be false?!

Finally it is more than clear (as I've shown before) that scientists are embracing Quantum information theory more and more. Which basically says that reality is not made of matter but information - Immaterial. If you can grasp the true meaning of the double slit experiment you may wonder the same.

There is a difference between physics and physicalism and you seem to be mixing the two.

Physics: "knowledge, science of nature"

Physicalism: "Physicalism is a philosophical theory holding that everything that exists is physical, that is, that there are no things other than physical things. Physicalism is often called "materialism"

I can see the not so crazy possibility that the definition of physics in the future changes from "the study of matter" to "the study of information" or something similar.

I think it's important for websites like this to exist, to counter the insanities of religious thought in society. But please don't you be guilty of the same sins of those you wish to destroy. Let the mind wonder into possibilities and don't be afraid of considering interpretations which are not intuitive when everything else fails. Studies that you think cannot bring anything usefull must be done despite, if others think otherwise.


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"In the foundations of

"In the foundations of science there is philosophy. There would be no science without philosophy! http://en.wikipedia.org/wiki/Science"

Wrong. The foundation of science is observation. The foundation of philosophy is also observation.
But you are excused for making such a comment, because you are certainly not a scientist!

"The scientific method itself was developed by philosophy! That is the most innacurate comment I've seen from you!"

Strawman. I never said philosophy has nothing to do with science, I said it has little to do with science. Making up arguments will not serve your point.

"Finally it is more than clear (as I've shown before) that scientists are embracing Quantum information theory more and more. Which basically says that reality is not made of matter but information - Immaterial."

Bullshit. Quantum physics depends completely upon "physicalism" or "materialism". However you want to call it.
All information requires material to exist, hence it is material. Your continuous inability to...

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...show anything which is

...show anything which is not material continuously invalidates your argument.

"There is a difference between physics and physicalism and you seem to be mixing the two."

Not in the context we are discussing. The laws of physics describe the physical nature of nature. Which requires a 'materialist' point of view.

"I can see the not so crazy possibility that the definition of physics in the future changes from "the study of matter" to "the study of information" or something similar."

Only because you don't understand either information or physics can you be forgiven for making such an ignorant claim.

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 Your logic and fanaticism

 Your logic and fanaticism is thick like a brick. I rest my case, no point discussing this further with you.


Vastet
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Teralek wrote: Your logic

Teralek wrote:

 Your logic and fanaticism is thick like a brick. I rest my case, no point discussing this further with you.

The final refuge of the theist: Projection.

Thanks for conceding the argument. Smiling

Enlightened Atheist, Gaming God.


Teralek
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 say what you like. you

 say what you like. you people just show over and over your prejudice. The true strawman here is your waving of the Theist flag out of the blue.

You attack the badge not the idea.

It's pointless to proceed further. We would be just saying "no. you're wrong" back and forward.

Nothing of what you said was true. I presented my evidence. What you said were plain all untruths or missinformation.

Basically what you said was your opinion.

https://en.wikipedia.org/wiki/Karl_Popper


Vastet
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Slinging ad hominems only

Slinging ad hominems only weakens your position further. I presented proof and logic, you presented incoherent thoughts and irrational propositions.

I win.

Enlightened Atheist, Gaming God.